API MPMS 14.3.4

A P I MPMS*L4-3-4 92 W 0732290 0506280 O31 W

Manual of Petroleum Measurement Standards Chapter 14-Natural Gas Fluids

Measurement

Sect ion 3-Concent ric, Square-Edged Orifice Meters

Part 4-Background, Development, Implementation Procedures and Subroutine Documentation

THIRD EDITION, NOVEMBER, 1992

AGCI American Gas Association Report No. 3, Part 4

GPA 81 85-92, Pari 4 Gas Processors Association

American Petroleum Institute 1220 L Street, Northwest Washington, D.C. 20005

COPYRIGHT American Petroleum InstituteLicensed by Information Handling ServicesCOPYRIGHT American Petroleum InstituteLicensed by Information Handling Services

A P I MPMS*L4-3=4 92 9 0732290 0506283 T78

Manual of Petroleum Measurement Standards Chapter 14-Natural Gas Fluids

Measurement

Section 3-Concentric, Square-Edged Orifice Meters

Part 4-BackgroundY Development, Implementation Procedures and Subroutine Documentation

THIRD EDITION, NOVEMBER, 1992

American Petroleum Institute


- -- - - API MPMS*L4.3*V 72 0732270 050b282 904

SPECIAL NOTES

1. API PUBLICATIONS NECESSARILY ADDRESS PROBLEMS OF A GENERAL NATURE. WITH RESPECT TO PARTICULAR CIRCUMSTANCES, LOCAL, STATE, AND FEDERAL LAWS AND REGULATIONS SHOULD BE REVIEWED.

2. API IS NOT UNDERTAKING TO MEET THE DUTIES OF EMPLOYERS, MAN- UFACTURERS, OR SUPPLIERS TO WARN AND PROPERLY TRAIN AND EQUIP THEIR EMPLOYEES, AND OTHERS EXPOSED, CONCERNING HEALTH AND SAFETY RISKS AND PRECAUTIONS, NOR UNDERTAKING THEIR OBLIGATIONS UNDER LOCAL, STATE, OR FEDERAL LAWS.

3. INFORMATION CONCERNING SAFETY AND HEALTH RISKS AND PROPER

TIONS SHOULD BE OBTAINED FROM THE EMPLOYER, THE MANUFACTURER OR SUPPLIER OF THAT MATERIAL, OR THE MATERIAL SAFETY DATA SHEET.

4. NOTHING CONTAINED IN ANY API PUBLICATION IS TO BE CONSTRUED AS

UFACTURE, SALE, OR USE OF ANY METHOD, APPARATUS, OR PRODUCT COVERED BY LETTERS PATENT. NEITHER SHOULD ANYTHING CONTAINED IN THE PUBLICATION BE CONSTRUED AS INSURING ANYONE AGAINST LIABILITY FOR INFRINGEMENT OF LE'ITERS PATENT.

PRECAUTIONS WITH RESPECT TO PARTICULAR MATERIALS AND CONDI-

GRANTING ANY RIGHT, BY IMPLICATION OR OTHERWISE, FOR THE MAN-

5. GENERALLY, API STANDARDS ARE REVIEWED AND REVISED, REAF- FIRMED, OR WITHDRAWN AT LEAST EVERY FIVE YEARS. SOMETIMES A ONE- TIME EXTENSION OF UP TO TWO YEARS WILL BE ADDED TO THIS REVIEW CYCLE. THIS PUBLICATION WILL NO LONGER BE IN EFFECT FIVE YEARS AFTER ITS PUBLICATION DATE AS AN OPERATIVE API STANDARD OR, WHERE AN EXTENSION HAS BEEN GRANTED, UPON REPUBLICATION. STATUS OF THE PUBLICATION CAN BE ASCERTAINED FROM THE API AUTHORING DEPART- MENT [TELEPHONE (202) 682-8000]. A CATALOG OF API PUBLICATIONS AND MATERIALS IS PUBLISHED ANNUALLY AND UPDATED QUARTERLY BY API, 1220 L STREET, N.W., WASHINGTON, D.C. 20005.

Copyright O 1992 American Petroleum Institute


A P I MPMS*L4e3.4 92 0732290 0506283 840

FOREWORD

This foreword is for information and is not part of this standard. Chapter 14, Section 3, Part 4 of the Manual of Petroleum Measurement Standards

describes the background and development of the equation for the coefficient of discharge of flange-tapped square-edged concentric orifice meters and recommends a flow rate calculation procedure. The recommended procedures provide consistent computational results for the quantification of fluid flow under defined conditions, regardless of the point of origin or destination, or the units of measure required by governmental customs or statute. The procedures allow different users with different computer languages on different computing hardware to arrive at almost identical results using the same standardized input data.

This standard has been developed through the cooperative efforts of many individuals under the sponsorship of the American Petroleum Institute, API, and the American Gas Association, A.G.A., with contributions from the Gas Processors Association, GPA, and others.

API publications may be used by anyone desiring to do so. Every effort has been made by the Institute to assure the accuracy and reliability of the data contained in them; however, the Institute makes no representation, warranty, or guarantee in connection with this publication and hereby expressly disclaims any liability or responsibility for loss or damage resulting from its use or for the violation of any federal, state, or municipal regulation with which this publication may conflict.

Suggested revisions are invited and should be submitted to the director of the Meas- urement Coordination Department, American Petroleum Institute, 1220 L Street, N.W., Washington, D.C. 20005.

iii


__ -~~ -- - __ I I A P I M P M S * L 4 - 3 . 4 72 W 0732290 O506284 787 W

ACKNOWLEDGMENTS

From the initial data-collection phase through the final publication of this revision of Chapter 14, Section 3, of the Manual of Petroleum Measurement Standards, many individuals have devoted time and technical expertise. However, a small group of individuals has been very active for much of the project life. This group includes the following people:

H. Bean, El Paso Natural Gas Company (Retired) R. Beaty, Amoco Production Company, Committee Chairman D. Bell, NOVA corporation T. Coker, Phillips Petroleum Company W. Fling, OXY USA, Inc. (Retired), Project Manager J. Gallagher, Shell Pipe Line Corporation L. Hillburn, Phillips Petroleum Company (Retired) P. Hoglund, Washington Natural Gas Company (Retired) P. LaNasa G. Less, Natural Gas Pipeline Company of America (Retired) J. Messmer, Chevron U.S.A. Inc. (Retired) R. Teyssandier, Texaco Inc.

K. West, Mobil Research and Development Corporation E. UPP

During much of the corresponding time period, a similar effort occurred in Europe. The following individuals provided valuable liaison between the two efforts:

D. Gould, Commission of the European Communities F. Kinghorn, National Engineering Laboratory M. Reader-Harris, National Engineering Laboratory J. Sattary, National Engineering Laboratory E. Spencer, Consultant J. Stolz, Consultant P. van der Kam, Gasunie

The American Petroleum Institute provided most of the funding for the research project. Additional support was provided by the Gas Processors Association and the American Gas Association. Special thanks is given to the Gas Research Institute and K. Kothari for providing funding and manpower for the natural gas calculations used in this project and to the National Institute of Standards and Technology in Boulder, Colorado, for additional flow work.

J. Whetstone and J. Brennan were responsible for the collection of water data at the National Institute of Standards and Technology in Gaithersburg, Maryland. C. Britton, S . Caldwell, and W. Seid1 of the Colorado Engineering Experiment Station Inc. were responsible for the oil data. G. Less, J. Brennan, J. Ely, C. Sindt, K. Starling, and R. Ellington were responsible for the Natural Gas Pipeline Company of America test data on natural gas.

Over the years many individuals have been a part of the Chapter 14.3 Working Group and its many task forces. The list below is the roster of the working group and its task forces at the time of publication but is by no means a complete list of the individuals who partic- ipated in the development of this document.

R. Adamski, Exxon Chemical Americas-BOP R. Bass M. Bayliss, Occidental Petroleum (Caldonia) Ltd. R. Beaty, Amoco Production Company D. Bell, NOVA Corporation B. Berry

iv


A P I M P M S * L 4 - 3 . 4 92 0732290 050b285 613

J. Bosio, Statoil J. Brennan, National Institute of Standards and Technology E. Buxton S. Caidweli R. Chittum, American Petroleum Institute T. Coker, Phillips Petroleum Company H. Colvard, Exxon Company, U.S.A. L. Datta-Bania, United Gas Pipeline Company D. Embry, Phillips Petroleum Company W. Fling J. Gallagher, Shell Pipe Line Corporation V. Gebben, Kerr-McGee Corporation B. George, Amoco Production Company G. Givens, CNG Transmission Corporation T. Glazebrook, Tenneco Gas Transportation Company D. Goedde, Texas Gas Transmission Corporation D. Gould, Commission of the European Communities K. Gray, Phillips Petroleum Company R. Hankinson, Phillips 66 Natural Gas Company R. Haworth E. Hickl, Union Carbide Corporation L. Hillburn P. Hoglund, Washington Natural Gas Company J. Hord, National Institute of Standards and Technology E. Jones, Jr., Chevron Oil Field Research Company M. Keady K. Kothari, Gas Research Institute P. LaNasa G. Less G. Lynn, Oklahoma Natural Gas Company R. Maddox G. Mattingly, National Institute of Standards and Technugy E, McConaghy, NOVA Corporation C. Mentz L. Norris, Exxon Production Research Company K. Olson, Chemical Manufacturers Association A. Raether, Gas Company of New Mexico E. Raper, OXY USA, Inc. W. Ryan, El Paso Natural Gas Company R. Segers J. Sheffield S. Stark, Williams Natural Gas Company K. Starling J. Stolz J. Stuart, Pacific Gas and Electric Company W. Studzinski, NOVA/Husky Research Company M. Sutton, Gas Processors Association R. Teyssandier, Texaco Inc. V. Ting, Chevron Oil Field Research Company L. Traweek, American Gas Association

E Van Orsdol, Chevron U.S.A. Inc. N. Watanabe, National Research Laboratory of Metrology, Japan

E. VPP

V


- _-___ A P I f lPf lS* l14.3.4 72 H 0732290 0506286 55T

K. West, Mobil Research and Development Corporation P. Wilcox, Total of France J. Williams, Oryx Energy Company M. Williams, Amoco Production Company E. Woomer, United Gas Pipeline Company C. Worrell, OXY USA, Inc.


CONTENTS

CHAPTER 14--NATW GAS FLUIDS MEASUREMENT SECTION 3.CONCENTRIC. SQUARE-EDGED

ORIFICE METERS 4.1 Introduction and Nomenclature

4.1.1 Introduction ................................................................................................ 4.1.2 Nomenclature .............................................................................................

4.2.1 Background ................................................................................................. 4.2.2 Historical Data Base ................................................................................... 4.2.3 Recent Data Collection Efforts .................................................................. 4.2.4 Basis for Equation ......................................................................................

4.2 History and Development

4.2.5 Reader-Harris/Gallagher Equation .............................................................

4.3.1 Introduction ................................................................................................. 4.3.2 Solution for Mass or Volume Flow Rafe .................................................... 4.3.3 Special Procedures and Example Calculations for Natural Gas

4.3.4 Example Calculations .................................................................................

4.3 Implementation Procedures

Applications ...............................................................................................

APPENDIX 4-A-DEVELOPMENT OF FLOW EQUATION SOLUTION ALGOEUTHM .......................................................

APPENDIX 4-B-RECOMMENDED ROUNDING PROCEDURES .................... APPENDIX 4-C-ROUND ROBIN TESTING ....................................................... Figures

4-1-Flange Tap Data Comparison-Mean Deviation (%) versus

4-2-Flange Tap Data Comparison-Mean Deviation (%) versus

4-3-Flange Tap Data Comparison-Mean Deviation (%) versus Reynolds Number Ranges ............................................................................

4-4-Corner Tap Data Comparison-Mean Deviation (%) versus Nominal Beta Ratio ......................................................................................

4-5-Corner Tap Data Comparison-Mean Deviation (%) versus Reynolds Number Ranges ............................................................................

4-6-0-D/2 (Radius) Tap Data Comparison-Mean Deviation (%) versus Nominal Beta Ratios .........................................................................

4-7-0-0/2 (Radius) Tap Data Comparison-Mean Deviation (%) versus Reynolds Number Ranges .................................................................

4-8Ccatter Diagram Based on Buckingham Equation ....................................... 4-9Ccatter Diagram Based on Reader-HarridGallagher Equation .................... 4-A-1-Number of Iterations Required to Solve for Orifice Plate

Coefficient of Discharge-Direct Substitution Method ............................. 4-A-2-Number of Iterations Required to Solve for Orifice Plate

Nominal Beta Ratio ......................................................................................

Nominal Pipe Diameter ................................................................................

Coefficient of Discharge-Newton-Raphson Method ............................... Tables

4- 1-Regression Database Point Distribution for flange Taps ............................. 4-2-Regression Database Point Distribution for Corner Taps ............................. 4-3-Regression Database Point Distribution for D-D/2 (Radius) Taps ...............

Page

1 1

3 5 6

10 13

20 20

31 48

63 71 75

16

16

16

17

17

18

18 19 19

68

70

9 10 11

vii


._-. . .- . ___

A P I MPMS*L4.3-4 72 0732270 O506288 322

4-4-Typical Values of Linear Coefficients of Thermal Expansion ...................... 4.5-Units. Conversion Constants. and Universal Constants ...............................

Tables (continued) 4-&Input Parameters for Six Example Test Cases (US. IP. Metric.

and SI Units) ................................................................................................. 4-7-Intermediate Output for Example Test Case Number 1 ................................ 4-8-Intermediate Output for Example Test Case Number 2 ................................ 4-9-Intermediate Output for Example Test Case Number 3 ................................ 4-10-Intermediate Output for Example Test Case Number 4 .............................. 4-11-Intermediate Output for Example Test Case Number 5 .............................. 4-12-Intermediate Output for Example Test Case Number 6 .............................. 4-B- 1-Recommended Rounding Tolerances ....................................................... 4-C-1-Round Robin Test Parameters (US Units) ................................................ 4-C-2-Round Robin Test Parameters (IP Units) .................................................. 4-C-3-Round Robin Test Parameters (Metric Units) ........................................... 4-C-”Round Robin Test Parameters (SI Units) .................................................. 4-C-5-Selected Round Robin Test Results Matrix (US Units) ............................ 4-CdSelec ted Round Robin Test Results Matrix (SI Units) .............................

22 23

Page

49 51 53 55 57 59 61 74 76 77 78 79 81

111

.


API MPMS*L4-3-'4 92 0732290 0506289 269

Chapter 14-Natural Gas Fluids Measurement

SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS

PART 4-BACKGROUND, DEVELOPMENT, IMPLEMENTATION PROCEDURES AND SUBROUTINE DOCUMENTATION

4.1 Introduction and Nomenclature 4.1.1 INTRODUCTION

This part of the standard for Concentric Square-Edged Orifice Meters provides the background and history of the development of the standard and recommends a method to solve the flow equations for mass and volumetric flow.

4.1.2 NOMENCLATURE

The symbols used have, in some cases, been given a more general definition than that used in other parts of API 2530. Some symbols have a different meaning than that defined elsewhere in the standard. Care should therefore be given to the meaning of variables used in this document.

Represented Quantity

Line& coefficient of thermal expansion of the orifice plate material. Linear coefficient of thermal expansion of the meter tube material. Ratio of orifice plate bore diameter to meter tube internal diameter (&I) calculated at flowing temperature, $. Ratio of orifice plate bore diameter to meter tube internal diameter (dD) calculated at measured temperature, T,t. Ratio of orifice plate bore diameter to meter tube internal diameter (d/D) calculated at reference temperature, T,. Orifice plate coefficient of discharge. Coefficient of discharge at a specified pipe Reynolds number for flange-tapped orifice meter. First flange-tapped orifice plate coefficient of discharge constant within iteration scheme. Second flange-tapped orifice plate coefficient of discharge constant within iteration scheme. Third flange-tapped orifice plate coefficient of discharge constant within iteration scheme. Fourth flange-tapped orifice plate coefficient of discharge constant within iteration scheme. Fifth flange-tapped orifice plate coefficient of discharge constant within iteration scheme. Orifice plate coefficient of discharge bounds flag within iteration scheme. Orifice plate bore diameter calculated at flowing temperature $. Meter tube internal diameter calculated at flowing temperature $. Orifice plate bore diameter calculated at reference temperature T,. Meter tube internal diameter calculated at reference temperature T,. Orifice plate bore diameter calculated at measured temperature Tm . Meter tube internal diameter calculated at measured temperature T,, . Orifice plate coefficient of discharge convergence function derivative.

1


A P I M P M S * 1 4 - 3 * 4 92 0732290 050b290 T B O

2 CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT

Orifice differential pressure. Napierian constant, 2.71828. Velocity of approach factor. Orifice plate coefficient of discharge convergence function. Iteration flow factor. Iteration flow factor pressure-independent factor. Iteration flow factor pressure-dependent factor. Mass flow factor. Ideal gas relative density (specific gravity). Real gas relative density (specific gravity). Real relative density (specific gravity), % carbon dioxide, and % nitrogen. Isentropic exponent. Mass. Absolute viscosity of flowing fluid. Molar mass (molecular weight) of dry air. Dimensionless downstream dam height. Number of moles. Unit conversion factor (orifice flow). Unit conversion factor (Reynolds number). Unit conversion factor (expansion factor). Unit conversion factor (discharge coefficient). Unit conversion factor (absolute temperature). Base pressure. Static pressure of fluid at the pressure tap. Absolute static pressure at the orifice upstream differential pressure tap. Absolute static pressure at the orifice downstream differential pressure tap. Measured air pressure. Measured gas pressure. Pi, 3.14159 ... . Mass flow rate. Volume flow rate per hour at base conditions. Volume flow rate flowing (actual) conditions. Universal gas constant. Pipe Reynolds number. Density of the fluid at base conditions, (6 , G). Air density at base conditions, (8 , G). Gas density at base conditions, (4 , Tb). Density at standard conditions, (P, , TJ. Density at flowing conditions, (9, Tf). Base temperature. Measured orifice plate bore diameter temperature. Measured meter tube internal diameter temperature. Measured temperature of air. Measured temperature of gas. Rowing temperature. Reference temperature of the orifice plate bore diameter and/or meter tube internal diameter. Downstream tap correction factor. Small meter tube correction factor.


API f lP f lS*14.3 .4 92 m 0732290 0506291 917 m

SECTION &CONCENTRIC. SQU RE-EDGED ORIFICE METERS. PART 4-43 CKGROUND 3

I;, Upstream tap correction factor. X Reduced reciprocal Reynolds number (4,000/ReD). X, Value of X where change in orifice plate coefficient of discharge correlation

occurs. Y Expansion factor. Yp Expansion factor pressure constant. Zb Compressibility (base conditions).

2, Compressibility at flowing conditions (9, T f > . Air compressibility at air measurement conditions.

ZnlgOs Gas compressibility at gas measurement conditions. Z"leir

4.2 History and Development 4.2.1 BACKGROUND

In May 1924, the Board of Directors of the Natural Gas Association (this later became the Natural Gas Department of the American Gas Association') directed its Main Technical and Research Committee to establish a new subcommittee to be known as the Gas Meas- urement Committee. The duties of this new committee were outlined by the directors as:

Determine the correct methods of installing orifice meters for measuring natural gas. Determine the necessary corrective factors and operative requirements in the use of orifice meters, using natural gas in all experimental work. Secure the cooperation and assistance of the National Bureau of Standards2 and the United States Bureau of Mines3, and secure, if possible, the assignment of members of their staffs to the Gas Measurement Committee to assist in this work.

The Gas Measurement Committee held ifs first meefing in November 1924 and discussed various features of the work assigned to it. Beginning in the summer of 1925, and extending over a period of six years, this committee conducted several research projects on orifice meters.

The Gas Measurement Committee published a preliminary report in 1927, which was revised in 1929, and Report No. 1 was issued in 1930. In the introduction to Report No. 1, the following statement was made:

'This is not a final report, but it is made with the understanding that the committee will continue its analytical studies of the data already developed, The committee also fully expects that it will be necessary for it to conduct further work of its own. This will make necessary one or more supplemental reports, in which the data will be summarized and the mathematical principles announced, which are thebasis for the present report, and such modifications and extensions will be made as additional data and further study may require."

rn September 193 1, this committee joined with the Special Research Committee of Fluid Meters of the American Society of Mechanical Engineers4 in the formation of a Joint Com- mittee on Orifice Meters so that future publications on orifice meters by these two parent committees might be in harmony. This joint committee found that a few additional research projects on orifice meters, especially for the determination of the absolute values of orifice coefficients, were needed. Thereafter, the committee formally requested representatives of the National Bureau of Standards to review the data obtained in these later research projects and report their findings to the committee.

Gas Measurement Committee Report No. 2 was published on May 6, 1935 and was intended to supplement Report No. 1. Within certain limits explained in that report, any orifice meter installed in accordance with the recommendations in Report No. 1 would

'American Gas Association, 1515 Wilson Boulevard, Arlington, Virginia 22209. 'National Bureau of Standards (is now the National institute of Standards and Technology). NiST publications are available from the US. Government Printing Office, Washington, D.C. 20402. 3United States Bureau of Mines. Bureau of Mines publications are available from the U.S. Government Printing Office, Washington, D.C. 20402. 4American Society of Mechanical Engineers, 345 East 47th Street, New York, New York 10017.



fulfill all the requirements stated in Report No. 2. The use of factors given in Report No. 2 made possible the use of orifice meters over a much wider range of conditions than had been possible before.

The material in Report No. 2 was based on a special engineering report made by the Joint American Gas AssociatiodAmerican Society of Mechanical Engineers Committee on Orifice Coefficients to the Gas Measurement Committee in October 1934 and was presented to and accepted by the Main Technical and Research Committee in January 1935. The analysis of the data presented in the report of that joint committee was made by Dr. Edgar Buckingham and Mr. Howard S. Bean of the National Bureau of Standards and checked by Professor Samuel R. Beitler for the committee. The report of the joint committee in its original form passed through the editorial committee of the bureau and was approved for publication by the director of the bureau.

Since publication of Report No. 2, new types of equipment have been made available for use in the construction of orifice meter stations, Further, the need developed for larger meter tube diameters and heavier wall pipe to measure the larger volumes of gas at higher metering pressures. It was recognized by the industry that Report No. 2 should be brought up to date. Thus, early in 1953, the PAR Plan’s Pipeline Research Committee appointed the Supervising Committee for PAR Project NX-7, for the purpose of developing Gas Meas- urement Committee Report No. 3. To maintain cooperation between the American Society of Mechanical Engineers and the American Gas Association in the development of publications on orifice meters, the members of the supervising committee had dual membership on the American Society of Mechanical Engineers Research Committee on Fluid Meters, Subcommittee No. 15, as well as the NX-7 Committee.

Report No. 3 supplemented Report No. 2. Generally, all of the data in this report were the same as included in Report No. 2, except that it was expanded to cover a wider range of conditions. In many instances, slight changes were made and statements added to clarify some of the conditions brought about from practical application of Reports No. 1 and 2. In Report No. 3, a pressure base of 14.73 pounds per square inch absolute was adopted to replace the former pressure base of 14.4 pounds per square inch absolute. The results are consistent with those obtained from Report No. 2.

Since the publication of Report No. 3 in 1955, there have been refinements and new developments in the measurement of natural gas. The 1969 revision updated the report and provided additional information which had been developed since the original publication. The basic concepts in Report No. 3 were not changed. The use of large pipe diameters and new manufacturing techniques as well as the use of computers, required additional material to make the report more useful. Fundamentally, however, these revisions did not make any appreciable changes. The compressibility material presented was abstracted from the Manual for Determining Supercompressibility Factors for Natural Gas.

During 1975, the American Petroleum Institute’s Committee on Petroleum Measurement adopted Report No. 3 and approved it as API Standard 2530, and for publication as Chapter 14.3 of the American Petroleum Institute’s Manual of Petroleum Measurement Standards. Subsequently, Report No, 3 was submitted by the American Petroleum Institute to the American National Standards Institute’ for endorsement as an American National Stan- dard. The American National Standards Institute approved Report No. 3 as an American National Standard on June 28, 1977, identified as ANSUAPI 2530.

During 1982-1983, API’s Committee on Petroleum Measurement worked in cooperation with the American Gas Association and the Gas Processors Association‘ to revise the standard. API adopted the revised standard by ballot of its Committee on Petroleum Meas- urement on November 23, 1983. The 1983 revision updated the standard and altered the format to improve its clarity and ease of application. Several forms of the flow equations

5American National Standards Institute, 1430 Broadway, New York, New York 10018. 6Gas Processors Association, 6526 East 60th Street, Tulsa, Oklahoma 74145.


A P I MPMS*L4*3*4 92 0732290 0506293 79T M

SECTION &CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART &BACKGROUND 5

were provided. The calculated flow rate results were equivalent for any of the forms presented and were also equivalent to those obtained with the first edition.

The empirical equation of state for natural gas, or compressibility factors was also updated in the 1983 revision. Gas compressibility work was completed on an expanded list of gas compositions and for pressures up to 20,000 pounds per square inch. These experiments were supported with facilities, technology, expertise, and funds supplied by the National Bureau of Standards, the University of Oklahoma, Texas A & M University, the Compressed Gas Association7, the Gas Research Institute*, the American Gas Association, and others. The resultant empirical equation of state for natural gas was adopted as A.G.A. Transmission Measurement Report No. 8. No other substantive technical revisions to the standard were undertaken at that time. The American National Standards Institute approved the 1983 revision as an American National Standard on May 16, 1985.

The empirical coefficient of discharge equation for flange-tapped orifice meters has been updated in the present revision. Extensive test work on orifice meters using oil, water, air, and natural gas as test fíuids was conducted by an international set of laboratories. Two sets of meter tubes in nominal 2 ,3 ,4 ,6 , and 10 inch sizes with two sets of eight orifice plates in nominal beta (ß) ratios from 0.05 to 0.75 were tested. The U.S. experiments were supported with facilities, technology, expertise, and funds supplied by the National Bureau of Standards, the American Petroleum Institute, the Gas Processors Association, the Gas Research Institute, the American Gas Association, and others. The new coefficient of discharge equation is based on the most extensive, high quality data ever collected.

The approach length, piping configuration, and flow conditioning recommendations are unchanged from the 1983 revision. A restatement of uncertainty will result from the current installation research and will offer a basis for future changes in this standard.

4.2.2 HISTORICAL DATA BASE

4.2.2.1 OSU Data Base

The largest single collection of industry-sponsored experiments to determine orifice discharge coefficients was conducted from 1932 to 1933 under the direction of Professor S.R. Beider at Ohio State University (OSU). These experiments used water in seven pipe diameters ranging from 25 to 350 millimeters (1 to 14 inch). The test results are commonly referred to as the OSU data base.

Orifice plates with a wide range of diameters were studied in each of the pipe sizes. While little is known of the detail of the pipework condition or of the plates themselves, the tests were undertaken with considerable care. All flange-tapped orifice metering standards published prior to 1990 (A.G.A. Report No. 3, ANSI/API 2530, and IS09 5167) were based on this sixty year old OSU data base.

The results from these experiments were used by Dr. Edgar Buckingham and Mr, Howard Bean of NBS to develop a mathematical equation to calculate the flow coefficient for orifice meters. They derived the equation by cross-plotting the data on large sheets of graph paper to obtain the best curve fit. The quality of the work done by Beitler, Buck- ingham, and Bean is obvious from the fact that their results were used for almost 60 years.

4.2.2.2 Data Reevaluation

In the late 1960s and early 1970s, attempts were made to mathematically rationalize the variety of discharge coefficient data then available. Equations using a power series form evolved. These provided excellent fits to specific data bases, but could not be used for

7Compressed Gas Association, 1725 Jefferson Davis Highway, Arlington, Virginia 22202. *Gas Research Institute, 8600 West Bryn Mawr Avenue, Chicago, Illinois 60631. 'International Organization for Standardization. IS0 publications are available from ANSI.


A P I MPMS*L4.3-4 %2 m 0732270 0506274 626 m


extrapolations. These attempts did not replace the Buckingham equation for flange-tapped orifice meters.

In the early 1970s, a joint committee of the American Gas Association, the American Petroleum Institute, and the International Organization for Standardization (ISO) was formed to address perceived problems associated with the OSU data base. Wayne Fling of the USA and Jean Stolz of France were selected to evaluate the OSU data base.

In their evaluation, Stolz and Fling discovered a number of physical reasons to question some of the data points of the OSU Data Set. Several installations and plates were found that did not meet the requirements of ANSUAPI 2530 and IS0 5 167. The F%ng/Stolz analysis identified 303 technically defensible data points from the OSU experiments. Unfortunately, it is not known which points were selected by Buckingham/Bean to generate the discharge coefficient equation. The 303 defensible data points were from 4 meter tubes covering a p ratio range of 0.2 to 0.75 and a pipe Reynolds number range of 16,000 to 1,600,000. This data was developed using water.

4.2.3 RECENT DATA COLLECTION EFFORTS

In the late 1970s, recognizing from the Fling/Stolz analysis the availability of only a small amount of definitive data, API and GPA initiated a multimillion dollar project to develop a new archival discharge coefficient data base for concentric, square-edged, flange- tapped, orifice meters. At about the same time, a similar experimental program was initiated by the Commission of European Communities'' (CEC). The goal of both research efforts was to develop a high quality archival data base of orifice meter discharge coefficients covering the broadest possible range of pipe Reynolds numbers. The data base was generated over a ten year period at eleven laboratories using oil, water, air, and natural gases as test fluids.

The experiments were randomized to eliminate experimental bias within a laboratory. Randomization assured valid estimates of the experimental error and allowed the application of statistical tests of significance, confidence levels, and time-dependent analyses. Replication of independent bivariate data points (Cd,ReD) was conducted to measure precision and to assess uncontrolled variables which could affect the find results. By using different laboratories, the possibility of systematic bias originating from any one laboratory could be identified, investigated, and corrected.

The experimental pattern was designed to vary in a controlled fashion the correlating parameters of p, pipe size, and Reynolds number for a given tapping system. All orifice plates were quantified with respect to concentricity, flatness, bore diameter, surface roughness, edge sharpness, and other characteristics. The edge sharpness was quantified by lead foil, casting, beam of light, and fingernail methods. The meter tubes were quantified with respect to circularity, diameter, stepdgaps, pipe wall roughness, and so forth. The wall roughness was quantified by the profilometer and the artifact methods.

The experimental design recognized the importance of the data taken on each of the four basis fluids. The water data were viewed as the most important of the research effort. The water experiments occupied the intermediate Reynolds number range. It was decided not to test all tube/plate combinations in all four fluids. The API/GPA experiments were restricted to flange-tapped orifice meters, using oil, water, and natural gas as the test fluids,

The CEC experiments covered orifice meters equipped with corner, radius (D-D/2), and flange tappings. Test fluids included water, dry air, and natural gas.

The combined data base which resulted is based on a combination of 12 meter tubes covering five nominal pipe diameters. It contains data from 106 orifice plates covering eight p ratios for both liquids and gases. The data base was collected from eleven different laboratories over a pipe Reynolds number range of 100 to 35,000,000.

"Commission of European Communities, rue de la Loi, B-1049, Brussels, Belgium.


SECTION SCONCENTRIC. SQUARE-EDGED ORIFICE METERS. PART 4-BACKGROUND 7

Full descriptions of the research projects may be found in the documents referenced in the appendix to Pari 1.

4.2.3.1 APVGPA Discharge Coefficient Research

The API/GPA discharge coeffficient research was restricted to flange-tapped orifice meters. Only those experiments conducted using oil and water were used in the final regression data base. For several technical reasons, the originators of the high Reynolds number experiments at Joliet considered the natural gas experiments to be comparison quality, rather than regression quality.

Since theresults of the project were to be applied in commerce, the experimental pattern included two sets of five nominal pipe diameters (2,3,4,6, and 10 inches). A three-section meter tube design was selected to facilitate inspection of internal surface conditions and for future experiments on installation conditions. Tube roughness values were representative of commercial installations.

Two sets of orifice plates having nominal p ratios (0.050, 0.100, 0.200, 0.375, 0.500, 0.575, 0.660, 0.750) were selected to produce a statistically consistent data base which could be used to develop an equation for the discharge coefficient. Plates were replaced when they were damaged or when the edge sharpness had deteriorated beyond acceptable levels. The nominal pratios and nominal tube diameters for the experimental patterns were:

0.050 o. 100 0.200 0.375 0.500 0.575 0.660 0.750

x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x

To ensure uniformity of the velocity profile at each laboratory, Sprenkle flow conditioners were constructed by the NBS mechanical shop in accordance with the original specifications of the Bailey Meter Company. These Sprenkle flow conditioners assured isolation from laboratory induced piping configurations. Additionally, velocity profile tests were performed to confirm the presence of uniform, fully-developed, swirl-free flow profiles.

Flow rates were selected for each pipe size and plate combination to produce Reynolds numbers spread equally over the relevant range of the laboratories' capabilities. The resulting test matrix sought to correct any possible bias in the existing OSU data base and minimize or eliminate aíl sources of bias in the new experimental data.

4.2.3.1.1 Low Reynolds Number Experiments

The low Reynolds number experiments were conducted at the Colorado Engineering Experimental Station Incorporated (CEESI) Flow Laboratory located in Nunn, Colorado. The viscous fluid selected was a white mineral oil with a nominal viscosity of 8 centipoise.

The mass flow rate for the oil experiments was calculated using a traditional liquid turbine meter, small volume prover, and empirical density arrangement. The density and viscosity of the white mineral oil was characterized to empirically predict flowing density and viscosity.



4.2.3.1 -2 Intermediate Reynolds Number Experiments

The intermediate Reynolds number experiments were conducted at the National Institute of Science and Technology (NIST) Flow Laboratory located in Gaithersburg, Maryland. The test fluid was potable water with a nominal viscosity of 1 centipoise.

The mass flow rate was calculated using the traditional weigh tank and empirical density method. Water density as a function of temperature was predicted using George S. Kell’s water density equation, combined with a zero offset attributable to dissolved minerals in the sump water.

4.2.3.1.3 High Reynolds Number Verification Experiments

The high Reynolds number experiments were conducted at Natural Gas Pipeline of America’s (NGPLA) Natural Gas Facility located at Joliet, Illinois. f i o natural gases were utilized, Gulf Coast and Amarillo, both having a nominal viscosity of 0.01 centipoise.

The mass flow rate was determined using sonic flow nozzles and an empirical PVT arrangement. The density and viscosities of the natural gases were continuously characterized by an on-line gas chromatograph which reported the composition in mole percent.

4.2.3.2 CEC Discharge Coefficient Research

The CEC Discharge Coefficient Research experiments used two tube sizes (100 millimeters and 250 millimeters) over a prange of 0.2 to 0.75 at eight laboratories.

To ensure a uniform velocity profile at each laboratory, long upstream lengths of straight pipe (greater than SOD) and flow conditioners were used to assure isolation from laboratory induced piping configurations. Again, velocity profile tests were performed to confirm the presence of uniform, fully-developed, swirl-free flow profiles.

Flow rates were selected for each pipe size and plate combination to produce Reynolds numbers spread equally over the relevant range of the laboratories’ capabilities. As in the APUGPA experiments, the resulting test matrix was designed to correct any possible bias in the existing OSU data base and to minimize or eliminate all sources of bias in the new experimental data.

The combined data base includes data from eleven different laboratories, for four basic fluid types with different sources, on twelve different meter tubes of differing origins, and over one-hundred orifice plates of differing origins.

4.2.3.3 Laboratory Bias

Before proceeding with equation regression, the researchers analyzed laboratory bias within the individual data bases as weil as the combined API/GPA and CEC data bases. Laboratory bias would be evident if the discharge coefficient curve for a given p ratio exhibited offsets between fluid data or between laboratories.

The traceability chain and method of determining mass flow, instrumentation calibration, and operating procedures were unique for each laboratory. Pipe sizes and p ratios common to both the APUGPA and CEC data bases were used to test the assumption that laboratory bias within the regression data set has been randomized.

Analysis of the APUGPA data base exhibited no laboratoq bias between the low and intermediate Reynolds number laboratories. A statistical analysis by the AEWGPA technical experts confirmed the lack of bias. Graphical analysis of the CEC data base indicated that the laboratory biases were randomized.

Comparison of the APUGPA and CEC data graphically confirmed the assumption of randomized laboratory bias between data bases. Additionally, a statistical comparison using any of the candidate equations confirmed the extremely compatible level between data bases.


SECTION %-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART &BACKGROUND 9

4.2.3.4 Regression Data Set

mutually agreed that the Regression Data Set be defined as follows: A meeting of interested international orifice metering experts in November, 1988,

T h e Regression Data Set shall consist of those data points contained in the APWGPA and CEC discharge coefficient experiments which were performed on orifice plates whose diameter was greater than 11.4 millimeters (0.45 inches) and if the pipe Reynolds number was equal to or greater than 4,000 (furbulent flow regime).”

Tests which contained uncontrolled independent variables and operator errors were excluded from the data base. Points were discarded only if a physical cause could be identified and both the laboratory and APUGPA or CEC experts concurred on the evidence. Questionable points which were considered to be statistical outliers were not discarded from the data base.

This does not mean that other data were of inferior qualify. Insufficient information existed for other data sets to determine if the independent variables were controlled and quantified. Examples of comparison quality data include the OSU 303 points, the 1983 NBS Boulder Experiments, the AFWGPA Joliet Data, and the Japanese Water data base.

The Regression Data Set defined above consists of data generated on orifice meters equipped with flange and D-D/2 (radius) tappings. The number of regression data points are summarized as follows:

Tapping Number of points

flange 5,734 comer 2,298 D-D/2 2,160

Total Poinfs 10,192

Tables 4-1 through 4-3 show the range of data used to generate the RG correlation.

Table 4-I-Regression Database Point Distribution for Flange Taps

Tube Size

2 3 4 6 10 summary Beta inches inches inches inches inches bvBeta o. 100 0.200 0.375 0.500 0.575 0.660

Summary by Tube

.0.750

Pipe

O 60

104 113 90

196 212

775

4000 to

loo00

O 57

106 69 72 64

101

469

io4 lo5 to

O 27 1 287 164 435 289 458

1904

Reg io5 lo6 to

29 83

122 109 136 92

130

701

lo6

io7 to

79 257 202 164 390 303 490

1885

io7 io8 to

108 728 821 619

1123 944

1391

5734

summary by Pipe

2.000 112 414 249 O O 775 3.000 22 209 238 O O 469 4.000 95 622 1004 183 O 1904 6.000 68 275 328 30 O 701 10.000 41 300 927 467 150 1885

summary byReD 338 1820 2746 680 150 5734


A P I N P N S * L 4 - 3 = 4 92 0732290 0506298 2 7 1


4.2.3.5 Interpretation of Research Data

For high values of p, the data follows a pattern similar to the Moody Friction Factor Diagram. This similarity is greatest at a p of 0.750 and continuously diminishes and becomes imperceptible at a p ratio of 0.500.

For low p ratios, the data is erratic. Closer examination indicated that the ability to reproduce an orifice plate with a sharp edge decreases with decreasing plate bore diameter. Based upon lead foil and video imaging analyses, a reasonable low limit for commercial plates was thought to be 11.4 millimeters (0.45 inches).

Data associated with the 50 millimeter and 75 millimeter (2 inch and 3 inch) tubes exhibit an anomaly. Further analysis indicated that this anomaly may be caused by the dimensionless tap hole size and dimensional location for flange taps.

The experiments confirmed the uncertainty guidelines used by the petroleum, chemical, and natural gas industries, Improvement in accuracy below this level under normal operating conditions is unrealistic without in situ calibration of the device and secondary instrumentation.

4.2.4 BASIS FOR EQUATION

The underlying principle for present day theoretical and experimental fluid mechanics is dynamic similarity. This principle states that two geometrically similar meters, with identical dimensionless flow parameters will display geometrically similar streamlines regardless of differences in density, viscosity, flow rate, and so forth, between the two fluids.

Dynamic similarity implies a correspondence of fluid forces between the two metering systems. Within the application limitations of this standard, the inertial and viscous forces are those considered to be significant for the orifice meter. As a result, the Reynolds number, which measures the ratio of the inertial to viscous forces, is the term which correlates dynamic similarity in all empirical coefficient of discharge and flow coefficient equations.

Table 4-2-Regression Database Point Distribution for Corner Taps

Tube Size

2 3 4 6 10 Summary Beta inches inches inches inches inches by Beta o. 100 0.200 O O 192 O 182 374 0.375 O O 78 O 96 174 0.500 O O 73 O 89 162 0.575 O o 300 O 275 575 0.660 O O 183 O 199 382 0.750 O O 270 O 361 63 1

Summary byTube O O 1096 o 1202 2298

Reg 4000 io4 lo5 io6 io7

to to to to to Summary Pipe 10000 lo5 lo6 lo7 10' byPipe 2.000 3.000 4.000 27 278 629 162 O 1096 6.000 1o.Ooo 12 166 519 371 134 1202

Summary by Reg 39 444 1148 533 134 2298


A P I M P M S * L 4 - 3 e 4 92 0732290 0506299 L O B

SECTION &CONCENTRIC. SQUARE-EDGED ORIFICE METERS. PART &BACKGROUND 11 ~ ~

Table 4-3-Regression Database Point Distribution for 0-012 (Radius) Taps

Tube Size

2 3 4 6 Beta inches inches inches inches o. 100 0.200 O O 169 O 0.375 O O 50 O 0.500 O O 48 O 0.575 O O 276 O 0.660 O O 158 O 0.750 O O 243 O

10 summary inches by Beta

186 355 97 147 90 138

274 550 198 356 37 1 614

Summary byTube O o 944 O 1216 2160

Ren

4000 io4 io5 lo6 io7 to to to to summary

Pipe loo00 :i5 lo6 lo7 lo8 bypipe 2.000 3.000 4.000 24 229 529 162 O 944 6.000 10.000 12 167 534 367 i36 1216

Summary byReg 36 396 1063 529 136 2160

Provided the physics of the fluid does not change, the Reynolds number correlation provides a rational basis for extrapolation of the empirical equation.

The originators of the APVGPA and CEC experiments considered fully developed velocity profiles as the foundation for the experiments. This decision was discussed extensively, as were the definition and determination of fully developed flow. Fully developed flow conditions were assured by the use of straight lengths of meter tube both upstream and downstream from the orifice and by the use of flow sfraighteners.

The theoretical definition of fully developed velocity profiles is based largely on the accumulated results of experimental observations of time-averaged velocity profile and, parficularly, of the pressure gradient (or friction factor). It is well established that both the velocity profile and the pressure gradient are sensitive to the condition of the pipe wall, whether smooth, partially rough, or fully rough, and the nature of the roughness.

4.2.4.1 Form of Equation

Previous discharge coefficient equation forms (Buckingham, Murdock, Dowdell, and others) were empirically derived expressions with minimal mathematical correlation to fluid dynamic phenomena. In 1978, Jean Stolz derived an empirical orifice equation based on the physics of an orifice meter. Stolz postulated that discharge coefficients obtained with different sets of near field pressure tappings must be related to one another based on the physics. The expression has been termed the Stolz linkage form. The coefficient of discharge (C,) equation for the concentric, square-edged orifice plafe developed by M. J. Reader-Harris and J. E. Gallagher, the RG equation, evolved from the work of Stolz.

The RG equation contains a coefficient of discharge at Reynolds number for corner taps, C;,(CT), a slope term consisting of a throat Reynolds Number term and velocity profile term, the near field tap t e m , and a “tap” size term for meter tubes less than 2.8 inches. A brief description of the physical understanding for the equation is presented in 4.2.4.2 and 4.2.4.3.


12 CHAPTER 14-NATURAL GAS FLUIDS b%EASUREMENT

4.2.4.2 Tap Terms

The near field tap terms were derived first since it was necessary to determine them before regression of the slope and q(CT) terms. The best-fit terms were derived statistically using the Regression data base and the Gasunie 600 millimeter flange tapping term data. The total tapping term data set consisted of 11,346 points, nominal diameter ratios (j) from 0.10 to 0.75, nominal pipe diameters from 50 to 600 millimeters, and pipe Reynolds numbers which ranged from approximately 200 to 50,000,000.

Stolz's postulate states that the near field tapping terms are equal to the difference between the discharge coefficient for the corner taps and the flange (or radius taps). The values of the terms were determined from the CEC data which included all three sets of tappings. However, the form of the tapping terms was based on data collected by several researchers. Because the data aplied to only one pair of tappings (flange), the value of the tapping terms in the APUGPA data could only be calculated for comparison.

The upstream term has a form which is essentially identical to that of IS0 5167. The downstream form is based on a suggestion by R. G. Teyssandier and Z. D. Husain. Also, it was agreed that the upstream and downstream tap terms should have a continuous first derivative.

No effect of Reynolds number on the tap terms is evident from analysis of the CEC data. However, data in the low Reynolds number range in the API/GPA experiments show the effect of Reynolds number on the tap term. The effect of low Reynolds number on the upstream and downstream wail pressure gradient has been reported by Witte, Schroeder, and Johansen. Perfect low Reynolds number tapping terms cannot be produced due to lack of data. However, it is important to produce the best ones possible.

4.2.4.3 Ci (CT) Term

The infinite discharge coefficient for corner taps, q(CT), increases with pratio to a maximum near p of 0.55 and then decreases rapidly with increasing p. The form of the equation, without taking into account the tap hole diameter term, is:

Ci (CT) = A,, + A l p 2 +A-#'

The constant exponents of 2 and 8 were chosen to enable a good fit to the data while keeping the exponents reasonable.

The 50 millimeter flange tap data differed significantly from the radius tap terms by as much as 0.4 percent for small values of b. Gallagher and Teyssandier postulated that this difference was a result of dimensional tap effects, An additional term was added to account for the tap hole diameter effect for 50 millimeter tubes. It is debatable whether this term should be in the tap term or G(CT) term. A proposal by Reader-H&s to add a tap hole diameter term to the C,(CT) term was accepted and has been implemented.

4.2.4.4 Slope Term

Intuitively, for small p ratios, the Cd should depend only on throat Reynolds Number (Re,). However, for large p ratios the velocity profile or friction factor is the correlating parameter.

Several scientists have attempted to correlate C, as a function of friction factor. While theoretically correct, the practical application would be unpopular. Also, the ability to measure friction factor is impractical in the field and difficult in the laboratory.

The slope term form should also provide a transition from laminar to turbulent flow because the velocity profile changes rapidly in the transitional flow regime. The data indicated that the slope for pipe Reynolds number (ReD) greater than 3,500 was very different from the slope for pipe Reynolds number (Re,) less than 3,500.


SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 4-BACKGROUND 13

The final slope term form is as follows:

The '%" term for Re, c 3,500 is different from Re, > 3,500 to correct for the velocity profile changes from laminar to turbulent flow regime.

4.2.5 READER-HARRIWGALLAGHER EQUATION

The equation for the coefficient of discharge (C,) for concentric square-edged orifice plates developed by Reader-HarridGallagher (RG) is structured into distinct linkage terms and is considered to best represent the current regression data base. The RG equation, as ballotted within API in 1989, is valid for the three tappings represented by the regression database and is acceptable for low flow conditions if a higher uncertainty is acceptable. The bailoted equation is given below.

c, = ci + SIX] + s,x, Ci = Ci(CT) + Tap Term

C;:(CT) = 0.5961 + 0.0291ß2- 0.2290ß8+ 0.003 (1 - ß) Ml

Tap T e m = Upstrm + Dnstrm

Upstrm = [ 0.0433 + 0.0712e-8'5L' - 0.1145e-6'0L1 ] (1 - 0.23A) B

Dnstrm = -0.0116

S2X, = (0.0210 + 0.0049A)ß4C

Also,

0.8 19, Wß

A = [ ReD ] For Re, greater than or equal to 3,500,

0.35

c = [E]



For Re, less than 3,500,

C = 30.0-6,500

Diameter ratio. d1D. Coefficient of discharge at a specified pipe Reynolds number. Coefficient of discharge at infinite pipe Reynolds number. Coefficient of discharge at infinite pipe Reynolds number for corner-tapped orifice meter. Orifice plate bore diameter calculated at Tf. Meter tube internal diameter calculated at Tf. Naperian constant, 2.71828. O for corner taps. N4/D for flange taps. 1 for 0-012 (radius) taps. O for corner taps. N4/Dfor flange taps. 0.47 for 0-012 (radius) taps. 1.0 when D is in inches; 25.4 when D is in millimeters, pipe Reynolds number.

By restricting the RG equation to flange-tapped orifice meters with pipe Reynolds numbers greater than or equal to 4,000, the RG equation becomes:

cd = cj + SIXI + S2x2 Ci = Ci(CT) + Tap Term

C;(CT) = 0.5961 + 0.0291ß2- 0.2290ß8+ 0.003 (1 - ß) Ml

Tap Term = Upstrm i- Dnstrm

Upstrm = [ 0.0433 + 0.07 12 - O. 1 145 e-6'oL' ] ( 1 - 0.23A) B

Dnstrm = -0.0116 M2 - 0.52M:.3 'J 1 -0.14A) lß

S2X, = (0.0210 + 0.0049A)ß4C

Also,

D M1 = max (2.8--,O.O) N4


A P I f l P M S * 1 4 * 3 . 4 92 W 0732290 0506303 469 W


0.8 19, Oooß A = [ Re, ]

Where: A = B' = ß =

c, =

- - C =

c. = G(CT) =

d = D = e =

LI = 4 ! = N4 =

Re, =

Small throat Reynolds number correlation function. Fluid momentum ratio. Diameter ratio. dlD. Generalized Reynolds number correlation function. Coefficient of discharge at a specified pipe Reynolds number. Coefficient of discharge at infinite pipe Reynolds number. Coefficient of discharge at infinite pipe Reynolds number for corner-tapped orifice meter. Orifice plate bore diameter calculated at ïj. Meter tube internal diameter calculated at Tf. Naperian constant, 2.71828. N41D for flange taps. N,lD for flange taps. 1.0 when D is in inches; 25.4 when D is in millimeters. pipe Reynolds number.

The downstream tap term, M,, is the distance between the downstream face of the plate and the downstream tap location. The tap hole term, M , , is significant only for nominal meter tubes less than 75 millimeter (3 inch) equipped with 9.525 millimeter (0.375 inch) flange taps holes.

The equation is applicable to nominal pipe sizes of 2 inches (50 millimeters) and larger, diameter ratios (p) of 0.10 through 0.75 provided the orifice plate bore diameter,d,, is greater than 0.45 inches (1 1.4 millimeters), and for pipe Reynolds numbers greater than or equal to 4,000. Those interested in applications with Re, less than 4000, d, less than 0.45 inches, or for corner or 0-012 (radius) taps, all of which are outside the range of this standard, are referred to Appendix 4-A.

4.2.5.1 Statistical Analysis

Since the mid 1930's, the correlation published by Dr. E. Buckingham and Mr. Howard S. Bean has been used by A.G.A. Report No. 3 (ANSUAPI 2530). In 1980, IS0 replaced the Buckingham equation with the Stolz linkage equation in the international orifice standard (IS0 5167). Statistical analysis of the Regression Data Set showed that in several regions, neither the Buckingham nor Stolz equations accurately represented the data for flange-tapped orifices (Figures 4-1 through 4-3). The figures indicate that the data does not substantiate the uncertainty statement published in both the IS0 and 1985 ANSI standards. The figures show that the RG equation provides an excellent fit to the data for flange-tapped orifice meters. Figure 4-9 shows that the RG equation fits the data much better over the entire Reynolds number range than the previous equation (Figure 4-8).

Figures 4-4,4-5,4-6, and 4-7 show the superior fit of the RG equation to the corner and 0-012 (radius) tap data.

(text continued on page 20)



0.8

0.6

0.4 op c 0.2 .9 ‘5 o a” g -0.2

Y

c m

a ’ -0.4

-0.6

-0.8

(LI Buckingham ~- IS0 5167-Stolz

0.1 0.2 0.375 0.5 0.575 0.66 0.75

Beta ratio

Figure 4-1 -Flange Tap Data Comparison-Mean Deviation (“A) versus Nominal Beta Ratio

0.6

o’8 * 0.4

op

‘5 o

Y 8 0.2 .- c m a> U

I I I I . ‘ . ’ RG Equation

Buckingham -0.4

-- ISO5167-Stolz -0.6 -

-n R I I I I ~~

V.”

2 3 4 6 10 Pipe diameter (inches)

Figure 4-2-Flange Tap Data Comparison-Mean Deviation (“h) versus Nominal Pipe Diameter

0.8 . 0.6

0.4 Oe 8 0.2 .- ;a g o 5 -0.2

v

.-

U

a> ’ -0.4

-0.6 I i 1 IS0 5167-Stolz I I I I I I I

104 I 05 106 107 108 Reynolds number ranges

Figure 4-3-Flange Tap Data Comparison-Mean Deviation (“YO) versus Reynolds Number Ranges


A P I NPMS*L4.3.4 92 0732290 0506305 231 m

SECTION %-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 4-BACKGROUND 17

V."

0.6

0.4 IS0 51 67-StOlz

9 L g 0.2 .- m o 5

I - C.

n $j -0.2

-0.4

-0.6

"." 0.2 0.375 0.5 0.575 0.66 0.75

Beta ratio

Figure 4-4-Corner Tap Data Comparison-Mean Deviation (%) versus Nominal Beta Ratio

0.8

0.6

0.4 8 c 0.2

'5 o 5 -0.2

Y

O m Q) U

0

.- c

-0.4

-0.6

-0.8

I .

104 105 106 107 108 Reynolds number ranges

Figure 4-5-Corner Tap Data Comparison-Mean Deviation ("70) versus Reynolds Number Ranges


0.8

0.6

0.4 8 8 0.2

Ei '5 o 8 5 -0.2

v

.-

a> ' -0.4 -0.6 11 -0.8

0.2 0.375 0.5 0.575 0.66 0.75 Beta ratio

Figure 4-6-D-D/2 (Radius) Tap Data Comparison-Mean Deviation (%) versus Nominal Beta Ratios

0.8

0.6

0.4 8

id '5 o

= -0.2 8 -0.4

v 8 0.2 .- a> U

-0.8 -OB 3 i 04 105 106 i 07 108

Reynolds number ranges

Figure 4-7-D-D/2 (Radius) Tap Data Comparison-Mean Deviation (%) versus Reynolds Number Ranges


' O

SECTION 3--CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 4-BACKGROUND 19

6

4

2 c O <-

id

e n o -2

-4

.e- - ---- WE?-- y y B

o

-6 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8

Log,,, Reynolds number

Figure 4-8-Scatter Diagram Based on Buckingham Equation

6

4

2 c O .- .- id 5 E O

n

c

! -2

-4

-6

o

3 3.5 4 4.5 5 5.5 6 6.5 . 7 7.5 8 Log,, Reynolds number

Figure 4-9-Scatter Diagram Based on Reader-HarridGallagher Equation



4.3 Implementation Procedures

4.3.1 INTRODUCTION

The implementation procedures in this document provide consistent computed flow rates for orifice meter installations which comply with other parts of this standard. A particular implementation may deviate from the supplied procedures only to the extent that final calculated flow rate does not differ from that calculated using the presented implementation procedure using IEEE Standard 754" double precision arithmetic by more than 50 parts per million in any case covered by the standard. This discrepancy is allowed in recognition of the need for real-time flow measurement computers to perform the required computations in a continuous manner with minimal computations.

This implementation procedure is divided into three subsections: solution for mass or volumetric flow rate (Section 4.3.2), special procedures for natural gas applications (Sec- tion 4.3.3), and implementation example calculations (Section 4.3.4). Three different rounding procedures are provided for rounding of input and output variables. Recommend- ed rounding tolerances for each of the variables are given in Appendix B. Section 4.3.2 demonstrates the general method for solving the mass flow equation used in orifice metering for either mass flow or standard volumetric flow. Since several additional standards are used when metering natural gas, the additional requirements and methods shown in Part 3 of this standard are presented in Section 4.3.3 of Part 4. Section 4.3.4 provides sample test cases that can be used to verify any computer logic developed to represent the implementation procedures.

4.3.2 SOLUTION FOR MASS OR VOLUME FLOW RATE

In Part 1, the equation for mass flow rate through an orifice meter was given as:

qm = : N , C d E v Y d 2 d v (4- 1)

Where:

Cd = orifice plate coefficient of discharge. d = orifice plate bore diameter calculated at flowing temperature, T f .

Al' = orifice differential pressure. E, = velocity of approach factor. N, = unit conversion constant.

qm = mass flow rate. pt,p = density of the fluid at flowing conditions (P,, T f ) .

The expansion factor,

z = universal constant (3.14159 ...).

Y = expansion factor.

is a function of the fluid being measured. If the metered fluid is considered incompressible (for example, water), the factor has a constant value of one. Otherwise, Y is a function of the orifice meter geometry, the fluid properties, and the ratio of the differential pressure to the static pressure. For the purposes of this standard, natural gas is considered to be a compressible fluid.

The volume flow rate at flowing (actual) conditions is related to the mass flow rate by:

I ' IEEE Standard 754-1985, IEEEStandard for Binary Floating Point Arithmetic, Institute for Electrical and Elec- tronic Engineers, New York, New York. See IEEE Standard 854-1987, IEEE Standard for Radix Independent Floating Point Arithmetic for discussion of non-binq machines.


API MPMS*14.3.4 92 0732290 0506309 987

SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS. PART 4-BACKGROUND 21

Where:

qm = mass flowrate. qv = volumetric flow rate at flowing (actual) conditions.

pt,p = densiiy of the fluid at flowing Conditions (q and Tf) . The volume flow rate at standard conditions is related to the mass flow rate by:

Q b = q m / P b (4-3) Where:

qm = mass flow rate. Qb = volume flow rate at base (standard) conditions. pb = density of the fluid at base conditions.

In Part 1, the orifice plate coefficient of discharge, C,, is given as a function of the orifice geometry and the pipe Reynolds number, Re,. The pipe Reynolds number is defined as:

- 4 q m ReD = - nuD (4-4)

Where:

p = absolute viscosity of the flowing fluid. D = meter tube internal diameter calculated at flowing temperature, Tf. In custody transfer applications, the mass flow rate is unknown and must therefore be

calculated using an iterative procedure. This section indicates how to solve for the mass flow rate in a reliable manner that yields consistent results. It is assumed for the purposes of this section that the following orifice geometry data is available:

dm = average orifice plate bore diameter measured in accordance with Part 2. Td, = measured orifice plate bore diameter temperature. a, = linear coefficient of thermal expansion of the orifice plate material. Dm = average meter tube internal diameter measured in accordance with Part 2 of this

TD, = measured meter tube internal diameter temperature. standard.

a, = linear coefficient of thermal expansion of the meter tube material.

Or:

d, = orifice plate bore diameter at reference temperature, Tf, determined according to

a, = linear coefficient of thermal expansion of the orifice plate material. D, = meter tube internal diameter at reference temperature, T,, determined according

a,! = linear coefficient of thermal expansion of the meter tube material. T, = reference temperature of orifice plate bore diameter and/or meter tube internal

diameter. According to Part 2, the reference temperature is 68°F (20°C).

Unlike previous versions of ANSI 2530, both the onfice plate bore diameter and meter tube intemal diameter must be corrected for temperature. Table 4-4 lists several typical values for the linear coefficient of thermal expansion that may be used in the application of this standard.

Application of this part requires the following data to be measured in accordance with the methods outlined in Part 2:

Part 2.

to Part 2.

= flowing temperature measured in accordance with Part 2. A.?' = orifice differential pressure.


22 CHAPTER 14-NATUFIAL GAS FLUIDS MEASUREMENT

Table 4-4-Typical Values of Linear Coefficients of Thermal Expansion

Linear Coefficient of Thermal Expansion (a)

US Units Metric Units íin/in-"F) (mm/mm-'C)

Type 304 & 3 16 stainless steela 0.00000925 O.OOO0 I67 Monela O.OoooO795 O.oooO143 Carbon Steelb 0.00000620 o.ooo0112

aFor flowing conditions between -1OO'F and +300"F, refer to ASME

bFor flowing Conditions between -7'F and +154'F, refer to Chapter 12, Section 2. Note: For flowing temperature conditions outside those stated above and for other materials, refer to the American Society for Metals Metals Handbook Desk Edition, 1985.

PTC 19.5; 4-1959.

And either:

P', = flowing pressure (upstream tap).

Pf2 = flowing pressure (downstream tap).

The following fluid property data is required as a function of Tf and p f : pr,p = density of the fluid at flowing conditions ( T f , p f ) ,

p = absolute viscosity of the flowing fluid. k = isentropic exponent (required for compressible fluids only), This is a dimension-

Additional data andor parameters required to determine the above quantities must either be made available as measured data or be determined by some other appropriate technical method. Acceptable methods for natural gas applications are specified in Section 4.3.3.

If volumetric flow at standard conditions is desired, then either the value of pb or the method of determining pb must be determined either by direct measurements, appropriate technical standards, or equations of state. Multiple parties involved in the measurement shall mutually agree upon the appropriate technical method to determine the base density of the fluid. Recommended methods for natural gas applications are specified in Part 3..

Four basic sets of units are provided for in this standard; U.S. practical engineering units, inch-pound (IP) units, practical metric (MT or metric) units, and System International units. Table 4-5 shows the expected units of each piece of data and the required unit conversion constants for each of these units sets. Other units sets may be used provided that the values for the units conversion constants are based on the SI units table and are converted using the full precision of the constants in ASTM-E380 or API Publication 2564 and then rounding the final result to six significant figures.

Basic input data used to determine the flow rate that is either input as text or transmitted as text may be rounded according to the specifications in Appendix 4-B. All other data should be retained to the full calculation precision being used.

The solution procedure given is not the only solution procedure acceptable, but it is believed to be the most reliable and predictable. Other solution techniques such as direct substitution have been investigated, but were not adopted except for natural gas applications for reasons given in Appendix 4-A. The outline of the solution procedure is given in 4.3.2.1.

less quantity.


A P I MPMS*14-3.4 92 m 0732290 0506333 535 m

SECTION %CONCENTRIC. SQUARE-EDGED ORIFICE METERS. PART 4-BACKGROUND 23

4.3.2.1 Outline of Solution Procedure for Flange-Tapped Orifice Meters

The general outline of the solution procedures for flange-tapped orifice meters is as follows: a. At Tf, calculate terms that depend only upon orifice geometry: d, D, b, E, and orifice coefficient correlation terms. These steps are outlined in Procedures 4.3.2.1 through 4.3.2.5. b. Calculate flowing pressure, Pf, from either QI or from QI and AP. Use Procedure 4.3.2.6A if QI is known. Otherwise use Procedure 4.3.2.6B. c. Calculate required fluid properties at Tf, p f and other specified fluid conditions. For natural gas as defined in Part 3, these methods are specified in Section 4.3.3. d. Calculate the appropriate fluid expansion factor. If the fluid is compressible follow Procedure 4.3.2.7A, otherwise follow Procedure 4.3.2.7B. e. Calculate the iteration flow factor, FI, and its component parts, FIc and Flp, used in the Cd(FT) convergence scheme according to Procedure 4.3.2.8. f. Determine the converged value of Cd(FT) using Procedure 4.3.2.9. Ifthe value is outside the range of applicability given in Part 1, the value of Cd(FT) should be flagged as being outside the uncertainty statement given in Part 1. g. Calculate the final value of qni (Procedure 4.3.2.10), qv (Procedure 4.3.2.11), or Qb (Procedure 4.3.2.12) as required.

Procedure 4.3.2.1 A Calculation of Orifice Plate Bore Diameter from Measured Diameter

Input: al = linear coefficient of thermal expansion of the orifice plate material. dn1 = orifice plate bore diameter measured at Tn,. Td, = orifice plate bore diameter measurement temperature.

Tf = flowing temperature.

d = orifice plate bore diameter calculated at flowing temperature, Tf. output:

Table 4-5-Units, Conversion Constants, and Universal Constants Variable(s) US. IP Metric S.I.

psia in H20 at 60°F

Ibm/ft3 l b m h

ftlhr3 OF

idin-"F CP

10.7316 psia-ft3Abmol-"F

28.9625 lbllbmol 323.279

6.23582 x lo4 27.7070

1 .o 459.67 68°F

3.14159

ft mm psia

in H20 at 60°F Ibm/ft3 I b m h

f t 3 h

O F ft/ft-"F lbmlft-s 10.7316

psia-ft3Abmol-"F 28.9625 IbAbmol 46552.1

0.0773327 27.7070

0.08333333 459.67 68°F

3.14159

bar millibar k g h 3 kg/hr m 3 h

OC mm/mm-"C

CP 0.083 145 1

bar-m3/kmol-"C 28.9625 kgkmol

0.036oooO 0.100000 1000.00

25.4 273.15 20°C

3.14159

m Pa Pa

k g h 3 kgls m3/s

K m/m-K

Pa-s 83 14.5 1

Jlkmol-K 28.9625 kgikmol

1 .o 1 .o 1.0

0.0254 0.0

293.15 K 3.14159



Procedure: Step 1 . Calculate orifice plate bore diameter at Tf according to:

(4-5)

Procedure 4.3.2.1 B Calculation of Orifice Plate Bore Diameter from Reference Diameter

Input: al = linear coefficient of thermal expansion of the orifice plate material. d, = orifice plate bore diameter calculated at reference temperature, T,. T, = reference temperature of orifice plate bore diameter and/or meter tube internal

diameter-680F (20°C). Tf = flowing temperature.

d = orifice plate bore diameter calculated at flowing temperature, Tf. output:

Procedure: Step 1 . Calculate orifice plate bore diameter at Tf according to:

1 d = d, l + a , ( T f - T , . ) [ Procedure 4.3.2.2A Calculation of Meter Tube Internal Diameter from

Measured Diameter Input:

cx, = linear coefficient of thermal expansion of the meter tube material. Dm = meter tube internal diameter measured at T,. TO,, = meter tube intemal diameter measurement temperature.

= flowing temperature. output: D = meter tube internal diameter calculated at flowing temperature, ïj.

Step 1. Calculate meter tube internal diameter at T f according to: Procedure:

D = .III[ Ita, ( T f - 'Dm ) ] Procedure 4.3.2.28 Calculation of Meter Tube Internal Diameter from

Reference Diameter Input: q = linear coefficient of thermal expansion of the meter tube material. D, = meter tube internal diameter at reference temperature, T,. T, = reference temperature of orifice plate bore diameter andor meter tube internal

Tf = flowing temperature.

D = meter tube internal diameter calculated at flowing temperature, Tf.

Step I . Calculate meter tube internal diameter at

diameter.

output:

Procedure: according to:

D = D r [ l + a , ( ï j - T , ) 1 (4-8) L J


SECTION &CONCENTRIC. SQUARE-EDGED ORIFICE METERS. PART 4-BACKGROUND 25

Procedure 4.3.2.344 Calculation of Diameter Ratio (ß) Input:

output:

d = orifice plate bore diameter calculated at flowing temperature, Tf. D = meter tube internal diameter calculated at flowing temperature, q. ß = ratio of orifice plafe bore diameter to meter tube internal diameter calculated at

flowing conditions. Procedure:

Step 1. Calculate ß using the formula:

ß= dlD (4-9)

Procedure 4.3.2.3B Calculation of Flowing Diameter Ratio (ß) from Measured Meter Tube and Orifice Bore Diameters

Input: a, = linear coefficient of thermal expansion of the orifice plate material. a, = linear coefficient of thermal expansion of the meter tube material. dm = orifice plate bore diameter at T,. D,, = meter tube internal diameter at T,, Td,, = orifice plate bore diameter measurement temperature. TD,, = meter tube internal diameter measurement temperature.

= flowing temperature. output:

ßm = ratio of orifice plate bore diameter to meter tube internal diameter calculated at flowing temperature, T f .

Procedure: Step 1. Calculate measured diameter ratio, ß,, according to the formula:

ß m = drnJDrn (4-10)

Step 2. Calculate /3 at flowing conditions according to the formula:

(4-1 1)

Procedure 4.3.2.3C Calculation of Flowing Diameter Ratio, ß, from Reference Meter Tube and Orifice Bore Diameters

Input: al = linear coefficient of thermal expansion of the orifice plate material. a, = linear coefficient of thermal expansion of the meter tube material. d, = orifice plate bore diameter at reference temperature, T,. D, = meter tube internal diameter at reference temperature, T,.

T, = reference temperature of orifice plate bore diameter andor meter tube intemal = flowing temperature.

diameter. output:

ß = ratio of orifice plate bore diameter to meter tube internal diameter calculated at flowing conditions.

Procedure: Step 1. Calculate reference diameter ratio, ßr , according to the formula:


__ ____. ----- - --- .. _I - __ A P I MPMS*L4-3-4 92 W 0732290 0506334 244 9


ß r = 4fDr (4-12)

Step 2. Calculate diameter ratio, ß, at flowing temperature according to the formula:

(4- 13)

Procedure 4.3.2.4 Calculation of Velocity of Approach Factor, E,

Input: B = ratio of orifice plate bore diameter to meter tube internal diameter calculated at

flowing conditions.

E, = velocity of approach factor.

Step I. Calculate velocity of approach factor, E,, by the following formula:

output:

Procedure:

(4-14)

Procedure 4.3.2.5 Calculation of Flange-Tapped Orifice Plate Coefficient of Discharge Constants

Input: D = meter tube internal diameter calculated at flowing temperature, Tf. p = ratio of orifice plate bore diameter to meter tube internal diameter calculated at

flowing conditions. Parameter Values:

Ao = 0.5961 Si = 0.0049 Al = 0.0291 S2 = 0.0433 A2 = -0.229 S, = 0.0712 A3 = 0.003 S4 = -0.1145 A4 = 2.8 S, = -0.2300 A5 = 0.000511 S, = -0.0116 A6 = 0.021 S, = -0.5200

s8 = -0.1400

Terms Ao through A6 and SI through & are numeric constants in the RG flange-tapped orifice meter coefficient of discharge equation. For details see Appendix 4-A.

output: c d = first orifice plate coefficient of discharge constant. Cd, = second orifice plate coefficient of discharge constant. Cdz = third orifice plate coefficient of discharge constant. cd3 = fourth orifice plate coefficient of discharge constant. Cd4 = fifth orifice plate coefficient of discharge constant.

N4 = unit conversion factor (discharge coefficient).

Step I. Calculate the dimensionless upstream tap position, L I , and dimensionless

O

Constants:

Procedure:

downstream tap position, L2. For flange-tapped orifices:

Li = N4fD (4- 15)

L2 = N4ID (4- 16)


. A P I M P M S * 3 4 * 3 - 4 92 = 0732290 0506335 L B O E

SECTION SCONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART +BACKGROUND 27

For other orifice meter tap configurations, see Appendix 4-A.

Step 2. Calculate the dimensionless downstream dam height, M2, according to the following formula:

2L2 M2 = - 1-ß

(4-17)

Step 3. Calculate upstream tap correction factor, Tu, according to the foilowing formula:

TU = [ s2+ s3e -8.5L, + ~ ~ ë ~ . ~ ~ l (4- 18)

Step 4. Calculate the downstream tap correction factor, TD, according to the following formula:

Step 5. Calculate small pipe correction factor, T,:

IfD > (A4 N4)

Then Ts .= 0.0

E l seq = A 3 ( l - ß ) ( A 4 - D / N 4 )

(4-19)

(4-20)

(4-21)

Step 6. Calculate the orifice plate coefficient of discharge constants at Reynolds number of 4,000 according to the following formulae:

(4-22)

(4-23)

(4-24)

(4-25)

(4-26)

Note: Library functions for calculating exponentials, powers, or square roots may be used if they are at least as accurate as the seven decimal versions presented in Sofhyare Manual for the Elementary Functions by William J. Cody and William Waite, Prentice- Hall, Englewood Cliffs, New Jersey (1980).

The FORTRAN library routines supplied by International Business Machines, Control Data Corporation, Digital Equipment Corporation, and UNISYS meet these requirements.

Procedure 4.3.2.6A Calculation of Upstream Flowing Fluid Pressure from Downstream Static Pressure

Input: 4, = flowing pressure (downstream tap). AP = orifice differential pressure.

4, = flowing pressure (upstream tap).

N3 = unit conversion factor (expansion factor).

output:

Constants:


. - __--- --- A P I MPMS*Lq.3.Y 92 W 0732290 05063Lb 017 W


Procedure: Step I. Calculate 5, according to the following formula:

AP f i N3 f i P = - + P (4-27)

Procedure 4.3.2.7A Calculation of Compressible Fluid Expansion Factor

Input: ß = ratio of orifice plate bore diameter to meter tube internal diameter calculated at

flowing conditions. AP = orifice differential pressure. f) = flowing pressure. k = isentropic exponent.

Y = expansion factor. output:

Constants:

Procedure:

to the formula:

N3 = unit conversion factor (expansion factor).

Step I. Calculate the orifice differential pressure to flowing pressure ratio, x, according

AP x = -

N3 5 (4-28)

Step 2. Calculate expansion factor pressure constant, 5, according to the formula:

0.41 + 0.35p4 (4-29) k y p =

Step 3. Calculate the expansion factor according to the formula:

Y = l - Y , x (4-30)

Procedure 4.3.2.7B Calculation of Incompressible Fluid Expansion Factor

Input:

output:

Procedure:

None


Step I . Expansion factor for incompressible fluid is defined to be unity.

Y = 1.0

Procedure 4.3.2.8 Calculation of Iteration Flow Factor

Input: d = orifice plate bore diameter calculated at flowing temperature, Tf. D = meter tube internal diameter calculated at flowing temperature, Tf. AP = orifice differential pressure. E, = velocity of approach factor. ,u = absolute viscosity of fluid flowing.


FI = iteration flow factor.

pt,p = density of the fluid at flowing conditions, Pf, Tf.

output:

Constants:

(4-31)


API MPMS*34*3.4 92 0732290 O506337 T53

SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART &BACKGROUND 29

Nrc = unit conversion constant for iteration flow factor.

Step 1. Calculate iteration flow factor intermediate values according to the formulae: Procedure:

4000 NlcDp F = 4 E, Yd2

5, = Al-

Step 2. Test for limiting value of iteration flow factor and limit accordingly:

If FI, < 1000 Frp Then 4 = FI,IFr,

(4-32)

(4-33)

(4-34)

Else FI = 1000 (4-35)

Procedure 4.3.2.9 Calculation of Flange-Tapped Orifice Plate Coefficient of Discharge

Input: Cd, = first orifice plate coefficient of discharge constant. C d , = second orifice plate coefficient of discharge constant. c d z = third orifice plate coefficient of discharge constant. c d 3 = fourth orifice plate coefficient of discharge constant. c d 4 = fifth orifice plate coefficient of discharge constant. 4 = iteration flow factor.

output: c d ( f l ) = orifice plate coefficient of discharge.

Constants: c d - f = onfice plate coefficient of discharge bounds flag.

X, = value of X where low Reynolds number switch occurs, 1.142 139 337 256 165 (Reynolds number of 3502.2) (4-36)

A, B = correlation constants for low Reynolds number factor A = 4.343 524 261 523 267 B = 3.764 387 693 320 165

(4-37) (4-38)

Procedure: Step 1 . Initialize cd(F?î) to a value at infinite Reynolds number.

c d ( m ) = c d ,

Step 2. Calculate X , the ratio of 4,000 to the assumed Reynolds number, according to the formula:

x = FI/ c d ( m ) (4-39)

Step 3. Calculate the correlation value of c d w ) , F, , at the assumed flow, X, and the derivative of the correlation with respect to the assumed value of C d m ) , O,, using the following formulae:

If (X<X,) then,


-.--I__- II-~. - -- A P I MPMS*34.3-4 92 m 0732290 O506338 99T

30 CHAPTER 14-NATUR GAS FLUIDS MEASUREMENT

Else,

(4-42)

0, = 0.7C,,X0'7+ X o * 8 + 0 . 8 ~ 4 X o ' 8 (4-43)

Step 4. Calculate the amount to change the guess for C,(J?ï), SC,, using the following formula:

cd (ml -Fc Scd = 0,

c, (Fu 1+-

Update the guess for C,(FT) according to:

cd(m) = cd(m) - SC, (4-44)

Step 5. Repeat Steps 2,3, and 4 until the absolute value of õcd is less than 0.000005. Step 6. If the value of X is greater than 1.0,

Then set C,-f Else clear Cd- f

Procedure 4.3.2.10 Calculation of Mass Flow Rate

Input: Cd(FT) = converged orifice plate coefficient of discharge.

d = orifice plate bore diameter calculated at flowing temperature, Tf. Aí' = orifice differential pressure. E, = velocity of approach factor.

P , , ~ = density of the fluid at flowing conditions (Pf, ïj). Y = expansion factor.

output: qm = mass flow rate.

N, = unit conversion factor (orifice flow). Constants:

Procedure: Step I. Calculate mass flow factor according to the formula:

n F,,,, = - N E d2 4 C "

Step 2. Calculate mass flow rate according to the formula:

Note: The term under the radical has been calculated in procedure 3.2.8 as Flp.

Procedure 4.3.2.11 Calculation of Volume Flow Rate at Flowing (Actual) Conditions

Input: Cd(Fï) = converged orifice plate coefficient of discharge.

d = orifice plate bore diameter calculated at flowing temperature, 5. AZ' = orifice differential pressure. E, = velocity of approach factor.

(4-45)

(4 - 46a)


A P I MPMS*34.3=4 92 W 0732290 0506339 8 2 6 W

SECTION INCENTRIC, WARE-ED ED RIFICE ZTERS,


qv = volume flow rate at flowing (actual) conditions. output:

Constants:

Procedure: N, = unit conversion factor (orifice flow).

Step 1. Calculate mass flow factor according to the formula:

4RT 4-BA - K

pt,p = density of the fluid at flowing conditions ( p f , Tf).

Step 2. Calculate volume flow rate according to the formula:

ROUND 31

(4-45)

(4-46b) Fmasscd (ml yd2Pt,pAp q v =

Pt,P

Note: The term under the radical has been calculated in procedure 4.3.2.8 as FIP.

Procedure 4.3.2.12 Calculation of Volume Flow Rate at Base (Standard) Conditions

Input: Cd(FT) = converged orifice plate coefficient of discharge.

d = orifice plate bore diameter calculated at flowing temperature, q. AP = orifice differential pressure. E, = velocity of approach factor. p b = density of the fluid at base conditions (4, Tb).

pt,p = density of the fluid at flowing conditions (Pf, Tf). Y = expansion factor.

output: Qb = volume flow rate at base conditions.

N, = unit conversion factor (orifice flow). Constants:

Procedure: Step 1. Calculate mass flow factor according to the formula:

Step 2. Calculate volume flow rate according to the formula:

(4-45)

(4-46c)

Note: The term under the radical has been calculated in procedure 4.3.2.8 as FIP.

4.3.3 SPECIAL PROCEDURES AND EXAMPLE CALCULATIONS FOR NATURAL GAS APPLICATIONS

Procedure 4.3.3.1 Calculation of Natural Gas Flowing Density Using Ideal Gas Relative Density (Specific Gravity), GI

Input: Gi = ideal gas relative density (specific gravity). Tj = flowing temperature. 9, = flowing pressure (upstream tap).



output: pf,p = density of the fluid at flowing conditions (Pf, Tf).

Constants: Mr,, = molecular weight of air.

R = universal gas constant. N5 = unit conversion factor (absolute temperature).

Step 1. Use appropriate A.G.A. Transmission Measurement Report No. 8 procedure

Step 2. Calculate the density of the fluid at flowing conditions according to the

Procedure:

to calculate the compressibility at flowing conditions, Zf , at G i , Tf, and 4.

formula:

(4-47)

Procedure 4.3.3.2 Calculation of Natural Gas Base Density Using Ideal Gas Relative Density (Specific Gravity), G,

Input: Gi = ideal gas relative density (specific gravity). G = base temperature. Pb = base pressure.

pb = density of the fluid at base conditions (4, Tb). output:

Constants: Mr,, = molecular weight of air.


Step 1. Use appropriate A.G.A. Transmission Measurement Report No. 8 procedure to

Step 2. Calculate the density of the fluid at base conditions according to the formula:

Procedure:

calculate the compressibility at base conditions, z b , at G , G, and pb .

Procedure 4.3.3.3 Calculation of Natural Gas Flowing Density Using Real Gas Relative Density (Specific Gravity), G,

Input: Gr = real gas relative density (specific gravity). 9, = flowing pressure (upstream tap).

Pm,, = measured air pressure. Pmglls = measured gas pressure.

Tf E flowing temperature. Tmair = measured air temperature. Tmgas = measured gas temperature. output:

Constants: Mair = molecular weight of air.


P , , ~ = density of the fluid at flowing conditions (P,, Tf).

(4-47)


SECTION SCONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 4-BACKGROUND 33

Procedure: Step I . Use the appropriate procedure from A.G.A. Transmission Measurement Report

No. 8 to calculate the air compressibility at air measurement conditions, Zma,, at &,;,. Since air is amixture of other gases, the full analysis method of A.G.A. Transmission Measurement Report No. 8 can be utilized to determine its compressibility. For those versions of A.G.A. Transmission Measurement Report No. 8 which do not contain Argon as a component, combine the Argon fraction and ail other missing fractions into the Carbon Dioxide fraction.

Step 2. Use the appropriate procedure fr0mA.G.A. Transmission Measurement Report No. 8 to calculate the gas compressibility at gas measurement conditions, Z,jlgas, at Gr, Tmga,,

Step 3. Calculate the ideal gas relative density (specific gravity), Gi, using the follow-

e

and elga. ing formula:

Gi = G, (4-48)

Step 4. Use the appropriate procedure fr0mA.G.A. Transmission Measurement Report

Step 5. Calculate the density of the fluid at flowing conditions according to the No. 8 to calculate the compressibility at flowing conditions, Zf, at Gi, Tf, and P

formula:

f:

(4-49)

Procedure 4.3.3.4 Calculation of Natural Gas Base Density Using Real Gas Relative Density (Specific Gravity), G,

Input: G, = real gas relative density (specific gravity). Pb = base pressure.

Pmair = measured air pressure. ejlgm = measured gas pressure. = base temperature.

Tmair = measured air temperature. Tmgm = measured gas temperature. output:

pb = density of the fluid at base conditions (4 , q). Constants: Mrair = molecular weight of air.


Step I . Use the appropriate procedure from A.G.A. Transmission Measurement Report No. 8 to calculate the air compressibility at air measurement conditions, Zmajr, at Tma, and Ga,, Since air is a mixture of other gases, the full analysis method of A.G.A. Transmission Measurement Report No. 8 can be utilized to determine its compressibility. For those versions of A.G.A. Transmission Measurement Report No. 8 which do not contain Argon as a component, combine the Argon fraction and all other missing fractions into the Carbon Dioxide fraction.

Procedure:


_I ___ -

API MPMSM14-3-4 72 W 0732270 0506322 310

34 CHAPTER 14-NATURAL GAS FLUIDS AEASUREMENT

Step 2. Use the appropriate procedure from A.G.A. Transmission Measurement Report No. 8 to calculate the gas compressibility at gas measurement conditions, Zmga,r, at G,, Tmga,r, and PmRi. Assume that G, is an ideal gas relative density (specific gravity) for this calculation.

Step 3. Calculate the ideal gas relative density (specific gravity), Gi, using the following formula:

(4-50)

Step 4. Use appropriate A.G.A. Transmission Measurement Report No. 8 to calculate

Step 5. Calculate the density of the fluid at base conditions according to the formula: the compressibility at base conditions, z b at Gj , & and Pb .

(4-5 1)

Procedure 4.3.3.5 Natural Gas Isentropic Exponent

Input: k = isentropic exponent, for calculation of expansion factor.

k = isentropic exponent, for calculation of expansion factor. output:

Procedure: Step 1. Recommended procedure is to use k = 1.3.

Procedure 4.3.3.6 Natural Gas Viscosity

Input: p = absolute viscosity of the flowing fluid, for calculation of Reynolds number or

iteration flow factor. output:

p = absolute viscosity of the flowing fluid, for calculation of Reynolds number or iteration flow factor.

Procedure: Step 1. Recommended procedure is to use

y = 0.0000069 lbm/ft*sec or p = 0.010268 cP.

4.3.3.7 Example Calculations Using Natural Gas Procedures

4.3.3.7.1 U.S. Units Examples

bore diameter is assumed. The geometric data for the meter is as follows: For the following two examples, a nominal 4 inch meter tube having a nominal 2 inch

meter tube internal diameter orifice plate bore diameter meter tube material

orifice plate material

4.025 inches at 68°F 2.000 inches at 68°F carbon steel pipe

austenitic stainless steel 6.20 x lod iníin -OF coefficient of thermal expansion (&)

9.25 x lo6 idin -OF coefficient of thermal expansion (a,)


API MPMS*L4.3-4 72 m 0732270 O506323 257 m

SECTION %CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART &BACKGROUND 35

Example 1

Calculate the mass flow rate and base volume flow rate of a natural gas having an ideal gas relative density (specific gravity) of 0.65 with 2.0% mole carbon dioxide and 5.0% mole nitrogen. The gas is flowing at 86'F and a downstream pressure of 199.3 psia with an orifice differential pressure of 20 inches of water column at 60°F. Base conditions are 60°F and 14.73 psia.

In this example, the flowing pressure must be calculated according to Procedure 4.3.2.6A. Procedure4.3.3.1 can then be used to calculate the density of the fluid at flowing conditions and Procedure 4.3.3.2 can be used to calculate the density of the fluid at base conditions.

20 27,707 p f = 199.3 + -

200.022 psia

Using A.G.A. Transmission Measurement Report No, 8 GCN [real relative density (specific gravity), % carbon dioxide, and % nitrogen] composition characterization procedure:

Zj = 0.973174

AGA-8 (1985) requires input in terms of real gas gravity rather than ideal gas gravity. It is necessary to iteratively solve for the real gas gravity at the AGA-8 base conditions of 60°F and 14.73 psia using the formula:

Gr = ci * zbair~zbgas

For the first iteration assume that Gr = Ci to calculate the initial value of This procedure must be repeated until the assumed and calcuIated values of Gr agree within 2 x lod. The value of to be used for this procedure is 0.999590. For this example the iteration history is as follows:

Iter Gr zbenv

Pt.

O 0.65 0.997646 1 0.65 1267 0.997634 2 0.65 1275 0.997634 3 0.65 1275 0.997634

200.022 x 28.9625 x 0.65 0.973174 x 10.7316 x (86 + 459.67)

- - = 0.660758 lbmlft3

z b = 0.997634

14.73 x 28.9625 x 0.65 pb = 0.997634 x 10.7316 x (60 + 459;67)

= 0.0498412 lbm/ft3

At flowing conditions, the orifice plate bore diameter and the meter tube internal diameter are calculated using Procedures 4.3.2.1B and 4.3.2.2B and the p ratio is calculated according to Procedure 4.3.2.3A.

d = 2.00 x [ 1 + 9.25 x (86 - 68) ] = 2.00033


- - A P I MPMS*L4-3-4 92 W 0732290 0506324 193 W


D = 4.025 X [ 1 + 6.20 x (86 - 68) ] = 4.02545

2.00033 ß = 4.02545

= 0.496921

The velocity of approach factor is calculated according to Procedure 4.3.2.4.

1 =

J- = 1.03195

The expansion factor is calculated according to Procedure 4.3.2.7A using the isentropic exponent value provided by Procedure 4.3.3.5.

k = 1.30 20.0

27.707 x 200.022

0.41 -k 0.35 x 0.4969214

x =

= 3.6088 x

1.30 Yp =

= 0.331801

Y = 1 - 0.331801 x 3.6088 x iob3

= 0.998803

The iteration flow factor is calculated using Procedure 4.3.2.8 with the absolute viscosity provided by Procedure 4.3.3.6.

p = 0.010268cP

4000 x 6.23582 x lop4 x 4.02545 x 0.010268 1.03195 x 2.000332 x 0.998803

FI, =

= 0.0249984

FrP = d 2 x 0 . 6 6 0 7 5 8 ~ 2 0 = 5.14104

0.0249984 5.14104

= 4.86252 x lo-’

6 - -

Procedure 4.3.2.5 is used to calculate the orifice plate coefficient of discharge correlation constants.

L1 = Lz 1 .o

4.02545 = -


37 SECTION M O N C E N T R I C , SQUARE-EDGED ORIFICE METERS, PART &BACKGROUND

= 0.248419

2 x 0.248419 Mz = 1 - 0.496921

= 0.987594

= 1.69652 x

To = -0.0116 (0.987594 -0.52 x O.987594la3) 0.496921"'

= -2.55828 x

T, = 0.0

cd,, = 0.5961 -k 0,0291 x 0.496921'- 0.229 X 0.496921'1- 1.69652 X w3- 2.55828 X

= 0.601573

c d , = 0.000511 x 0.496921°'7 x 250°*7

= 0.0149410

c d , = 0.021 x 0.4969214 x 250°.35

= 8.84398 x

cd3 = 0.0049 x 0.4969214.8 x 4.75°'8 x 250°.3J

= 4.10213 x loy3

c4 = ( -0.23 x 1.69652 x I- 0.14 x 2.55828 x 0.496921°.8 X 4.75"¿?

= -6.36917 x i r 5

Using Procedure 4.3,2.9 to calculate tbe orifice plate coefficient of discharge results in the following iteration history:

c d = 0.601573

X = 8.08301 x

F, = 0.603738

0, = 9.49450~ lo4

scd = -0.00216159

c d = 0.603735

X = 8.05406 x loy3

F, = 0.603735

0, = 9.47757 x lo4

scd = - o . ~ o ( ) c d = 0.603735


_ - -

A P I M P M S * L 4 - 3 - 4 92 m 0732290 0506326 Tbb m


The mass flow rate can now be Calculated using Procedure 4.3.2.10.

323.279.~ 3.14159 x 1.03195 x 2.000332 4 Fmoss =

= 1048.40

qm = 1048.40 x 0.998803 x 0.603735 x 5.14104

= 3250.16 lbm/hr

The base (standard) volume flow rate is calculated using Procedure 4.3.2.12.

Q b = 1048.40 x 0.998803 x 0.603735 x 5.14104

0.0498412

= 65.2102 x lo3 f?/hr

Example 2

Calculate the mass flow rate and base volume flow rate of a natural gas having a real gas relative density (specific gravity) of 0.65 with 2.0% mole carbon dioxide and 5.0% mole nitrogen. The real gas relative density (specific gravity) was measured at 60°F and 14.73 psia. The gas is flowing at 86°F and an upstream pressure of 200.0 psia with an orifice differential pressure of 20 inches of water column at 60°F. Base conditions are 60°F and 14.73 psia.

In this example, the flowing pressure must be calculated according to Procedure 4.3.2.6B. Procedure 4.3.3.3 can then be used to calculate the density of the fluid at flowing conditions, and Procedure 4.3.3.4 can be used to calculate the density of the fluid at base conditions.

Pf z 200.0

Using the A.G.A. Transmission Measurement Report No. 8 compositional characterization procedure for air and the composition for air given by Jones", the air compressibility for air at gravity measurement conditions is:

= 0.999590

Using the A.G.A. Transmission Measurement Report No. 8 GCN composition characterization procedure, assuming that the ideal gas relative density (specific gravity), Gj , is the same as the real gas relative density (specific gravity), G,:

Zmgos = 0.997646

Using these values to calculate the ideal gas relative density:

Gì = 0.65 x 0.997646

0.999590

= 0.648736

Using A.G.A. Transmission Measurement Report No. 8 GCN composition characterization procedure: .

Zf = 0.973311

200.0 x 28,9625 x 0.648736 ' t p = 0.97331 1 x 10.7316 x (86 + 459.67)

= 0.659307 l bd f?

I* Jones, Frank E., "The Air Density Equation and the Transfer of the Mass Unit," Journal of Research of the National Bureau of Standards, Vol. 83, No. 5, 1978, pp. 419-428.


A P I MPMS*14-3=4 92 W 0732290 0506327 9T2

SECTION &CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 4-BACKGROUND 39

Zb = 0.997646

14.73 x 28.9625 x 0.648736 pb = 0.997646 x 10.7316 x (60 + 459.67)

= 0.0497437 Ibdf?

At flowing conditions, the orifice pIate bore diameter and the meter tube internal diameter are calculated using procedures 4.3.2.1B and 4.3.2.2B and the ßratio is calculated using Procedure 4.3.2.3A.

d = 2.00 x [ 1 + 9.25 X (86 - 68) ] = 2.00033

D = 4.025 x I] 1 + 6.20 x (86 - 68) ] = 4.02545

2.00033 ß = 4.02545

= 0.496921

The velocity of approach factor is calculated according to Procedure 4.3.2.4.

1

= 1.03195


k = 1.30

20.0 27.707 x 200.0 x =

= 3.60920 x iod3 0.41 f 0.35 x 0.496921 Yp =

1.30

= 0.331801

Y = 1 - 0.331801 x 3.60920 x

= 0.998802


p = 0.010268cP

4000 x 6.23582 x x 4.02545 x 0.010268 FIc =

1.03195 x 2.000332 x 0.998802 = 0.0249984



FIP = A2 x 0.659307 x 20

= 5.13540

0.0249984 5.13540

= 4.86786 x

FI =


LI = L,

1 .o 4.02545

= 0.248419

- - -

2 x 0.248419 M2 = 1 - 0.496921

= 0.987594

Tu = ( 0.0433 + 0.0712

= 1.69652 x 10"

0,1145~-6.0~0.248419 0.4969214 -8.5~0.248419 - 1 - 0.4969214

TO = -00116 ( 0.987594 - 0.52 x 0,987594'.3) 0.496921"'

= -2.55828 x

TS = 0.0

cd0 = 0.5961 0.0291 x 0.4969212- 0.229 X 0.4969218+ 1.69652 X w3- 2.55828 X 10-

= 0.601573

cd, = 0.0005 11 x 0.496921°'7 x 250°a7

= 0.0149410

C& = 0.021 x 0.4969214 x 250°.35

= 8.84398 x lou3

Cd, = 0.0049 x 0.4969214" x 4.75°.8 x '

= 4.10213 X ¡O-3

cd4 = ( -0.23 x 1.69652 x + 0.14 x 2.55828 x ) 0.496921°*8 x 4.75'"

= -6.36917 x 10"

Using Procedure 4.3.2.9 to calculate the orífice plate coefficient of discharge results in the following iteration history:

Cd = 0.601573

X = 8.09189x lod3

F, = 0.603739


A P I MPMS*14*3-4 92 W 0732290 0506329 775


0, = 9.49968 x lo4

6 c d = -0.00216258

c d = 0.603736

X = 8.06290 x

F, = 0.603736

0, = 9.48274 x lo4 s c d = - 0 . 0 0 0 ~

c d = 0.603736

The mass flow rate can now be calculated using Procedure 4.3.2.10.

323.279 x 3.14159 x 1.03195 x 2.00033* 4 F",O, =

= 1048.40

qm = 1048.40 x 0.998802 x 0.603736 x 5.13540

= 3246.59lbmíhr


Qb = 1048.40 x 0.998802 x 0.603736 x 5.13540

0.497437

= 65.2664 x lo3 f?/hr

4.3.3.7.2 Metric Units Examples

50 millimeter bore diameter is assumed. The geometric data for the meter is as follows: For the following two examples, a nominal 100 millimeter tube having a nominal

meter tube internal diameter orifice plate bore diameter meter tube material

orifice plate material

102.24 millimeters at 20°C 50.8 millimeters at 20°C carbon steel pipe

austenitic stainless steel 11.16 x lo4 mím - O C coefficient of thermal expansion (q)

16.65 x lod m/m -OC coefficient of thermal expansion (a,)

Example 1

Calculate the mass flow rate and base volume flow rate of a natural gas having an ideal gas relative density (specific gravity) of 0.65 with 2.0% mole carbon dioxide and 5.0% mole nitrogen. The gas is flowing at 30°C and a downstream pressure of 13.74 bar with an orifice differential pressure of 49.8 millibar. Base conditions are 15°C and 1.01325 bar.

In this example, the flowing pressure must be calculated according to Procedure 4.3.2.6A. Procedure 4.3.3.1 can then be used to calculate the density of the fluid at flowing conditions, and Procedure 4.3.3.2 can be used to calculate the density of the fluid at base conditions.

49.8 Pf = 13.74+- 1000.0

= 13.7898bar


- -_____ __ __-.I_----

A P I MPMS*LY-3-4 92 - 0732290 0506330 LI97 - 42 CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT

AGA-8 (1985) requires input in terms of real gas gravity rather than ideal gas gravity. It is necessary to iteratively solve for the real gas gravity at the AGA-8 base conditions of 60°F and 14.73 psia using the formula:

G r = zbR;r/zbgns

For the first iteration assume that G, = Gj to calculate the initial value of Zbg,,. This procedure must be repeated until the assumed and calculated values of G, agree within 2 x lo4. The value of ZbRir to be used for this procedure is 0.999590. For this example the iteration history is as follows:

Iter

O 0.65 0.997635 1 0.65 1267 0.997634 2 0.651275 0.997634 3 0.651275 0.997634

Using A.G.A. Transmission Measurement Report No. 8 GCN composition characterization procedure:

Zf = 0.973174

13.7898 x 28.9625 x 0.65 pr*p = 0.973174 x 0.0831451 x (30 + 273.15)

= 10.5834 kg/m3

z b = 0.997624

1.01325 x 28.9625 x 0.65 pb = 0.997624 x 0.0831451 x (15 + 273.15)

= 0.798078 kg/m3

At flowing conditions, the orifice plate bore diameter and the meter tube internal diameter are calculated using procedures 4.3.2.1B and 4.3.2.2B and the diameter ratio, ß, is calculated using procedure 4.3.2.3A.

d = 50.8 x [ 1 + 16.65 x (30 - 15) ] = 50.8085

D = 102.24 X [ 1 + 1 1 . 1 6 ~ (30- 15)]

= 102.251

50.8085 ß = 102.251

= 0.496900

The velocity of approach factor is calculated according to Procedure 4.3,2.4.

1

J- = 1.03195


A P I f l P M S * 3 4 - 3 - 4 92 0732290 O506333 323

43 SECTION SCONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 4-BACKGROUND


k = 1.30

49.8 1000.0 x 13.7898

0.41 + 0.35 x 0.4969004 1.30

x =

= 3.61136 x loL3

y p =

= 0.331798

Y = 1 - 0.331798 x 3.61136 x lod3

= 0.998802


/i = 0.010268cP

4000 x 0.10000 x 102.251 x 0.010268 1.03195 x 50.80852 x 0.998802

F;, =

= 0.157835

= 2/2 x 10.5834 x 49.8

= 32.4671

0.157835 32.4671

FI =

= 4.86138 x

Procedure 4.3.2.5 is used constants.

0 alculate the orifice pl^; coefficient of discharge correlation

- 25.4

= 0.248408

- - 102.25 1

2 x 0.248408 M2 = 1 - 0.496900

= 0.987509

TO = -0.0116 ( 0.987509 - 0.52 x 0.9875091.3) 0.4969001.'

= -2.55802 x


CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT

T, = 0.0

Cdo = 0.5961 + 0.0291 x 0.4969002- 0.229 x 0.496900’+ 1.69615 x 2.55802 x 10”

= 0.601572

Cd, = 0.0005 11 x 0.496900°‘7 x

= 0.0149406

Cdz = 0.021 x 0.4969004 x

= 8.84248 x

Cd3 = 0.0049 x 0.4969004” x 4.75’“ x 250°.35

= 4.10130 x

cd4 = ( -0.23 x 1.69652 x + 0.14 x .2.55828 x 0.496921O” x 4.75”’

= -6.35927 x lo-’

Using Procedure 4.3.2.9 to calculate the orifice plate coefficient of discharge results in the following iteration history:

C, = 0.601572

X = 8.08113 x

F, = 0.603737

0, = 9.49231 x lo4

6cd = -0.00216159

Cd = 0.603734

X = 8.05219 x 10”

F, = 0.603733

0, = 9.47539 x lo4

sc, = 0.00000

Cd = 0.603733

O’

The mass flow rate can now be calculated using Procedure 4.3.2.1 O.

. - 0.003600 x 3.14159 x 50.80852 4 mass -

= 75.3223

qm = 75.3223 x 0.998802 x 0.603733 x 32.4671

= 1474.66kgíhr 1

The base (standard) volume flow rate is calculated using Procedure 4.3.2.12. 1 75.3223 x 0.998802 x 0.603733 x 32.4671

0.798078 Q b =

= 1847.76 x m3/hr ad W


A P I MPMS*14-3-4 92 = 0732290 0506333 LTb

SECTION

Example 2

-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 4-BACKGROUND 45

Calculate the mass flow rate and base volume flow rate of a natural gas having a real gas relative density (specific gravity) of 0.65 with 2.0% mole carbon dioxide and 5.0% mole nitrogen. The real gas relative density (specific gravity) was measured at 15°C and 1.01325 bar. The gas is flowing at 30°C and an upstream pressure of 13.79 bar with an orifice differential pressure of 49.8 millibar. Base conditions are 15°C and 1.01325 bar.

In this example, the flowing pressure must be calculated according to Procedure 4.3.2.6B. Procedure 4.3.3.1 can then be used to calculate the density of the fluid at flowing conditions and Procedure 4.3.3.2 can be used to calculate the density of the fluid at base conditions.

p f = 13.79 bar

Using the compositional characterization procedure for air from A.G.A. Transmission Measurement Report No. 8 and the composition for air given by Jones (see footnote 12), the compressibility for air at gravity measurement conditions is:

Z,,zair = 0.999586 (SI basis) and 0.999590 (AGA-8 basis)

AGA-8 (1985) requires input in terms of real gas gravity at 60°F and 14.73 psia rather than the specified base conditions of 15°C and 101.325 kPa. It is necessary to iteratively solve for the real gas gravity at the AGA-8 base conditions using the formula:

GrAcAm, = GrSI/ @ba, zbgas)SL (zba;r/zbgas)AGA-8

For the first iteration assume that GrAGA-, = GrSI to calculate the initial value of zbgos at both sets of base conditions. The compressibility factor for air, zba;,, at the AGA-8 conditions is 0.999590 and at SI base conditions is 0.999586. The procedure must be repeated until the assumed and calculated values ofGr agree within 2 x lo-'. The value OfZbair to be used for this procedure is 0.999590. For this example the iteration history is as follows:

AGA-8 Basis SI Basis Iter Gr 'bPos zbpa.r

O 0.65 0.997646 0.997635 1 0.649996 0.997646 0.997635 2 0.649996 0.997646 0.997635

Using the A.G.A. Transmission Measurement Report No. 8 GCN composition characterization procedure, assuming that the ideal gas relative density (specific gravity), Gi, is the same as the real gas relative density (specific gravity), G, :

ZmgaS = 0.997635 (SI basis) and 0.997646 (AGA-8 basis)

Using these values to calculate the ideal gas relative density (specific gravity):

0.65 x 0.997635 0.999586

Gi =

= 0.648731

Using A.G.A. Transmission Measurement Report - . J. 8 GCN composition characterization procedure:

z f = 0.973312

13.79 x 28.9625 x 0.648731 pt ,p = 0.973312 x 0.0831451 x (30 + 273.15)



= 10.5614 k g h 3 Zb = 0.997635

1.01325 x 28.9625 x 0.648731 pb = 0.997635 x 0.0831451 x (15 + 273.15)

= 0.796511 kg/m3

At flowing conditions, the orifice plate bore diameter and the meter tube internal diameter are calculated using procedures 4.3.2.1B and 4.3.2.2B and the p ratio is calculated using Procedure 4.3.2.3A.

d = 50.8 x [ 1 + 16.65 x (30 - 15) ] = 50.8085

D = 102.24 x [ 1 + 11.16 x (30 - 15) ] = 102.251

50.8085 ß = 102.251

= 0.496900

The velocity of approach factor is calculated using Procedure 4.3.2.4.

E, = 1

J1-orl.969004 = 1.03195


k = 1.30

49.8 1000.0 x 13.79

0.41 + 0.35 x O.4969OO4 1.30

x =

= 3.61131 x

y p =

= 0.331798

Y = 1 - 0.301635 x 3.61131 x

= 0.998802

The iteration flow factor is calculated using Procedure 4.3.2.8. The absolute viscosity is calculated using Procedure 4.3.3.6.

,li = 0.010268cP

4000 x 0.1ooOO x 102.251 x 0.010268 1 .O3 195 x 50.8085' x 0.998802 FI, =


A P I f l P M S * 1 4 = 3 - 4 92 m 0732290 0506335 T79 =

47 SECTION &CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 4-BACKGROUND

= 0.157835

FIp = A2 x 10.5614 x 49.8

= 32.4333

0.157835 32.4333

FI =

= 4.86645 x


- 25.4 102,251

= 0.248408

- -

2 x 0.248408 MZ = 1 - 0.496900

= 0.987509

T, = ( 0.0433 + 0,0712 e-8.5 X 0.248408 - 0.1145 e-6.0 x 0.248408 0*4969004 1 - O.4969OO4

)

= 1.69615 x

TO = -0.01 16 ( 0.987509 - 0.52 x 0.9875091.3 ) 0.496900

= -2.55802 x

T, = 0.0

cdo = 0.5961 -k 0.0291 X 0.496900’- 0.229 X 0.4969008+ 1.69615 X m3- 2.55802 X 10”

= 0.601572

Cdi = 0.0005 11 X 0.496900°’7 x 250°’7

= 0.0149406

cd, = 0.021 x 0.4969004 x 250°.35

= 8.84248 x

c d , = 0.0049 x 0.4969004‘8 x 4.75°‘8 x

= 4.10130 x

cd, = (-0.23 x 1.69615 x + 0.14 X 2.55802 X 0.496900°‘8 x4.75°’8

= -6.35927 x lo9 l Using Procedure 4.3.2.9 to calculate the orifice plate coefficient of discharge results in the

following iteration history:

c d = 0.601572

X = 8.08956 x

F, = 0.603738


48 CHAPTER . -NATURAL AS FLUIC MEASUREMENT

0, = 9.49723 x 10"

SC, = -0.00216259

C, = 0.603735

X = 8.06057 x

F, = 0.603734

0, = 9.48029 x lo4

sc, = 0.0000

C, = 0.603734

The mass flow rate can now be calculated using Procedure 4.3.2.10.

0.003600 x 3.14159 x 50.80852 4 Fm, =

= 75.3223

4m - - 75.3223 x 0.998802 x 0.603734 x 32.4333

= 1473.13 k g k


Qsb = 0.7965 11 75.3223 x 0.998802 x 0.603734 x 32.4333

= 1849.47 x m3/hr

4.3.4 EXAMPLE CALCULATIONS

This section provides sample test cases that can be used to verify computer logic developed to represent the implementation procedure. The final computed flow rates obtained from a computerized solution must agree with the final solutions in these example cases to within 50 parts per million. The values for all key parameters as well as the values for the intermediate terms are provided so the cause of deviations in final results outside the acceptable tolerance can be resolved. A possible source of difference between two independent calculations may be input precision. A set of acceptable input precision levels is presented in Table 4-B-1 of Appendix 4-B. If computed rates continue to differ by more than 50 parts per million, check the deviation of the following intermediate values:

a. Orifice diameter (d) should be within 25 ppm. b. Velocity of approach factor (E,) should be within 50 ppm. c. Expansion factor (Y) should be within 50 ppm. d. Orifice coefficient (C,) should be within 50 ppm. e. Flowing densiiy ( P ~ , ~ ) should be within 100 ppm.

input values for the six examples are given in Table 4-6. The values for constants given in Table 4-5 must be used to the precision stated. The

4.3.4.1 Example Test Case Number 1

Calculate the mass and volumetric flow rate for a liquid hydrocarbon stream fiowing through a mild carbon steel two inch schedule 80 pipe with a 316 SS plate (see Table 4-4). Assume the reference diameters were measured at standard conditions. Output for example test case number 1 is shown in Table 4-7. The input physical parameters and flowing conditions are noted with an asterisk (*). See Table 4-5 for the US, IF', metric, and SI units.



Table 4-ô-Input Parameters for Six Example Test Cases (US, iP, Metric, and Si Units)

US Units

"2 dm ai APinches of in/in-"F in in/in-"F H?O at 60°F

Pf4J P k p6 qn Case No. "F mia lb/ft3 CP lb/ft3 in ExampleTest T/ 9

1 210.00 14.696 58.792 2.8250E-01 -1.0 62.366 1.93945 0.00000620 1.45311 O.OoooO925 110.1736 2 0.00 14.696 58.199 1.8650E+03 -1.0 56.861 7.98146 0.00000620 1.59374 O.oooO0925 8.9938 3 0.00 200.00 2.0466 1.3520E-02 1.3198 0.116198 4.02638 0.00000620 2.66406 O.OoooO925 56.21 10 4 0.00 200.00 2.0466 1.3520E-02 1.3198 0.116198 1.93945 O.OoooO620 0.19531 0.00000925 2.2484 5 0.00 200.00 2.0466 1.3520E-02 1.3198 0.116198 1.93945 O.OoooO620 0.19531 0.00000925 440.6943 6 0.00 14.696 58.199 1.8650E+03 -1.0 56.861 7.98146 0.0oooO620 0.79689 0.00000925 2.2484

iP Units G p l e Test-- T/ Case No. O F

1 210.00 2 0.00 3 0.00 4 0.00 5 0.00 6 0.00

9 psia

14.696 14.696

200.00 200.00 200.00

14.696

P i:% lbdft-s

58.792 1.8983E-04 58.199 í.2532 2.0466 9.0850E-06 2.0466 9.0850E-06 2.0466 9.0850E-06

58.199 1.2532

k

-1.0 -1.0

1.3198 1.3198 1.3198

-1.0

P6 lb/ft3

62.366 0.1616208 56.861 0.6651217 0.116198 0.3355317 0.116198 0.1616208 0.116198 0.1616208

56.861 0.6651217

" 2 ftlft -OF

O.OoooO620 0.0oooO620 O.OoooO620 0.00000620 0.00000620 0.00000620

dl11 ft

O. 1210925 O. 13281 17 0.2220050 0.0162758 0.0162758 0.0664075

a, APinches of ft/ft-"F H,O at 60°F

~ ~

0.00000925 110.1736 O.oooO0925 8.9938 0.00000925 56.21 10 0.00000925 2.2484 O.OoooO925 440.6943 0.00000925 2.2484

Metric Units

Case No. "C bar kg/m3 CP kg/m3 mm mm/mm°C mm mm/m-"C millibar Example Test 7

1 98.89 1.01325 941.75 2.8250E-01 -1.0 999.01 49.262 O.oooO112 36.909 O.ooOo167 274.159 2 -17.78 1.01325 932.26 1.8650E+03 -1.0 910.83 202.729 0.0000112 40.481 0.0000167 22.380 3 -17.78 13.7895 32.783 1.3520E-02 1.3198 1.86131 102.270 O.oooO112 67.667 O.oooO167 139.877 4 -17.78 13.7895 32.783 1.3520E-02 1.3198 1.86131 49.262 O.ooOo112 4.961 O.oooO167 5.595 5 -17.78 13.7895 32.783 1.3520E-02 1.3198 1.86131 49.262 O.oooO112 4.961 0.0000167 1096.635 6 -17.78 1.01325 932.26 1.8650E+03 -1.0 910.83 202.729 0.0000112 20.241 O.ooOo167 5.595

Pt,p P k P6 Dni "2 d,, "i AP Pr

SI Units a 2 4 1 "i AP

m/m-K m m/m-K Pa PCP P k P6 Drn

kdm Pa-s kdm3 m ExampleTest T/ 9 Case No. "K Pa

1 372.04 1.01325E+05 941.75 2.82503-04 -1.0 999.01 0.049262 O.ooOo112 0.036909 O.oooO167 27415.9 2 255.37 1.01325E+05 932.26 1.8650 -1.0 910.83 0.202729 O.oooO112 0.040481 0.0000167 2238.0 3 255.37 1.37895E+06 32.783 1.3520E-05 1.3198 1.86131 0.102270 O.oooO112 0.067667 O.oooO167 13987.7 4 255.37 lt37895E+06 32.783 1.3520E-05 1.3198 1.86131 0.049262 0.0000112 0.004961 O.ooOo167 559.5 5 255.37 1.37895E+06 32.783 1.3520E-05 1.3198 1.86131 0.049262 0.0000112 0.004961 O.oooO167 109663.5 6 255.37 1.01325E+05 932.26 1.8650 -1.0 910.83 0.202729 O.oooO112 0.020241 O.oooO167 559.5

Note: For al l cases, the reference diameters (& and DnJ are assumed to be at standard conditions. A value of -1 .O for the isentropic exponent (k) indicates that the fluid is incompressible.


A P I M P M S * L 4 - 3 . 4 92 W 0732290 050b338 788 W



Calculate the mass and volumetric flow rate for a liquid hydrocarbon stream flowing through a mild carbon steel eight inch schedule 40 pipe with a 316 SS plate (see Table 4-4). Assume the reference diameters were measured at standard conditions. Output for example test case number 2 is shown in Table 4-8. The input physical parameters and flowing conditions are noted with an asterisk (*). See Table 4-5 for the US, IP, metric, and SI units,


Calculate the mass and volumetric flow rate for a gas hydrocarbon stream flowing 8

through a mild carbon steel four inch schedule 40 pipe with a 316 SS plate (see Table 4-4). Assume the reference diameters were measured at standard conditions. Output for example test case number 3 is shown in Table 4-9. The input physical parameters and flowing conditions are noted with an asterisk (*). See Table 4-5 for the US, IP, metric, and SI units,


Calculate the mass and volumetric flow rate for a gas hydrocarbon stream flowing through a mild carbon steel two inch schedule 80 pipe with a 316 SS plate (see Table 4-4). Assume the reference diameters were measured at standard conditions. Output for example test case number 4 is shown in Table 4-10. The input physical parameters and flowing conditions are noted with an asterisk (*). See Table 4-5 for the US, IP, metric, and SI units.

4.3.4.1

pressure. Output for example test case number 5 is shown in Table 4-11.

Example Test Case Number 5

This example calculation is the same as example 4 but with a much higher differential

4.3.4.1

This example calculation is the same as example 2 but with a lower differential pressure and a smaller orifice diameter, causing the iteration flow factor to exceed the 1000 maximum limit. Output for example test case number 6 is shown in Table 4-12.

Example Test Case Number 6


SECTION %CONCENTRIC. SQUARE-EDGED ORIFICE METERS. PART &BACKGROUND 51

Table 4-7-Intermediate Output for Example Test Case No. 1

Symbol us Units IP units Metric Units SI Units

Calculate temperature corrected diameters *Measured pipe diameter *Coefficient of thermal expansion *Pipe diameter measurement temperature *Flowing fluid Pipe diameter *Measured orifice diameter *Pipe coefficient of thermal expansion *Orifice diameter measurement temperature Orifice diameter

Calculate diameter ratio (ß) Orifice diameter Pipe diameter Diameter ratio, p

Calculate cd correlation constants Upstream tap position Downstream tap position Dam height Upstream tap term Downstream tap term Small pipe diameter correction term Pipe diameter Diameter ratio, p Conversion factor Correlation constant 1 Correlation constant 2 Correlation constant 3 Correlation constant 4 Correlation constant 5

Calculate velocity of approach factor Diameter ratio, ß ß squared ß raised to fourth power Velocity of approach factor

Calculate fluid expansion factor *Compressible fluid switch (1 = yes) Units conversion factor Diameter ratio, ß *Isentropic exponent *Differential pressure *Flowing pressure Expansion factor

Calculate iteration flow factor Unit conversion constant Pipe diameter Orifice diameter Velocity of approach factor Huid expansion factor *Fluid viscosity *Huid density Differential pressure AP independent part of 4 AP dependent part of 4 Maximum value of i$ Iteration flow factor

Calculate the orifice coefficient Iteration flow factor Correlation constant 1 Correlation constant 2 Correlation constant 3

1.939450E+00 6.200000E-06 6.8ooOoOE+01 2.100000E+02 1.941157E+00 1.453110E+00 9.250000E-06 6.800000E+01 1.455019E+00

1.455019E+OO 1.941157E+00 7.495624E-01

5.151566E-01 5.151566E-01 4.1 14051E+OO 1.798428E-02

6.452594E-04 1.941157E+00 7.495624E-01 1.000000E+00 6.011301E-01 1.99225OE-02 4.578563E-02 2.950576E-02

-7.13OO30E-03

-8.667194E-03

7.495624E-01 5.6 18438E-01 3.156684E-01 1.208834E+OO

O 2.770709E+01 7.495624E-01

1.101736E+02 1.4696OOE+01 1.000000E+00

-1.000000E+00

6.235820Eo4 1.941157E+OO 1.455019E+00 1.208834E+oO 1.000000E+00 2.825000E-01 5.8792OOE+Ol 1.101736E+02 5.344769E-01 1.138185E+02 1.000000E+03 4.695870E-03

4.695870E-03 6.011301E-01 1.992250E-02 4.578563E-02

1.616208E-01 6.200000E-06 6.800000E+01 2.100000E+02 1.617631E-01 1.210925E-01 9.25oooOE-06 6.800000E+01 1.212516E-01

1.2125 16E-01 1.617631E-01 7.495626E-01

5.151565E-01 5.151565E-01 4.114053E+ûO 1.79843OE-02

6.452587E-04 1.61763 1E-01 7.495626E-01 8.333330E-02 6.011301E-01 1.992250E-02 4.578567E-02 2.950579E-02

-7.130031E-03

-8.667208E-03

7.495626E-01 5.618440E-01 3.156687E-01 1.208834E+00

O 2.770700E+01 7.495626501

1.101736E+02 1.4696OOE+Ol 1.OOOO00E+00

-1.000000E+00

7.733270E-02 1.617631E-01 1.212516E-01 1.208834E+00 1.000000Em 1.8983ûOl%O4 5.879200E+Ol 1.101736E+02 5.344733E-01 1.138185E+02 1 .OCKKIOOE+03 4.695838E-03

4.695838E-03 6.011301E-01 1.99225OEXQ 4.578567E-02

4.9262OOE+O 1 1.116000E-05 2.000000E+01 9.8 89000E+O 1 4.930537E+01 3.690900E+01 1.665000E-05 2.000000E+01 3.695748E+01

3.695748E+Ol 4.930537E+01 7.495630E-01

5.15 1569-1 5.151569E-01 4.1 14063E+00 1.798436E-02

6.452587E-04 4.930537E+OI 7.495630E-01 2.54oooOE+01 6.011301E-01 1.99225 1E-02 4.578578E-02 2.950587E-02

-8.667252E-03

-7.130033E-03

7.495630E-01 5.618447E-01 3.156694E-01 1.208835E+3+00

O 1.000000E+03 7.495630E-01

-1.000000E+OO 2.741590E+02 l.O1325OE+OO 1.000000E+OO

1.000000E-01 4.930537E+Ol 3.695748E+O 1 1.208835Em 1.000000E+00 2.825OOOE-O 1 9.4175OOE+02 2.741590E+02 3.374434E+00 7.185948E+02 1.000000E+03 4.695879E-03

4.695879E-03 6.011301E-01 1.99225 1E-02 4.5785780-02

4.926200E-02 1.116OOOE-05 2.931500E+02 3.720400E+02 4.930537E-02 3.690900E-02 1.665000E-05 2.93 15OOE+02 3.695748E-02

3.695748E-02 4.930537E-02 7.495630E-01

5.15 1569H1 5.15 1569E-01 4.114063E+OO 1.798436E-02

-7.130033E-03 6.452587E-04 4.930537E-02 7.495630E-01 2.54oooOE-02 6.011301E-01 1.992251E-02 4.578578E-02 2.950587E-02

-8.667252E-03

7.495630E-01 5.618447501 3.156694E-01 1.208835E+CKl

O 1.000000E+00 7.495630E-01

2.741590E+04 1.013250E+05 l.OCKKIOOE+OO

-1.000000E+00

1.000000E+00 4.930537E-02 3.695748E-02 1.208835E+00 1.000000E+00 2.825000E-04 9.417500E+02 2.741590E+04 3.374434E+Ol 7.185948E+03 l.OOOOOOE+03 4.695879E-03

4.695879E-03 6.011301E-01 1.992251E-02 4.578578E-02


_ _ _ _ I - - - __ __ __ ___ A P I MPMS*L4-3*4 72 W 0732270 0506340 336 W

52 CHAPTER NATUF TU FI AL GAS FLUIDS MEASUREMENT

Table 4-7-Intermediate Output for Example Test Case No. 1 (continued)

Symbol US Units IP Units Metric Units SI Units

Correlation constant 4 Correlation constant 5 Initial orifice coefficient Convergence flag (counter)

Calculate the orifice coefficient Reduced reciprocal Reynolds no. Term raised to power of .35 Term raised to power of -80 Calculated orifice coefficient Derivative of orifice coefficient resid Change in C, for an iteration Calculated orifice coefficient Convergence flag (counter)

Calculate the orifice coefficient Reduced reciprocal Reynolds no. Term raised to power of .35 Term raised to power of -80 Calculated orifice coefficient Derivative of orifice coefficient resid Change in cd for an iteration Calculated orifice coefficient Convergence flag (counter)

Calculate the mass flow rate Unit conversion constant Entrance flow factor Orifice diameter Fluid expansion factor Fluid density Differential pressure Converged orifice coefficient Intermediate mass flow factor Universal constant, n Mass flow rate

Calculate the volumetric flow rate Unit conversion constant Entrance flow factor Orifice diameter Fluid expansion factor Fluid density Differential pressure Converged orifice coefficient *Fluid density at base conditions Intermediate mass flow factor Universal constant, n Volumetric flow rate

cd3 cd4 cd ICD

X

xO.80

F C

D C

sc,

~ 0 . 3 5

cd ICD

X ~0.35 xo.80

Fc D C

SC,

ICD

NI E d Y P l , P AP

FI,, ,

Q",

cd

E

NI E d Y P1.P AP cd

Pb

n FI,,,,

Q"

2.950576E-02 -8.667 194E-03

6.011301E-01 O

7.81 1737E-03 1.830045E-01 2.061570E-02 6.101089E-01 3.384765E-03

6.100587E-01 1

-8.928556E-03

7.697407E-03 1.820625E-01 2.037397E-02 6.100592EcOl 3.364399E-03

-5.171605E-07 6.1OO592E-01 2

3.232790E+02 1.208834E+OO 1.455019E+OO 1.000000E+00 5.879200E+O 1 1.101736E+02 6.100592E-01 6.497867E+02 3.141590E+OO 4.51 1861E+3+04

3.232790E+02 1.208834E+00 1.455019E+OO 1.000000E+00 5.879200E+01 1.101736E+02 6.100592E-01 6.2366OOE+Ol 6.497861E+02 3.141590E+00 7.234488E+02

2.950579E-02

6.01 1301E-01 O

-8.667208E-03

7.811684E-03 1.83OO40E-01 2.061559E-02 6.101089E-01 3.384758E-03

6.100586E-01 1

-8.928540E-03

7.697356E-03 1.820621E-01 2.037386E-02 6.100591E-01 3.364392E-03

6.10059 1E-01 2

-5.171575E-07

4.655210E+04 1.208834E+00 1.2125 16FA1 1.OOOOOOE+OO 5.879200EtOl 1.101736E+02 6.100591E-01 6.497858E+02 3.141590E+00 4.5 11 854E+3+O4

4.655210E+04 1.208834E+Oo 1.212516E-01 1.OOOOOOE+00 5.879200E+O 1 1.101736E+02 6.100591E-01 6.236600E+01 6.497858E+02 3.14159OE+OO 7.234477E+02

2.950587E-02

6.011301E-01 O

-8.667252503

7.811751E-03 1.830O46E-01 2.061573E-02 6.101089E-01 3.384777E-03

6.100586E-01 1

-8.928588E-03

7.697422E-03 1.820626E-01 2.037400E-02 6.1 OO592E-O 1 3.364410E-03

6.1OO592E-01 2

-5.171659E-07

3.6OOOOOE-02 1.208835E+00 3.695748E+01 l.OOOOOOE+OO 9.417500E+02 2.741 590E+02 6.100592E-01 4.668354E+01 3.141590E+00 2.046538E+04

3.600000E-02 1.208835E+00 3.695748E+O 1 l.OOOOOOE+OO 9.417500E+02 2.741590E+02 6.1OO592E-01 9.990100E+02 4.668354E+Ol 3.141590E+00 2.048566E+Ol

2.950587E-02

6.011301E-01 O

-8.667252E-03

7.81 1751E-03 1.83OO46E-01 2.06 1573E-02 6.101089E-01 3.3 84777E-03

6.100586E-01 1

-8.928588E-03

7.697422E-03 1.820626E-01 2.037400E-02 6.100592E-01 3.364410E-03

6.100592E-01 2

-5.171659E-07

l.OOOOOOE+OO 1.208835E+OO 3.695748E-02 1.OOOOOOE+OO 9.417500E+02 2.741590E+04 6.100592E-01 1.296765E-03 3.141590E+00 5.684827E+OO

1.000000E+00 1.208835E+00 3.695748E-02 1.000000E+00 9.4175OOE+02 2.741590E+04 6.100592E-01 9.9901 OOE+02 1.296765E-03 3.141590E+00 5.69046 1E-03


A P I M P M S * 1 4 - 3 - 4 92 m 0732290 0506343 272 m

SECTION %CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 4-BACKGROUND


53

Calculate temperature corrected diameters *Measured pipe diameter "Coefficient of thermal expansion *Pipe diameter measurement temperature *Flowing fluid Pipe diameter *Measured orifice diameter *Pipe coefficient of thermal expansion *Orifice diameter measurement temperature Orifice diameter

Calculate diameter ratio (P, Orifice diameter Pipe diameter Diameter ratio, ß

Calculate cd correlation constants Upstream tap position Downstream tap position Dam height Upstream tap term Downstream tap term Small pipe diameter correction term pipe diameter Diameter ratio, ß Conversion factor Correlation constant 1 Correlation constant 2 Correlation constant 3 Correlation constant 4 Correlation constant 5

Symbol us units IP Units Metric Units SI Units

Calculate velocity of approach factor Diameter ratio, ß ß squared fl raised to fourth power Velocity of approach factor

Calculate fluid expansion factor *Compressible fluid switch (I = yes) Units conversion factor Diameter ratio, p *Isentropic exponent *Differential pressure *Flowing pressure Expansion factor

Calculate iteration flow factor Unit conversion constant Pipe diameter Orifice diameter Velocity of approach factor Fluid expansion factor *Fluid viscosity *Fluid density Differential pressure AP independent part of F, AP dependent part of F, Maximum value of F, Iteration flow factor


7.981460E+00 6.200000E-06 6.800000E+01 0.000000E+00 7.978095E+00 1.59374OE+00 9.250000E-06 6.800000E+01 1.592738E+00

1.592738E+OO 7.978095E+00 1.996388E-01

1.253432E-O 1 1.253432E-01 3.132166E-01 2.205076E-05

0.000000E+00 7.978095E+OO 1.996388E-01 1.000000E+00 5.968905E-01 7.891325E-03 2.303977E-04 5.152351E-05 4.757 194E-05

-3.907720E-04

1.996388E-01 3.985566E-02 1.588474E-O3 1.000795E+00

O 2.7707OOE+O 1 1.996388E-01

8.993800E+00 1.469600E+Ol 1.000000E+00

-1.000000E+00

6.235820E-04 7.978095E+00 1.592738E+OO 1.000795E+00 1.000000E-FOO 1.865000E+03 5.819900E+Ol 8.993800E+Oo 1.46 1834E+O4 3.235522E+01 LOOOOOOE+03 4.518077E+02

4.518077E+02 5.968905E-01 7.891325E-03 2.303977E-04

6.651217E-01 6.200000E-06 6.800000E+01 0.000000E+00 6.648413E-01 1.3281 17E-01 9.25oooOE-06 6.800000E+Ol 1.327282E-01

1.327282E-01 6.648413E-01 1.996389E-01

1.253431E-01 1.25343 1E-01 3.132165E-01 2.205076E-05

-3.907719E-04 0.000000E+00 6.648413E-01 1.996389E-01 8.333330E-02 5.968905E-01 7.89 1326E-03 2.303979E-04 5.152356E-05 4.757194E-05

1.996389E-01 3.985568E-02 1.588475E-03 1.000795E+00

O 2.770700E+01 1.996389E-01

8.993800E+00 1.469600E+Ol 1.000000E+00

-1.000000E+00

7.733270E-02 6.648413E-01 1.327282E-01 l.O00795E+00 1.000000E+00 1.253200E+OO 5.819900E+Ol 8.993 800E+00 1.461807E+04 3.235522E+Ol l.OOOOOOE+03 4.517996E+02

4.517996E+û2 5.968905E-01 7.891326E-03 2.303979E-04

2.027290E+02 1,116000E-05 2.000000E+01

2.026435E+02 4.048100E+01 1.665000E-05 2.000000E+01 4.045554E+Ol

-1.778CKKlE+01

4.045554E+OI 2.026435E+02 1.996389E-01

1.253433E-01 1.253433E-01 3.132168E-01 2.205081E-05

0.000000E+00 2.026435E+02 1.996389E-01 2.54oooOE+O 1 5.968905E-01 7.891328E-03 2.303981E-04 5.152364E-05 4.757200E-05

-3.907724E-W

1.996389E-01 3.985570E-02 1.588477E-03 1.000795E+00

O 1.000000E+03 1.996389E-01

-1.000000E+00 2.238000E+01 1.013250E+00 1.000OOOE+00

1.000000E-01 2.026435E+02 4.045554E+Ol 1.000795E-1.00 1.000000E+Oo 1.865ooOE+O3 9.322600E+02 2.238000E+01 9.229335E+04 2.042742E+02 l.OOOOOOE+03 4.5 18 11 1E+02

4.5 18 11 1E+02 5.968905E-01 7.891328E-03 2.303981E-04

2.027290E-0 1 1.116OOOE-O5 2.93 1500E+02 2.553700E+02 2.026435E-01 4.048 100E-02 1.665000E-05 2.93 15OOE+O2 4.045554E-02

4.045554E-02 2.026435E-01 1.99638950 1

1.253433E-0 1 1.253433E-o 1 3.132168E-01 2.205081E-05

0.000000E+00 2.026435E-01 1.996389E-01 2.54oooOE-02 5.968905E-01 7.89 1328E-03 2.303981E-04 5.152364E-05 4.757200E-05

-3.907724E-04

1.996389E-01 3.985570E-02 1.588477E-03 1.000795E+00

O 1.000000E+00 1.996389E-01

-1.000000E+ûO 2.238000E+03 l.O1325OE+05 1.000000E+00

1.000000E+00 2.026435E-01 4.045554E-02 1.000795E+00 1.000000E+00 1.865OOOE+00 9.322600E+02 2.238000E+03 9.229335E+05 2.042742E+03 1.000000E+03 4.518111E+02

4.5 181 llE+02 5.968905E-01 7.891328E-03 2.303981E-04





Correlation constant 4 Correlation constant 5 Initial orifice Coefficient Convergence flag (counter)

Calculate the orifice coefficient Reduced reciprocal Reynolds no. Term raised to power of .35 Term raised to power of .80 Calculated orifice coefficient Derivative of orifice coefficient resid Change in Cd for an iteration Calculated orifice coefficient Convergence flag (counter)

Calculate the orifice coefficient Reduced reciprocal Reynolds no. Term raised to power of .35 Term raised to power of -80 Calculated orifice coefficient Derivative of orifice coefficient resid Change in Cd for an iteration Calculated orifice coefficient Convergence flag (counter)


Calculate the orifice coefficient Reduced reciprocal Reynolds no. Term raised to power of .35 Term raised to power of .80 Calculated orifice coefficient Derivative of orifice coefficient resid Change in cd for an iteration Calculated orifice coefficient Convergence flag (counter)


Unit conversion constant Entrance flow factor Orifice diameter Fluid expansion factor Huid density Differential pressure Converged orifice coefficient *Fluid density at base conditions Intermediate mass flow factor Universal constant, n Volumetric flow rate

Calculate the volumetric flow rate

Cd3 Cd4 cd ICD

X ~0.35 xo.80

F, DE

Cd SC,

ICD

X xO.80

F, Dc SCd

~0.35

cd ICD

X ~0.35 xO.80

F, De

ICD

cd cd

X ~0.35 xo.80

E? Dc SCd cd ICD

NI E d Y Pt .P AP cd

F;,,,, n Q",

NI E d Y Pt. P AP cd Pb

n F m m s

Q"

5.152351E-05 4.757194E-05 5.968905E-01 O

7.569356E+02 1 .O 178 l9E+01 2.0 10236E+02 1.469896E+00 6.159067E-01

-4.296585E-01 l.O26549E+00 1

4,401 228E+02 8.418813E+00 1.302744E+02 1.192493E+00 4. I98 112E-01

1.144327E+00 2

3.948239E+02 8.104780E+00 1.194326E+O2 1.148601E+00

-1.177779E-01

3.887946E-0 I -3.1904 16E-03

1. l47517E+OO 3

3.937262E+02 8.096886E+00 I. 19 1669E+02 1 I 147520E+00 3.880304E-01

1.147519E+00 4

-1.922336E-06

3.232790E+02 l.O00795E+OO 1.592738E+00 l.OOOOOOE+OO 5.8 l99OOE+01 8.9938OOE+00 1.1475 l9E+00 6.446154E+02 3.141590E+00 2.393343E+04

3.232790E+02 1,000795E+OO 1.592738E+W 1.000000E+00 5.819900E+Ol 8.993800E+00 I. 147519E+W 5.6861OOE+Ol 6.446 154E+02 3.141590E+00 4.209 112E+02

5.152356E-05 4.757 194E-05 5.968905E-01 O

7.569220E+02 1.0178 13E+01 2.010208E+02 1.469885E+OO 6.158990E-0 1

4.296559E-01 l.O26546E+0 1

4.401 16IEi02 8.4 18768B+m 1.302728E+02 1.192486Ed 4.198067E-01

1.144322E+00 2

3.948186E+02 8.10474 1E+00 1.194313E+02 1.148596E+00 3.887909E-01

I. 1475 12E+00 3

-1.177755E-01

-3.190279E-03

3.937209E+02 8.096848E+00 1.19 1656E+02 1.1475 15E+00 3.880268E-01

1,1475 l4E+OO 4

-1.922173E-06

4.655210E+04 1.000795E+00 1.327282E-01 1.000000E+QO 5.8 199OOE+01 8.993800E+00 1.147514E+OO 6.446146E+02 3.141590E+00 2.393330E+04

4.655210E+04 1.000795E+ûO 1.327282E-01 1.000000E+00 5.819900E+01 8.993800E+OO 1.147514E+00 5.686100E+01 6.446146E+02 3.141590E+00 4.209089E+02

5.152364E-05 4.757200E-05 5.968905E-O 1 O

7.569413E+02 1.017822E+OI 2.0 10249E+02 1.469901E+00 6.159103E-01

4.296597E-01 1.026550E+OO 1

4.401256E+02 8.418832E+OO 1.30275 1E+02 1.192496E+00 4. I98 133E-01

1.144329E+OO 2

3.948261E+02 8.104795E+00 1.194331E+02 1.148604E+00

-1.177790E-01

3.887963E-01

l,14752OE+OO 3

-3.190479E-03

3.937284E+02 8.096901E+00 1.191674E+02 1.147522E+00 3.880321E-O 1

1.147522E+00 4

-1.922411E-06

3.6oooOOE-02 1.000795E+00 4.045554E+01 1.000000E+00 9.322600E+02 2.23 8oOOE+O 1 I. 147522E+00 4.631 196E+01 3.14159OE+OO l.O85594E+04

3.600000E-02 1.000795E+00 4.045554E+01 1.OOOOOOE+00 9.322600E+02 2.238000E+01 1.147522E+OO 9.108300E+02 4.63 1196E+01 3.14159OE+OO 1.19 1874E+O 1

5.152364E-05 4.757200E-05 5.968905E-0 1 O

7.5694 13E+02 l.OI7822E+Ol 2.010249E+02 1.469901E+00 6,159103E-01

-4.296597E-01 1.026550E+00 1

4.401256E+02 8.418832E+00 1.30275 1E+02 1,192496E+00 4.198133E-01

I. 144329E+00 2

3.948261E+02 8.104795E+00 1.194331E+02 I. 148604E+00 3.887963E-01

1.14752OEd 3

-1.177790E-01

-3.190479E-03

3.937284E+02 8.096901E+00 1.191674E+02 1.147522E+00 3.880321E-01

1.147522E+OO 4

-1.922411E-M

1.000000E+00 1.000795E+00 4.045554E-02 1.000000E+00 9.322600E+02 2.238000E+03 1.147522E+00 1.286443E-03 3.141590E+00 3.015540E+00

1.000000E+00 1.000795E+OO 4.045554E-02 1.oOOOOOE+00 9.322600E+02 2.238000E+03 1.147522E+00 9.108300E+02 1.286443E-03 3.141590E+00 3.3 10760E-03




Symbol us Units iP Units Metric Units SI Units



Calculate cd correlation constants Upstream tap position Downstream tap position Dam height Upstream tap term Downstream tap term Small pipe diameter correction term Pipe diameter Diameter ratio, ß Conversion factor Correlation constant 1 Correlation constant 2 Correlation constant 3 Correlation constant 4 Correlation constant 5

Calculate velocity of approach factor Diameter ratio, ß ß squared ß raised to fourth power Velocity of approach factor

Calculate fluid expansion factor *Compressible fluid switch (1 = yes) Units conversion factor Diameter ratio, ß *Isentropic exponent *Differential pressure *Flowing pressure Expansion factor Pressure independent term Pressure ratio Expansion factor

Calculate iteration flow factor Unit conversion constant Pipe diameter Orifice diameter Velocity of approach factor Fluid expansion factor *Fluid viscosity *Fluid density Differential pressure AP independent part of 4. AP dependent part of 4 Maximum value of 4 Iteration flow factor

Calculate the orifice coefficient Iteration flow factor

4.026380E+00 6.200000E-06 6.800000E+01 O.OOOOOOE+OO 4.024682E+OO 2.664060E+00 9.25oooOE-06 6.800000E+01 2.662384E+00

2.662384E+00 4.024682E+OO 6.615141E-01

2.484668E-01 2.484668E-01 1.468 107E+OO 6.189049E-03

4.502338E-03 O.O00000E+00 4.024682Et00 6.615141E-01 1.000000E+00 6.021234E-01 1.82539 1 E-02 2.777503E-02 1.619635E-02

-1.982181E-03

6.615141E-01 4.376009E-01 1.9 14946E-O 1 1.112138E+OO

1 2.770700E+Ol 6.615141E-01 1.3 198oOE+oO 5.6211OOE+Ol 2.000000E+02 3.614359E-01 1.014383E-02 4.376009E-01 9.963337E-01

6.235820E-04 4.024682E+00 2.662384E+00 I. 1 12138E+W 9.963337E-01 1.352000E-02 2.046600E+00 5.621100E+01 1.728053E-02 1.516848E+Ol 1.000000E+03 1.139239E-03

1.139239E-03

3.355317E-01 6.200000E-06 6.800000E+Ol O.O00000E+NJ 3.353902E-01 2.220050E-01 9.25oooOE-06 6.800000E+01 2.218654E-01

2.218654E-01 3.353902E-01 6.615141E-01

2.484667E-01 2.484667E-01 1.468106E+00 6.189044-3

-4.502336E-05 O.OOOOOOE+OO 3.353902E-01 6.615141E-01 8.333330E-02 6.021234E-0 1 1.825390E-02 2.777502502 1.619634E-02

-1.982179E-03

6.615141E-01 4.376009E-01 1.9 14945E-01 1.112138E+oO

1 2.770700E+Ol 6.615141E-01 1.319800E+00 5.621 100E+O1 2.000000E-tO2 3.614359E-01 1.014383E-02 4.376009E41 9.963337E-01

7.733270E-02 3.353902E-01 2.218654E-01 1.112138E+M) 9.963337E-01 9.085000E-06 2.046600E+00 5.621 100E+O1 1.728050E-02 1.5 16848E+Ol 1.000000E+03 1.139237E-03

1.139237E-03

1.022700E+02 1.116000E-05 2.000000E+01

l.O22269E+O2 6.76670OE+Ol 1.665000E-05 2.000000E+01 6.762443E+Ol

-1.7780OOE+Ol

6.762443E+Ol l.O22269E+O2 6.615132E-01

2.484669E-01 2.484669E-01 1.468104E+00 6.189011E-03

-4.502326E-03 O.OOOOOOE+OO 1.022269E+02 6.615132E-01 2.54000OE+Ol 6.021235E-01 1.825389E-02 2.777488E-02 1.6 19625E-02

-1.982161E-03

6.615132E-01 4.375998E-01 1.914936E-01 1.112137E+OO

1 1.OOOOOOE+O3 6.615132E-01 1.3 19800E+oO 1.398770E+02 1.37895OE+O 1 3.614356E-01 1.014373E-02 4.375998E-01 9.963337E-01

1.000000E-01 1.022269E+02 6.762443E+01 1.112137E+00 9.963337E-01 1.352000E-02 3.2783OOE+Ol 1.398770E+02 1.091017E-01 9.576625E+Ol 1.000000E+03 1.13925OE-03

1.139250E-03

1.0227OOE-01 1.116000E-05 2.931500E+02 2.553700E+02 1.022269E-01 6.766700E-02 1.665000E-05 2.931500E+02 6.762443E-02

6.762443E-02 1.022269E-01 6.6 15 1 32E-0 1

2.484669E-01 2.484669E-01 1.468 104E+OO 6.189011E-03

-4.502326E-03 0.000000E+00 1.022269E-01 6.615132E-01 2.54oooOE-02 6.021235E-01 1.825389E-02 2.777488E-02 1.6 19625E-02

-1.982161E-03

6.6 15 132E-01 4.375998E-01 1.914936E-01 1.1 12 137E+00

1 1.000000E+00 6.615 132E-01 1.3 19800E+00 1.398770E+W 1.378950E+06 3.614356E-01 1.014373E42 4.375998E-01 9.963337501

l.OOOOOOE+OO 1.022269E-01 6.762443E-02 1.112137E+OO 9.963337E-01 1.352000E-05 3.278300E+01 1.398770E+3+04 1.091017E+00 9.576625E+02 1.000000E+03 1.13925OE-03

1.13925OE-03





Correlation constant 1 Correlation constant 2 Correlation constant 3 Correlation constant 4 Correlation constant 5 Initial orifice coefficient Convergence flag (counter)



Calculate the mass flow rate Unit conversion constant Entrance flow factor Orifice diameter Fluid expansion factor Fluid density Differential pressure Converged orifice coefficient Intermediate mass flow factor Universal constant, A Mass flow rate

Calculate the volumetric flow rate Unit conversion constant Entrance flow factor Orifice diameter Fluid expansion factor Fluid density Differential pressure Converged orifice coefficient *Fluid density at base conditions Intermediate mass flow factor Universal constant, n Volumetric flow rate

6.021 234E-O 1 3.825391E-02 2.777503E-02 1.619635E-02

6.021234E-01 O

-1.9821 8 1E-03

1.892036E-03 1.1 14 103E-01 6.630458E-03 6.054432E-01 1.244894E-03

6.054364E-O1 1

-3.3 12968E-03

1.88 1683E-03 1.11 1965E-01 6.601416E-03 6.054364E-01 1.2421 67E-03

6.054364E-01 2

-2.620428E-08

3.232790E+02 1.112138E+00 2.662384E+OO

2.046600E+OO 5.62 1 1OOE+O 1

9.963337E-01

6.054364E-O1 2.001553E+03 3.14159OE+OO 1.831397E+M

3.232790E+02 1.112138E+OO 2.662384E+OO 9.963337E-01 2.0466OOE+OO 5.6211OOE+01 6.054364E-01 1.161980E-01 2.001553E+03 3.141590E+OO 1.576 1OOE+05

6.02 1234E-01 1.825390E-02 2.777502E-02 1.619634E-02

6.021234E-0 1 O

-1.982179E-03

1.892032E-03 1.1 141 02E-o 1 6.630447E-03 6.054432E-01 1.244892E-03

6.054364E-01 1

-3.3 12964E-03

1.88 1679E-03 I. 11 1965E-01 6.601406E-03 6.054364E-01 1.242166E-03

6.054364E-01 2

-2.620419-8

4.6552 10E+04 1.112138E+3+00 2.218654E-01 9.963337E-ol 2.046600E+00 5.621 lOOE+Ol 6.054364E-O 1 2.001549E+03 3.141590E+OO 1.831394E+M

4.655210E+04 1.112138E+OO 2.218654E-01 9.963337E-01 2.046600E+OO 5.6211OOE+01 6.054364E-01 1.161980E-01 2.001549E+03 3.141590E+OO 1.576098E+05

6.021235E-01 1.825389E-02 2.777488E-02 1.619625E-02

6.02 1235E-0 1 O

-1.982161E-03

1.892053E-03 1.1'14106E-O1 6.630506E-03 6.054433E-01 1.244892E-03

6.054364E-01 1

-3.312963E-03

1.88 17OOE-03 1.11 l969E-01

6.054364E-O 1 1.242166E-03

6.054364E-01 2

6.601465E-03

-2.620417E-08

3.6OWOOE-02 I. 112137E+00 6.762443E+Ol

3.2783OOE+Ol 1.398770E+02 6.054364E-01 1.437996E+02 3.14 1590E+OO 8.306985E+03

9.963337E-01

3.600000E-02 1.112137E+OO 6.762443E+01 9.963337E-01 3.278300E+01 1.398770E+02 6.054364E-O 1 1.8613 lOE+OO 1.437996E+02 3.141590E+OO 4.462978E+03

6.021235E-01 1.825389E-02 2.777488E-02 1.619625E-02

6.021235E-01 O

-1.982161E-03

1.892053E-03 1.1 14106E-01 6.630506E-03 6.054433E-01 1.244892E-03

6.054364E-01 1

-3.312963E-03

1.881700E-03 1.1 11969E-01 6.601465E-03 6.054364E-01 1.242 166E-03

6.054364E-0 1 2

-2.620417E-08

1.000000E+00 1.112137E+00 6.762443E-02 9.963337E-01 3.278300E+O 1 1.398770E+04 6.054364E-01 3.994432E-03 3.141 590E+OO 2.307496E+00

1.000000E+00 1.112137E+00 6.762443E-02 9.963337E-01 3.278300E+Ol 1.398770E+04 6.054364E-01 1.861310E+OO 3.994432E-03 3.141590E+OO 1.239716E+OO


SECTION 3--CONCENTRIC, SQUARE-EDGED ORIFICE METERS. PART 4-BACKGROUND 57

Table 4-1 O-Intermediate Oufput for Example Test Case No. 4

Symbol US Units IF'Units Metric Units SI Units


Calculate diameter ratio (P, Orifice diameter pipe diameter Diameter ratio, ß

Calculate cd correlation constants .

Upstream tap position Downstream tap position Dam height Upstream tap term Downstream tap term Small pipe diameter correction term Pipe diameter Diameter ratio, ß Conversion factor Correlation constant 1 Correlation constant 2 Correlation constant 3 Correlation constant 4 Correlation constant 5

Calculate velocity of approach factor Diameter ratio, fl ß squared ß raised to fourth power Velocity of approach factor

Calculate fluid expansion factor *Compressible fluid switch (1 = yes) Units conversion factor Diameter ratio, ß *Isentropic exponent *Differential pressure *Flowing pressure Expansion factor Pressure independent term Pressure ratio Expansion factor

Calculate iteration flow factor Unit conversion constant Pipe diameter Orifice. diameter Velocity of approach factor Fluid expansion factor *Huid viscosity *Fluid density Differential pressure AP independent part of F, AP dependent part of F, Maximum value of 4 Iteration flow factor


1.93945OE+OO 6.200000E-06 6.800000E+01 0.000000E+00 1.938632E+00 1.953100E-01 9.25oooOE-ûó 6.800000E+01 1.951872E-01

1.951872E-01 1.938632E+00 1.006829E-01

5,158276E-0 1 5.158276E-01 1.147 154E+OO 4.008413E-06 -4.878946E-04 2.323928E-03 1.938632E+00 1.006829E-01 1.000000E+00 5.982350E-01 4.887058E-03 1.490463E-05 1.927601%06 3.734835E-05

1.006829E-01 1 .O 13705E-02 1.027598E-04 1 .oooO5 1 E+ûû

1 2.770700E+Ol 1.006829E-01 1.319800E+00 2.248400E+Oo 2.000000E+02 3.106804E-01 4.057458E-04 1.013705Eo2 9.998739E-01

6.235820E-M 1.938632E+00 1.951 872E-01 l.oooO51E+oO 9.998739E-01 1.352000E-02 2.046600E+00 2.248400E+Oû 1.716152Em 3.03367OE+OO 1.000000E+03 5.65701-1

5.657016M1

1.616208E-01 6.200000E-06 6.800000E+01 0.000000E+00 1.615527E-01 1.6275 80E-02 9.25oooOE-06 6.800000E+01 1.626556E-02

1.626556E-02 1.615527E-01 1.006827E-01

5.158275E-01 5.158275E-01 1.147 153E+00 4.008383E-06 -4.878935E-04 2.323927E-03 1.6 15527E-01 1.006827E-01 8.333330E-02 5.982350E-01 4.88705 1E-03 1.490452E-05 1.927584E-06 3.734822E-05

1.006827E-O 1 1.013701E-02 1.027590E-04 1 .oooO51E+OO

1 2.770700E+Ol 1.006827E-01 1.3í9800E+00 2.248400E+Oû 2.000000E+02 3.106804E-01 4.057458E-04 1.013701E-02 9.9987390-01

7.733270E-02 1.615527E-01 1.626556E-02 l.oooO51E+00 9.998739E-01 9.085000E-06 2.046600E+OO 2.248400E+00 1.716155E+Oû 3.033670E+00 1.000000E+03 5.657026E-01

5.657026E-01

1.616208E-01 6.200000E-06 6.800000E+01 0.000000E+00 1.6 15527E-01 1.62758OE-02 9.25oooOE-06 6.800000E+01 1.626556E-02

1.626556E-02 1.615527E-01 1.006827E-01

5.158275E-01 5.1582750101 1.147153E+OO 4.008383E-06 4.878935E-04 2.323927E-03 1.615527E-01 1.006827E-01 8.333330E-02 5.982350E-01 4.88705 1E-03 1.490452E-05 1.927584E-06 3.734822E-05

1.006827E-01 1.013701E-02 1.027590E-04 l.oooO51E+OO

1 2.770700E+Ol 1.006827E-01 1.3 198OOE+OO 2.248400E+Cû 2.000000E+02 3.106804E-01 4.057458E-04 1.013701E-02 9.998739E-01

7.733270E-02 1.615527E-01 1.6265563-02 l.oooO51E+00 9.998739E-01 9.085000E-06 2.046600E+00 2.248400E+00 1.716155E+00 3.033670E+00 1.000000E+03 5.657026E-01

5.657026E-01

4.926200E-02 1.116000E-05 2.931500E+02 2.553700E+02 4.924123E-02 4.96 1OOOE-03 1.665000E-05 2.93 1500E+02 4.957879E-03

4.957879E-03 4.924 123E-02 1.006855E-01

5.158279E-0 1 5.158279E-01 1.147 158E+oO 4.008830E-06 -4.879096E-04 2.323925E-03 4.924 123E-02 1.006855E-01 2.54oooOE-02 5.982350E-01 4.887147E-03 1.4906 18E-05 1.927841E-06 3.735025E-05

1.006855E-01 1.013758E-02 1.027704E-04 1.oooO51E+OO

1 1.000000E+00 1.006855E-01 1.319800E+OO 5.595000E+02 1.378950E+06 3.106804E-01 4.057435E-04 1.013758E-02 9.998739E-01

1.000000E+00 4.924123E-02 4.957879E-03 1.oooO5 1E+00 9.998739E-01 1.352000E-05 3.278300E+O 1 5.595000E+02 1.083443E+02 1.915311E+02 1.000000E+03 5.656746E-0 1

5.656746E-01


A P I M P M S * L 4 - 3 * 4 92 0732290 050634b 854 =


Table 4-1 &Intermediate Output for Example Test Case No. 4 (continued)



Calculate the orifice coefficient Reduced reciprocal Reynolds no. Term raised to power of .35 Term raised to power of .80 Calculated orifice coefficient Derivative of orifice coefficient resid Change in C, for an iteration Calculated orifice coefficient Convergence flag (counter)

Calculate the orifice coefficient Reduced reciprocal Reynolds no. Term raised to power of -35 Term raised to power of .80 Calculated orifice coefficient Derivative of orifice coefficient resid Change in Cd for an iteration Calculated orifice coefficient Convergence flag (counter)


Calculate the volumetric flow rate Unit conversion constant Entrance flow factor Orifice diameter Fluid expansion factor Fluid density Differential pressure Converged orifice coefficient *Fluid density at base conditions Intermediate mass flow factor Universal constant, n volumetric flow rate

~

5.982350E-01 4.887058E-03 1.490463505 1.927601E-06 3.734835505 5.982350E-01 O

9.456177E-01 9.806193E-01 9.562522E-01 6.029866E-O 1 3.325391E-03

-4.725336E-03 6.029604E-O 1 1

9.382070E-01 9.779227E-01 9.502523E-01 6.029605E-0 1 3.3071 llE-03

6.029605E-01 2

-1.742147E-07

3.232790E+02 1 .OOOo5 1E+OO 1.951872E-01 9.998739E-01 2.0466OOE+OO 2.248400E+OO 6.029605E-0 1 9.673681E+OO 3.14159OE+OO 1.769270E+01

3.232790E+02 1 .OW5 1E+OO 1.951872E-01 9.998739E-01 2.0466OOE+OO 2.2484OOEtûO

9.673681E+OO 3.141590E+OO 1.522634E+02

6.029605E-01 1.16 198OE-O 1

5.982350E-01 4.887051E-03 1.490452E-05 1.927584E-06 3.734822E-05 5.982350E-01 O

9.456 194E-0 1 9.806200E-01 9.562536E-01 6.029866E-01 3.32539 IE-03

-4.725335E-03 6.0296ME-O I I

9.3 82087E-O 1 9.779233E-O 1 9.502537E-01 6.029605E-01 3.307 11 1E-03

-1.742147E-07 6.029605E-O I 2

4.655210E+04 1 .O0005 1E+OO 1.626556E-02 9.998739E-01 2.046600E+00 2.248400E+00 6.029605E-O 1 9.673626E+OO 3.14 1590E+OO 1.769260E+Ol

4.655210E+04 1.000051E+OO 1.626556E-02 9.998739E-01 2.046600E+00 2.248400E+00 6.029605E-01 1.161980E-01 9.673626E+00 3.14159OE+OO 1.522625E+02

5.982350E-01 4.887051E-03 1.490452E-05 1.927584E-06 3.734822E-05 5.982350E-01 O

9.456 l94E-01 9.8062OOE-0 1 9.562536E-01 6.029866E-01 3.325391E-03

4725335E-03 6.029604E-01 1

9.382087E-01 9.779233E-01 9.502537E-01 6.029605E-01 3.307111E-03

6.029605E-01 2

-1.742147E-07

4.655210E+04 1.00005 lE+OO 1.626556E-02 9.998739E-01 2.0466OOE+OO 2.2484OOE+OO 6.029605Ml 9.673626E+00 3.14159OE+OO 1.76926OE+Ol

4.655210E+04 1.000051E+00 1.626556E-02 9.998739E-01 2.046600E+00 2.248400E+OO 6.029605E-01 1.161980E-01 9.673626Ei00 3.141590E+00 1.522625E+O2

5.982350E-0 1 4.887 147E-03 1.4906 18E-05 1.927841E-06 3.735025E-05 5.9823503-0 I O

9.455726E-01 9.806030E-O 1 9.562 158E-O 1 6.029866E-0 1 3.325342E-03

-4.725267E-03 6.029603E-O 1 1

9.381623E-01 9.779064E-01 9.502161E-01 6.029605E-01 3.307063E-03

6.029605E-0 1 2

-1.742071E-07

l.O00000E+OO 1.000051E+OO 4.957879E-03 9.998739E-01 3.2783OOE+01 5.595000E+02 6.029605E-01 1.93065 1E-05 3.141590E+OO 2.229345E-03

1.00000OE+00 l.ooOo51E+OO 4.957879E-03 9.998739E-01 3.278300E+01 5.595000E+02 6.029605E-01 1.86 I3 10E+00 1.93065 1 5 0 5 3.14 1590E+00 1.197729E-03


SECTION SCONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART &BACKGROUND 59

Table 4-Il-Intermediate Output for Example Test Case No. 5



Calculate diameter ratio (ß) Orifice diameter Pipe diameter Diameter ratio, ß

Calculate C , correlation constants Upstream tap position Downstream tap position Dam height Upstream tap term Downstream tap term Small pipe diameter correction term Pipe diameter Diameter ratio, ß Conversion factor Correlation constant 1 Correlation constant 2 Correlation constant 3 Correlation constant 4 Correlation constant 5

Calculate velocity of approach factor Dinmefer ratio, ß ß squared ß raised to fourth power Velocity of approach factor

Calculate ñuid expansion factor *Compressible fluid switch (1 = yes) Units conversion factor Diameter ratio, ß *Isentropic exponent *Differential pressure *Flowing pressure Expansion factor Pressure independent term Pressure ratio Expansion factor

Calculate iteration flow factor Unit conversion constant Pipe diameter Orifice diameter Velocity of approach factor Fluid expansion factor *Fluid viscosity *Fluid density Differential pressure AP independent part of 4 AP dependent part of l$ Maximum value of 4 Iteration flow factor


1.939450E+OO 6.200000E-06 6.800000E+01 0.000000E+00 1.938632E+00 1.953100E-01 9.250000E-06 6.800000E+01 1.951 872E-01

1.951872E-01

1.006829E-01 1.938632E+OO

5.158276E-01 5.158276E-O 1 1.147154E+00 4.008413E-06

-4.878946E-04 2.323928E-03 1.938632E+OO 1.006829E-01 l.OOOOOOE+00 5.982350E-01 4.887058E-03 1.490463E-05 1.927601E-06 3.734835E-05

1.006829E-01 1.013705E-02 1.027598E-04 1.oooO5 1E+00

1 2.77070OE+Ol 1.006829E-01 1.3 198OOE+OO 4.406943E+02 2.000000E+02 3.106804E-0 1 7.952761E-02 ' 1 .O 13705E-02 9.752923E-01

6.235820E-04

1.951872E-01

9.752923E-01 1.352OOOE-02 2.046600E+00 4.406943Et02 1.759406E+00 4.247 175E+Ol l.OOOOOOE+03 4.142533E-02

1.938632E+Oû

1.000051E+00

4.142533E-02

1.616208E-01 6.200000E-06 6.800000E+01 O.OM1000E+OO 1.615527E-01 1.627580E-02 9.250000E-06 6.8000OOE+Ol 1.626556E-02

1.626556E-02 1.615527E-01 1.006827E-01

5.158275E-0 1 5.158275E-01 1.147 153E+OO 4.008383E-06

4.878935E-04 2.323927E-03 1.615527E-01 1.006827E-01 8.333330E-02 5.982350E-01 4.887051E-03 1.490452E-05 1.927584E-06 3.734822E-05

1.006827E-01 1.013701E-02 1.027590E-04 l.oooO51E+00

1 2.770700E+O 1 1.006827E-01 1.319800E+00 4.406943E+02 2.oooOOOE+O2 3.106804E-0 1 7.952761E-02 1.013701E-02 9.752923E-01

7.733270E-02 1.6 15527E-O 1 1.626556E-02 l.oooO51E+00 9.752923E-01 9.085000E-06 2.046600E+00 4.406943E+02 1.759409E+00 4.247 175Ei01 1.000000E+03 4.142540E-02

4.142540E-02

4.926200E+Ol 1.116000E-05 2.oooOOOE+Ol

4.924 123E+01 4.961000E+00 1.665000E-05 2.000000E+Ol 4.957879E+00

-1.7780OOE+Ol

4.957879E+00 4.924123E+01 1.006855E-01

5.158279E-01 5.158279E-01 1.147 158E+OO 4.008830E-06

-4.879096E-04 2.323925E-03 4.924123E+Ol 1.006855E-01 2.54ooOOE+Ol 5.982350E-O 1 4.887147E-03 1.490618E-05 1.92784 1E-06 3.735025E-05

1.006855E-01 1.013758E-02 1.027704E-04 1 .O0005 1E+00

1 1 .oooOOOE+03 1.006855E-01 1.3 19800E+OO 1.096635E+03 1.37895OE+Ol 3.1068O4E-01 7.95268 1E-02 1.013758E-02 9.752926E-01

1.000000E-01 4.924123E+Ol 4.957879E+ûO 1 .O0005 1E+00 9.752926501 1.352000E-02 3.2783OOE+Ol 1.096635E+03 l.l10750E+01 2.68 1454E+02 1.000000E+03 4.142343E-02

4.142343E-02

4.926200E-02 1.116OOOE-O5 2.93 1500E+02 2.553700E+02 4.924123E-02 4.961OOOE-03 1.66500OE-05 2.931500E+02 4.957879E-03

4.957879E-03 4.924123E-02 1.006855E-01

5.158279E-01 5.158279E-01 1.147 158E+OO 4.008830lW6

4.879096E-04 2.323925E-03 4.924 123E-02 1.006855E-01 2.540000E-02 5.982350E-O 1 4.887 147E-03 1.4906 18E-05 1.92784 1E-06 3.735025E-05

1.006855E-01 1 .O 13758E-02 1.027704E-04 l.ooOO5 1E+00

1 1.000000E+00 1.006855E-01 1.319800E+00 1.096635E+05 1.378950E+06 3.106804E-01 7.952681E-02 1.013758E-02 9.752926E-01

l.O00000E+00 4.924 123E-02 4.957879E-03

9.752926E-01 1.352OOOE-05

1 .OoOO5 1E+00

3.278300E+01 1.096635E+05 1.110750E+O2 2.681454E+03 1.000000E+03 4.142343E-02

4.142343E-02


60 CHAPTER 1 &NATURAL GAS FLUIDS MEASUREMENT

Table 4-il-Intermediate Output for Example Test Case No. 5 (continued)

Symbol US Units iP Units Metric Units SI Units


Calculate the orifice coefficient Reduced reciprocal Reynolds no. Term raised to power of .35 Term raised to power of .80 Calculated orifice coefficient Derivative of orifice coefficient resid Change in c d for an iteration Calculated orifice coefficient Convergence flag (counter)

Calculate the orifice coefficient Reduced reciprocal Reynolds no. Term raised to power of .35 Term raised to power of .80 Calculated orifice coefficient Derivative of orifice coefficient resid Change in c d for an iteration Calculated orifice coefficient . Convergence flag (counter)


Unit conversion constant Entrance flow factor Orifice diameter Fluid expansion factor Fluid density Differential pressure Converged orifice coefficient *Fluid density at base conditions Intermediate mass flow factor Universal constant, n Volumetric flow rate


5.982350E-01 4.887058E-03 1.490463E-05 1.927601E-06 3.734835E-05 5.982350E-01 O

6.924591E-02 3.927697E-01 1.181178E-01 5.989993E-01 5.334226E-04

5.989986E-01 1

-7.635908E-04

6.915763E-02 3.925943E-01 1.179973E-01 5.989986E-01 5.329469E-04

5.989986E-01 2

3.232790E+02 l.ooOo51E+OO 1.951872E-01 9.752923E-01 2.046600E+OO 4.406943E+02 5.989986E-01 9.673681E+OO 3.14 1590E+OO 2.400229E+02

3.232790E+02 1.ooOo51E+OO 1.95 1872E-01 9.752923E-01 2.046600Etûû 4.406943E+02 5.989986E-01 1.16 1980E4ll 9.673681EtOO 3.141590E+OO 2.065637E+03

-7,369381610

5.982350E-01 4.8 8705 1 E-03 1.490452E-05 1.927584E-06 3.734822E-05 5.982350E-01 O

6.924603E-02 3.927699E-01 1.181 179E-01 5.989993E-01 5.334226E-04

5.989986E-01 1

-7.635907E-04

6.915776E-02 3.925946E-01 1.179975E-01 5.989986E-01 5.329469-

5.989986E-01 2

4.655210Ei04 l.ooOo51E+00 1.626556E-02 9.752923E-01 2.046600E+ûO 4.406943E+02 5.989986E-01 9.673626E+OO 3.141590E+OO 2.400215E+02

4.655210E+04 1.000051E+Oû 1.626556E-02 9.752923E-01 2.046600Etûû 4.406943E+02 5.989986E-01 1.161980E41 9.673626EtOO 3.141590E+Oo 2.065625E+03

-7.369379E-10

5.982350E-01 4.887147E-03 1,490618E-05 1.927841E-06 3.735025E-05 5.982350E-01 O

6.92427333-02 3.927634E-01 1.181135E-01 5.989993E-01 5.334155E-04

5.989986E-01 1

-7.635809E-04

6.915446E-02 3.925881E-01 1.179930E-01 5.989986E-01 5.329399E-04

5.989986E-01 2

3.600000E-02 1.000051E+00 4.957879E+W 9.752926E-01 3.278300E+01 1.096635E+03 5.989986E-01 6.950343E-01 3.141590E+OO 1.088773E+02

3.6oooOOE-02 1.oooO51Etoo 4.957879E+OO 9.752926E-01 3.2783ûûE+Ol 1.096635E-tO3 5.989986E-01 1.861310E+00 6.950343E-01 3.141590E+OO 5.849499E+01

-7.369093E-10

5.982350E-01 4.8 87 147Ei-03 1.490618E-05 1.927841E-06 3.735025E-05 5.982350E-01 O

6.9242730-02 3.927634E-0 1 1.181 135E-01 5.989993E-01 5.334155E-04

5.989986E-01 1

-7.635809-

6.915446502 3.925881E-01 1.179930E-01 5.989986E-01 5.329399E-04

-7.369093E10 5.989986E-01 n L

1.000000E+00 1.oooO51E+00 4.957879E-03 9.752926E-01 3.278300E+01 1.096635E+05 5.989986E-ûl 1.93065 1E-05 3.141590B+OO 3.024370E-02

l.OOOOOOE+OO 1 . ~ 5 1 E i O O 4.957879E03 9.752926E-01 3.278300E+01 1.096635E+05 5.989986E-01 1.861310E+00 1.930651E-05 3.141590E+00 1.624861Eo2


SECTION %CONCENTRIC. SQUARE-EDGED VFICE METERS, PART 4-BACKGROUND 61

Table 4-í2-lntermediate Output for ExampleTest Case No. 6

Symbol us units IP units Metric Units SI Units



Calculate cd correIation constants Upstream tap position Downstream tap position Dam height Upstream tap term Downstream tap term Small pipe diameter correction term Pipe diameter Diameter ratio, ß Conversion factor Correlation constant 1 Correlation constant 2 Correlation constant 3 Correlation constant 4 Correlation constant 5

Calculate velocity of approach factor Diameter ratio, p ß squared ß raised to fourth power Velocity of approach factor

Calculate fluid expansion factor *Compressible fluid switch (1 =yes) Units conversion factor Diameter ratio, ß *Isentropic exponent *Differential pressure *Flowing pressure Expansion factor

Calculate iteration flow factor Unit conversion constant Pipe diameter Orifice diameter Velocity of approach factor Fluid expansion factor *Fluid viscosity *Fluid density Differential pressure Mindependent part of 4 AP dependent part of F, Maximum value of F, Iteration flow factor


7.981460E+00 6.200000E-06 6.8oooM1E+01 0.000000E+ûO 7.978095E+OO 7.968900E-01 9.25oooOE-06 6.800000E+01 7.963888E-01

7.963888E-01 7.978095E+00 9.982192E-02

1.253432E-01 1.253432E-01 2.784854E-01 1.376258E-06

0.000000E+00 7.978095E+00 9.982192E-02 1.000000E+CQ 5.962260E-01 4.857766E-03 1.440130E-05 1.849753E-06 1.25685OE-05

-1.653483E-04

9.982192E-02 9.964416-3 9.928958E-05 l.oooO5OE+00

O 2.770700E+Ol 9.982192E-02

2.2484OOE+00 1.469600E+01 1.000000E+00

-1.000000E+00

6.235820E-04 7.978095E+00 7.963888E-01 1 .oooO50E+OO 1.000000E+00 1.865000E+03 5.819900E+OI 2.248400E+00 5.851400E+04 1.617743E+01 1 .ocQOOOE+03 1 .-E+03

1.000000E+03 5.962260E-O 1 4.857766E-03 1.440130E-05

6.651217E-01 6.200000E-06 6.800000E+Ol 0.000000E+00 6.648413E-01 6.640750E-02 9.25oooOE-06 6.800000E+01 6.636573E-02

6.636573E-02 6.648413E-01 9.982 19 1E-02

1.253431E-01 1.253431E-01 2.784852E-01 1.376257E-06

0.000000E+00 6.6484 13E-0 1 9.982191E-02 8.333330E-02 5.962260E-O 1 4.857766E-03 1.440130E-05 1.849753E-06 1.256849E-05

-1.653482E-M

9.982191E-02 9.964415E-03 9.928956E-05 l.oooO5OE+00

O 2.770700E+Ol 9.982191E-02

2.248400E+00 1.469600E+O1 l.oooOOOE+ûû

-1.000000E+00

7.733270E-02 6.648413E-01 6.636573E-02 l.ooo05OE+00 1.000000E+00 1.253200E+00 5.819900E+01 2.248400E+ûO 5.851298E+04 1.617743E+01 1.000000E+03 1.000000E+03

1 .OC#OOE+03 5.962260E-01 4.857766E-03 1.440130E-05

2.027290E+02 1.116OOOE-05 2.000000E+01

-1.778000E+01 2.026435E+02 2.024100E+01 1.665OOOE-05 2.000000E+01 2.022827E+01

2.022827E+Ol 2.026435E+02 9.982193E-02

1.253433E-01 1.253433E-01 2.784855E-01 1.376259E-06

0.000000E+CQ 2.026435E+02 9.982193E-02 2.540000E+01 5.962260E-0 1 4.857766E-03 1.44013 1E-05 1.849754E-06 1.256851E-05

-1.653483E-M

9.982193E-02 9.964418E-03 9.928962E-05 1 .OOO050E+OO

O 1.000000E+03 9.982193E-02

-l.OOOOOOE+W 5.595000E+ûO 1.013250E+ûO 1.000000E+00

1.000000E-01 2.026435E+02 2.02282íE+01 l.oooO5OE+00 1.000000E+00 1.865000E+03 9.322600E+02 5.595000E+00 3.694304E+05 1.021371E+02 l.OOO000E+O3 l.OOOOOOE+03

1.000000E+03 5.962260E-01 4.857766E-03 1.4401 3 1E-05

2.027290E-0 1 1.1160OOE-05 2.931500E+02 2.553700E+02 2.026435E-01 2.024 1 00E-02 1.665000E-05 2.93 15OOE+02 2.022827E-02

2.022827E-02 2.026435E-01 9.982193E-02

1.253433E-01 1.253433E-01 2.784855-1 1.376259E-06

0.000000E+00 2.026435E-01 9.982193E-02 2.54oooOE-02 5.962260E-01 4.857766E-03 1.440 13 1E-05 1.849754E-06 1.256851E-05

-1.653483E-04

9.982193E-02 9.964418E-03 9.928962E-05 1.000050E+00

O 1.000000E+00 9.982193E-02

5.595000E+02 1 .O 13250E+05 1.000000E+00

-1.000000E+00

1.000000E+00 2.026435E-01 2.022827E-02 1.000050E+00 1.000000E+00 1.865000E+OO 9.322600E+02 5.595000E+02 3.694304E+06 1 .O2 137 1E+03 1.000000E+03 1 .OC#OOE+03

1.000000E+03 5.962260E-0 1 4.857766E-03 1.440131E-05


62 CH PTER 14-NATURAL GAS FLUIDS ME SUREMENT

Table 4-1 2-Intermediate Output for Example Test Case No. 6 (continued)


Correlation constant 4 Correlation constant 5 Initial orifice coefficient Convergence flag (counter)



Calculate.the orifice coefficient Reduced reciprocal Reynolds no. Term raised to power of .35 Term raised to power of .80 Calculated orifice coefficient Derivative of orifice coefficient resid Change in C, for an iteration Calculated orifice coefficient Convergence flag (counter)


Calculate the mass flow rate Unit conversion constant Entrance flow factor Orifice diameter Fluid expansion factor Fluid density Differential pressure Converged orifice coefficient Intermediate mass flow factor Universal constant, it Mass flow rate

Unit conversion constant Entrance flow factor Orifice diameter Fluid expansion factor Fluid density Differential pressure Converged orifice coefficient *Fluid density at base conditions Intermediate mass flow factor Universal constant, A Volumetric flow rate


1.849753E-06 1.25685OE-05 5.962260E-O I O

1.6772 16E+03 1.344640E+01 3.799017E+02 1.482426E+OO 6.210806E-01

4.340531E-01 I .030279E+00 1

9.706 I 08E+02 1.110365E+OI 2.452653E+02 1.200259E+OO 4.232863E-01

1.150760E+OO 2

-1.204809E-01

8.689910E+02 l.O68207E+Ol 2.244979E+02 1.155215E+00 3.917128E-01

-3.323755E-03 1.154084E+00 3

8.664883E+02 1.067 129E+O 1 2.239805E+02 1.154086E+OO 3.909217E-01

-2.070598E-06 1.154086E+00 4

3.232790E+02 l.O00050E+00 7.963888E-01 1.000000E+OO 5.8 199OOE+01 2.248400E+00 1.154086E+00 1.610419E+02 3.141590E+OO 3.006675E+03

3.232790E+02 l.O00050E+OO 7.963888E-01 1.OOOOOOE+OO 5.819900E+Ol 2.2484OOE+OO 1.154086E+00 5.686100E+OI 1.6 10419E+02 3.141590E+00 5.287762E+Ol

1.849753E-06 I .256849E-05 5.962260E-o 1 O

1.6772 16E+03 1.344640E+0 1 3.799017E+02 I .482426E+OO 6.2 I 0806E-o 1

4.340530E-01 l.O30279E+OO 1

9.706108E+02 I . 1 lO365E+Ol 2.452653E+02 1.200259E+OO 4.232863E-01

I. 150760E+OO 2

-1.204808E-01

8.6899fOE+02 1.068207E+01 2.244979E+02 1.155215E+OO 3.917128E-01

1.154084E+00 3

-3.323754E-03

8.664883E+02 1 .O67 129E+01 2.239805E+02 1.154086E+00 3.909217E-01

1.154086E+OO 4

-2.070597E-06

4.655210E+04 1.000050E+00 6.636573E-02 1.000000E+00 5.819900E+01 2.2484OOE+OO 1.154086E+00 1.6104 16E+02 3.141590E+00 3.006670E+03

4.6552 10E+04 l.OOoO50E+OO 6.636573E-02 1.000000E+00 5.8199OOE+01 2.248400E+OO 1.154086E+00 5.686 100E+01 1.6104 16E+02 3.141590E+OO 5.287754E+Ol

1.849754E-06 1.25685 1E-05 5.962260E-O 1 O

1.677216E+03 1.34464OE+Ol 3.7990 17E+02 1.482426E+OO 6.2 10806E-0 1

434053 1E-01 1.030279E+00 1

9.706108E+02 1.1 10365E+01 2.452653E+02 1.2OO259E+OO 4.232864E-01

1.150760E+00 2

-1.204809E-01

8.689910E+02 l.O68207E+Ol 2.244979E+02 1.155215E+00 3.917128E-01

1.154084E+00 3

-3.323756E-03

8.664883E+02 1.067 129E+01 2.239805E+02 1.154086E+OO 3.9092 17E-O 1

-2.070599E-06 1.154086E+00 4

3.600000E-02 1.00005OE+OO 2.022827E+01 1.OoooOOE+OO 9.322600E+02 5.595000E+00 1.154086E+00 1,156994E+01 3.141590E+00 1.363806E+03

3.6oooOOE-02 1.000050E+00 2.022827E+01 1.000000E+00 9.322600E+02 5.595000E+00 1.154086E+OO 9.108300E+02 1.156994E+Ol 3.141590E+OO 1.497322E+00

1.849754E-06 1.25685 I EX5 5.962260E-O I O

1.6772 16E+03 1.344640E+01 3,7990 17E+02 1.482426E+00 6.210806E-01

434053 1E-01 1.030279E+00 1

9.706108E+02 1.110365E+Ol 2.452653E+02 1.200259E+OO 4.232864E-01

1.150760E+00 2

-1.204809E-01

8.689910E+02 l.O68207E+Ol 2.244979E+02 1.155215E+OO 3.917128E-01

-3.323756E-03 1.154084E+00 3

8.664883E+02 1 .O67 129E+01 2.239805E+02 1.154086E+00 3.909217E-01

1.154086E+00 4

-2.070599E-06

l.OOOOOOE+OO 1.000050E+00 2.022827E-02 l.O00000E+OO 9.3226OOE+02 5.595000E+02 1.154086E+OO 3.213871E-04 3.141590E+00 3.788350E-01

1.000000E+00 l.OOO05OE+00 2.022827E-02 1.000000E+00 9.322600E+02 5.595OOOE+O2 1.154086E+00 9.108300E+02 3.213871E-04 3.141 590E+OO 4.159229E-04


A P I f l P f l S * 1 4 . 3 - 4 42 m 0732240 0506353 3 3 3 m

APPENDIX 4-A-DEVELOPMENT OF FLOW EQUATION SOLUTION ALGORITHM

4-A.l General Flow Equations

In Part 1 of this standard, the flow equation is written as:

Where: Cd = d =

A P = E, =

n = 4m =

Y =

N, =

Pt,p =

orifice plate coefficient of discharge. orifice plate bore diameter at flowing temperature (Tf. orifice differential pressure. velocity of approach factor. unit conversion factorI3. universal constant (3.14159 ...). mass flow rate. density of fluid at flowing conditions (9, q). expansion factor.

(4A-1)

Part 1 also shows that c d is a function of the orifice plate bore diameter (d), the meter tube internal diameter (D), and the pipe Reynolds number (Re,). For practical application of the flow equation, Re, can be expressed as:

Where: D = Y =

4m = x =

Re, =

meter tube internal diameter at flowing temperature ( T f ) , absolute viscosity of flowing fluid. universal constant (3.14159 ... ). mass flow rate. pipe Reynolds number.

(4A-2)

The discharge coefficient equation for flange tapped orifice meters is presented in Part 1 of ANSI 2530 in the following form:

(4A-3) 106ß

Cd(FT) = C i F ) + 0.00051 1 [ - Re, ] + (0.0210 + 0.0049A) p4C

C i F ) = C,(CT) + Tup Term

G(CT) = 0.5961 + 0.0291 ß2 - 0.2290ß8 + 0.003 (1 -p ) 4 Tap Term = Upstrm + Dnstrm

(4A-4)

(4A-5)

(4A-6)

Upstnn = [ 0.0433 + 0.0712

Dnstrm = -0.01 16 [ M2 - 0.52Mk3 ] ß ( 1 - O. 14A)

- 0.1 145 ë6.OL' ] ( 1 - 0.23A) B (4A-7)

(4A-8)

l3 Note that definition for N, is different from the NI used in Part 1. In Part 1, N, contained the constants ?ü4 and 3. in Appendix 4-A, N, is strictly a units conversion constant. The g, shown in Part 1 is a units conversion constant and is therefore included in N, .

63


~ I_~ __ ______ - A P I MPMS*L4-3.4 92 W 0732290 O506352 O58 W


Also,

ß4 1 -p4

B = - (4A-9)

M, = max (2.8--, D 0.0) , (4A- 10) N4

0.8 19, OOOß ' = [ Re, ]

(4A- 11)

(4A-12)

(4A- 13)

According to Part 1, the equations and their associated uncertainty statements are limited to ß ratios of O. 10 to 0.75, d greater than 0.45 inches (1 1.4 millimeters), and pipe Reynolds numbers greater than or equal to 4,000.

Equation 4A-13 can also be used for pipe Reynolds numbers between 3500 and 4000. For Reynolds numbers less than 3500 the following equation for C is provided:

C = 30-6500 - [::I (4A-13B)

The results of the Cd(FT) calculation for Reynolds numbers less than 4000 is not covered by the uncertainty statement of Part 1.

Where:

A = high bore Reynolds number correlation function. B = fluid momentum ratio. ß = ratio of orifice plate bore diameter to meter tube internal diameter.

C = low bore Reynolds number correlation function. = (d/D) calculated at flowing temperature, q.

Cd(FT) = coefficient of discharge at a specified pipe Reynolds number for flange-

Cj(FT) = coefficient of discharge at infinite pipe Reynolds number for flange-tapped

C;:(CT) = coefficient of discharge at infinite pipe Reynolds number for corner-tapped

tapped orifice meter.

orifice meter.

orifice meter. d = orifice plate bore diameter calculated at flowing temperature, Tf. D = meter tube internal diameter calculated at flowing temperature, Tf. e = Napierian constant (2.71828 ...).

LI, L2 = N,/D for flange taps. N4 = 1.0 when D is in inches.

= 25.4 when D is in millimeters. ReD = pipe Reynolds number.

Note: For corner-tapped orifice meters LI , L2 = O, and for radius-tapped (0-012) orifice meters L, = 1 andL2 = 0.47.


A P I MPMS*14.3.4 92 m 0732290 0506353 T 9 4 W

SECTION %CONCENTRIC, SQUARE-EDGED ORIFICE METERS. PART &BACKGROUND 65

As is apparent, the orifice plate coefficient of discharge is a non-linear function of the pipe Reynolds number and the pipe Reynolds number is a function of the orifice plate coefficient of discharge. This means that an iterative solution technique must be used to determine either the pipe Reynolds number and/or the orifice plate coefficient of discharge. This appendix shows the development of the solution algorithm presented in-& document.

4-A.2 Rearrangement of Orifice Plate Coefficient of Discharge Correlation

As presented, the orifice plate coefficient of discharge equation requires a number of terms to be computed each time the assumed Reynolds number changes. It is not apparent what the contribution of each term might be for a change in Reynolds number. For these reasons, the equation was rearranged for presentation in this document, by introducing the following intermediate terms:

Tu = [ 0.0433 + 0.07 12 ë8'5L' - O. 1145 ë6'OL1 ] B (4A-14)

TD = -0.0116 [ M,- 0.52~4:'~ ] pi.' (4A-15)

T, = 0.003 (1 - p ) Ml (4A- 16)

With the introduction of these terms, the Tap Term now becomes:

Tup Tenn = Tu(l - 0.23A) + TD(1- 0.14A) (4A- 17)

And Ci(FT) becomes:

Ci (FT) = 0.5961 + 0.0291p2 - 0.2290p8 -t T, + Tu ( 1 - 0.23A) + T,( 1 - 0.14A)

(4A- 18)

By defining to contain all terms in C,(Fï) that are independent of Reynolds number, the following is obtained:

Cdo = 0.5961 + 0.0291p2 -0.2290p8 + T, + Tu + To (4A- 19)

And,

CI,(CT) cd + (-0.23Tu - O.l4T,)A O

Using this new expression for Ci(FT) in Cd(FT),

c d ( F T ) = cdo+ (-0.23Tu -O.l4T~)A+0~000511

+ (0.0210 + 0.0049A) ß4C

(4A-20)

Since in this expression, the pipe Reynolds number appears in several terms raised to several exponents combined with several additional factors, it is convenient to define a new variable, X, which is equal to 4,000 divided by the pipe Reynolds number. Substituting X into the expressions for A and C yield:

0.8 19, ow

A = [ Re, ]



For Reynolds numbers greater than 4,000:

0.35

c = [E] 0.35

4000

(4A-22)

(4A-23)

Similarly, [ @ ] 0.7 = [ io6 ~ O O O ] 0.7

- - Re, 4000 Re,

= [250/3]0.7X07 (4A-24)

By grouping all terms having X raised to similar powers together, the orifice plate coefficient of discharge equation is transformed into:

c, = c,, + cd4xo.80 + c,,x0.70 + c,2x0*35 + cd3x'.'5 (4A-25)

Where the coefficients are given by:

Cd, = (- 0.14Tu - 0.23TD) [4.758] o.8o (4A-26)

Cd, = 0.000511 250°.70 (4A-27)

cd, = 0.0210 p425~0.35 (4A-28)

C& = 0.0049 [ 4.75 p] p4p0.7 250°.35 (4A-29)

Since the fractional exponents ase relatively impractical calculations, it is advantageous to rewsite equation 4A-25 in the following manner so that only two fractional exponents are required:


A P I MPMS*L4-3-4 92 W 0732290 0506355 Ab7 W

SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFLCE METERS. PART &BACKGROUND 67

This method of formulating the equations makes the relative importance of terms more succinct. Within the bounds of the standard, X will always be less than or equal to one and greater than zero. Therefore, it is apparent how much each term contributes to the calculated value of the orifice plate coefficient of discharge. This compact form also makes it easier to solve for the coefficient of discharge.

In order to handle the case where the Reynolds number is below 4,000, a modification must be made to the algorithm to account for the switching function used for the C term. For functional smoothness, the transition takes place when the two functional forms used for Care equal. This occurs when:

0.35

Or, in terms of the reduced Reynolds number, when:

~ 0 . 3 5 B = * - X

Where: A = 4.343252

B = 3.764387 = 30 (4 1 0 - ~ ) ~ . ~ ~

= 6500 (4 1 0 - ~ ) ~ . ~ ~

(4A-3 1)

(4A-32)

(4A-32a)

It can be shown that the crossover point, X,, occurs at X = 1.142129 or a Reynolds

Therefore, the solution algorithm must be modified to compute c d as shown in equation number of 3502.20.

4A-30 for X less than X , as:

For X greater than X,.

4-A.3 Development of Solution Equations By combining equations (4A-1) and (4A-2), it can be shown that:

(4A-34)

where N, is a unit conversion factor for Reynolds number. The reduced Reynolds number used in the modified orifice plate coefficient of discharge correlation is:

(4A-35)

For a given set of flow conditions, aíi terms on the right hand side of equation 4A-35, except the orifice plate coefficient of discharge, are constant. It is convenient to define an iteration constant, FI such that:

(4A-36)


68 CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT ~ ~ ~~ ~ ~~ ~ ~ ~~

Equation 4A-36 can then be substituted into the orifice plate coefficient of discharge correlation equation, equations 4A-30 and 4A-33, to get a single equation which can then be solved for C, using any one of a number of numerical techniques.

Two numerical techniques were investigated, direct substitution and Newton-Raphson. The direct substitution algorithm can be summarized as:

Step 1: Guess a î d . Step 2: Calculate X using equation 4A-36. Step 3: Calculate a new C, using equation 4A-30 or 4A-33. Step 4: Repeat steps 2 and 3 until C, changes less than some specified tolerance

between iterations (for example, 0.000005 ).

As can be seen in Figure 4-A-1, the number of iterations needed to solve for the orifice plate coefficient of discharge varies strongly with the beta ratio ( p ) and the pipe Reynolds number. For many, if not most, natural gas applications (ReD > lo5), the direct substitution method converges in relatively few iterations. However, many more iterations are required for liquid applications (Re, > lo5). In the case of a very viscous fluid, the method will not converge in 50 iterations.

A Newton-Raphson method requires an explicit statement of the function to be solved and the first derivative of that function with respect to the solution variable. The function to be solved is:

(4A-37) FI f(C,) = c, - 9 ( c, )

Where:

For X < X,: g (x) = Cd, + c d , x0'70 f- c,2x0'35 + c,3x0'70 + cd4xo'80 (4A-38A)

1x100 1XIOi 1x102 1x103 1x104 1x105 1x106 1x107 1x108

Pipe Reynolds Number

Figure 4-A-1-Number of Iterations Required to Solve for Orifice Plate Coefficient of Discharge-Direct Substitution Method


SECTION 3-CONCENTRIC. SQUARE-EDGED ORIFICE METERS. PART 4--BACKGROUND 69

For X > X,:

The first derivative of the function f with respect to c d is:

(4A-39)

Where:

For X e X,:

For X > Xc:

(4A-40B)

This formulation allows both the function and its derivative to be calculated using only two fractional powers, X0‘3s and Xo‘80. The value of X0’7 is calculated by taking the square of X0’35. This calculation scheme allows the iterations to be performed very economically.

Figure 4-A-2 shows the number of iterations required to solve equation 4A-35 as a function of p ratio and pipe Reynolds number. The Newton-Raphson algorithm never requires more than 10 iterations to solve any case that falls within the bounds of the standard. Even at extremely low Reynolds numbers, the algorithm is able to solve for the orifice plate coefficient of discharge in fewer than 10 iterations in any case tested.. The stability in number of iterations required for solution as well as the economy of the iterations, makes the Newton-Raphson algorithm the preferred solution algorithm.

The Newton-Raphson algorithm can be summarized as follows:

Step 1: Guess a c d .

Step 2: Calculate X using equation 4A-36. Step 3: Calculate f and f’ according to equations 4A-37 through 4A-40. Step 4: Calculate the change in c d for the next iteration, 6 c d .

Step 5: Update the guess for c d .

Step 6: Repeat steps 2 through 5 until 6 c d is less than some predetermined tolerance

6 c d = f/f‘

c d = cd - 6 c d .

(for example, 0.000005).

4-A.4 Additional Precautions Required In cases where either very low flow or no flow is encountered, the iteration factor for c d ,

6, as defined by equation 4A-36, will become very large or infinite. Therefore, it is necessary to limit the iteration flow factor to some maximum value, qlirn. This limit has been arbitrarily set to 1000 in this standard to allow computation of the orifice plate coefficient



of discharge outside the range of applicability of this standard. This limit is sufficiently large that only a small number of cases will actually use this value. The limit also ensures that all computations will occur within the machine floating point range without causing any exceptions (for example, overflow or underflow).

8

7

6

v>

.- 5 5

5 4

5 3

c 2

f

(I> -

z 2

1

O

1x10’ 1x102 1x103 1x104 1x105 1x106 I XI 07 1x10* Pipe Reynolds Number

Figure 4-A-2-Number of Iterations Required to Solve for Orifice Plate Coefficient of Discharge-Newton-Raphson Method


~~

API f lPf lS*L4.3.4 92 m 0732290 0506359 402 m

APPENDIX 4-B-RECOMMENDED ROUNDING PROCEDURES

The rounding procedures presented must be implemented in a manner such that only decimal (base 10) arithmetic is used in all operations. Ifthe input and/or output data are not in decimal form, the implementation must provide a method for converting the input data to andíor from a decimal representation. These procedures will not give consistent results unless decimal arithmetic is used. The number of decimal digits used in the implementation shall be atleast two more than required for output.

4-B.l Absolute Rounding Absolute rounding shall be used for those quantities that have a fixed magnitude and a

fixed precision. The output result will be an exact multiple of the input precision, rounded from zero or towards infinity. This rounding procedure is outlined in Procedure 1.

Examples of the results of applying the procedure are:

2.3451 t 0,001 + 2,345 f 0.001 6.5435 f 0.002 3 6,544 f 0.002 6.5430 f 0.002 + 6.544 f 0.002

Procedure 1 -Absolute Rounding

x = value to be rounded. y = absolute rounding factor.

z = roundedvalue.

Input:

output:

Procedure: Step I . If x = O then set z = O and return. Step 2. Divide x by y. Step 3. I f x > O then add 0.5 to the result of Step 2,

else subtract 0.5 from result of Step 2. Step 4. Truncate the result of Step 3 to an integer value. Step 5. Multiply the result of Step 4 by y. This is the returned value z.

4-B.2 Relative Rounding Relative rounding is to be used for those quantities that have a variable magnitude and a

fixed relative precision. For these types of quantities, the precision is often expressed as a percentage of the final value. This procedure multiplies the relative precision by the value to obtain a nominal absolute precision for the observation. The nominal absolute precision is converted to the final rounding precision by truncating to 1,2, or 5 times an appropriate power of ten. The final rounding precision is then used according to the absolute rounding procedure to develop the properly rounded value. These rounding increments were chosen such that numbers which rounded up with one increment would exactly match numbers rounded down using the next larger increment. The output result will be an exact multiple of the final rounding precision, rounded towards infinity. This rounding procedure is outlined in Procedure 2.

Examples of the results of applying the procedure are:

2.3451 f 0.1% + 2.3451 f 0.0023 + 2.345 1 f 0.002 3 2.346 f 0.002 + 2.346 f O. 1%

71


~ - _ ___II_ __ -- A P I MPMS*L4=3-4 92 0732290 0506360 124 H


2.3451 f 0.05% 3 2.3451 k 0.00118 3 2.3451 f 0.001 3 2.345 f 0.001 3 2.345 f 0.05%

Procedure 2 - Relative Rounding

Input: x = value to be rounded. y = absolute rounding factor.

z = roundedvalue. output:

Procedure: Step 1. I f x = O then set z = O and return. Step 2. Multiply x times y and take the absolute value of the result. Step 3. If ( x < O ) then set w = -1 else set w = 1. Step 4. Determine q and w such that the result of Step 2 equals the absolute value of

q times w. q will be between 1 and 10 and w will equal some integral power of ten. w will have the same sign as x.

a. set q = result of Step 2 b. while (q c: 1)

s e t q = q x 1 0 s e t w = w x 1 0

end-while c. while (q > 10)

set q = q / 10 set w = w / 10

end-while

if (q < 2) then set ix = trunc( x x w + 0.5 ) else if (q < 5) then set ix = 2 x trunc( x x w/2 + 0.5 ) else if (q > 5 + 5 x y) then set ix = 5 x trunc(x x w/5 + 0.5) else begin

Step 5. Truncate q to either 1,2, or 5 and round x. This is accomplished by:

set n2 = 10 x trunc( x x w/10 + 0.5 ) set ix = 2 x trunc( x x w/2 -+ 0.5 ) if ( ix > n2 ) then set ix = 5 x trunc( x x w/5 + 0.5 ) end.

Step 6. Setz = idw.

Note: The function trunc(x) returns the largest integer value less than or equal to x.

4-8.3 Mixed Rounding Mixed rounding shall be used for those quantities that have a variable magnitude and the

precision is expressed as a combination of a fixed relative precision for large values and a fixed absolute precision for smaller values. The rounding increment used is the larger of the input absolute rounding factor or the absolute rounding factor determined according to Procedure 3.2.2. In order to maintain consistency, the fixed absolute precision must be equal to the rounding factor determined using the relative precision at the cross-over point. The output resuIt will be an exact multiple of the final rounding precision, rounded towards infinity. This rounding procedure is outlined in Procedure B-3.



Examples of the results of applying the procedure are: 2.3451 f (0.1% or 0.005)

3 2.3451 f (0.0023 or 0.005) + 2.345 f 0.005

2.3451 k (0.05% or 0.0005) a 2.3451 f (0,00118 or 0.0005) * 2.3451 f (0.001 or 0.0005) 3 2.345 f 0.001

2.345 f 0.05%

Procedure 3 -Mixed Rounding

Input: x = value to be rounded.

yl = relative rounding factor. y2 = absolute rounding factor.

output: z = roundedvalue.

Procedure: Step 1. If x = O then set z = O and return. Step 2. Multiply x times yl and take the absolute value of the result. Step 3. If the result of Step 2 is greater than y2.

then go to Step 6, else go to Step 4.

Step 4. If( x > O ) then set z=yz x trunc( x/y2 + 0.5 ) else setz = y2 x trunc( x/y2 - 0.5 ).

Step 5. Go to Step 10. Step 6. If( x < O ) then set w = -1

Step 7. Determine q and IV such that the result of Step 2 equals the absolute value of q times w. q wili be between 1 and 10 and w wiU equal some integral power of ten. w will have the same sign as x.

else set w = 1.

a. set q = result of Step 2 b. while (q < 1)

set q = q x 10 set IV = w x 10

end-while c. while (q > 10)

set q = q / 10 set w = w / 10

end-while

if (q < 2) then set ix = trunc( x x w + 0.5 ) else if (q < 5) then set rh = 2 x trunc( x x w/2 + 0.5 ) else if (q > 5 + 5 x y> then set ix = 5 x trunc(x x w/5 + 0.5) else begin

Step 8. Truncate q to either 1,2, or 5 and round x. This is accomplished b:

set n2 = 10 x frunc( x x w/10 + 0.5 ) set ix = 2 xtrunc( x x w/2 + 0.5 ) if ( ix > n2) then setix = 5 x trunc( x x w/5 + 0.5 ) end.

Step 9. Setz = i x h . Step 10. Return vdue of z.



Table 4-B-1-Recommended Rounding Tolerances Item us IP Metric SI

0.001 Rel. cw,, cc, 0.001 Re1 0.001 Rel. 0.001 Rel.

dm 3 di < 0.5 0.0010 Re1 e 0.05 0.0010 Rel. 10 0.0010 Rel. 0,010 0,0010 Rel. > 0.10 0.0005 Rel. > 1.0 0.0005 Rel. > 25 0.0005 Rel. > 0.025 0.0005 Rel.

0.05 to 0.1 0.00005 Abs. 0.5 to 1.0 0.0005 Abs. 10 to 25 0.0100 Abs. 0.010 to 0.025 O.oooO1 Abs.

D m 9 4 0.0025 Rei. 0.0025 Rel. 0.0025 Rei. 0.0025 Rel. k 0.01 Abs. 0.01 Abs. 0.01 Abs. 0.01 Abs. Pi, Pz. 4, 0.001 Rel. 0.001 Rel. 0.001 Rel. 0.001 Rel.

Lip > 20 0.001 Rel. e 20 0.02Abs. >20 0.001 Rel. < 20 0.02 Abs.

pb, &iair 9 %I,,,

> 50 0.001 Rel. 50 0.05Abs. > 5000 0.001 Rel. < 5000 5.0Abs.

0.001 Rel. 0.001 Rel. 0.1 Abs.

0.001 Rel. 0.001 Rel.

0.001 Rel. 0.001 Rel. 0.05 Abs.

0.001 Rei. 0.001 Rel.

0.001 Rel. 0.001 Rei. 0.05 Abs.

0.001 Rel. 0.001 Rei.


A P I MPMS*14.3.4 92 W 0732290 0506363 9 3 3

APPENDIX 4-C-ROUND ROBIN TESTING

To test the recommended implementation, an extensive round robin test procedure was conducted. Participants were solicited from the Committee on Petroleum Measurement, the Committee on Gas Measurement, and the Chapter 14.3 Working Group and other interested parties. Each participant was provided with a test matrix of values which would provide a wide variety of conditions of pipe geometry, flow conditions, and differential pressures. The matrix was designed to test results within normal operating ranges, extreme operating ranges, and outside the bounds of the RG equation. The test matrix was available in US, IP, metric, and SI units.

In addition, the participants were provided with a draft version of Part 4 and both FOR- TRAN and C versions of the implementation procedure. Also included in the test package were the baseline output results from the test matrix in each of the four systems of input units.

The implementation procedure was tested on a variety of computers ranging from 286 PCs to large mainframes and implemented in several different programming languages. Some of the computers used in the round robin test included:

Dell 8 MMHZ 286 Gateway 33 MHz 486 IBM RSl6000 - 320 DEC VAX 6220 VMS 5.3 Dataworld 25 MMHz 386

Dell 310 20 MHz 386 Gateway 25 MHz 486 IBM PSI2 Mod 70 20 MHz 386 DEC VAX 8800 VMS 5.3 Apollo DN10000

Toshiba 25 MHz 386 IBM 3090 - 600s LandMark v2.0 CPU 110.34 MHz

This list is representative but not inclusive of all computer systems that would be capable of making the necessary calculations to the required reproducibility. Several vendors of rack-mounted and low-powered field-mounted flow computers also tested the procedures on their systems.

Regardless of the equipment or the language used to program the calculational procedure, the final computed flow rates, calculated using single precision arithmetic, agreed with the baseline output results to within the stated 50 parts per million. Thus the calculational procedure was deemed to be of the desired accuracy and reproducibility.

At the time the round robin testing was begun, it was hoped that statistics concerning execution times could be provided. It was found that execution times were varying widely and were híghIy dependent on the speed of the processor, the programming language, and the VO requirements. As a result, insufficient data was collected within any particular operating environment to be meaningful. Therefore, no timing information is being presented. It should be noted that none of the participants expressed a concern about execution time.

Tables 4-C-1,4-C-2,4-C-3, and 4-C-4 present the actual test matrices used in the round robin testing. Since each matrix represents 10,080 test points, and there are five unique values output for each point, the output from an individual test matrix is substantial. To be able to provide a reasonable number of values to verify calculational accuracy and provide a means of testing for the full realm of conditions, a subset of the output results is presented in Tables 4-C-5 and 4-C-6. Each cell in the output results matrix contains values of the following quantities:

C, Discharge coefficient qin Mass flow rate Q, Y Expansion factor ICD Convergence flag

Volume flow rate at flowing conditions

A value of convergence flag, ICD, less than zero means outside correlation range. The absolute value is the number of iterations to convergence.

75


Table 4-C-1-Round Robin Test Parameters (US Units)

4 1 4, in in

i ,04882 0.10157 1,93945 O. 1953 1 2.90039 0.28906 4.02638 0.40626 7.98146 O. 7 9 6 8 9

14.31154 1.42969 29.37598 2.93752 47.25000 4.72657

1.04882 0.21094 1.93945 0.39063 2.90039 0.5781 1 4.02638 0.80469 7.98146 1.59374

14.31154 2.85937

Pipe Geometry

Dl11 4 1 ,

in in

29.37598 5.87500 47.25000 9.453 1 1

1.04882 0.42969 1.93945 0.78906 2.90039 1.17969 4.02638 1.64063 7.98 146 3.25000

14.31154 5.8281 1 29.37598 11.96094 47.25000 19.23437

1.04882 0.56252 1.93945 1.03126 2.90039 1.54689 4.02638 2.14843

Dl11 4 1 ,

in in

7.98 I46 4;25000 14.3 1 I54 7.62500 29.37598 15.65626 47.25000 25.17969

i .O4882 0.6953 1 1.93945 1.28126 2.90039 1.921 89 4.02638 2.66406 7.98146 5.28906

14.31 154 9.47657 29.37598 19.46094 47.25000 3 1.29689

1.04882 0.78906 1.93945 1.453 1 i

2.90039 4.02638 7.98146

14.31154 29.37598 47.25000

1.04882 1.93945 2.90039 4.02638 7.98146

14.31154 29.37598 47.25000

2.17189 3.02343 5.98437

10.73437 22.03 126 35.43752 0.83594 1.55469 2.3203 1 3.2 1874 6.38280

11.4551 1 23.5oooO 37.79689

Meter tube material is carbon steel pipe, cq? = 9.25 x 1O4in/in-"F. Orifice plate material is austenitic stainless steel, al = 6.20 x IO4in/in-"E

Flowing Conditions lu ka

"F

0.00 14.696 58.199 1.8650E+03 -1.0 68.00 14.696 56.660 2.1220E+02 -1.0

176.00 14.696 54.214 1.7490E+01 -1-0 60.00 14.696 62.366 1.1990 -1.0

2 10.00 14.696 58.792 2.8250E-01 -1.0

psia 4 2 t 3 CP T/

0.00 14.696 O. I3223 I .3070E-02 1.3198 50.00 100.00 0.31 109 1.0670E-02 1.3622 0.00 1000.00 65.072 1.5430E-01 -1.0 0.00 200.00 2.0466 1.3520E-02 1.3198

50.00 500.00 1.6623 1.13 10E-02 1.3622 150.00 1000.00 2.7573 1.3650E-02 - 1.3622 140.00 2000.00 32.465 4.17 10E-02 -1.0

aA value of -1.0 for the isentropic exponent k indicates that the fluid is incompressible.

Differential Pressures

Pb ib/f?

56.861 56.861 56.861 62.366 62.366 0.116198 0.044210 0.116198 0.1 16198 0.044210 0.044210 0.1 16198

0.0000 2.2484 8.9938

20.2360 35.9750

AP inches H20 at 60°F

80.9438 110.1736 143.9002 182.1236

~~

224.8440 272.0613 323.7754 379.9864 440.6943

The test matrix of 10,080 data points is formed by using all combinations of the 56 pipe geometry values, the 12 values for flowing conditions, and the 15 differential pressures (56 x 12 x 15 = 10,080).


API MPMS*1q-3-q 92 m 0732290 0506365 706 m

4, 4, ft ft


DI,, 4 1 ,

ft ft

Table 4-CP-Round Robin Test Parameters (IP Units)

Piue Geometrv Dm 4 1 , ft ft

0.0874017 0.0084642 O. 1616208 0.0162758 0.2416992 0.0240883 0.3355317 0.0338550 0.665 1217 0.0664075 1.1926283 0.1191408 2.4479983 0.2447933 3.9375000 0.3938808 0.0874017 0.0175783 O. 16 16208 0.0325525 0.2416992 0.0481758 0.3355317 0.0670575 0.6651217 O. 13281 17 1.1926283 0.2382808

2.4479983 3.9375000 0.0874017 & 16 16208 0.2416992 0.3355317 0.6651217 1.1926283 2.4479983 3.9375000 0.0874017 O. 1616208 0.2416992 0.3355317

0.4895833 0.7877592 0.0358075 0.0657550 0.0983075 0.1367192 0.2708333 0.4856758 0.9967450 1.6028642 0.0468767 0.0859383 O. 1289075 0.1790358

0.6651217 1.1926283 2.4479983 3.9375000 0.0874017 O. 1616208 0.2416992 0.3355317 0.6651217 1.1926283 2.4479983 3.9375000 0.0874017 O. 1616208

0.3541667 0.6354167 1.3046883 2.0983075 0.0579425 0.1067717 O. 1601575 0.2220050 0.4407550 0.7897142 1.6217450 2.6080742 0.0657550 0.1210925

0.2416992 0.3355317 0.6651217 1.1926283 2.4479983 3.9375000 0.0874017 O. 1616208 0.2416992 0.3355317 0.665 1217 I. 1926283 2.4479983 3.9375000

0.1809908 0.25 19525 0.4986975 0.8945308 1.8359383 2.9531267 0.0696617 O. 1295575 0.1933592 0.2682283 0.5319000 0.9544258 1.9583333 3.1497408

Meter tube matenal is carbon steel pipe, a, = 9.25 X 104idi-oF. Orifice plafe material is austenitic stainless steel, a, = 6.20 x 10dinlin-oF.

Flowing Conditions

0.00 68.00

176.00 60.00

210.00 0.00

50.00 0.00 0.00

50.00 150.00 140.00

14.696 14.696 14.696 14.696 14.696 14.696

100.00 1000.00 200.00 500.00

1000.00 2000.00

58.199 56.660 54.214 62.366 58.792

O. 13223 0.31109

2.0466 1.6623 2.7573

65.072

32.465

1.2530 1.4260E-01 1.1750E-02 8.0560E-04 1.8980E-04 8.7850M6 7.1720E-06 1.0370E-04 9.0840E-06 7.6000E-06 9.1740E-06 2.8030E-05

-1.0 -1.0 -1.0 -1.0 -1.0

1.3198 1.3622

1.3198 1.3622 1.3622

-1.0

-1.0

56.861 56.861 56.861 62.366 62.366 0.1 16198 0.044210 0.116198 0.116198 0.044210 0.044210 0,116198


Differential Pressures AP

inches H-O at 60°F

O.oo00 2.2484 8.9938

20.2360 35.9750

56.2110 80.9438

110.1736 143.9002 182.1236

~~~

224.8440 272.06 13 323.7154 379.9864 440.6943




Table 4-C-3-Round Robin Test Parameters (Metric Units)

Pipe Geometry

Din 4 1 1 Dl11 4 1 Dlll dni Dm dni mm mm mm mm mm mm mm mm

26.640 49.262 73.670

102.270 202.729 363.5 13 746.150

1200.150 26.640 49.262 73.670

102.270 202.729 363.513

2.580 4.961 7.342

10.319 20.241 36.314 74.613

120.055 5.358 9.922

14.684 20.439 40.48 1 72.628

746.150 149.225 1200.150 240.109

26.640 10.914 49.262 20.042 73.670 29.964

102.270 41.672 202.729 82.550 363.513 148.034 746. I50 303.808

1200.150 488.553 26.640 ,14.288 49.262 26.194 73.670 39.29 i

102.270 54.570

202.729 363.513 746.150

1200.150 26.640 49.262 73.670

102.270 202.729 363.513 746.150

1200.150 26.640 49.262

107.950 193.675 397.669 639.564

17.661 32.544 48.816 67.667

134.342 240.705 494.308 794.941 20.042 36.909

73.670 102.270 202.729 363.5 13 746. I50

1200.150 26.640 49.262 73.670

102.270 202.729 363.5 13 746.150

1200.150

Meter tube material is carbon steel pipe, a, = 9.25 x 104idin-oF. Orifice plate material is austenitic stainless steel, a, = 6.20 x lO4in/in-'F.

Flowing Conditions Pl# P ka Pb

kdm3 CP kg/m3 9 bar

? "C

-17.78 20.00 80.00 15.56 98.89

-17.78 10.00

-17.78 -17.78

10.00 65.56 60.00

1.01325 1.01325 1.01325 1.01325 1.01325 1.01325 6.895

68.9476 13.7895 34.474 68.948

137.895

932.26 907.60 868.43 999.01 941.75

2.1181 4.9831

1042.35 32.783 26.627 44.168

520.04

1.8650E+03 2.1220E+02 1.7490E+01 1.1990 2.8250E-01 1.3070E-02 1.0670Eo2 1.5430E-01 1.3520E-02 1.13 1 0 W 2 1.3650E-02 4.1710E-02

-1.0 -1.0 -1.0 -1.0 -1.0

1.3198 1.3622

1.3198 1.3622 1.3622

-1.0

-1 .o

910.83 910.83 910.83 999.01 999.01

1.86131 0.70817 1.8613 1 1.86131 0.70817 0.70817 1.86131

'A value of -1.0 for the isentropic exponent k indicates that the fluid is incompressible.

Differential Pressures AP

millibar

0.000 139.877 559.508 5.595 201.423 677.004

22.380 274.159 805.691 50.356 358.085 945.568 89,521 453.20 1 1096.635

55.166 76.795

152.003 272.653 559.594 900.113 21.233 39.489 58.936 8 1.756

162. I23 290.909 596.900 960.041



A P I MPMS*L4.3.4 72 0732290 050b367 587

0.0 559.5

2238.0 5035.6 8952.1


13987.7 55950.8 20142.3 67700.4 27415.9 80569.1 35808.5 94556.8 45320.1 109663.5

Table 4-C-4-Round Robin Test Parameters (SI Units)

Pipe Geometry D m dm m m

0.026640 0.002580 0.049262 0.004961 0.073670 0.007342 0.102270 0.010319 0.202729 0.020241 0.363513 0.036314 0.746150 0.074613 1.200150 0.120055 0.026640 0.005358 0.049262 0.009922 0.073670 0.014684 O. 102270 0.020439 0.202729 0.040481 0.363513 0.072628

D m dm m m

0.746150 0.149225 1.200150 0.240109 0.026640 0.010914 0.049262 0.020042 0.073670 0.029964 0.102270 0.041672 0.202729 0.082550 0.363513 0.148034 0.746150 0.303808 1.200150 0.488553 0.026640 0.014288 0.049262 0.026194 0.073670 0.039291 0.102270 0.054570

D m d* m m

O. 107950 0.202729 0.363513 O. 193675 0.746150 0.397669 1.200 150 0.639564 0.026640 0.017661 0.049262 0.032544 0.073670 0.048816 0.102270 0.067667 0.202729 0.134342 0.363513 0.240705 0.746150 0.494308 1.200150 0.794941 0.026640 0.020042 0.049262 0.036909

0.073670 O. 102270 0.202729 0.363513 0.746150 1.200150 0.026640 0.049262 0.073670 O. 102270 0.202729 0.363513 0.746150 1.200150

Meter tube material i s carbon steel pipe, cc, = 9.25 x 10"in/ii-°F. Orifice plate material is austenitic stainless steel, a, = 6.20 x 104in/in-"F.

Flowing Conditions

PUJ P ka pb kdm3 Pa-s kdm3

í7 pr OK Pa

255.37 293.15 353.15 288.71 372.04 255.37 283.15 255.37 255.37 283.15 338.71 333.15

932.26 907.60 868.43 999.01 941.75

2.1181 4.9831

1042.35 32.783 26.627 44.168

520.04

1.8650 2.1220-1 I .7490E-02 1.1990E-03 2.8250E-04 1.30703-05 1.0670E-05 1.5430- 1.3520E-05 1.1310E-05 1.3650E-05 4.1710E-05

-1.0 -1.0 -1.0 -1.0 -1.0

1.3198 1.3622

1.3198 1.3622 1.3622

-1.0

-1.0

910.83 910.83 910.83 999.01 999.01

1.86131 0.70817 1.86131 1.86131 0.70817 0.70817 1.86131


Differential Pressures AP Pa

0.055166 0.076795 0.152003 0.272653 0.559594 0.900113 0.021233 0.039489 0.058936 0.081756 O. 162123 0.290909 0.596900 0.960041




440.6943 ?.3 I O4 1 E-0 I 1.78852E+04 3.14543E+02 I .00000E+OO 4 5.87257E-01 1.30428E+04 2.2938 1E+02 1 .OOOOOE+OO -3 5.14002E-01 1.14211E+O4 2.00860E+02 I .ooOOOE+OO -3 5.99032E-0 1 1.19254E+O4 1.91217E+02 I .OOOOOE+00 2 5.97441E-01 1.158OE+O4 1.85679E+02 1 .ooO00E+OO 2 5.97734E-01 3.6305 1 E+02 3.12442E+03 6.63327E-01 2 5.97111E-01 7.99160E+02 1.80765E+04 9.52062E-01 2 5.97090E-01 1.21284E+04 1.04377E+05 1 .OOooOE+OO 2 5.96859E-01 2.09690E+03 1.80459E+O4 9.7526 1E-01 2 5.96836E-01 1.92086E+03 4.34486E+O4 9.904 12E-0 1 2 5.96820E-01 2.49042E+03 5.63315E+04 9.95206E-01 2 5.96792E-01 8.58468E+03 7.38797E+04 l.OOOOOE+OO 2

Table 4-C-&Selected Round Robin Test Results Matrix-US Units (Dm = 2.90039 in, % = 0.00000620 in/in-"F, d,,, = 0.57811 in, al = 0.00000925 in/in-"F)

9.60971E+03 1.69004E+02 1 .OOOOOE+OO -3 6.18538E-01 8.21819E+03 1.4453 1E+02 1.00000E+00 -3 5.99699E-01 8.52765E+03 1.36736E+02 I.O(IOOOE+OO 2 5.97692E-01 8.27492E+03 1.32683E+02 1 .00000E+00 2 5.97837E-01 3.23845E+02 2.78701E+03 8.28228E-01 2 5.97264E-01 5.85056E+02 1.32336E+04 9.75542E-01

Flow Conditions

1.13322E+04 1.99297E+02 1.00000E+00 -3 6.15959E-01 9.82072E+03 I .727 14E+02 1.00000E+00 -3 5.993 18E-01 1.02267E+04 1.63979E+02 l.OOOOOE+OO 2 5.97549E-01 9.92753E+03 1.59182E+02 1 .OOOOOE+OO 2 5.97758E-01 3.53 105E+02 3.03882E+03 7.52648E-01 2 5.97 176E-0 1 6.94220E+02 1.57028E+O4 9.64781E-01

T/ = O.OO"F, PJ = 14.696 psh, pf,p = 58.199 lb/f?, p = 1.8650E+03 cP, k = -1 .o, pb = 56.86 1 lb/ft3

6.9729 1E-01 9.26447E+02 1.62932E+01 1.00000E+OO -3 6.1271 6E-01 8.7 1268E+02 I .39702E+Ol 1.OoooOE+OO -3 6.02411E-01 8.34018E+02 1.33730E+01 1.OOOOOE+00 2 6.02323E-01 3.93263E+01~ 3.38443E+02 9.98282E-01 2 6.00256E-01 6.02575E+01 1.36298E+03 9.99755E-01 2 6.0O256E-O 1 8.70902E+02 7.49498E+03 1.00000E+00 2 5.98801E-01 1.54057E+02 1.32581E+ü3 9.99874E-01 2 5.98685E-01 I.38954E+02 3.14304E+03 9.99951501 2 5.98588E-01 1.79267E+02 4.05490E+03 9.99976E-01

ïj = 68.W°F, 9 = 14.696 psia, pf,p = 56.660 Ib/ft3, p = 2.1220E+02 cP, k = -1.0, pb = 56.861 Ib/ft3

6.4588 1E-01 2.57445E+03 4.52762E+OI 1.00000E+00 -3 6.03868E-01 2.57608E+03 4.13059E+Ol l.OOOOOE+OO 2 5.99259E-01 2.48899E+03 3.99094E+OI 1 .OOOOOE+OO 2 5.99244E-01 1.1576€E+02 9.96242E+02 9.84540E-01 2 5.98252E-01 1.79818E+02 4.06737E+03 9.97799E-01 2 5.98249E-O 1 2.60400E+03 2.24100E+04 1.00000E+00 2 5.97568E-01 4.60757E+02 3.96528E+03 9.98864E-01 2 5.97514E-01 4.15886E+02 9.40707E+03 9.99560E-01 2 5.97468E-01 5.36696E+02 1.21397E+04 9.99780E-01

T/ = 176.00'F, PJ = 14.696 psia, pf,p = 54.214 lb/ft3, p = 1.749OE+OI cP, k =-i .o, pb = 56.86 i lb/ft3

2 5.97466E-01 6.06804E+03 5.22215E+O4 l,OOOOOE+00 2 5.97088E-01 1.06880E+03 9.19813E+03 9.93815E-01

T/ = 60.00°F, ìf = 14.696 p i a , pf,p = 62.366 ib/ft3, p = 1.1990 cP, k = -1.0, pb = 62.366 lb/ft3

2 2 5.97250E-01 5.97159E-01 8.66549E+03 1.03970E+04 7.45752E+O4 8.94766E+04 1 . O ~ E + o O l.OOOOOE+W 2 2 5.96956E-01 5.96901E-01 1.51664E+03 1.80956E+03 1.30522E+04 1.55731E+04 9.87378E-01 9.81825E-01

T/ = 210.0O0F, ìf = 14.696 psia,

k = -1.0, pb = 62.366 lb/ft3 = 58.792 lb/ft3, p = 2.8250E-01 cP,

5.97056E-01 9.67759E+02 2.18901E+O4 9.97603501 2 5.97030E-01 1.25015E+03 2.82775E+M 9.98802E-01 2 5.96987E-01 4.29374E+03 3.69519E+O4 l.OOOOOE+00 2

= O.OOF, PJ = 14.696 psia, pf+ = 0.13223 Ib/ft3, p = 1.3070E-02 cP, k = 1.3198,pb=0.1161981b/ft3

5.96930E-01 5.96876E-01 1.37876E+03 1.65079E+03 3.11867E+O4 3.73398E+04 9.95108E-01 9.92956MI 2 2 5.96910E-01 5.96858E-01 1.78333E+03 2.13751E+03 4.03378E+O4 4.83490E+04 9.97554E-01 9.96478E-01 2 2 5.96875-1 5.96828E-01 6.13277E+03 7.35874E+03 5.27786E+04 6.33293E+04 l.OOOOOE+OO 1.00000E+OC 2 2

T/ = 50.00°F, 4 = 100.00 psia, pf,p = 0.31 109 ib/ft3, /i = 1.0670E-02 cP, k = 1.3622, pb = 0.044210 ib/ft3

T/ = O.OO°F, 4 = 1ooO.00 psia, pf,p = 65.072 lb/ft3, p = 1.5430E-01 cP, k=-1.0, pb = 0.116198 Ib/ft3

T/ = O.QQ°F, PJ = 200.00 psia, p,,p = 2.0466 lb/ft3, p = 1.3520E-02 cP, k = 1.3198,pb=0.1161981b/ft3

T/ = 50.00°F, PJ = 500.00 psia, P,,~ = 1.6623 iblf?, p = 1.1310E-02 cP, k = 1,3622, pb = 0.044210 lb/ff3

T/ = lSO.OO'F, PJ = 1OOO.00 psia, pf,p = 2.7573 Ib/ft3, p = 1.3650E-02 cP, k = 1.3622, pb = 0.044210 lb/ft3

T/ = 140.00°F, 9 = 2000.00 psia, P,,~ = 32.465 lb/ft3, j i = 4.1710E-02 cP, &=-1.0, pb = 0.116198 ib/ft3

- Cell iralue

cd b r

Y iCD cd 8 r Qv Y iCD

cd 8 1

Y tCD

cd 7nr Qv Y ICD

QV

-

-

Q,*

-

cd Pnr Qv Y tCD cd 4111

Qv Y ICD c, %Il

Qv Y ICD cd %,i

Qv Y ICD cd Qi

Y ICD cd 4111

Qv Y ICD

cd 4 1

Qv Y ICD cd 9111

Qv Y ICD

-

-

-

-

e, -

-

-

-

2.2484 20.2360

1.03233E+001 8.30723E-O1

-4

AP(inches H,O at 60"E)

56.21 10 I. I8 122E+OO 1.10400E+03 1.42523E+02 l.OOOE+OO 4 7.69 144E-01 5.213 18E+03 ?. 16828E+Ol 1.00000E+OO 4 5.3 166 1E-01 $.19628E+O3 7.37989E+OI l.OOOOOE+OO -3 5.01 673E-01 $.27786E+03 5.85929E+01 I.O(IOOOE+W 2 5.98434E-01 1.14260E+03 6.6424OE+Ol I.OOOOOE+00 2 5.98461E-01 1.87305E+M 1.61 194E+03 9.57057E-01 2 5.97729E-01 2.98261E+02 6.74645E+03 9.93886E-01 2 5.97724E-0 1 4.33618E+03 3.73172E+04 I.OOOOOE+OC 2 5.97246E-01 7.65961E+02 6.59186E+03 9.96845E-01 2 5.97206E-01 6.92245E+02 1.56581E+04 9.98777E-01 2 5.97 174E-01 8.93703E+@ 2.02149E+04 9.99389E-01 2 5.97121E-01 3.06764E+O? 2.64001E+04 1 .OOOOOE+O( 2

323.7754

1.58261E+M 2.78330E+02 1 .OOOOOE+OO

9.61 16OE-O1

d I '

7.36966E-0 I I 7.0890 I E 4 I I 6.9664 I E-O I 6.993 1 1E+03 1.22986E+02 1.00000E+00 -3 6.24554E-01 5.80869E+03 1.02156E+02 1.00000E+OC -3 6.00597E-01 5.97830E+03 9.58583E+01 1.00000E+OC 2 5.9803OE-O 1 5.79572E+03 9.29308E+01 I.oOoOOE+OC 2 5.98099E-01 2.50779E+02 2.15821E+03 9.15832E-01 2 5.97474E-01 4.14922E+02 9.38524E+01 9.88016E-01


82

A P I MPMS*L4.3*4 92 0732290 050b3b9 351 m


Table 4-C-5-Selected Round Robin Test Results Matrix-US Units (D, = 4.02638 in, a;! = 0.00000620 in/in-"F, d, = 0.80469 in, al = 0.00000925 in/in-"F)

Flow Conditions T/ = O.W°F, 9 = 14.696 psia, prp = 58.199 Ib/ft3, p = 1.8650E+03 cP, k = -1.0, pb = 56.861 Ib/ft3

T/ = 68.00"F. i j = 14.696 psia, pl,p = 56.660 lb/ft3, /.i = 2.1220E+02 cP, k = -1.0, pb = 56.861 Ib/ft3

T/ = 176.00°F, 9 = 14.696 psia, pI,p = 54.214 Ib/ft3, /.i = 1.7490E+01 cP, k = -1.0, pb = 56.861 Ib/ft3

r f = GO.OO°F, 9 = 14.696 psia, P,,~ = 62.366 Ib/ft3, /.i = 1.1990 cP, k =-imo, pb = 62.366 ib/f$

= 210.ûû°F, 9 = 14.696 psia, pl,p = 58.792 Ib/ft3, p = 2.8250E-01 cP, k = -1.0, pb = 62.366 Ib/ft3

r/ = O.OO"F, 9 ='14.696 psia, P,,~ = 0.13223 lb/f$, /.i = 1.3070E-02 cP, k = 1.3198, pb = 0.116198 Ib/ft3

~~

7j = 50.00'F, 9 = 100.00 psia, o , , ~ = 0.31 109 Ib/ft3, p = 1.0670E-02 cP, k = 1.3622, pb = 0.044210 Ib/ft3

7j = O.OO°F, 9 = 1000.00 pcia, g,,p = 65.072 Ib/ft3, p = 1.5430E-01 cP, '(=-1.0,pb=0.1161981b/ft3

7 j = O.OO°F, 4 = 200.00 psia, 'I,p = 2.0466 lb/ft3, p = 1.3520E-02 cP, i = 1,3198, pb = 0.116198 Ib/ft3

rf = 50.00°F, 9 = 500.00 psia, 't,p = 1.6623 ib/ft3, /.i = 1.1310E-02 cP, : = 1.3622, pb = 0.044210 lb/ft3

7 = 150.00°F, p f = 1OOO.00 psia, ),,p = 2.7573 Ib/ft3, /.i = 1.3650E-02 cP, : = 1.3622, pb = 0.044210 lb/ft3

y = 140.00"F. 4 = 2000.00 psia, I , , ~ = 32.465 lb/ft3, /.i = 4.1710E-02 cP, :=-1.o, pb = 0.116198 lb/ft3

- Cell valu1

cd qn,

Y ICD

4111

Y ICD

-

Q"

- cd

Qv

- cd 4nr Qv Y ICD

%Il

Y ICD cd 4nr Qv Y ICD

- cd

Qv

-

- cd Qin

Qv Y ICD cd 9ni Qv Y [CD cd ~ J J J

Qv Y iCD

-

-

- cd b r

Y [CD :d ?nt

Y CD

-d Im

2"

-

2,

- n

3, f

CD -d Im

- -I

3 V

CD -

AP(inches H,O at 60'F) 1 2.2484 I 20.2360 I 56.2110 I 110.1736

1.42942E+00 3.8O1 OE+03 6.683 14E+01 l.OOOOOE+OO

9.58872E-01 2.51838E+03 4.42901E+Ol i 1.00000E+00

1.23678E+00 1.08598E+00 1.00447E+0 9.86394E+03 1.44354E+04 1.86928E+O 1.73475E+02 2.53872E+02 3.28745E+O 1.OOOOOE+00 l.OOOOOE+OO 1.00000E+O -5 -4 -4 7.88535E-01 7.37202501 7.10577E-0 6.21 308E+03 9.68 102E+03 1.30639E+O 1.09268E+02 1.70258E+02 2.29752E+O l.OOOOOE+OO l.OOOOOE+OO l.OOOOOE+Oi -d -2 -2

6.77984E-01 6.36219E-01 6.24766E-01 6.19050E-0 1.74528E+03 4.91336E+03 8.04150E+03 1.1 1551E+O 3.06938E+Ol 8.64100E+01 1.41424E+02 1.96182E+0 l.OOOOOE+ûû l.OOOOOE+OO l.OOOOOE+OO l.OOOOOE+Oi -3 -3 -3 -3 6.09491E-01 6.02522E-01 6.00780E-01 5.99926E-0 1.67919E+03 4.98002E+03 8.27602E+03 1.15700E+O 2.69248E+Ol 7.98515E+01 1.32701E+02 1.85517E+0: 1.00000E+OO l.OOOOOE+ûû l.OOOOOE+OO l.OOOOOE+O( -2 12 12 12 5.01365E-01 I5.98864I5-01 I5.98209E-01 I5.97888E-o 1.61330E+03 4.81922E+03 8.02323E+03 3.122658+0 2.58650E+Ol 7.72731E+Ol 1.28648E+02 1.80010E+O: 1 .OOO00E+OO 1,0OOOOE+00 I .00000E+OO 1 .OoooOE+O( 2 2 2 2 5.01295E-01 5.98851E-O1 5.98230M1 5.97942E-01 7.60645B+01 2.24140E+02 3.62761E+02 4.85755E+O: 5.5461 IE+02 1.92895E+03 3.121928+03 4.18041E+O: >.98282E-01 9.8454OE-O1 9.57056E-01 9.15830E-01 1 12 12 ( 2 2.99655E-01 I5.98064E-01 I 5.97648E-01 I5.97446E-01 I. 1G632E+02 3.48287E+02 5.777998+02 8.03869B+K l.638 13E+03 7.878018+03 1.306948+04 1.81830E+@ ).99755E-01 9.97799E-01 9.93885E-O1 9.88015E-01 ! 2 2 2 j.99655E-01 5.98062E-03 5.97644E-01 5.97439B-01 1.68568E+03 5.04364E+03 8.40019E+03 1.17562E+@ 1.45069E+04 4.34056E+04 7.22921E+W 1.01 l74E+O: I .OOO00E+00 1.00000E+OO 1.00000Et00 1.00000E+O( ! 12 12 12 i.98500E4lI5.975208-OlI5.97264E-01 I5.97138E-01 !.98333E+02 8.92641E+02 1.48409E+03 2.07097E+0: !.56746E+03 7.68207E+03 1.27721E+04 1.78228E+OL 1.99874E-01 9.98864E-01 9.96845E-01 9.93815E-01 ! 2 2 2 i.98408E-01 5.97477E-01 5.97232E-01 5.971 12E-01 !.69097E+02 8.05727E+02 1.34128E+03 1.8752OE+Ol 1.08679E+03 1.82250E+04 3.03388E+04 4.24158E+04 1.99951E-01 9.99560E-01 9.98777E-01 9.97603E-01

1.98331E-01 5.97441E-01 5.97207E-01 5.97092E-01 ~47180E+02 1.03980E+03 1.73164E+03 2.42240E+03 '.85297E+03 2.35195E+04 3.91684E+04 5.47931E+04 1.99976E-01 9.99780E-01 9.99389E-01 9.98802E-01

2 2 2 ,98202E-01 5.97380E-01 5.97164E-01 5.97058E-01 .19085E+03 3.56768E+03 5.94397E+03 8.32008E+03 .02485E+04 3.07034E+04 5.1 1538E+04 7.16026E+04 . O ~ E + O O 1.OOOOOE+00 1.00000E+00 l.OOOOOE+OO

2 2 2

( 2 12 12

224.8440 323.7754 440.6943

9.31233E-01 8.98444E-01 8.72953E-01 2.47569E+04 2.86622E+04 3.24905E+04 4.35393E+02 5.04075E+02 5.71402E+02 1.00000E+00 1.00000E+00 l.OOOOOE+OC -4 -4 -4 6.87491E-01 6.77452E-01 6.69787E-01 1.80564E+04 2.13513E+04 2.46280E+04 3.17554E+02 3.75500E+02 4.33127E+02 1.00000E+00 l.OOOOOE+OO l.OOOOOE+C€ -3 1-3 1-3 6.14205E-01 I6.12122E-01~6.10537E-01

-3 5.99213E-01 5.9891 1E-01 5.98683E-01 1.65089E+04 1.98007E+04 2.30920E+04 2.64709E+02 3.17491E+02 3.70266E+02 l.OOOOOE+00 1.00000E+00 1.00000E+00 2 2 2 5.97619E-01 5.97505E-01 5.97419E-01 1.60306E+04 1.92331E+04 2.24354E+04 2.57041E+02 3.08391E+02 3.59738E+02 l.OOOOOE+OO 1.00000E+00 l.OoooOE+OO 2 2 2 5.97734E-01 5.97671E-01 5.97652E-01 6.27337E+02 6.84035E+02 7.03308E+02 5.39887E+03 5.88680E+03 6.05267E+03 8.28225E-01 7.52645E-01 6.63322E-01 2 2 2 5.97278E-01 5.97208E-01 5.97157E-01 1.13357E+03 1.34512E+03 1.54848E+03 2.56405E+04 3.04256E+04 3.50256E+04 9.75542E-01 9.64780E-01 9.52062E-01 2 2 2 5.97267E-01 5.97 194E-01 5.97 140E-01 1.67898E+04 2.01453E+04 2.35007E+04 1.44493E+05 1.73370E+05 2.02247E+05 1.00000E+00 l.OOOOOE+OO l.OOOM)E+OO 2 2 2 5.97033E-01 5.96989E-01 5.96956E-01 2.93885E+03 3.50653E+03 4.06338E+03 2.52918E+04 3.01772E+04 3.49694E+04 9.87378E-01 9.81824Eol 9.75261E-01 2 2 2 5.97012E-01 5.96969Eo1 5.969370-01 2.67171E+03 3.19889E+03 3.72228E+03 6.04323E+04 7.23568E+04 8.41955E+04 9.95108E-01 9.92956E-01 9.90412E-01 2 2 2 5.96996E-01 5.96955E-01 5.96924E-01 3.45569E+03 4.14208E+03 4.82601E+03 7.81655E+û4 9.36910E+04 1.09161E+05 9.97554E-01 9.96478E-01 9.95206E-01 2 2 2 5.96969E-01 5.96931E-01 5.96902E-01 l.I884OE+O4 1.426OOE+O4 1.66358E+04 1.02274E+05 1.22721E+05 1.43168E+05 1.00000E+OO 1.00000E+00 1.00000E+00 2 2 2


A P I MPMS*L4-3 .4 92 W 0732290 050b370 073 W

7.98381E-01 ).99092E+04 I .75708E+03 I .OOOOOE+00 4 5.48378M1 3.01587E+04 I .40973E+03 1.000OOE+00 -3 5.06292E-01 7.34665E+04 I .29204E+03 I .00000E+00 -2 5.983 19E-01 7.75938E+04 1.244 17E+03 1 .oMxH)E+00 2

SECTION %-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 4-BACKGROUND 83

7.80600E-01 1.13965E+05 2.00427E+03 1 .OoooOE+00 4 6.43399E-01 9.28004E+04 1.63206E+03 1.00000E+00 -3 6.05308E-01 8.557 19E+O4 1.50493E+03 1 .ooOOOE+W -2 5.98 I78E-01 9.05046E+04 1.45 1 19E+03 I.OOOOOE+W 2

Table 4-C-5-Selected Round Robin Test Results Matrix-US Units (O, = 7.98146 in, Q = 0.00000620 in/in-"F, d, = 1.59374 in, al = 0.00000925 in/in-OF)

6.14499E-01 3.10254E+04 5.45637E+02 1.00000E+00

Now Conditions lj = 0.ûO0F, 4 = 14.696 psia, D,,~ = 58.199 ib/ft3, p = 1.8650E+03 cP, ke-1.0, pb = 56.861 ib/ft3

6.10828E-01 6.07674E-01 4.31761E+04 6.13617E+04 7.59328E+02 1.07915E+03 1 .OOOOOE+00 1 .OOOOOE+OO

r f = 68.00'F. 4 = 14.696 psia, D ~ , ~ = 56.660 Ib/ft3, p = 2.1220E+02 cP, k = -1 .o, pb = 56.861 ib/ft3

3.23935E+04 5.19410E+02 1 .000OOE+00 2 5.97883E-01 3.14549E+04 5.04361E+02 1 .OOOOOE+00

lj = 176.0O0F, 4 = 14.696 psia, = 54.2 14 ib/f$, p = 1.749OE+O 1 cP,

k=-1.0, pb = 56.861 Ib/ft3

4.53108E+04 6.46818E+04 7.26530E+02 1 .O37 13E+03 1 .OOOOOE+OO 1.00000E+00 2 2 5.97682E-01 5.975 15E-01 4.40222E+04 6.28712E+04 7.05868E+02 1.00810E+03 1 .oooOOE+00 1 .000OOE+00

r f = 60.0o0F, if = 14.696 psia,

k = -1.0, pb = 62.366 Ib/ft3 = 62.366 Ib/ft3, p = 1.1990 cP,

5.97444E-01 7.54365E+04 1.20958E+03 1 .OOO00E+OO

r f =210.0O0F, 4 = 14.696 psia, p,,p = 58.792 ib/ft3, p = 2.8250E-01 cP, k=-l.o, pb = 62.366 Ib/ft3

5.97390E-01 8.80013E+04 1.41 105E+03 1 .00OOOE+00

r f = 0.OOoF, 4 = 14.696 psia,

k = 1.3198, pb = 0.116198 Ib/ft3 = 0.13223 Ib/ft3, p = 1.3070E-02 cP, 1.42218E+03

1.22393E+04 9.57057E-01 2 5.97533E-01 2.26605E+03 5.12565E+04 9.93885E-01 2 5.97530E-01 3.29445E+04 2.83520E+05 l.OOOOOE+OO 2 5.97292E-01 5.82180E+03 5.01024E+04 9.96845E-01

r/ = 50.00'F, 6 = 100.00 psia, ptP = 0.31109 lb/ft3, /i = 1.0670E-02 cP, k 1.3622, pb = 0.044210 Ib/ft3

1.90471E+03 2.46020E+03 1.63920E+04 2.11725E+04 9.15831E-01 8.28226E-01 2 2 5.97406E-01 5.97301E-01 3.15307E+03 4.44673E+03 7.13202E+04 1.00582E+05 9.88016E-0í 9.75542E-01 2 2 5.97402E-01 5.97294E-01 4.61124E+04 6.58631E+04 3.96844E+05 5.66817E+05 l.OOOOOE+OO l.OOOOOE+W 2 2 5.97213E-01 5.97147E-01 8.12468E+03 1.15302E+04 6.99210E+04 9.92291E+04 9.93815E-01 9.87378E-01

r/ = O.W"F, 4 = 1OOO.00 psia, = 65.072 ib/ft3, p = 1.5430E-01 cP,

k=-1.0, pb = 0.116198 ib/ft3

5.97273E-01 5.26168E+03 1.19016E+05 9.98777E-01

r f = 0.00"F, 4 = 200.00 psia, P , , ~ = 2.0466 Ib/ft3, p k = 1.3198, pb =0.116198 Ib/ft3

1.3520EX2 cP,

5.97 197E-01 5.97 134E-0 I 7.35677E+03 1.04823E+04 1.66405E+05 2.37102E+05 9.97603E-01 9.95108E-01

T/ = 50.W°F, p f = 500.00 psia, prP = 1.6623 ib/fe, p = 1.1310E-02 cP, k L 1.3622, pb = 0.044210 ib/ft3

6.79313E+03 1.53656E+05 9.99389E-01 2 5.97230E-01 2.33185E+04 2.00679E+05 1.000OOE+00 2

= 150.00"F, 4 = 1000.00 psia, pi,p = 2.7573 lb/ft3, p = 1.3650E-02 cP, k = 1.3622, pb = 0.044210 Ib/ft3

9.50365E+03 1.35583E+04 2.14966E+05 3.06680E+05 9.98802E-01 9.97554E-01 2 2 5.97164E-01 5.97108E-01 3.26423E+04 4.66275E+04 2.80920E+05 4.01276E+05 l.OOOOOE+00 I.OOOOOE+OC 2 2

Tf = 140.00"F. 9 = 2000.00 psia, P , , ~ = 32.465 ib/ft3, p = 4.1710E-02 cP, k=-l .O,pb = 0.116198 ib/ft3

- Cell talue

cd 4ni Qv Y [CD Cd q r r , Qv Y ICD cd 4m

Qv Y ICD

cd %I,

Qv Y ICD

-

-

-

-

cd 4rri Qv Y ICD cd e, Qv Y ICD cd 41n

Qv Y ICD cd e, Qv Y ICD cd 4ra Qv Y ICD

cd 9lli

Qv Y ICD cd G'n'nt Qv Y ICD cd 4m

Y ICD

-

-

-

-

-

-

-

QV

-

2.2484 [.3836OE+OO 1.44285E+04 1.53750E+02 I .OOOM)E+00 -5 3.40868E-01 3.66295E+03 1.52353E+û2 I .OOOOOE+OO 4 5.48724E-01 5.55063E+03 I . 15204E+02 I .OOOOOE+00 -3 5.04694E-01 5.53499E+03 1.04784E+O2 I.OOO00E+OO 2 5.99845E-01 5.31 158E+03 l.O1202E+O2 l.OOOOOE+OO 2 5.9980 1E-O 1 2.9763 1E+02 2.56 14 1E+03 9.98282E-01 2 5.98782E-01 4.56835E+02 1.03333E+04 9.99755E-01

5.98781E-01 6.60264E+03 5.68223E+04 1.000OOE+W 2 5.98063E-01 1.16940E+03 1.00638E+04 9.99874E-01 2 5.98006E-01 1.05486E+03 2.38601E+04 9.99951E-01 2 5.97958E-01 1.36101E+O? 3.07851E+04 9.99976E-01 2 5.97878E-01 4.66872E+03 4.01790E+04 1.00000E+OC 2

20.2360 1.04031E+00 3.25461E+04 5.72379E+02 I .00000E+00 4 7.22461E-01 2.23294E+04 3.92702E+02 l.OOOOOE+OO -3 5.218 15E-01 1.88369E+04 3.31280E+02 1.000OOE+Oû -3 5.00563E-01 1.947 12E+04 3.12209E+02 1 .OOOOE+OO 2 5.98290E-01 1.88859E+04 3.02823E+02 l.OOOOOE+CG 2 5.98282E-01 8.78380E+02 7.55934E+03 9.84540E-01 2 5.97792E-O 1 1.36558E+03 3.08884E+04 9.97799E-01 2 5.97790E-01 1.97753E+04 1.70187E+05 I.OOOOOE+OC 2 5.97453E-0 1 3.501 10E+03 3.01305E+04 9.98864E-01 2 5.97426E-01 3.16029E+O? 7.14837E+04 9.99560E-01 2 5.9740450 1 4.07848E+O: 9.22523E+Of 9.99780E-01 2 5.97366E-01 1.39943E+W 1.20435E+O: 1.00000E+O( 2

AP(inches H,O at 60°F)

56.2110 I 110.1736 I 224.8440 3.3 1428E-01 8.73 195E-01 6.8566 1 E+04 6.3741 6E+04 8.54120E+02 1.12101E+03 1 .oooOOE+00 1.00000E+OC

6.87816E-01 6.701 11E-01 3.543 1OE+04 4.83266E+04 6.23 1 16E+02 8.49907E+02 + 1 .OOOOOE+OO 1 .OOOOOE+OC

8.2 1 3 8 1 E-0 I 8.56562E+04 1.50641E+03 1.00000E+00 4 6.54928E-01 6.74737E+04 1.18664E+03 1 . O E + 0 0 -3

-3 1 -2 I -2 5.99481E-01~5.98950E-01 15.98507E-01

2 12 12 5.97895E-01 I 5.97716E-01 I 5.97586E-01

2 12 12 5.97257E-0115.97185E-011 5.97125-1

323.7754 I 440.6943 I

2 5.97258E-01 5.97225E-01 5.27683E+03 6.0748 1E+03 1.19358E+05 1.37408E+05 9.64780E-O 1 I I 9.52062E-O 1

5.97108E-01 1.255 1OE+04

9.92956E-01

5.97099E-01

9.75261E-01

5.97088E-01

9.90412E-01


--_____- - _ -- A P I MPMS*34-3*4 92 m 0732290 0506373 T O T m

a4 CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT

Table 4-C-5-Selected Round Robin Test Results Matrix-US Units Dm = 14.31154 in, CS = 0.00000620 in/in-"F, d, = 2.85937 in, al = 0.00000925 idin-"F

Flow Conditions

q = 0.00'F, 4 = 14.696 psia, pl,p = 58.199 ib/ft3, /.i = 1.8650E+03 cP, k = -1.0, pb = 56.861 Ib/ft3

T/ = 68.00'F, 4 = 14.696 psia,

k = -1.0, pb = 56.861 Ib/ft3 = 56.660 Ib/ft3, /.i = 2.1220E+02 cP,

lj = 176.00°F, 4 = 14.696 psia, P, ,~ = 54.214 Ib/ft3, /.i = 1.749OE+Ol cP, k = -1.0, pb = 56.861 Ib/ft3

7 = 60.00'F, 8 = 14.696 psia, pl,p = 62.366 Ib/ft3, /.i = 1.1990 cP, k = -1.0, pb = 62.366 Ib/ft3

r f = 210.00°F, 4 = 14.696 psia,

i( = -1.0, pb = 62.366 Ib/ft3 = 58.792 Ib/ft3, j i = 2.8250E-01 cP,

g = O.OO°F, 4 = 14.696 psia, = 0.13223 ib/ft3, j i = 1.3070E-02 cP,

k = 1.3198, pb = 0.116198 lb/ft3

rf = 50.00"F, p f = 100.00 psia, P,,~ = 0.31 109 Ib/ft3, /.i = 1.0670E-02 cP, i( = 1.3622, pb = 0.044210 Ib/ft3

7 j = O.OO"F, p f = 1000.00 psia, ?f,p = 65.072 Ib/ft3, j i = 1.5430E-01 cP, i = -1.0, pb = 0.116198 Ib/ft3

rf = O.OO°F, íj = 200.00 psia, >f,p = 2.0466 Ib/ft3, /.i = 1,3520E-02 cP, I = 1.3198, pb = 0.116198 Ib/ft3

r/ = 50.00'F, p f = 500.00 psia, ) f , p = 1.6623 Ib/ft3, j i = 1.1310E-02 cP, : = 1.3622, pb = 0.044210 Ib/ft3

y = 15O.0O0F, 9 = 1OOO.00 psia, = 2.7573 Ib/ft3, /.i = 1.3650E-02 cP,

: = 1.3622, pb = 0.044210 Ib/ft3

= 140.00°F, 9 = 2000.00 psia, = 32.465 Ib/ft3, /.i = 4.1710E-02 cP,

: = -1.0, pb = 0.116198 Ib/ft3

Cell Valut

cd

Q v

-

%I

Y ICD cd %,I

Y ICD

4111

Y ICD

Qlri

Y ICD

-

Q"

Cd

Qv

-

- cd

Qv

- cd !?Ili

Q" Y [CD

Cd qlll

Q v Y [CD

c, BI Q v Y [CD cd bi

Y [CD -d ?Ili

Y .CD

?I ?ni

-

-

2,

- P

2,

- n

2, Y CD *d bi

- - + CD -d 1111

- r.

3,

CD -

2.2484 20.2360

1.17826E+OO 9.17031E-0 3.9551 1E+04 9.23478E+@ 6.95574E+02 1.6241OE+O: 1.00000E+00 l.OOOOOE+OI -4 -4 7.68831E-O1 6.83523E-01 2.54962E+04 6.80022E+01 4.48395E+02 1.19594E+O: 1.00000E+00 1.00000E+O( -4 -3 6.32128E-01 6.13732E-01 2.05463E+04 5.98458E+ol 3.6 I343E+02 l.O5249E+O: 1 .00000E+00 1 .0000OE+o( -? -? ., I "

6.02246E-01 I 5.99492E-01

2 5.98984E-01 9.56737E+oi 8.23368E+O: 9.98282E-01 2 5.98304E-O1 1.46933E+O? 3.32353E+04 9.99755E-01

2 5.9797OE-O1 2.82594E+O: 2.43200E+OL 9.84540E-01 2 5.97643E-01 4.39455E+O? 9.94017E+OL 9.97799E-01

5.98304E-0 1 2.12363E+04 1.82759E+05 l.OOOOOE+OC 2 5.97824E-O 1 3.76265E+03 3.23 8 14E+04 9.99874E-01 2 5.97786E-01 3.39422E+03 7.67750E+04 9.99951E-01

5.97642E-01 6.36389E+3+04 5.47676E+05 l.OOOOOE+OC 2 5.974 16E-0 1 1.12690E+04 9.69807E+04 9.98864E-01 2 5.97397E-01 1.01722E+04 2.30087E+05 9.99560E-01

5.97755E-01 5.97383E-01 4.37944E+03 1.31277E+04 3.90600E+04 2.96940E+05 3.99976E-01 9.99780E-01 .I * L I' 5.97701E-01I5.97357E-01

@(inches H,O at 6OoF)

56.21 10 110.1736 224.8440 323.7754 440.6943

8.35608E-01 7.92546E-01 7.54610E-01 7.37907E-01 7.25060E-01 1.40247E+05 1.86227E+05 2.53305E+05 2.97237E+05 3.40740E+05 2.46649E+03 3.27513E+03 4.45480E+03 5.22744E+03 5.99250E+03 l.OOOOOE+OO l.OOOOOE+CO l.OOOOOE+OO 1.00000E+00 l.OOOOOE+OC -4 -4 -3 -3 -3 6.59173E-01 6.46865E-01 6.36388E-01 6.31890E-01 6.28479E-01 1.09299E+05 1.50162E+05 2.1 1043E+05 2.51461E+05 2.91788E+05 1.92222E+03 2.64086E+03 3.71 155E+03 4.42238E+03 5.13160E+03 l.OOOOOE+00 1.00000E+00 l.OOOOOE+OO 1.00000E+00 l.OOOOOE+W -3 -3 -3 -3 -3

6.08682E-01 6.06089E-01 6.041 17E-01 6.03284E-01 6.02656E-01 9.89222E+04 1.37901E+05 1.96361E+05 2.35308E+05 2.74240E+05 1.73972E+03 2.42523E+03 3.45334E+03 4.13830E+03 4.82299E+03 1.0OooOE-1-00 1.OOOOOE+00 l.OOOOOE+00 l.O0000E+00 1.0OOOOE+00 -2 1 -2 12 12 12 5.98771E-01 I 5.98417E-01 I 5.98121E-01 I 5.97995E-01 I5.97901E-01 1.04148E+05 1.45721E+05 2.08069E+05 2.49631E+05 2.91 190E+05 1.66994E+03 2.33654E+03 3.33626E+03 4.00268E+03 4.66905E+03 l.OOOOOE+0O 1.OOOOOE+00 l.OOOOOE+OO 1.OOOOOE+00 1.00000E+OO 2 2 2 2 2 5.97704E-01 5.97570E-01 5.97458E-01 5.97410E-01 5.97374E-01 1.01220E+05 1.41676E+05 2.02356E+05 2.42808E+05 2.83259E+05 1.62300E+03 2.27169E+03 3.24466E+03 3.89328E+03 4.54188E+03 1.00000E+00 l.OOOOOE+OO 1.00000E+00 1.00000E+00 1.0OOOOE+00 2 12 12 12 12 j.97712E-01 I 5.97592E-01 I 5.97505E-01 I 5.97479E-OlI5.97471E-01 $.57643E+03 6.12979E+03 7.91805E+03 8.63419E+O? 3.93848E+04 5.27530E+04 6.81427E+04 7.43059E+M 9.57056E-01 9.15831E-01 8.28226E-01 7.52645E-01 1 2 2 2

5.97469E-01 5.97384E-01 5.97314E-01 5.97285E-01 7.29340E+03 1.01490E+04 1.43139E+04 1.69863E+04 I .64972E+05 2.29564E+05 3.23770E+05 3.84219E+05 3.93885E-01 9.88015E-01 9.75542E-01 9.64780E-01 1 2 2 2 5.97467E-01 5.97381E-01 5.97309E-01 5.97278E-01 i.O6034E+O5 1.48426E+05 2.1201 1E+05 2.54401E+05 ).12526E+05 1.27735E+06 1.82457E+06 2.18937E+06 L.OOOOOE+OO 1.00000E+00 l.OOOOOE+OO l.OOOOOE+OC l 2 2 2 i97308E-01 5.97254E-01 5.97210E-01 5.97191E-01 1.87402E+04 2.61543E+04 3.71 185E+04 4.42902E+04 1.61278E+05 2.25084E+05 3.19441E+05 3.81162E+05 P.96845E-01 9.93815E-01 9.87378E-01 9.81824E-01

* * m

8.87763E+03 7.64009E+04 6.63322E-01 2 5.97263E-0 1 1.95554E+04 4.42330E+05 9.52062E-01 2 5.97255E-01 2.96789E+05 2.55417E+06 l.OOOOOE+OO 2 5.97177E-01 5.13253E+04 4.41706E+05 9.75261E-01 m .

I ' I ' I ' I ' i.97295E-0II5.97244E-01 I5.97201B41 I5.97183E-01 I5.97170&01 1.69374E+04 2.36825E+04 3.37451E+04 4.04053E+04 4.70177E+04 I . 83 1 13E+05 5.35682E+05 7.6329 1 E+05 9.1394 1E+05 1 .O635 1 E+06 ).98777E-01 I l I I I 9.97603E-01 9.95108E-01 9.92956E-01 9.90412E-01

i.97284E-01 5.97236E-01 5.97195E-01 5.97178E-01 5.97165E-01 !.18674E+04 3.05938E+04 4.36479E+04 5.23194E+04 6.09601E+04 1.94625E+05 6.9201 1E+05 9.87286E+05 1.18343E+06 1.37888E+06 1.99389E-01 9.98802E-01 9.97554E-01 9.96478E-01 9.95206E-01

2 2 2 2 i.97266E-01 5.97221E-01 5.97183E-01 5.97167E-01 5.97155E-01 '.50644E+04 1.05082E+05 1.50108E+05 1.80125E+05 2.10141E+05 i.46004E+05 9.04338E+05 1.29183E+06 1.55015E+06 1.80847E+M .OOOOOE+00 l.OOOOOE+OO 1.OOOOOE+OO l.OOOOOE+OO l.OOO00E+OO

1


API MPMS*14-3-4 92 m 0732290 O506372 9Llb =

9.91422E-01 1.40492E+05 2.47080E+03 1 .OOOOOE+Oo -4 7.06945E-01 9.89705E+04 1.74057E+03 1.00000E+00 -3 6.18734E-01 8.49004E+04 1.493 12E+03 1 .OOOOOE+00 -3 6.00321E-01 8.81607E+04 1.41360E+03 1.00000E+00 2 5.98357E-01 8.55544Et04 1.37181E+03 1 .OOOOOE+00 2 5.98338E-01 4.03460E+03 3.472 17E+04 9.98282E-01


Table 4-C-&Selected Round Robin Test Results Matrix-US Units Dm = 29.37598 in, a;! = 0.00000620 in/in°F, d,,, = 5.87500 in, a1 = 0.00000925 in/in-"F

8.07597E-01 3.43331E+05 6.03808E+03 1.00000E+W -4 6.5 12 18E-0 1 2.73509E+05 4.81014E+03 I .00000E+W -3 6.07105E-01 2.499 16E+05 4.39522E+03 1.00000E+W -2 5.98647E-01 2.63747E+05 4.22903E+03 1 .OOOM)E+W 2 5.97725E-01 2.56395E+05 4.11113E+03 1 .OOOOOE+W 2 5.97720E-01 l,1925OE+04 1.02626E+05 9.84540E-01

Flow Conditions

6.35725E-01 4.45004E+05 7.82617E+03 1 .OOOOOE+00

T = O.GOOF, p/ = 14.696 psia, = 58.199 lb/ft3, p = 1.8650E+03 cP,

k=-1.0, pb = 56.861 Ib/ft3

TJ = 68.00"F, 4 = 14.696 psia, p f p = 56.660 Ib/ft3, p = 2.1220E+02 cP, k=-1.0, pb = 56.861 Ib/ft3

6.27969E-01 6.21400E-01 6.18585E-01 6.15405E+05 8.69952E+05 l.O3921E+O6 l.O823OE+04 1.52996E+04 1.82764E+04 1 .OOOOOE+00 I .00OOOE+00 I .00000E+W

T f = 176.00"F. 4 = 14.696 psia, pf,p = 54.214 Ib/ft3, p = 1.749OE+OI cP, k = -1.0, pb = 56.861 lb/ft3

TJ = 60.00"F, pf,p = 62.366 Ib/ft3, p = 1.1990 cP, k = -1.0, p b = 62.366 lb/ft3

= 14.696 psia,

4.14454E+05 7.28890E+03 1.00000E+00 2 5.98208E-01 4.39256E+05 7.04320E+03 1.00000E+00

?j = 21O.OO0F, 4 = 14.696 psia, pfp = 58.792 Ib/ft3, j i = 2.8250E-01 cP, k = -1.0, pb = 62.366 Ib/ft3

TJ = O.OO"F, 4 = 14.696 psia, pf,p = 0.13223 lb/ft3, p = 1.3070E-02 cP, k = 1.3198,pb=0.1161981b/ft3

5.78862E+05 8.25305E+05 9.89532E+05 1 .O 1803E+O4 1.45 144E+04 1.74027E+04 1 .OOOOOE+00 1 .OOOOOE+00 1 .OOOOOE+W 2 2 2 5.97992E-01 5.97812E-01 5.97736E-01 6.14737E+05 8.7793 lE+05 1.05338E+06 9.85693E+03 1.4077 1E+04 1.68903E+M 1 .oooOOE+00 1.00000E+00 1.00000E+W

TJ = 50.00"F. p / = 100.00 psia,

k = 1.3622, pb = 0.044210 Ib/ft3 = 0.31 109 ib/ft3, p = 1.0670E-02 cP,

5.97924E-O 1 6.19898E+03 1.40217E+05 9.99755E-0 1 2 5.97924E-01 8.95938E+04 7.71045E+05 l.OOOOOE+OO 2 5.9763 1E-0 1 1.58793E+04 1.36657E+05 9.99874E-01 .-i

TJ = O.OO"F, p/ = 1OOO.00 psia, pf,p = 65.072 lb/ft3, j i = 1.5430E-01 cP, k=-1.0, jib = 0.1 16198 ib/ft3

TJ = O.ûO°F, p / = 200.00 psia, pf,p = 2.0466 lb/ft3, p = 1.3520E-02 cP, k = 1.3198,pb=0.1161981b/ft3

5.97520E-O 1 1.85482E+04 4.19547E+05 9.97799E-O 1 2 5.97519Ero 1 2.68602E+05 2.31159E+O6 l.OOOOOE+C€ 2 5.9738050 1 4.75702E+04 4.09389E+05 9.98864E-01 +

TJ = 50.00"F, 4 = 500.00 psia, pf,p = 1.6623 ib/ft3, f l = 1.1310E-02 cP, k = 1.3622, pb = 0.044210 ib/ft3

TJ = 150.00"F, 4 = 1OOO.00 psia, pf,p = 2.7573 Ib/ft3, p = 1.3650E-02 cP, k = 1.3622, pb = 0.044210 Ib/ft3

5.97281E-01 1.10418E+05 9.50254E+05 9.93815E-01 2 5.97275E-01 9.99830E+04 2.26155E+06 9.97603E-01

TI = 140.00°F, p / = 2000.00 psia, pf,p = 32.465 lb/ft3, p = 4.1710E-02 cP, k=-1.0,p~=0.1161981b/ft3

5.97254E-01 5.97242E-01 1.56710E+05 1.86991E+05 1.34865E+06 1.60925E+06 9.87378E-01 9.81824E-01 2 2 5.97248E-01 5.97237E-01 1.42469E+05 1.70590E+05 3.22256E+06 3.85863E+06 9.95108E-01 9.92956E-01

Cell Value

1.43248E+04 3.24016E+05 9.99951E-01 2 5.97589E-01 1.84831E+04 4.18075E+05 9.99976E-01 2 5.97556E-01 6.34084E+04 5.45693E+05 l.OOOOOE+OO 2

cd 9111

Qv Y ICD cd 9111

Y ICD cd 4111

Y ICD

-

QV

-

Q,,

4.29407E+04 9.71290E+05 9.99560E-01 2 5.97361E-01 5.54179E+04 1.25351E+06 9.99780E-01 2 5.97345E-01 1.90160E+05 1.63652E+06 l.OOOOOE+ûC 2

Cd

Qv 4111

Y ICD cd 4111

Qv Y ICD

-

5.97300E-O1 9.23175E-cO4 2.08816E+06 9.99389E-01 2 5.97289E-01 3.16903E+05 2.72727E+06 l.OOOOOE+OO 2

cd 4111

Qv Y ICD c, 4111

Qv Y ICD Cd 4111

Qv Y ICD c, 4111

Qv Y ICD cd 4"L Qv Y ICD cd 4ni

Y ICD

4111

Y ICD

-

-

-

-

-

Q"

Cd

Qv

-

-

5.97270E-01 5.97245E-01 5.97234E-01 1.29162E+05 1.84279E+05 2.20892E+05 2.92156E+06 4.16826E+06 4.99643E+06 9.98802E-01 9.97554E-01 9.96478E-01 2 2 2 5.97261E-01 5.97237E-01 5.97227E-01 4.43644E+05 6.33752E+05 7.60490E+05 3.8 18OOE+06 5.45407E+06 6.54477E+06 1.00000E+00 l.OOOOOE+OO I.OOOOOE+ûC 2 2 2

2.2484 I 20.2360

L IL

5.97608501 I 5.97369EM1

AP(inches H?O at 60°F)

56.21 10 7.5 1815E-01 5.32694E+05 9.36836E+03 1 .OOO00E+OC -3

110.1736 224.8440 323.7754

7.16964E+05 9.88442E+05 1.16741E+06 I .26091E+04 I.73835E+04 2.053098+04 i 1.00000E+00 1 .OoooOE+00 1.00000E+W

7.22773E-O1 6.975 16E-01 6.86507E-01

-3 1-3 1-3 1-3 6.04084E-01 I6.02653E-OlI6.01458E-01 I6.00951E-01

2 ( 2 12 12 5.97558E-01 I 5.97476E-01 I 5.97407E-01 I 5.97378E-01

1.66225E+05

3.07869E+04 6.96378E+05 9.93885E-01

5.97412E-01 4.47590E+05

5.97489E-01 5.97435E-01 5.97419E-01 2.58730E+04 3.34228E+04 3.64464E+04 2.22663E+05 2.87637E+05 3.13657E+05 9.15830EMl 8.28225E-01 7.52644E-01 2 2 2 5.97361E-01 5.97318E-01 5.97300E-01 4.28433E+04 6.04277E+04 7.171 11E+04 9.69087E+05 1.36683E+06 1.62206E+06 9.88015E-01 9.75542E-01 9.64780E-01 2 2 2 5.97359E-01 5.97315E-01 5.97296E-01 6.26571E+05 8.95034E+05 1.07401E+M

3.85 1968t06 5.392278+06 7.70266E+06 9.24291 E+O6 1 .ooOo8++0 1.00000E+00 I 1.0008+00 I .WOWE+Oa

5.97314E-01 7.91 144E+04

9.96844E-O 1

9.98777E-01

440.6943 6.78091E-01 1.34528E+06 2.36591E+04 I .OOOOOE+OO -3 6.16449E-0 I I .20823E+06 2.12488E+04 I .OOOOOE+00 -3 6.00570E-01 I . 15372E+06 2.02902E+04 1.00000E+00 2 5.97678E-O1 1.22883E+06 1.97035E+04 1 .OoooOE+OO 2 5.97355E-01 1.19577E+06 1.91734E+04 1 .OOOOOE+00 2 5.974 14E-O 1 3.74741E+04 3.22502E+05 6.63320E-01 2 5.97286E-01 8.25582E+04 1.8674 1 E+06 9.52062E-01 2 5.97282E-01 1.25298E+06 1.0783 1E+07 1.00000E+00 2 5.97233E-01 2.16695E+05 1.864888+06 9.75261E-01 2 5.97229E-O1 1.98509E+05 4.49014E+06 9.904 12E-0 1 2 5.97226E-O 1 2.57375E+05 5.82165E+06 9.95206E-01 2 5.97220E-O 1 8.87227E+05 7.63547E+06 1.0OOOOE+00 2


_ _

A P I MPMS*L4 .3 .4 72 W 0732270 0506373 8 8 2


Table 4-C-5-Selected Round Robin Test Results Matrix-US Units ( D, = 1.93945 in, cc;! = 0.00000620 in/in-"F, d, = 0.78906 in, al = 0.00000925 in/in-OF)

Cell Value

AP (inches H,O at 60°F) I Flow Conditions 2.2484

TJ-= O.W°F, PJ= 14.696 pia , P,,~ = 58.199 lb/ft3, p = 1.8650E+03 CP, k = -1.0. pb = 56.861 Ib/ft3

cd 4111

Qv Y ICD

Cd 411,

Qv Y ICD

cd 4111

Qv Y ICD

Cd 4111

Qv Y ICD

cd Qi

Y ICD cd 4ni Qv Y ICD cd 4111

Qv Y ICD

-

-

-

-

Q"

-

-

9.91422E-01 1.40492E+O: 2.4708OE+O: 1.00000E+O( -4 7.06945E-03 9.89705E+oL 1.74057E+O: l.OOOOOE+o(

I - l - I " I " I "

6.51218E-01 I6.35725E-01 I6.27969E-O1 16.214WE-01 I6.18585E41 16.16449E-01 ïj= 68.0O0F, PJ= 14.696 p i a , pl,p = 56.660 Ib/ft3, p = 2.1220E+02 cP, k = -1.0, pb = 56.861 Ib/ft3

2.73509E+05 4.45004E+05 6.15405E+05 8.69952E+05 1.03921E+06 1.20823E+06 4.81014E+03 7.82617E+03 1.08230E+04 1.52996E+04 1.82764E+04 2.12488E+04 1.00000E+OO l.OOOOOE+OO 1.OOOOOE+00 l.OOOOOE+OO 1.00000E+00 l . O ~ E + W -3 -3 -3 -3 -3 -3

ïj= 176.iN°F, PJ= 14.696 psia, pl,p = 54.214 Ib/ft3, p = 1.749OE+Ol cP, k = -1.0, pb = 56.861 Ib/ft3

6.07105E-01 6.04084E-01 6.02653E-01 2.49916E+05 4.14454E+05 5.78862E+05 4.39522E+03 7.28890E+03 1.01803E+04 l.OOOOOE+00 1.00000E+00 l.OOOOOE+OC -2 2 2 5.98647E-01 5.98208E-01 5.97992E-01 2.63747E+05 4.39256E+05 6.14737E+05 4.22903Et03 7.04320E+03 9.85693E+03 l.OOOOOE+OO 1.OoooOE+00 1.00000E+W

6.01458E-01 6.00951E-01 6.00570E-01 8.25305E+05 9.89532E+05 1.15372E+06 1.45144E+04 1.74027E+04 2.02902E+04 1.00000E+00 1.OOOWE+00 1.00MX)E+00 2 2 2 5.97812E-01 5.97736E-01 5.97678E-01 8.77931E+05 1.05338E+06 1.22883E+06 1.40771E+04 1.68903E+04 1.97035E+04 l.OOOOOE+OO l.oM)0(1E+00 1.00000E+00

6.18734E-03 8.49004E+oL 1.49312E+0: 1.00000E+O( -3 6.00321E-03 8.81607E+oL 1.41360E+0: l.OOOOOE+O( 2 5.98357E-01 8.55544E+oL 1.37 18 1E+O: 1 .OOOOOE+O( 2

TJ-= 60.W°F, PJ= 14.696 psia, P,,~ = 62.366 Ib/ft3, p = 1.1990 cP, k = -1.0, pb = 62.366 Ib/ft3

2 2 2 2 5.97725E-01 5.97558E-01 5.97476E-01 5.97407E-01 2.56395E+05 4.27205E+05 5.98004E+05 8.54193E+05 4.1 11 13E+03 6.84996E+03 9.58863E+03 1.36965E+04 l.OOOOOE+OO l.O00OOE+00 1 .OOOOOE+00 l.OOOOOE+OC 2 2 2 2 5.97720E-01 5.97562E-01 5.97489E-01 5.97435E-01 1.19250E+04 1.93150E+04 2.58730E+04 3.34228E+04 1.02626E+05 1.66225E+05 2.22663E+05 2.87637E+05 9.84540E-01 9.57056E-01 9.15830E-01 8.28225E-01

Tf= 210.00'F, PJ= 14.696 psia, pl,p = 58.792 lb/ft3, p = 2.8250E-01 cP, k = -1.0, pb = 62.366 lb/ft3

TJ-= O.OO"F, PJ= 14.696 psia, P,,~ = 0.13223 lb/ft3, p = 1.3070E-02 cP, k = 1.3198, pb = 0.116198 lb/ft3

5.98338E-01 4.0346OE+O? 3.47217E+OL 9.98282E-01

5.97520E-01 5.97414E-01 5.97361E-01 5.97318E-01 1.85482E+04 3.07869E+04 4.28433E+04 6.04277E+04 4,19547E+05 6.96378E+05 9.69087E+05 1.36683E+06 9.97799E-01 9.93885E-01 9.88015E-01 9.75542E-01 2 2 2 2 5.97519E-01 5.97412E-01 5.97359E-01 5.97315E-01 2.68602E+05 4.47590E+05 6.26571E+05 8.95034E+05 2.31 159E+06 3.85196E+06 5.39227E+06 7.70266E+06 1.00000E+00 1.00000E+00 1.OOOOOE+00 1.00000E+W 2 2 2 2 5.97380E-01 5.97314E-01 5.97281E-01 5.97254-1 4.75702E+04 7.91 144E+04 1.10418E+05 1.56710E+05 4.09389E+05 6.80859E+05 9.50254E+05 1.34865E+06 9.98864E-01 9.96844E-01 9.93815E-01 9.87378E-01 n ?3 ?3 ?3

5.97300E-01 7.17111E+04 1.62206E+OC 9.64780E-01 2 5.97296E-01 l.O7401E+M 9.2429 1E+M 1.00000E+íX 2 5.97242E-0 1 1 A699 1E+05 1.60925E+Of 9.8 1824E-01 0

ïj= 50.00"F, PJ= 100.00 psia, pbp = 0.31 109 Ib/ft3, p = 1.0670E-02 cP, k = 1.3622, pb = 0.044210 3b/ft3

5.97924E-0 1 6.19898E+O? 1.40217E+O: 9.99755E-01 2 5.97924501 8.95938E+04 7.71045E+05 1.00000E+OC 2 5.9763 lE-01 1.58793E+04 1.36657E+O5 9.99874E-01 2 5.97608E-01 1.43248E+04 3.24016E+05 9.99951E-01

Tf= O.OO"F, P f = 1ooO.00 psia, P , , ~ = 65.072 lb/f$, p = 1.5430E-01 cP, k = -1 .O, pb = O. 1 16 198 1b/ft3

cd 4ni Qv Y ICD cd 4111

Qv Y ICD

cd 4m

Y ICD cd 4111

Qv Y ICD

cd 4111

Y ICD

-

-

Q"

-

13"

-

1.25298E+06

1.00000E+00

5.97233E-01 2.16695E+05 1.86488E+06 9.75261E-01

TJ-= 0.00'F, PJ= 200.00 psia, p,p = 2.0466 lb/ft3, p = 1.3520E-02 cP, k; 1.3198, pb = 0.116198 lb/ft3

I ' I ' I L 5.97369E-01 I5.97306E-01 I5.97275E-01 I5.97248EolI5.97237E-01 I5.97229E-01 Tf= 50.00"F, PJ= 500.00 psia,

pl,p = 1.6623 lb/f$, k = 1.3622, pb = 0.044210 lb/ft3

= 1.131OE-02 cP, 4.29407E+04 7.15042E+04 9.99830E+04 1.42469E+05 1.70590E+05 1.98509E+05 9.71290E+05 1.61738E+06 2.26155E+06 3.22256E+06 3.85863E+06 4.49014E+06 9.99560E-01 I l I l I l 9.98777E-01 9.97603E-01 9.95108E-01 9.92956E-01 9.90412E-01

5.97361E-01 5.54179E+W 1.2535 1E+M 9.99780E-01

5.97345E-01 1.90160E+05 1.63652E+06 i 1.OOooOE+00

5.97300E-01 5.97270E-01 5.97245E-01 5.97234E-01 9.23175E+W 1.29162E+05 1.84279E+05 2.20892E+05 2.08816E+06 2.92156E+06 4.16826E+06 4.99643E- 9.99389E-01 9.98802E-01 9.97554E-01 9.96478E-01 2 2 2 2 5.97289E-01 5.97261E-01 5.97237E-01 5.97227E-01 3.16903E+05 4.43644E+05 6.33752E+05 7.60490E+05 2.72727E+06 3.8 18OOE+06 5.45407E+06 6.54477E+06 1.00000E+00 l.OOOOOE+OO 1.OOOOOE+00 1.OOOOOE+OO

5.97226E-01

9.95206E-01

5.97589E-01 1.84831E+04 4.18075E+05 9.99976E-01 2 5.97556E-01 6.34084E+04 5.45693E+05 l.OOOOOE+OC 2

TJ-= 150.00°F, P f = 1000.00psia, pt,p = 2.7573 Ib/ft3, p = 1.3650E-02 cP, k = 1.3622, pb = 0.044210 lb/ft3

Tf= 140.00'F, Pf= 2000.00 psia, P,,~ = 32.465 lb/ft3, p = 4.1710E-02 cP, k=-1.0, pb = 0.116198 Ib/ft3


A P I MPMS*14.3.4 92 = 0732290 O506374 719 W

440.6943 ).45278E-01 7.66087E+04 1.3473OE+O3 I .OOOOOE+00 4 5.94472E-0 1 !.56039E+04 >.77892E+02 I .00000E+00 -3 3.13737E-0 1 1.8 1644E+O4 3.47055E+02 I .OOOOOE+00 2 3.02206E-01 5.05785E+04 3.10996E+O2 1.00000E+00 2 5.00740E-01 1.91257E+04 7.87700E+02 1 .00OOOE+00 2 5.01032E-O 1 1.52293E+03 1.3 1064E+04 6.55931E-01 2 6.00388E-01 3.38631E+03 7.65959E+04 9.5 1009E-0 1 2 6.00363E-01 5.14483E+04 4.42764E+05 1 .00OOOE+00 2 6.00095E-01 8.8 8947E+03 7.65028E+04 9.747 18E-0 1 2 6.00067E-01 8.1460 1E+03 1.84257E+05 9.90202E-O I 2 6.00049E-0 1 1.05627E+04 2.38920E+05 9.95101E-01 2 6.00013E-01 3.64137E+04 3.13376E+05 1 .00000E+00 2

SECTION %CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART &BACKGROUND a7

1.05155E+00 6.01380E+O3 1.05763E+02 1 .OOOOOE+00 -4 7.04770E-01 3.95056E+03 6.94776E+Ol 1.00000E+00 -3

Table 4-Cd-Selected Round Robin Test Results Matrix-US Units ( D, = 2.90039 in, = 0.00000620 in/in-"F, d, = 1 .I7969 in, al = 0.00000925 idin-OF)

8.41234E-01 7.77968E-01 7.45121E-01 7.16547E-01 7.04057E-01 1.44331E+04 2.22461E+04 2.98296E+04 4.09796E+04 4.83 183E+O4 2.53832E+02 3.91237E+O2 5.24606E+02 7.20697E+02 8.49762E+02 l.OOOOOE+00 1 .OOOOOE+00 I .00000E+00 1.00000E+00 1 .OOOOOE+00 4 -4 -3 -3 -3 6.50983E-01 6.34050E-01 6.24074E-01 6.17209E-01 6.15228E-01 I .09473E+04 1.77709E+O4 2.44878E+04 3.45977E+04 4.13840E+04 1.92527E+O2 3.12532E+02 4.30661E+02 6.08461E+02 7.27810E+02 l.OOOOOE+OO I.OOOWE+ûû 1 .OOOOOE+00 1.00000E+00 1.00000E+00 -3 -3 -3 3 3

Flow Conditions ïj= 0.00'F, PJ= 14.696 psia, p,,p = 58.199 Ib/ft3, p = 1.8650E+03 cP, k = -1 .O, pb = 56.861 ib/ft3

6.12758E-01 3.67602E+03 5.89427E+01 1.00000E+00 2 6.05019E-01 3.53394E+03 5.66645E+01 1.00000E+00 2 6.04938E-01 1.66626E+02 1.43398E+03 9.98245E-O1

TJ= 68.00"F, PJ= 14.696 psia, p,,p = 56.660 Ib/ft3, p = 2.1220E+02 cP, k = -1.0, pb = 56.861 ib/ft3

6.06179E-01 6.04415E-01 6.03532E-01 6.02779E-01 6.02454E-01 1.09098E+04 1.81300E+04 2.53450E+04 3.61619E+04 4.33709E+04 1.74932E+02 2.90704E+02 4.06391E+02 5.79834E+02 6.95425E+02 1.00000E+00 l.OOOOOE+OO 1 .OOOOOE+00 1 .OOOOOE+00 1 .OOOOOE+00 2 2 2 2 2 6.02409E-01 6.01682E-01 6.0131 1E-01 6.00989E-01 6.00848E-01 1.05562E+04 1.75724E+04 2.45862E+04 3.5 1043E+04 4.21 153E+04 1.69262E+02 2.81762E+02 3.94224E+02 5.62876E+02 6.75293E+02 1.OOOOOE+00 1.OOO00E+00 1 .00000E+00 1.00000E+00 1.00000E+00 2 2 2 2 2 6.02388E-01 6.01699E-01 6.01370E-01 6.01 125E-01 6.01052E-01 4.90771E+02 7.93701E+02 1.06164E+03 1.36751E+O3 1.48709E+03 4.22358E+03 6.83059E+03 9.13643E+03 1.17688E+04 1.27979E+04 9.84201E-01 9.56114E-01 9.13983E-01 8.24454E-01 7.47214E-01

T/= 176.oO0F, PJ= 14.696 psia, P,,~ = 54.214 Ib/ft3, p = 1.7490E+01 cP, k = -1.0, p b = 56.861 Ib/ft3

2.55485E+02 5.77889E+03 9.99750E-01 2 6.03246E-01 3.69250E+03 3.17776E+04 l.OOOOOE+00 .-I

T/= 60.0û0F, PJ= 14.696 psia, pt,p = 62.366 Ib/ft3, j i = 1.1990 cP, k = -1 .o, p b = 62.366 Ib/ft3

7.62725E+02 1.26508E+03 1.72523E+04 2.86152E+04 9.97750E-01 9.93751E-01 2 2 6.01506E-01 6.01012E-01 1.10457E+04 1.83943E+04 9.50589E+04 1.58301E+05 l.OOOOOE+OO 1.OOOOOE+OC I .-I

Tf= 210.00"F, PJ= 14.696 psia, P,,~ = 58.792 ib/ft3, p = 2.8250E-01 cP, k = -1.0, p b = 62.366 ib/ft3

1.75968E+O3 3.98028E+04 9.87752E-01 2 6.00758E-01 2.5741 1E+04 2.21528E+05 1.00000E+00 2 6.00360E-01 4.53320E+03 3.90128E+04 9.93679E-01 2 6.00326E-01 4.10500E+03 9.28522E+04 9.97550E-01

TJ= O.ûO°F, PJ= 14.696 psia, P,,~ = 0.13223 Ib/ft3, p = 1.3070E-02 cP, k = 1.3198, pb = 0.116198 ib/ft3

2.48050E+03 2.94256E+03 5.61071E+04 6.65587E+04 9.75004E-01 9.64006E-01 2 2 6.00536E-01 6.00438E-01 3.67594E+04 4.41041E+04 3.16352E+05 3.79560E+05 1.OOO00E+00 1.00000E+W 2 2 6.002 1OE-0 1 6.00 145E-O 1 6.43153E+03 7.67262E+03 5.53497E+04 6.60306E+04 9.87 101E-01 9.8 1425E-O 1 2 2 6.00181E-01 6.001 17E-01 5.84788E+03 7.00120E+03 1.32275E+05 1.58362E+05 9.9500 1 E-0 1 9.9280 1E-O 1

T/= 50.00"F, P'= 100.00 psia, ptP = 0.31109 lb/ft3, p = 1.0670E-02cP, k 2 1.3622, ph = 0.044210 Ib/ft3

Tf= O.OO'F, Pf= 1000.00 psia, P,,~ = 65.072 ib/ft3, ,ü = 1.5430E-01 cP, k=-1.0, pb = 0.116198 ib/ft3

Tf= O.W°F, P f = 200.00 psia, p,,+, = 2.0466 lb/ff3, p = 1.3520E-02 cP, k = 1.3198, pb = 0.116198 Ib/ft3

ïj= 50.00"F, PJ= 500.00 psia, pCp = 1.6623 ib/f?, j i = 1.1310E-02cP, k = 1.3622, pb = 0.044210 ib/f?

Tf= 150.00"F, i''= 1000.00 psia, P,,~ = 2.7573 ib/ft3, j i = 1.3650E-02 cP, k = 1.3622, pb = 0.044210 lb/ft3

T/= 14O.ûO0F, PJ= 2000.00 psia, p,,p = 32.465 ib/ft3, p = 4.1710E-02 cP, k = -1.0, p6 = 0.1 16198 Ib/ft3

- Cell lalue

cd

-

?ill

Y [CD cd b r

2,

-

Q" Y [CD

cd 7111

Q v Y LCD

cd 711,

Y iCD

cd %li

Qv Y [CD

cd 4ni

Y [CD cd 4rri

Qv Y ICD cd B i

Qv Y [CD cd 4nt

Y ICD

cd 4111

Qv Y ICD

cd 4111

Y ICD

cd 4111

Y ICD

-

-

QV

-

-

Q,

-

-

-

Q"

-

-

Q"

-

Q"

-

Ai' (inches H,O at 60°F)

2.2484 I 20.2360 I 56.2110 I 110.1736 I 224.8440 I 323.7754 I I I l I

1.9829 1 E+001 1.39638E+Wl 1.20891E+00l 1.10788E+001 1.01726E+0019.7675 1E-0 1

-5

2 12 12 12 12 12 6.03248E-01 I6.01510E-01I 6.01020E-01 I 6.00768E-01 I 6.00552E-01 I 6.00459E-01

6.0053IE-01 3.24902E+03 2.79610E+04 9.96775E-01 2 6.00491E-01 2.93647E+01 6.642 lOE+OI 9.98750E-01

2.24457E+04 6.72275E+04 I . 11992E+05 1.5675üE+05 2.238798+05 2.686298+05 1.00000E+00 I .OOOEt00 I I .00000E+00 I 1.00000E+00 I I .OOO0017+00 1 .OoooOB+oC



Table 4-C-5-Selected Round Robin Test Results Matrix-US Units ( Dm = 4.02638 in, CS = 0.00000620 in/in-"F, ú,,, = 1.64063 in, al = 0.00000925 in/in-"F)

Flow Conditions

r f = O.OO°F, Pf= 14.696 pia , P,,~ = 58.199 lb/f$, j i = 1.8650E+03 cP, k = -1.0, pb = 56.861 Ib/ft3

Tf= 68,00"F;Pf= 14.696 psia, P,,~ = 56.660 lb/ft3, j i = 2.1220E+02 cP, k = -1.0, pb = 56.861 Ib/ft3

Tf= 176.û0°F, Pf= 14.696 pia, P, ,~ = 54.214 lb/ft3, /i = 1.7490E+O1 cP, k = -1.0, pb = 56.861 lb/ft3

r f = 60.0O0~>f= 14.696 p i a , P,,~ = 62.366 lb/ft3, j i = 1.1990 cP, k = -1.0, pb = 62.366 lb/ft3

Tf= 210.00°F, Pf= 14.696 psia, P , , ~ = 58.792 Ib/ft3, j i = 2.8250E-01 cP, k = -1.0, pb = 62.366 lb/ft?

T,-= O.OO°F, Pf= 14.696 psia, P , , ~ = O. 13223 lb/ft3, ,ü = 1.307OE-02 CP, k = 1.3198, pb = 0.116198 lb/ft3

ïj= 50.OO0F, P'= 100.00 psia, P , , ~ = 0.31109 lb/ft3, j i = 1.0670E-02 cP, k = 1.3622, pb = 0.044210 lb/f$

Tf= O.OO°F, Pf= 1OOO.00 pia, P,,~ = 65.072 lb/f?, j i = 1.5430E-01 cP, k=-i.0,p~=0.1161981b/ft3

ïj= O.W°F, Pf= 200.00 p ia , P,,p = 2.0466 Ib/ft3, j i = 1.3520E-02 cP, k = 1.3198, pb = 0.116198 lb/ft3

ïj= 50.00"F, Pf= 500.00 psia, P, ,~ = 1.6623 lb/ft3, j i = 1.1310E-02 cP, k = 1,3622, pb = 0.044210 lb/ft3

r/= 150.00°F, P f = 1000.00 pia , o,,~ = 2.7573 Ib/ft3, j i = 1.3650E-02 cP, k = 1.3622, pb = 0.044210 lb/ft3

r f = 140.00"F, Pf= 2000.00 psia, o , , ~ = 32.465 lb/ft3, j i = 4.1710E-02 cP, G = -1.0, pb = 0.116198 Ib/ft3

Cell Value - Cd 4111 Q v Y ICD Cd %Il Q v Y ICD

Cd 4ni Q v Y ICD

41"

Y ICD

4111

Y ICD

4m

Y ICD

4111

Y ICD cd 4111 Q v Y ICD cd 4111 Q v Y ICD cd YllI Q v Y ICD

cd Yni Qv Y [CD

cd Ym Q v Y [CD

-

cd

Q v

- cd

Q v

- cd

Q"

- cd

Q v

-

-

-

-

-

-

AF' (inches H20 at 60°F)

2.2484 20.2360 56.2110 110.1736

1.77644E+00 1.27091E+OO 1.11027E+00 1.02406E+o( 1.98915E+04 4.26930E+04 6.21609E+04 8.02682E+04 3.49826E+02 7.50831E+02 1.09321E+03 1.41166E+O? 1.00000E+00 1.00000E+00 1.00000E+00 l.OOOOOE+OC -5 -5 -4 -4 9.76159E-01 7.98803E-01 7.46110E-01 7.18886E-01 1.07986E+04 2.65102E+04 4.12691E+04 5.56686E+W 1.89913E+02 4.66229E+02 7.25790E+02 9.79030E+02 l.OOOOOE+OO 1.00000E+00 1.00000E+00 1.00000E+OC -4 -4 -3 -3 6.85485E-01 6.40022E-01 6.24525E-01 6.17802E-01 7.43258E+03 2.08191E+04 3.38583E+04 4.68914E+04 1.30715E+02 3.66140E+02 5.95457E+02 8.24666E+OL 1.00000E+00 l.OOOOOE+OO 1.OOOOOE+OO l.OooOOE+OC -3 -3 -3 3 6.10538E-01 6.05266ENl 6.03840E-O1 6.03122E-01 7.08487E+03 2.107 13E+O4 3.50360E+04 4.89922E+W 1.13602E+02 3.37865E+02 5.61781E+02 7.85559E+02 l.OOOOOE+OO l.OOOOOE+OO l.OOOOOE+OO l.OooOoE+OC 2 2 2 2 6.04330E-O 1 6.02206E-0 1 6.0 1609E-O 1 6.0 1302E;O 1 6.82801E+03 2.04122E+04 3.39866E+04 4.75570E+04 1.09483E+02 3.27298E+02 5.44954E+02 7.62547E+02 1.OOOOOE+00 l.OOOOOE+OO 1.OOOOOE+OO l.OOOOOE+OC 2 2 2 2 6.04263E-01 6.02188E-01 6.01622E-01 6.01350E-01 3.21949E+02 9.48994E+02 1.53507E+03 2.05345E+03 2.77069E+03 8.16704E+03 1.32108Et04 1.76720E+04 9.98244501 9.84198E-01 9.56106E-01 9.13968E-01 2 2 2 2 6.02891E-01 6.01466E-01 6.01060E-01 6.00851E-01 4.93898E+02 1.47525E+03 2.44724E+03 3.40426E+03 1.1 1716E+04 3.33692E+04 5.53548E+04 7.70021E+04

L I ' I ' I ' 6.01871E-01 I6.00928E-01 I6.00652E-01 I6.00509E-01 1.26364E+03 3.78 110E+03 6.28592E+03 8.77086E+03 1.08749E+û4 3.25401E+04 5.40966E+04 7.54820E+04 9.99871E-01 9.98839E-01 9.96775E-01 9.93678E-01 2 2 2 2 6.01788E-01 6.00883E-01 6.00619E-01 6.00480E-01 1.13983E+03 3.41302E+03 5.68131E+03 7.94244E+03 2.57822E+04 7.72003E+04 1.28507E+05 1.79653E+05 9.99950E-01 9.99550E-01 9.98750E-01 9.97550E-01 2 2 12 12 6.017208-01 I 6.00849E-01 I 6.00593E-031 I 6.00459Eol

6.01600E-01 6.00784E-01 6.00543E-01 6.00417E-01 5.04440E+03 1.51128E+04 2.51779E+04 3.52417E+04 4.34121E+04 1.30061E+05 2.16681E+05 3.03290E+05 1.00000E+00 l.OOOOOE+OO l.OOOOOE+OO l.OOOOOE+00 2 /1 l 2 1)

224.8440-

9.47065E-03 l.O6047E+O: 1.86503E+O: l.OOOOOE+CH -4 6.95240E-01 7.69108E+oL 1.35261E+O: l.OOOOOE+O(

6.14082E-01 6.65843E+oL 1.17 lOOE+O: 1.00000E+O[ 2 6.02508E-01 6.99175E+oL 1.12108E+O: 1 .00000E+o( 2 6.01035E-01 6.79084E+W 1.08887E+OT l.OOOOOE+O( 2 6.01147E-01 2.64521B+O? 2.27647E+04 8,24425501 2 6.00670E-01 4.79901E+O? l.O855OE+O? 9.75000E-01

6.00656E-01 7.1119OE+W 6.12050E+05 1.OOOOOE+OC 2 6,003830-01 1.24442E+04 1.07095E+05 9.87099E-01 2 6.00358E-01 1.13 150E+O4 2.55938E+05 9.95000E-01 2 6.00340E-01 1.46363E+04 3.31063E+05 9.97500E-01 2 6.00305E-01 5.03358E+04 4.33190E+05 1.00000E+W 2

323.7754 I 440.6943 I 9.12766E-O1 8.86185E-01 1.22648E+05 1.38922E+05 2.15698E+03 2.44319E+03 1.OOOOOE+00 l.O0000E+OO 4 -4 6.84893E-01 6.76934E-01 9.09194E+04 1.04840E+05 1.59898E+03 1.84379E+03 l.OOOOOE+Oo 1.00000E+Oa -3 -3 6.12507E-01 6.11320E-01 7.96961E+04 9.27987E+04 1.40160E+03 1.63203E+03 l.OOOOOE+00 l.OOOOOE+Oa 2 2 6.02242E-01 6.02039E-01 8.38640E+04 9.78083E+04 1.34471E+03 1.56830E+03 1.00000E+00 1.00000E+00 I) 10 I L I' 6.00918E-01 I 6.00828E-01

5.693108+03 6.55174E+03 1.287748+05 1.481968+05 9.64000E-01 9.5 1001E-01 2 2 6.00574E-01 6.0051 IE-01 8.5331 IB+W 9.95425E+04 7.343600+05 8.566630+05 1.000008+00 1.00000E+00 2 2 6.00327E-01 6.00285Eol 1.484588+04 1.72005E+04 1.277638+05 1.48028E+05 9.81422Eol 9.74714E-01 2 2 6.00304E-01 6.00262Eo1 1.35468E+04 1.5762 1 E+04 3.06419E+05 3.56528E+05 9.92800E-01 9.90200E-01

6.00287E-01 1.75426E+04 3.96803E+05 9.96400E-01

6.00255E-01 6.03980E+04 5.19785E+05 i 1.00000E+00


API MPflS*14*3-4 92 m 0732290 0506376 591 m

8.53630E-01 3.70550E+04 6.5 1677E+02 l.OOOOOE+OO d

SECTION %CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART B BACKGROUND 89

7.3 1434E-01 6.95889E-01 6.77545E-01 9.52528E+04 1.51040E+05 2.05882E+05 1.67519E+03 2.65629E+03 3.62079E+03 1.00000E+00 l.OOOOOE+00 1.00000E+00 -? -2 -2

Table 4-C-&Selected Round Robin Test Results Matrix-US Units ( D, = 7.98146 in, % = 0.00000620 in/in-"F, d, = 3.25000 in, al = 0.00000925 in/in-OF)

6.54288E-01 3.40825E+05 5.99400E+03 I .00000E+00

Flow Conditions TJ= O.OO"F, P f = 14.696 psia, pf,p = 58.199 lb/ft3, p = 1.8650E+03 cP, k = -1 .o, pb = 56.86 1 Ib/ft3

6.48679E-01 3.94220E+05 6.93306E+03 1 .OOOOOE+00

Tf= 68.00"F. P f = 14.696 psia, P,,~ = 56.660 Ib/ft3, p = 2.1220E+02 cP, k = -1.0, pb = 56.861 Ib/ft3

2.78555E+04 4.898888+02 I .00000E+00 -3 6.071948-01 2.76487E+04 4.433308+02 1.000(X)E+00 2 6.03226E-01 2.6744 IE+M 4.288268+02 1.00000E+00 2 6.03 I80E-01 1.26106E+03 1.08527B+04 9.98244E-O1 .I

T/= 176.oO0F, Pf= 14.696 psia, pf.p = 54.214 Ib/ft3, p = 1.749OE+Ol cP, k=-l.O,pb = 56.861 Ib/ft3

7.91599E+04 I .30730E+05 1.82 1978+05 1.39217ö+03 2.299128+03 3.204258+03 I .00000E+00 1.00000E+00 I.OOOOOE+Oû -3 2 2 6.03831E-01 6.02905E-01 6.02434E-01 8.248778+04 1.37268Et05 I .92026E+05 1.322648+03 2.20101E+03 3.07901E+03 I.(KKH30E+00 1.00000E+00 l.OOüOOE+00 2 . 2 2 6.01 828E-01 6.01427E-O1 6.012 19E-01 8.00473E+W I .33323E+05 I .86588E+05 1.28351E+03 2.137758+03 2.99182E+03 1.00000E+00 1.00000E+00 1 .O(K")E+OC 2 2 2 6.018 14E-01 6.01434E-01 6.0 12508-01 3.721548+03 6.02174B+03 8.056448+03 3.202768+04 5.1823 1E+04 6.93337E+04 9.84199E-O1 9.56109E-01 9.13974E-01 o n n

T/= 60.00"F, Pf= 14.696 psia, pf,p = 62.366 Ib/ft3, p = 1.1990 cP, k = -1.0, pb = 62.366 Ib/ft3

3.10648E+05 5.46330E+03 1 .OOOOOE+OO 2 6.0185 IE-01 3.28868E+05 5.27320E+03 1 .OOO00E+00 2 6.00956E-0 1 3.19725E+05 5.12659E+03 l.OOOOOE+OO 2 6.0 1070E-O 1 1.12874E+04 9.7 139 1E+04 7.47 188E-0 1

Tf= 210.0û0F, Pf= 14.696 psia, pf,p = 58.792 lb/ft?, /.i = 2.8250E-01 cP, k = -1.0, pb = 62.366 Ib/ft3

3.61979E+O5 6.36603E+03 1.0OOOOE+00 2 6.017 15E-01 3.83593E+05 6.15067E+03 1 .OOOOOE+00 2 6.00893E-O 1 3.72974E+05 5.98040E+03 l.OOOOOE+OO 2 6.0 1059E-O 1 1.15594E+04 9.94802E+04 6.55895E-01

TI= 0.W0F, Pf= 14.696 psia, pfp = 0.13223 Ib/ft3, p = 1.3070E-02cP, k 2 1.3198, pb = O. 116198 lb/ft3

1.93609E+03 4.3793IE+04 9.99750E-01 2 6.02279E-01 2.79822E+04 2.40815E+05 1.OOOOOE+00 2 6.01601E-01 4.95629E+03 4.26538E+04 9.99871E-01 2 6.01546E-01 4.47090E+03 1.01 129E+05 9.99950E-01 2 6.01501E-01 5.76861E+03 1.30482E+05 9.99975EM1 2 6.01420E-01 1.97883E+04 1.70298E+05 1.00000E+00 2

Tf= 50.0O0F, P f = 100.00 psia, prp = 0.31 109 lb/ft3, p = 1.0670E-02 cP, k = 1.3622, pb = 0.044210 lb/ft3

5.78756E+03 9.60283E+03 1.33596E+04 1.3091 1E+05 2.17209E+05 3.02185E+05 9.97750E-01 9.93750E-01 9.87751E-01 2 2 2 6.01326E-01 6.01048E-01 6.00902E-01 8.38147E+04 1.39626E+05 1.95429E+05 7.21309E+05 1.20162E+06 1.68187E+06 1.00000E+00 l.OOOOOE+OO 1.OoooOE+oO 2 2 2 6.00961E-01 6.00770E-01 6.00670E-01 1.48378E+04 2.46708E+M 3.44261E+04 1.27695E+05 2.12317E+05 2.96271E+05 9.98839E-01 9.96775E-01 9.93679E-01 2 2 2 6.00931E-01 6.00747E-01 6.00650E-01 1.33937E+04 2.22982E+04 3.11749E+04 3.02957E+05 5.04370E+05 7.05156E+05 9.99550E-01 9.98750E-01 9.97550E-01 2 2 2 6.00908E-01~ 6.00730E-01 6.00636E-01 1.72855E+04 2.87890E+04 4.02741E+04 3.90985E+05 6.51188E+05 9.10974E+05 9.99775E-01 9.99375E-01 9.98775E-01 2 2 2 6.00863E-01 6.00695E-01 6.00606E-01 5.93104E+04 9.88230E+04 L38332E+O5 5.10425E+05 8.50471E+05 1.19048Em l.OOOOOE+OO l.OOOOOEt00 l.OOOOOE+OC 2 2 2

Tf= 0.00'F, PI= 1000.00 psia, pf,p = 65.072 Ib/ft3, p = 1.5430E-01 cP, k=-1.0,& = 0.1161981b/ft3

4.88472E+04 4.20379E+05 9.87100E-01 2 6.00564E-01 4.44154E+04 l.W65E+O6 9.95000E-01 2 6.00552E-01 5.74530E+04 1.29955E+06 9.97500E-01 2 6.00526E-01 197591E+05 1.70046E+06 l.OOOOOE+OO 2

Tf= O.OO"F, P/= 200.00 psia, P,,~ = 2.0466 ib/ft3, p = 1.3520-2 cP, k = 1.3198, & = 0.116198 Ib/ft3

5.82758E+04 6.75203E+04 5.01522E+05 5.81080E+05 9.81423E-01 9.74715E-01 2 2 6.00525E-01 6.00495E-01 5.31772E+04 6.18746E+04 1.20283E+06 1.39956E+06 9.92801E-01 9.90201E-01 2 2 6.00514E-01 6.00485E-01 6.88633E+04 8.02318E+04 1.55764E+06 1.81479E+06 9.96400E-01 9.95100E-01 2 2 6.00491E-01 6.W63E-01 2.37095E+05 2.76598E+05 2.04044E+06 2.38040E+06 1.OOOOOE+00 l.OOOOOE+OO 2 2

TJ= 50.C0°F, PJ= 500.00 psia, pf,p = 1.6623 lb/ft3, p = 1.1310E-02 cP, k = 1.3622, pb = 0.044210 Ib/ft3

TJ= 150.0O0F, Pf= 1OOO.00 psia, pf,p = 2.7573 lb/ft3, p = 1.3650E-02 cP, k = 1.3622, pb = 0.044210 lb/ft3

T/= 140.0O0F, Pf= 2000.00 psia, pf,p = 32.465 Ib/ft3, p = 4.1710E-02 cP, k=-1.0, p b = 0.116198 lb/ft3

Cell Value

cd 4nr Qu Y ICD cd 4rn

Y ICD cd %Ir

Qu Y ICD

cd 4irr

Y ICD cd %r Qv Y ICD

qnr

Y ICD

91,l

Y ICD

-

-

QU

-

_.

Q"

-

- cd

QP

- cd

Q"

cd e 1

Qv Y ICD c, %n Q" Y ICD

c d qm Qu Y ICD cd %n

Y ICD cd qm Qu Y ICD

-

-

-

Q"

-

-

Ai' (inches H,O at 60°F) I 2.2484 I 20.2360 I 56.2110 I 110.1736

I I I

1.43086E+OOl 1.06321E+00] 9.48255E-01 I 8.87250E-01

-5

I - I < I d

6.54699E-01 I 6.20169E-01 I 6.14514E-01 I 6.11743E-01

L I,& I ' I ' 6.02281E-01 I 6.01329E-01 I6.01052E-01 I 6.00908E-01

7.91 133E-01

1 .OOOOOE+00

6.61455E-01 2.87132E+05 5.0497 IE+03 1 .OOOOOE+ûC -3 1-3 1-3 6.09423E-01 I 6.08435E-01 I 6.07688E-01 2.59294E+05 4.560 14E+03 1.00000E+ûC 2 6.02028E-01 2.74137E+05 4.39562E+03 l.OOO00E+OC 2 6.01036E-01 2.66473E+05 4.27273E+03 l.OOOOOE+OC 2 6.01112E-01 1.03793E+04 8.93243E+04 8.24436E-O 1 2 12 12 6.00783E-01 I6.00728E-01 I 6.00687EMl 1.88349E+04 4.26032E+05 9.75002E-01 2 6.00773E-01 2.79125E+05 2.40215E+06 1.00000E+OC .-I ' I ' I' 6.00581E-01 I6.00541E-01 I6.00511E-01



Table 4-C-%Selected Round Robin Test Results Matrix-US Units ( Dm = 14.31154 in, % = 0.00000620 in/in-"F, d,,, = 5.82811 in, al = 0.00000925 in/in-"F)

Flow Conditions

T,== 0,00"F, PJ= 14.696 psia, P,,~ = 58.199 Ib/ft3, k = -1.0, /3b = 56.861 1b/ft3

= 1.8650E+03 cP,

T,== 68.00"F, PJ= 14.696 psia, pl,p = 56.660 ib/f$, j i = 2.1220E+02 cP, k = -1.0, pb = 56.861 Ib/ft3

TJ= 176.0O0F, PJ= 14.696 psia, P , , ~ = 54.214 Ib/ft3, j i = 1.749OE+Ol cP, k = -1.0, pb = 56.861 Ib/ft3

T,== 60.00°F, Pf= 14.696 psia, pl,p = 62.366 ib/f$, p = 1.1990 cP, k = -1.0, pb = 62.366 Ib/ft3

ï)= 210.00"F, P f = 14.696 psia, 4 p = 58.792 Ib/ft3, p = 2.8250E-01 cP, k = -1.0, pb = 62.366 Ib/ft3

ïj-= 0.00"F, P f = 14.696 psia, oIp = 0.13223 ib/f$, p = 1.3070E-02 cP, k2 1.3198, pb = 0.116198 ib/ft3

Q= 50.00"F, Pf= 100.00 psia, oY = 0.31109 Ib/ft3, j i = 1.0670E-02 cP, k = 1.3622, pb = 0.044210 Ib/ft3

rFO.OO'F, P'zÖOO.00 PST r & p = 65.072 ib/f$, p = 1.5430E-01 cl? = -1.0, pb = 0.116198 Ib/ft3

?)= O.OO"F, Pf= 200.00 psia, vIp = 2.0466 ib/ft3, p = 1.3520E-02 cP, k = 1.3198, pb = 0.116198 Ib/ft3

r f= 50.00"F, PJ= 500.00 psia, = 1.6623 lb/ft3, p = 1.1310E-02 cP,

¿ = 1.3622, pb = 0.044210 ib/ft3

rf= i50.OO0F, PJ= 1OOO.00 psia,

c = 1.3622, pb = 0.044210 Ib/ft3 = 2.7573 ib/f$, p = 1.3650E-02 cP,

TJ= 140.0O0F, PJ= 2000.00 psia, = 32.465 ib/ft3, p = 4.1710E02 cP,

;=-1.o, pb = 0.116198 lb/ft3

Cell Valut

cd 4111

Qv Y ICD cd 41n Qv Y ICD cd 4ni Qv Y ICD cd 4ni Qv Y ICD

_.

_.

-

~

-

4ni Qv Y ICD cd B Qv Y ICD cd 4ni Qv Y ICD cd 41n Qv Y ICD cd 4ni Qv Y ICD cd 4ni Qv Y ICD

4 Qv Y ICD

-

-

-

-

~

cd 4ni Qv Y ICD

2.2484

1.21145E+O( 1.71175E+O! 3.01041E+O: l.OOOOOE+Oí -5 7.79472E-03 1.08810E+O! 1.91361E+O: l.OOOOOE+O( -4 6.35173E-03 8.69066E+ol 1.52841E+O: l.OOOOOE+O( -3 6.05345E-01 8.86425E+O( 1.42133E+O: l.OOOOOE+O( 2 6.02602E-01 8.59153E+O~ 1.3776OE+O: l.OOOOOE+O( 2 6.02569E-01 4.05 123E+O: 3.48649E+OL 9.98244E-0 1 2 6.01933E-01 6.22253E+0: 1.40749E+O! 9.99750E-01 2 6.01932E-01 8.99337E+04 7.73970E+01 l.OOOOOE+OC 2 6.01446E-01 1.59344E+04 1.37131E+05 9.99871E-01 2 6.01407E-01 1.43742E+04 3.25 136E+05 9.99950E-01 2 6.01375E-01 1.85469E+O4 4.19518E+05 9.99975E-01

6.01316E-01 6.36245E+3+04 5.47552E+05 1.00000E+00 2

I ' I ' I - I - I -

6.9171OE-01 16.66211E-01 16.52776E-01 I6.40546E-01 I6.34848E-01 I6.30221F01 2.89680E+05 4.65001E+05 6.37873E+OS 5.09452E+03 8.17785E+03 1.12181E+04 1.00000E+00 l.OOOOOE+00 1.00000E+0(1 -3 -3 -3 6.14068E-01 6.10294E-01 6.08432E-01 2.52060E+05 4.17517E+05 5.82740E+05 4.43291E+03 7.34276E+03 1.02485E+04 l.OOOOOE+00 l.OOOOOE+ûO l.OOOOOE+OO II n n

8.94175E+05 1.06347E+06 1.23167E+06 1.57256E+04 1.87029E+O4 2.166 lOE+04 l.OOOOOE+OO 1.0OOOOE+00 l.OOOOOE+00 -3 -3 -3 6.06863E-01 6.06192E-01 6.05684E-01 8.30340E+05 9.95306E+05 1.16022E+06 1.46030E+04 1.75042E+04 2.04044E+04 l.OooOOE+00 1.OOOOOE+00 l.OOOOOE+OO * n n

L, I ' I ' I ' I ' I' 6.03025E-01 I 6.02375E-01 I 6.02042E-01 I 6.01753E-01 I 6.01626E-01 I 6.01528E-01 2.64911E+05 4.41042E+05 6.17117E+05 8.81173E+05 1.05718E+06 1.23318E+06 4.24768E+03 7.07183E+03 9.89509E+03 1.41291E+04 1.69513E+04 1.97733E+04 l.OOOOOE+OO 1 OOOOOE+00 1 OOOOOE+OO 1 OOOOOE+OO 100000E+00 1 OOOOOE+00 2 I2 I2 I 2 I 2 1 2 I -

I - I - , I

6.01611E-01 6.01321E-01 6.01170E-01 6.01036E-01 6.00977E-01 6.00931E-01 2.57324E+05 4.28667E+05 5.99983E+05 8.56928E+05 1.02821E+06 1.19949E+06

R L I ' I' I' I ' I' 6.01599Fr01 16.01325E-01 I6.01191E-01 I6.01090E4l I6.01060E-01 I6.01051E-01 1.19635E+04 1.9361 3E+04 2.59055E+04 3.33767E+04 1.02958E+05 1.66623E+05 2.22942E+05 2.87240E+05 9.84199E-01 9.56109E-01 9.13973E-01 8.24435E-01 2 2 2 2 6.01249E-01 6.01047E-01 6.00941E-01 6.00848E-01 1.86093E+04 3.08807E+04 4.29643E+04 6.05760E+04 4.20929E+05 6.98499E+05 9.71824E+05 1.37019E+M 9.97750E-01 9.93750E-01 9.87751E-01 9.75002E-01

3.62973E+04 3.12375E+05 7.47186E-01 2 6.00807E-01 7.18663E+04 1.62557E+OC 9.64002E-01

6.55892E-01

9.5 1OO3E-01 2 12 12 12 6.01247E-01 I6.01043E-01 I6.00936l%O1 I6.0084OE-0lI6.00797E-01 I6.00764F-01 2.69497E+05 4.49009E+05 6.28500E+05 8.97714E+05 1.07718E+06 2.31929E+06 3.86417E+06 5.40887E+06 7.72573E+06 9.27022E+M l.OOOOOE+00 1.OOOOOE+OO 1.OOOOOE+00 1.00000E+00 1.OOOOOE+OC 2 2 2 2 2 6.00979E-01 6.00838E-01 6.00763E-01 6.00696E-01 6.00666E-01 4.77172E+04 7.93456E+O4 1.10725E+05 1.57114E+05 1.87443E+05 4.10655E+05 6.82849E+05 9.52900E+05 1.35212E+O6 1.6 13 14E+06 9.98839E-01 9.96775E-01 9.93679E-01 9.87099E-01 9.81423E-01 2 2 2 2 2 6.00957E-01 6.00821E-01 6.00748E-01 6.00683E-01 6.00654E-01 4.30737E+04 7.17157E+04 1.00269E+05 1.42860E+05 1.71045E+05 9.74298E+05 1.62216E+06 2.26802E+06 3.23 140E+06 3.86892E+M 9.99550E-01 9.98750501 9.97550E-01 9.95OOOE-01 9.92800E-01 2 2 2 2 2

9.99775E-01

6.00809Eiol

9.99375E-01

6.00738E-01 6.00675E-01 6.00647E-01 1.29536E+05 1.84796E+05 2.21500E+05 2.93002E+06 4.17996E+06 5.01019E+06 9.98775E-01 9.97500E-01 9.96400E-01

6.00716E-01 6.00656E-01 6.00629E-01 2 Jj Ij

1.25664E+OC 1 .O8 147E+Oí l.OOOOOE+OC

6.00643E-01 2.17 18 1E+O5 1.86906E+OC 9.74715E-01 2 6.00632E-01 1.99022E+05 4.50175E+W 9.90201E-01 2 6.00624E-O 1 2.5807 1E+05 5.83738E+06 9.95 100Eo1 2 6.00608E-01

1.90746E+05 3.178438+05 4.44931B+05 6.355528+05 7.62628E+05 8.89701E+05 1.641568+06 2.735368+06 3.82907E+06 5.46956E+06 6.56318E+06 7.65677E+06 l,OOOOOE+00 1 .ooo(x)E+00 1.00000E+00 1.00000E+00 1.00000E+00 1 .OOOOOE+00 2 2 2 2 2 2


20.2360

8.19828E-01 1.4637 I E+06 2.57419E+04 í.OOOOOE+00 -4 6.57743E-01 1.16017E+06

56.21 10 110.1736 224.8440 323.7754 7.62126E-01 7.32247E-01 7.06287E-01 6.94938501 2.26782E+06 3.05047E+06 4.20332E+06 4.96293E+06 3.988358+04 5.36479E+04 7.39227E+04 8.72818E+04 1.00000E+00 l.ooOOOE+00 l.OOOOOE+00 1.00000E+OC -3 -3 -3 -3 6.39850E-01 6.29603E-01 6.20103E-01 6.17910E-01 1.88101E+06 2.59125E+06 3.64592E+06 4.35963E+M

-3 6.09276E-01 l.O5335E+06 1.85250E+04 I.OOOOOE+00 2 6.02357E-01 1.1 1452E+06 1.78707E+O4 l.OOOOOE+00

-3 -3 -3 6.06951E-01 6.05793E-01 6.048 1OE-01 1.74888E+06 2.44376E+06 3.48542E+06 3.07571E+04 4.29778E+04 6.12972E+04 1.00000E+00 l.OOOOOE+00 l.OOOOOE+Oll 2 2 2 6.01930E-0 1 6.01 709E-O 1 6.0 15 15E-0 1 1.85622E+06 2.59776E+M 3.70989E+06 2.97634E+04 4.16534E+04 5.94858E+04 1.00000E+00 1.00000E+00 l.OOOOOE+OC

4.17958E+06 7.35052E+04 1 .OOO00E+00 2 6.01430E-O I 4.45123E+06 7.13728E+04 I.OOOOOE+OO 2 6.00986E-01 4.33073E+06 6.94405E+04 1.00000E+00 2 6.01042E-0 1 1.52875E+05 1.31564E+06 7.47190E-01

4.87358E+06 8.57 1O4E+04 1 .OOOOOE+00 2 6.01364E-01 5.19254E+06 8.32591E+04 l.oOoOOE+00 2 6.00954E-01 5.05224E+06 8.10096E+04 1.00000E+00 2 6.0 1036E-0 1 1.56561E+05 1.34736E+06 6.55897E-01

6.01421E-01 1.08347E+06 1.73727E+O4 1 .OOOOOE+00 2 6.014 1 lE-0 1 5.03726E+M 4.33507E+05 9.84199E-01 2 6.01 174E-01 7.83692E+04 1.77266E+06 9.97750E-01

6.01224E-01 6.01120E-01 6.01028E-01 1.80518E+06 2.52682E+06 3.60919E+06 2.89450E+04 4.05 160E+O4 5.787 1 1E+04 1 .OOOOOE+00 1 .OOOOOE+00 1.00000E+0(3 2 2 2 6.0 1225E-01 6.0 1 133E-01 6.0 1064E-O 1 8.15330E+04 1.09099E+05 1.40571E+05 7.01673E+05 9.38907E+05 1.20976E+06 9.56109E-01 9.13974E-01 8.24437E-01 2 2 2 6.01034E-01 6.00960E-01 6.00895E-01 1.30061E+05 1.80964E+05 2.55 156E+05 2.94190E+06 4.09329E+06 5.77146E+06 9.93751E-01 9.87751E-01 9.75002E-01

3.78599E+05 3.25822E+06 I .00000E+OO 2

1.13493E+06 1.8911 1E+06 2.64723E+06 3.78133E+06 4.53737E+06 5.29339E+06 9.76724E+06 1.62749E+07 2.27820E+07 3.25421E+07 3.90486E+07 4.55549E+07 1.00000E+00 l.OOOOOE+OO 1 .OOO00E+00 1.00000E+00 1 .OOOOOE+00 1 .OOOOOE+00 2 2 2 2 2 2

6.05293E+04 1.36913E+06 9.99950E-01 2 6.01261E-01 7.81016E+04 1.76660E+06 9.99975E-01 2 6.01220E-01 2.67933E+05 2.30583E+06 I.o0000E+00 2

1.8 1424E+05 3.02082E+05 4.22371E+05 4.10368E+06 6.83289E+06 9.55374E+06 9.99550E-01 9.98750E-01 9.97550E-01 2 2 2 6.00961E-01 6.00868E-01 6.00818E-01 2.34143E+05 3.90022E+05 5.45658E+05 5.29616E+06 8.82203E+06 1.23424E+07 9.99775E-01 9.99375E-01 9.98775E-01 2 2 2 6.00937E-01 6.00849E-01 6.00802E-01 8.03429E+05 1.33885E+06 1.87424E+06 6.9 143 1E+06 1,1522 1E+07 1.6 1297E+07 l.OOOOOE+OO 1.00000E+00 1.00000E+C€ 2 2 2

7.20536E+05 1.62980E+07 9.9280 1 E-0 1 2 6.00752E-01 9.33087E+05 2.11058E+07 9.96400E-01 2 6.00739E-0 1 3.21265E+06 2.76481E+07 1 .OOOOOE+00 2

8.3840 1 E+05 1.89641E+O7 9.9020 1 E-0 1 2 6.00736E-01 1.08715E+06 2.45906E+07 9.95 100E-01 2 6.00724E-O 1 3.74800E+06 3.22553E+07 1.00000E+00 2

API MPflS*L'4m3-'4 72 W 0732270 050b378 36'4 =


Table 4-C-+Selected Round Robin Test Results Matrix-US Units (D, = 29.37598 in, c+ = 0.00000620 in/in-OF, d, = 11.96094 in, al = 0.00000925 in/in-OF)

- Cell

Value AP (inches H,O at 60°F) I

Flow Conditions 2.2484

1.01286E+ûC 6.02779E+05 1.06009E+04 1 .M)OE+OC 4 7.1601 8E-01 4.20982E+05

440.6943

1 .OOOOOE+00

ïj= O.OO"F, Pf= 14.696 psia, pl,p = 58.199 Ib/ft3, j i = 1.8650E+03 cP, k=-1.0, pb = 56.861 lb/ft3

Cd

Q v 4,111

Y ICD cd 4111

Qv Y ICD cd 4111

Qv Y ICD cd 4ili

Q v Y ICD cd 4m Qv Y ICD cd 4111

Qv Y ICD cd 41,, Q v Y ICD

cd 4111

Q v Y ICD cd 4111

Qv Y ICD cd %Il

Q v Y ICD cd 4ni Q v Y ICD cd 4111

Qv Y ICD

_.

-

-

-

-

-

-

-

-

-

-

ïj= 68.00"F, Pf= 14.696 psia, piep = 56.660 Ib/ft3, j i = 2.1220E+02 cP, k = -i .o, pb = 56.86 i ib/ft3 I 7.40370E+03 2.04036E+04 3.30809E+04 4.55716E+04 6.41 199E+04 7.66717E+04 8.921 17E+04

1 .OoooOE+00 I 1.00000E+00 I 1 .oooOOE+00 1 .OOO00E+00 I l.OOOOOE+Cû I 1.00000E+00 I 1.00000E+00 -3 6.18033E-01 3.561 59E+05 6.26367E+03 I.OOOOOE+OC 3 6.03849E-01 3.72425E+05 5.97 160E+OI l.oOoOOE+OC

Tf= 176.W°F, Pf= 14.696 psia, pf,p = 54.214 ib/fG, p = 1.749OE+Ol cP, k = -1.0, pb = 56.861 lb/ft3

ïj= 60.00"F, Pf= 14.696 psia, pf,p = 62.366 lb/ft3, j i = 1.1990 cP, k =-1.0, pb = 62.366 ib/ft3

T/= 210.00"F, Pf= 14.696 psia, pf,p = 58.792 ib/ft3, j i = 2.8250E-01 cP, k = -1.0, pb = 62.366 1b/ft3

6.02081E-01 3.61548E+05 5.79720E+03 l.OOOOOE+OC 2 6.02057E-01 1.70486E+04 1.46720E+05 9.98244E-01

Tf= 0.OOoF, Pf= 14.696 psia,

k = 1.3198, pb = 0.116198 lb/ft3 = 0.13223 ib/ft3, j i = 1.3070E-02 cP,

6.01636E-01 2.61953E+04 5.92520E+05 9.99750E-01

6.00866E-01 3.02719E+05 6.84729E+06 9.64003E-01

ïj= 50.00"F, Pf= 100.00 psia, pl,,, = 0.31109 ib/ft3, j i = 1.0670E-02 cP, k = 1.3622, pb = 0.044210 Ib/ft3

9.5 1OO4E-01 2 12 ( 2 12 12 12 12 6.01635E-01 I 6.01171E-01 I 6.01031E-01 I 6.00956E-01 I6.00889E-01 I6.00858E-01 I 6.00835E-01 ïj= O.OO°F, Pf= 1ooO.00 psia,

k = -1.0, pb = 0.1 16198 lb/ft3 = 65.072 ib/ft3, j i = 1.5430E-01 cP,

6.01308E-01 6.00986E-01 6.00887E-01 6.00834E-01 6.00786E-01 6.70976E+04 2.00979E+05 3.34218E+05 4.6641 lE+05 6.61837E+05 5.77442E+05 1.72963E+06 2.87628E+06 4.01393E+06 5.69577E+06 9.99871E-01 I I I / 9.98839E-01 9.96775E-01 9.93679E-01 9.87100E-01

ïj= 0.00"F, Pf= 200.00 psia,

k = 1.3198, pb = 0.116198 Ib/ft3 = 2.0466 lb/ft3, j i = 1.3520E-02 cP,

2 12 12 12 12 6.01281E-01 I 6.00972E-01 I 6.00876E-01~6.00824E-01~ 6.00778E-01 I 6.00757E-01~6.00740E-01 ïj= 50.00"F, Pf= 500.00 psia,

pf,p = 1.6623 lb/f?, j i = 1.1310E-02 cP, k= 1.3622, pb = 0.044210 ib/ft3

6.01798E+05 1.36123E+07 9.95000E-01 2

ïj= 150.00"F, Pf= 1OOO.00 psia, pf,p = 2.7573 lb/f?, /i = 1.3650E-02 cP, k = 1.3622, pb = 0.044210 Ib/ft3

6.00772E-01 7.78457E+05 1.76082E+Oí 9.97500E-01 2 6.00759E-01 2.67730E+Ot 2.30408E+Oí 1.00000E+OC 2

Tf= 140.00"F, Pf= 2000.00 psia, pl.p = 32.465 lb/ft3, j i = 4.1710E-W cP, k=-1.0, pb = 0.116198 lb/ft3



Table 4-Cd-Selected Round Robin Test Results Matrix-US Units ( Dm = 1.93945 in, % = 0.00000620 in/in-"F, dm = 1.03126 in, al = 0.00000925 in/in-"F)

- Cell Value

Ai' (inches H,O at 60°F)

2.2484 I 20.2360 I 56.2110 1 110.1736 Flow Conditions 323.7754 440.6943 I 224.8440

TJ-= O.OO"F, Pf= 14.696 psia, p r p = 58.199 lb/ft3, p = 1.8650E+03 cP, k 2 -1.0, pb = 56.861 Ib/ft3

cd 4111

Q v Y ICD

1.234 17E+O( 6.73598E+oL l.l8464E+O: l.OOOOOE+O( -5 7.90545E-01 4.26282E+oL 7.4969 lE+O: l.OOOOOE+O( -d

l118446E+û0 7.54212E+04 1.32641E+03 1 .OOOOOE+00 4 7.73776E-01 4.86779E+04 8.56087E+02 1.OOOOOE+00 -4 6.25659E-01 3.85802E+04 6.78500E+02 1.OOOOOE+00 3 6.08408E-01 4.01496E+04 6.43775E+02 1.00000Et00 2 6.05935E-01 3.89347E+04 6.24294E+02 1.00000E+00 2 6.06488E-01 1.17968E+03 1.01523E+04 6.40854E-01 2 6.05299-1 2.67637E+03 6.05376E+04 9.48861E-01 2 6.0525 1E-01 4.07520E+04 3.507 12E+05 1.00000E+00 2 6.04735E-01 7.03046E+03 6.05041E+04 9.73610E-01 2 6.04679E-01 6.44681E+03 1.45822E+05 9.89772-1 2 6.04639E-01 8.361 18E+03 1.89124E+05 9.94886E-01 2 6.04567E-01 2.88288E+04 2.48100E+05 l.OOOOOE+Oo 2

2.79017E+00 1.88676E+OO 1.59671E+ûC 1.26903E+04 2.57445E+04 3.631 14E+04 2.23 18 1E+02 4.5276 1E+02 6.38599E+02 l.OOOOOE+OO l.OOOOOE+OO l.OOOOOE+OC

1.35172E+00 1.01838E+00 9.15216E-01 6.07397E+03 1.37284E+04 2.05628E+O4

1.4396 lE+OC 4.58341E+04 8.06072E+02 1 .OOOOOE+OC -5 8.60579E-0 1 2.70694E+04

1.29789E+O( 5.903 16E+O4 1 .O38 17E+O? 1 .00000E+O( -5 8.12116E-01 3.64928E+O4 6.41790E+02 l.OOOOOE+O( -4 6.30764E-01 2.77821E+O4 4.88597E+02 1.OOOOOE+OC 3 6.09323E-01 2.87214E+04 4.60530E+02 l.OOOOOE+CK 2 6.06374E-01 2.78307E+04 4.46247E+02 l.OOOOOE+OC 2 6.06630E-01 l.O7417E+Ol 9.2443 1E+OI 8.16762-1

Cd 4111

Q v Y ICD cd e,, Q v Y ICD

Cd 4111

Q v Y ICD

cd 4111

Q v Y ICD cd Qi,i

Q v Y ICD cd 4nl Q v Y ICD cd 4111

Q v Y ICD cd 4tn Q v Y ICD

-

-

-

-

-

-

-

TJ-= 68.00"F, Pf= 14.696 psia, pf,p = 56.660 Ib/ft3, ,U = 2.1220E+02 cP, k = -1.0, pb = 56.861 lb/ft3 1.06821E+02 2.41438E+02 3.61 633Et02 4.76062Et02

i.OOOOOE+OO I l.OOOOOE+W I 1.000000+OO I .00000EtOC -5 -4 -4 7.91821E-01 6.93475E-01 6.58288E-01 3.48756E+03 9.16328E+03 1.44972E+04 6.13349E+Ol 1.61152E+02 2.54959E+02 1.00OOOE+00 l.OOOOOE+OO l.OOOOOE+OO -4 -3 -3 6.24217E-01 6.14514E-01 6.11855E-01 2.94232E+03 8.68984E+03 1.44204E+O4

-4 6.37689E-01 1.966 1 OE+04 3.45773E+02 1 .OOOOOE+OC -3 6.10500E-01 2.01438E+04

6.27849E-03 3.3 1845E+oL 5.83607EtO: 1.00000E+O( 3 6.08806E-01 3.44365E+oL 5.52168E+O: l.OOOOOE+O( 2 6.06127E-01 3.33832E+oL 5.35279E+O: l.OOOOOE+O( 2 6.0651 1E-01 1.16154E+O: 9.996 18E+O: 7.36138E-01

Tf= 176.OO0F, Pf= 14.696 psia, P,,~ = 54.214 Ib/ft3, p = 1.749OE+Ol cP, k = -1.0, ph = 56.861 Ib/f$

ïj= 60.00"F, Pf= 14.696 psia, P,,~ = 62.366 Ib/ft3, p = 1.1990 cP, k = -1.0, = 62.366 lb/fG 4.71783E+Ol 1.393368t02 2.31222EtO2 3.22994Et02

I.OOOOOE+OO I.OOOOOE+W 1.00000Et00 1.00000Et00 3 2 2 2 6.12772E-01 6.0873384 I 6.07550E-01 6.06928E-01 2.812408+03 8.38168E+03 1.39423E+04 1.94992E+04 4.5095 1E+01 i .34395Et02 2.23556E+02 3.12658EtO2 l.OOOOOEt00 I.O0000E+OO 1.000WEt00 1.00000EtûC 2 2 2 2 6.12650E-01 6.08703E-01 6.07587E-O1 6.07039E-01 1.32576Et02 3.893678+02 6.284458+02 8.385178+02 1,14095B+03 3.35089E+03 5.40839Et03 7.2 1628E+03 9.98 168E-0 1 9,83509131 9.54 l91E-0 1 9.102 l4E-0 1 2 2 2 2 6.10059E-01 6.07268E-01 6.06432E-O1 6.05991E-01 2.03002Et02 6.049598t02 1.00266E+03 1.39387Et03 4.59176E+03 1.36838E+04 2.26796B+04 3. l5283E+W 9.99739E-01 9.976528-01 9.93477E-O1 9.872 15E-O1 2 2 2 2 6.10055E-01 6.07261E-01 6.06421E-01 6.05973E-01 2.93394E+ü3 8.76159Et03 1.458248+04 2.04003E+W 2.524958+04 7.540228+04 1.25496E+05 1.75565E+05 1.00000E+00 1 .OOOOOE+üO i .00000Et00 I .00000E+Oû 2 2 2 2 6.08078E-01 6.06155E-01 6.05563E-01 6.05246E-O1 5.18564E+02 1.549128+03 2.573778+03 3.58972Et03 4.462768+03 1.333 17E+04 2.214998+04 3.0893 lE+W 9.99865E-01 9.98788E-01 9.96634E-O1 9.93402E-01 2 2 2 2 6.079 12E-0 1 6.06060E-0 1 6.05488Ero 1 6.05 180E-O 1 4.677048+02 1.39827Et03 2.32630E+03 3.25 108Et03 1.05791E+W 3.162788+04 5.26192E+04 7.3537 IE+W 9.99948E-01 9.99530E-01 9.98695501 9.97443E-01 2 2 2 2 6.07775E-01 6.05982E-01 6.05427E-01 6.05128E-01 6.03389E+02 I .80447E+03 3.00344E+03 4.2OíJlOE+03 i .36482E+M 4.081598+04 6.793578+04 9.500348+04 9.99974E-01 9.99765E-01 9.99348E-01 9.98721E-01 2 2 2 2 6.07534E-01 6.05843E-01 6.053 17FrOI 6.05033E-01 2.06928E+03 6.19064E+03 1.030888+04 1.44255E+W 1.78083E+W 5.32766E+04 8.87172E+W 1.24146E+05 1.00000E+00 l.OOOE+OO 1.000OOE+00 1.00000E+00 2 2 2 2

Tf= 210.00"F, Pf= 14.696 psia, P,,~ = 58.792 lb/ft3, p = 2.8250E-01 cP, k = -1.0, pb = 62.366 lb/ft3

r f = O.0OoF, Pf= 14.696 psia, pf,p = 0.13223 Ib/ft3, /i = 1.3070E-02 cP, k = 1.3198, p h = 0.116198 lb/ft3

6.05601E-01 1.96313E+Ol 4.44048Et04 9.73909E-01 2 6.05572E-01 2.9124OE+W 2.50641E+05 1.OOOOOE+OC

6.05430Ero1 2.32733E+O? 5.26427EtO4 9.62428E-01 2 6.05392E-01 3.49384E+3+04 3.00680E+05 l.OOOOOE+OC 2 6.04834E-01 6.07043E+03 5.2242 1E+04 9.80611E-01 2 6.04777E-01 5.54188E+Ol 1.25354E+05 9.92486E-01 2 6.04735E-01 7.17764E+03 1.62353E+05 9.96243501 2 6.04659E-01 2.47141E+W 2.12690E+05 l.OOOOOE+ûC

TJ-= 50.00"F, P f = 100.00 psia, pf,p = 0.31109 Ib/ft3, /A = 1.0670Eo2 cP, k = 1.3622, p,, = 0.044210 Ib/ft3

ïj= O.OO"F, Pf= 1000.00 psia, pf ,p = 65.072 ib/ft3, p = 1.5430E-01 cP, k=-l.O,pb= 0.1161981b/ft3

6.04962E-01 5.09033E+03 4.38073E+04 9.86536E-01 2 6.04902E-01 4.62988E+03 1.04725E+05 9.94782E-01 2 6.04857E-01 5.98947E+03 1.35478E+05 9.97391E-01 2 6.04776-1 2.05991E+O4 1.77276E+05 1.OOOOOE+OO 2

Tf= O.OO°F, Pf= 200.00 psia, pf ,p = 2.0466 Ib/ft3, p = 1.3520E-02 cP, k = 1,3198, p b = 0.116198 lb/ft3

ïj= 50.00"F, Pf= 500.00 psia, pf,p = 1.6623 lb/ft3, p = 1.1310E-02 cP, k = 1.3622, pb = 0.044210 Ib/ft3

cd 9ni Q v Y íCD cd 4"l

Q v Y [CD

'd Bi

Y [CD

-

-

Q"

-

ïj= 150.00°F, Pf= 1OOO.00 psia, = 2.7573 Ib/ft3, p = 1.3650E-02 cP,

r C = 1.3622, pb = 0.044210 Ib/ft3

ï j = 140.00"F, Pf= 2000.00 psia,

k = - l . O , pb = 0.116198 Ib/ft3 = 32.465 lb/ft3, p = 4.1710E-02 cP,


API MPMS*1q-3-4 92 0732290 0506380 T L 2

2.2484 2.41409E+Oo 2.47 177E+04 4.34704E+02 1.00000E+Oo 4 1.21094E+00 I .22496E+O4 2.1543OE+U2 1.00000E+00 -5 7.50248E-01 7.43895E+03


20.2360 1.65683E+W 5.08929E+04 8.95041E+02 I .OOOOOE+W -5 9.35896E-01 2.8402 1 E+04 4.9950IE+02 1 .00000E+W -4 6.64836E-01 1.97764E+04

Table 4-C-&Selected Round Robin Test Results Matrix-US Units ( D, = 2.90039 in, a;! = 0.00000620 in/in-"F, d, = 1.54689 in, al = 0.00000925 in/in-OF)

1.2839IE+00 9.20218E+04 1.61836E+03 I.OOOOOE+00 -5 8.06809E-01 5.71307E+04 1.00474E+03 1 .OOOOOE+00 -4

Flow Conditions TJ= 0.00"F, PJ= 14.696 psia, pISp = 58.199 Ib/ft', p = 1.8650E+03 cP, k = -1 .o, pb = 56.861 Ib/ft'

1.16631E+00 1.1 1358E+00 1.07252E+OC I . 19419E+05 1.36823E+05 I .5374lE+05 2.10019E+03 2.40628E+03 2.70381E+03 I .oooOOE+00 I .00000E+00 1.00000E+OC 4 4 -4 7.67033E-01 7.49192E-01 7.35212E-01 7.75917E+04 9.09443E+04 1.04122E+05 1.36459E+03 1.59941E+03 1.831 16E+03 I .000OOE+00 I .OOOOOE+Oo 1.00000E+OC -3 -3 -3

TJ= 68.00"F. Pj= 14.696 psia, pl,p = 56.660 Ib/ft', p = 2.1220E+02 cP, k=-i .O,pb t56.861 Ib/ft"

6.29207E-01 4.36720E+04 7.68048E+02 1.000OOE+OO

Tj= 176.ûOoF, PJ= 14.696 psia,

k = -1.0. pb = 56.861 Ib/ft3 = 54.2 I4 Ib/ft', p = I .7490E+O 1 cP,

6.23979E-01 6.21766E-01 6.20098E-01 6.18702E+04 7.39809E+04 8.60795E+04 1.08809E+03 1.30108E+03 1.51386E+03 I .000OOE+00 I .000OOE+OO 1.00000E+OC

Tj= 60.00°F, P j = 14.696 psia, pf,p = 62.366 Ib/ft3, p = I. 1990 cP, k = -i .o, & = 62.366 Ib/ft'

4.5 1844E+O4 7.24504E+02 l.OOOOOE+00 2 6.0541OE-01 4.37868E+04 7.02094E+02 l.OOOOOE+00

TJ= 210.00"F. PJ= 14.696 psia, pf ,p = 58.792 Ib/ft3, p = 2.8250E-01 cP, k=-1.0, pb = 62.366 Ib/ft3

6.44488E+04 7.72855E+04 9.01 184E+04 I.O3340E+03 1.23922E+03 1.44499E+03 1.00000E+00 1 .000OOE+00 1 .OOOOOE+OC 2 2 2 6.04954E-01 6.04749E-01 6.04589E-01 6.25054E+04 7.498 1 1E+04 8.74548E+û4 1.00223E+03 1.20227E+03 1.40228E+03 1.0OOOOE+00 1.00000E+00 1.00000E+OC

TJ= 0.00'F. PJ= 14.696 psia, pf,p = O. 13223 Ib/ft3, p = 1.3070E-02 cP, k = 1.3198, ph = 0.1 16198 Ib/ft3

2 6.10013E-01 2.97169E+02 2.55744E+03 9.98166E-01 2 6.07949E-01 4.554 15E+02 1.03012E+04 9.99739E-01

TJ= 50.W°F, Pj= 100.00 psia, pf,p = 0.31 109 Ib/ft3, p = 1.0670E-02 cP, k = 1.3622, pb = 0.044210 lb/ft3

2 2 6.06855E-01 6.05947E-01 8.73866E+02 1.41088E+03 7.52049E+03 1.21420E+3+04 9.83496E-01 9.54155E-01 2 2 6.05686E-01 6.04998E-01 1.35833E+03 2.25 184E+03 3.07245E+04 5.09350E+04 9.97650E-01 9.93472E-01

TJ= O . M I O F , PJ= 1000.00 psia, pf.p = 65.072 Ib/ft3, p = 1.5430E-01 cP, k=-1.0, pb = 0.116198 ib/ft3

2.41 189E+03 2.07567E+04 8.16620E-01 2 6.04308E-01 4.40986E+03 9.97480E+04 9.73888E-01

TJ= O.ûO°F, PJ= 200.00 psia, pf,+ = 2.0466 lb/ft3, p = 1.3520E-02 cP, k = 1.3198,ph = 0.116198 Ib/€t3

2.60787E+03 2.64820E+03 2.24433E+04 2.27904E+04 7.35933E-01 6.40575E-01 2 2 6.04165E-01 6.04055E-01 5.22816E+03 6.01238E+03 1.18257E+05 1.35996E+05 9.62399E-01 9.48821E-01

TJ= 50.00"F, PJ= 500.Ix) psia, pf,p = 1.6623 Ib/ft3, p = 1.1310E-02 cP, k = 1.3622, &, = 0.044210 Ib/ft3

6.07945E-01 6.58201E+03 5.66448E+04 1.OoooOE+00 2 6.06348E-01 1.16406E+03 I.00179E+04 9.99865E-01 2 6.06213E-01 1.04995E+03 2.37491E+04 9.99948E-01 2 6.06103E-01 1.35461E+03 3.06403E+04 9.99974E-01 2 6.05906E-01~ 4.64587E+03 3.99824E+04 1.00000E+00 2

î j= 150.00°F, PJ= lON& psia, pI,p = 2.7573 Ib/ft3, /i = 1.3650E-02 cP, k = 1.3622, pb = 0.044210 Ib/ft3

6.05680E-01 6.04988E-01 1.96726E+04 3.27502E+04 1.69303E+05 2.81849E+05 l.OOOOOE+ûû I.OOOOOE+OO 2 2 6.04768E-01 6.04275E-01 3.47937E+03 5.78171E+03 2.99435E+04 4.97574E+04 9.98787E-01 9.96631E-01 2 2 6.04690E-01 6.04213E-01 3.14065E+03 5.22591E+03 7.10393E+04 1.18206E+05 9.9953OE-O1 9.98694E-01 2 2 6.04627E-01 6.04164E-01 4.05312E+03 6.74720E+03 9.16789E+04 1.52617E+05 9.99765E-01 .9.99347E-01 2 2 6.04512S01 6.04072E-01 1.39057E+04 2.31592E+04 1.19672E+05 1.99308E+05 1.00000E+00 1.ooOOOE+Oû 2 2

TJ= 140.00"F, Pj= 2000.00 psia, pl+ = 32.465 Ib/ft3, p = 4.1710E-02 cP, k=-1.0,Pb=0.1161981b/ft3

6.54241E+04 5.63040E+05 1.00000E+00 2 6.03770E-01 1.14366E+04 9.84234E+04 9.86525E-O 1

Cell Value - Cd (ln Qv Y ICD c, %li

Qv Y ICD

-

7.84893E+04 9.15530E+04 6.75479E+05 7.87905E+05 I.OOOOOE+OO l.O0000E+OC 2 2 6.03663E-01 6.03580E-01 1.36390E+04 1.57963E+04 1.17377E+05 1.35943E+05 9.80596E-O 1 9.73589E-0 1

Cd qn1 QL. Y ICD Cd 4n1 Q,. Y ICD c;t Ba

Qv Y ICD cd Llrn

Y ICD

-

-

-

Q,?

Cd

Q"

Cd

QV

-

Q'nr

Y ICD

%Il

Y ICD cd GÍn

Y ICD cd 4111

Y ICD cd B I 1

Y ICD

-

-

Q"

-

Q"

-

Q"

- cd 4ni

Y ICD

QV

-

6.03721E-01 1.04023E+04 2.35294E+05 9.94778E-01 2 6.03685E-01 1.34573E+04 3.04395E+05 9.97389E-01 2 6.03616E-01 4.62835E+04 3.98316E+05 l.OOOOOE+OO 2

AP (inches H,O at 6OoF)

6.03615E-01 6.03533E-01 1.24518E+04 1.44854E+04 2.81651E+05 3.27649E+05 9.92480E-01 9.89764E-01 2 2 6.03581E-01 6.03500E-01 1.61274E+04 1.87871E+04 3.64790E+05 4.24951E+05 9.96240E-01 9.94882E-01 2 2 6.03517E-01 6.03439E-01 5.5531 1E+04 6.47780E+04 4.77901E+05 5.57479E+05 I.000OOE+OO 1.OoooOE+OC 2 2

56.21 I O

1.41467E+OC 7.24242E+04 1.27371E+03 I .OOOOOE+OC -5 8.5 1475E-01 4.30669E+04 7.57406E+02 1.00000E+OC 4 6.35508E-01 3.15066E+04

I .30827E+O2 3.47803E+02 5.540998+02 1.00000E+00 I I .OOOE+OO I I .oOOWE+OC

-3 6.09384E-01 3.233 19E+O4 5.18423E+02 1 .OOOOOE+OC 2 6.05921E-O I 3.13026E+04 5.01918E+02 l.OOOOOE+OC

110.1736 I 224.8440 I 323.7754 I 440.6943

3 13 13 13 6.08303E-01 I 6.07357E-01 I 6.06940E-01 I 6.06617E-01

2 6.05498E-01 1.88272E+O? 1.62027E+W 9.10144E-01 2 6.04633E-01 3.13079E+O? 7.08164E+04 9.87205E-01 2 6.046 17E-0 1 4.58222E+W 3.94346E+05 1.00000E+OC 2 6.04010E-01 8.06459E+07 6.94038E+3+04 9.93397E-01 2 6.03955501 7.30397E+O? 1.6521 1E+O5 9.97441E-01 2 6.039 13E-0 1 9.43624E+0+01 2.13441E+05 9.98720E-01 2 6.03833E-01 3.24101E+3+04 2.78922E+05 I.OOOOOE+OC 2

2 12 12 6.05161E-01 I6.05063E-01 I6.05044E-01

2 12 12 6.04283E-01 I 6.04132E-01 I 6.04014E-01


-~.I __- - A P I MPMS*14.3m4 92 m 0732290 0506341 959 m


Table 4-(2-5-Selected Round Robin Test Results Matrix-US Units ( D, = 4.02638 in, % = 0.00000620 in/in-"F, d, = 2.14843 in, al = 0.00000925 in/in-"F)

Flow Conditions

Tf= O.OO°F, Pf= 14.696 psia, p,+ = 58.199 Ib/ft3, p = 1.8650E+03 cP, k = -1.0, pb = 56.861 lb/ft3

Tf= 68.00"F, Pf= 14.696 psia,

k = -1.0, pb = 56.861 Ib/ft3 = 56.660 Ib/ft3, = 2.1220E+02 cP,

Tf= 176.Q0°F, Pf= 14.696 psia, pbp = 54,214 ib/ft3, p = 1.749OE+Ol cP, k = -1.0, pb = 56.861 Ib/ft3

Tf= 60.00"F, P f = 14.696 psia, pf,p = 62.366 lb/f?, p = 1.1990 cP, k = -1.0, pb = 62.366 Ib/ft3

Tf= 210.00"F, Pf= 14.696 psia, pf,p = 58.792 ib/f?, p = 2.8250E-01 cP, k = -1.0, pb = 62.366 ib/fe

Tf= O.OO°F, P f = 14.696 psia, pf,p = 0.13223 Ib/ft3, p = 1.3070E-02 cP, k = 1.3198, pb = 0.116198 lb/ft3

Tf= 50.00"F, P f = 100.00 psia, P , , ~ = 0.31 109 Ib/ft3, p = 1.0670E-02 cP, & = 1.3622, pb = 0.044210 Ib/ft3

Tf= O.OO°F, Pf= 1OOO.00 psia, pf,p = 65.072 ib/f$, p = 1.5430E-01 cP, k = -1.0, pb = 0.1 16198 Ib/ft3

Tf= O.0OoF, P f = 200.00 psia, pl,p = 2.0466 lb/f?, p = 1.3520E-02 cP, k = 1.3198,pb=0.1161981b/ft3

Tf= 50.0O0F, Pf= 500.00 psia, P , , ~ = 1.6623 ib/ft3, p = 1.1310E-02 cP, k = 1.3622, pb = 0.044210 lb/ft3

Tf= i50.0O0F, Pf= 1ooO.00 psia, pf,p = 2.7573 Ib/ft3, p = 1.3650E-02 cP, k = 1.3622, pb = 0.044210 Ib/ft3

Tf= 140.00"F, Pf= 2000.00 psia, pf,p = 32.465 lb/f?, p = 4.1710E-02 cP, k=-1.0, pb = 0.116198 Ib/ft3

Cell Value

cd 4111

Y ICD cd qn1

Y ICD cd qn1 Qv Y ICD

4111

Y ICD cd 4nt Qv Y ICD cd 4ni

Y ICD

cd 9n1 Qv Y ICD

Q"

-

Q"

-

- cd

Qv

-

-

Q"

-

cd 4111

Qv Y ICD cd 4ni

Y ICD cd 4ni Qv Y ICD cd 4i Qv Y ICD cd 4ni Qv Y ICD

-

Qv

-

-

-

-

I - I -

1.11396E+OOl 8.79898E-01 I 8.08397E-01

-4 7.21751E-01 6.42738E-01 1.38056E+04 3.68830E+04 2.42795E+02 6.48652E+02 1.OOOOOE+ûO l.OOOOOE+OO -3 -3 6.16303E-01 6.1017 1 E a l 1.26160E+04 3.74717E+04 2.02289E+02 6.00835E+02 l.OOOOOE+OO l.OOOOOE+W 2 2 6.09037E-01 6.06333E-01 1.21393E+04 3.62566E+O4 1.94647E+02 5.8 1352E+02 1.00000E+00 1.00000E+OC 2 2 6.08953E-01 6.06309E-01 5.72279E+02 1.68427E+03 4.92503E+03 1.44948E+04 9.98166Eo1 9,83494-1

6.29512E-01 6.02067E+04 1.05884E+03 l.ooOOOE+OC 3 6.08430E-01 6.22746E+04 9.98534E+02 l.OOOOOE+OC 2 6.05516E-01 6.03463E+04 9.676 15E+02 l.OOOOOE+OC 2 6.05539E-01 2.7 1990E+03 2.34075E+04 9.54149E-01

6.07230E-01 6.05317E-01 6.04729E-01 8.7751 IE+02 2.61878E+03 4.34213E+03 1.98487E+04 5.92350E+04 9.82159E+04 9.99739E-01 9.97650E-01 9.93471Eol 2 2 2 6.07227E-01 6.0531 1E-01 6.04720E-01 1.26825E+04 3.79278E+04 6.3151 1E+04 1.09145E+05 3.26407E+05 5.43479E+05 1.00000E+00 1.00000E+00 1.00000E+W 2 2 2 6.05879E-01 6.0453 lE-01 6.04 107E-01 2.24388E+03 6.70949E+03 1.1 1505E+M 1.93108E+û4 5.77419E+04 9.59612E+M 9.99865E-01 9.98787E-01 9.96631501 2 2 2 6.05765E-01 6.û4464E-01 6.04053E-01 2.02398E+03 6.05642E+03 1.00787E+M 4.57810E+04 1.36992E+05 2.27974E+05 9.99948E-01 9.99530E-01 9.98694E-01

6.05671E-01 6.04410E-01 6.04010E-01 2.6 11 34E+03 7.8 16 15E+03 1.30129E+CM 5.90668E+04 1.76796E+05 2.94342E+05 9.99974501 9.99765E-01 9.99347E-01 2 2 2 6.05504E-01 6.04310E-01 6.03931E-01 8.95650E+03 2.68168E+M 4.46665E+04 7.70796E+04 2.30785E+05 3.84400E+05 1.00000E+00 l.OOOOOE+00 1.00000E+00

iches H,O at 60°F) I 110.1736 224.8440 323.7754 440.6943

1.17639E+00 1.07584E+00 1.03086E+00 9.95885E-01 1.62656E+05 2.12503E+05 2.44341E+05 2.75394E+05 2.86058E+03 3.73723E+03 4.29717E+03 4.84329E+03 l.OOOOOE+OO l.OOOOOE+OO 1.OOO00E+00 l.OOOOOE+00 -4 -4 -4 -4 7.70446E-01 7.36338E-01 7.20837-1 7.08548E-01 1.05245E+05 1.43694E+05 1.68803E+05 1.93579E+05 1.85091E+03 2.5271 1E+03 2.96869E+03 3.40442E+03 l.OOOOOE+OO l.OOOOOE+OO l.OOOOOE+OO l.OOOOOE+00 -3 -3 -3 -3 6.24502E-01 6.20321E-01 6.18542E-01 6.17197E-01 8.36185E+04 1.18655E+05 1.41978E+05 1.65281E+05 1.47058E+03 2.08676E+03 2.49693E+03 2.90675E+03 1.00000E+00 l.OOOOOE+OO l.OOOOOE+OO 1.00000E+00 3 13 13 12 6.07527501 16.06732E-01 I6.06380E-01 I6.06107E-01 8.70550E+04 1.24202E+05 1.48955E+05 1.73703E+05 1.39587E+03 1.99150E+03 2.38841E+03 2.78522E+03 1.OOOOOE+00 1.00000E+00 l.OOOOOE+OO 1.OOOOOE+00 2 2 2 2 6.05081E-01 6.04690E-01 6.04514501 6.04377E-01 8.44241E+04 1.20528E+05 1.44591E+05 1.68652E+05 1.35369E+03 1.93259E+03 2.31843E+03 2.70422E+03 l.OOOOOE+ûO l.OOOOOE+OO l.OOOOOE+OO l.OOOOOE+OO 2 2 2 2 6.05156E-01 6.04868E-01 6.04784E-01 6.04768E-01 3.62991E+03 4.65044E+03 5.02836E+03 5.10602E+03 3.12390E+04 4.00217E+04 4.32740E+04 4.39424E+04 9.10133E-01 8.16598E-01 7.35901E-01 6.40532E-01 2 2 2 2 6.04415E-01

9.87204E-01

6 .04i35mi 6.04011~-0i 6.03916~-01 8.50468E+03 1.00831E+04 1.15959E+04 1.92370E+05 2.28074E+05 2.62290E+05 9.73885E-01 9.62395Ml 9.48815E-01 2 2 2 6.041 13E-01 6.03982E-01 6.03880E-01 1.26176E+05 1.51378E+05 1.76578E+05 1.08587E+06 1.30276E+06 1.51963E+06 I.OOOOOE+OO l.OOOOOE+OO I.OOOOOE+00 2 2 2 6.03669E-01 6.03576E-01 6.03503E-01 2.20588E+04 2.63074E+04 3.04690E+04 1.89838E+05 2.26402E+05 2.62216E+05 9.86524E-01 9.80594501 9.73586E-01 o 0 o

L I ' I ' I ' 6.03829E-01 I 6.03626E-01 I 6.03534E-O1 I 6.03462E-01

2

6.03793E-01 1.82000E+04 4. I 1672E+05 9.98720E-01 2 6.03723E-01 6.25117E+O4 5.37976E+05 1.00000E+OC 2

6.03594E-01 2.59568E+04 5.87 126E+05 9.97388E-01 2 6.03534E-01 8.92745E+04 7.68296E+05 l.OOOOOE+OC 2

2.40178E+04 2.79407E+04 5.43266E+05 6.32000E+05 9.92479E-01 9.89763E-01 2 2 6.03505E-01 6.03434E-01 3.11077E+04 3.62386E+04 7.03634E+05 8.19692E+05 9.96239E-01 9.94881E-01 2 2 6.03448E-01 6.03381E-01 1.071 14E+05 1.24952E+05 9.2 1824E+05 l.O7534E+OG l.OOOOOE+OO 1.00000E+00 2 2


API M P M S * 1 4 - 3 . 4 92 m 0732290 050b382 895 m

2.2484 20.2360 56.21 10 110.1736 224.8440 .70699E+00 1.22893E+OO 1.07845E+00 9.98074E-0 I 9.26480E-O 1 .31893E+O5 2.84869E+05 4.16645E+05 5.39829E+05 7.15865E+05 ..31957E+O3 5.00991E+03 7.32743E+03 9.49384E+03 1.25897E+04 .00000E+00 1 .OOOOOE+00 1.00000E+00 I .OOOOOE+OO 1 .OM")E+00

SECTION SCONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART &-BACKGROUND 95

323.7754 440.6943 8.946 13E-0 1 8.69902E-O 1 8.29491E+05 9.41009E+05 1.45880E+04 I .65493E+04 1.00000E+00 1.00000E+00

Table 4-C-5-Selected Round Robin Test Results Matrix-US Units ( Dm = 7.98146 in, GC;! = 0,00000620 in/in-OF, d, = 4.25000 in, ai = 0.00000925 in/in-OF)

;.83 199E+02 .00000E+W -3 i.12058E-01 1.901 13E+04 !.85866E+02 I .000008+00 ! i07200841 1.734348+04 1.59122E+02 I.OOOOOE+00 l 5.07141E-O1

:low Conditions

2.474838+03 4.082608+03 5.686578+03 8.088558+03 9.688 l4E+03 I . 12867E+M 1.00000E+00 I .oooOOE+00 I .00000E+W I .00000E+00 1 .OOOOO1:+00 I .00000E+00 3 3 2 2 2 2 6.07974E-01 6.06780FAl 6.06152E4I 6.05594E-01 6.053458-01 6.05151E-O1 1.46054E+05 2.429458+05 3.397728+05 4.8494 i E+05 5.8 1690E+05 6.7842 I E+05 2.34189E+03 3.895488+03 5.44803E+03 7.775738+03 9.327048+03 1.0878 IE+04 1 .OOOO0E+00 I .000008+00 1 .OOOOOE+00 I .00000E+00 1.000(K)E+00 I .O(XH)OE+OO 2 2 2 2 2 2 6.0531 1W1 6.04728E-01 6.04414E-01 6.04130E-01 6.04001E-01 6.03901E-01 1.41590E+05 2.35756E+05 3.29886E+05 4.7 10458+05 5.65 I34E+05 6.592 12E+05 2.27031E+03 3.78019E+03 5.289528+03 7.552918+03 9.061578+03 l.O57OlE+OM 1.00000E+00 1.000WE+OO 1.00000E+00 I .00000E+W I .OOOOOE+Oíl I .000000+00 2 2 2 2 2 2 6.05294E-01 6.04744E-01 6.04468B-01 6.042598-01 6.04198E-01 6.041 86E-01

/= O.OO"F, P'= 14.696 psia, %p - - 58.199 lb/ft3, p = 1.8650E+03 cP, : = -1.0, pb = 56.861 ib/ft3

5.05942E-01 $.95064E+04 4.26052E+05 1.00000E+00 2 6.04988E-01 8.76472E+03 7.54292E+04 9.99865E-01

'/= 68.ûû°F, Pf= 14.696 psia, >f,p = 56.660 lb/ft3, p = 2.1220E+02 cP, : = -1.0, pb = 56.861 lb/ft3

6.04580E-01 6.04151E-01 1.48187E+05 2.46803E+05 1.27530E+06 2.12399E+06 1.00000E+00 l.OOOOOE+00 2 2 6.04013E-01 6.03702E-01 2.62238E+04 4.35895E+04 2.25682E+05 3.75 131E+05 9.98788E-01 9.96633E-01

rf= i76.00°F,Pf= 14.696 psia, >,,p = 54.214 Ib/ft3, p = 1.749OE+Ol cP, : = -1.0, pb = 56.861 lb/ft3

6.03918E-01 3.45391E+05 2.97243E+06 1,00000E+00 2 6.03531E-01 6.08102E+04 5.233328+05 9.93400E-01 2 6.03496E-01 5.50764E+04 1.24579E+06 9.97442E-01 P.

rf= 60.0O0F, Pf= 14.696 psia, = 62.366 Iblft? 1 = 1.1990 cP,

i = -1 .o, pb = 62.366 lb/ft3

6.03706E-01 6.03610E-01 6.03534E-01 4.93242E+05 5.91796E+05 6.90342E+05 4.24484E+06 5.09300E+06 5.94108E+06 1.00000E+00 l.OOOOOE+OO 1.00000E+00 2 2 2 6.03377E-01 6.03307E-01 6.03253E-01 8.62488E+04 1.02865E+05 1.19141E+05 7.42258E+05 8.85256E+05 1.02533E+06 9.86531E-01 9.80604E-01 9.73600E-01 2 2 2 6.03345E-01 6.03276E-01 6.03222E-01 7.84510E+04 9.39131E+04 1.09256E+05 1.77451E+06 2.12425E+06 2.47129E+06 9.94780E-0 1 9.92483E-O 1 9.89768E-O 1 - 0

r/= 210.û0°F, PE= 14.696 psia, 7,,p = 58.792 ib/f?, p = 2.8250E-01 cP, i; = -1.0, pb = 62.366 ib/f?

6.04906E-01 7.90619E+03 1.78833E+05 9.99948E-01 "

r/= O.W°F, Pf= 14.696 psia, s ~ , ~ = 0.13223 ib/ft3, p = 1.3070E-02 cP, k = 1.3198, pb = 0.116198 lb/ft3

6.03964E-01 6.03662E-01 2.36720E+04 3.94005E+04 5.35444E+05 8.91213E+05 9.99530E-01 9.98695E-01 - r,

Tj= 50.W°F, i''= 100.00 psia,

k = 1.3622, pb = 0.044210 Ib/ft3 = 0.31 109 lb/ft3, p = 1.0670E-02 cP,

6.04719E-01 3.49907E+04 3.01 130E+05 l.OOOOOE+OO 2

Tf= O.0OoF, PJ= 1000.00 psia, pf,p = 65.072 Ib/ft3, /i = 1.5430E-01 cP, k=-1.0, Pb = 0,116198 lb/ft3

6.03852E-01 6.03571E-01 6.03417E-01 6.03276E-01 6.03212E-01 6.03161E-01 1.04822E+05 1.74623E+05 2.44410E+05 3.49075E+05 4.18845E+05 4.8861 1E+05 9.02102E+05 1.50280E+06 2.10339E+06 3.00414E+06 3.60458E+06 4.20499E+06 1.00000E+00 1.00000E+00 l.OOOOOE+oO 1.00000E+00 1.OOOOOE+00 l.OM")E+OO 2 2 2 2 2 2

q= O.W°F, Pf= 200.00 psia, pfp = 2.0466 ib/ft3, kk 1.3198, PI, = 0.116198 lb/@

= 1 . 3 5 2 0 m cP,

Tf= 50.Gû°F, Pf= 500.00 psia, pf,p = 1.6623 lb/ft3, p = 1.1310E-02 cP, k = 1.3622, pb = 0.044210 lb/ft3

Tf= 15O.0O0F, P f = 1000.00 psia, pf,p = 2.7513 lb/ft3, p = 1.3650E-02 cP, k = 1.3622, pb = 0.044210 lb/ft3

Tf= 140.W°F, i'/= 2000.00 psia, pf,p = 32.465 Ib/ft3, p = 4.1710E-02 cP, k=- i .O,pb= 0.1161981b/ft3

- :ell 'alue

-d lnr

- r.

7. CD -d !in

- ,. 2, Y CD -d 6 1 1

- "

2" Y [CD

Li

Y ICD

8 1

Y iCD

9m

Y ICD

4111

Q V Y ICD

- cd

9,

- cd

Qv

- cd

Qv

- cd

- cd 4 1

Qv Y ICD cd 4ni

Y ICD

cd qlll

Y ICD cd 4 r Qv Y ICE

cd qln Q v Y ICE

-

Q"

-

Q"

-

-

-

-5 1-5 14 i.53571E-01 I7.88144E-0I 17.37224E-01

d

I i.71 I65E-01 6.26888E-01 6.20488E-01 i.O2196E+04 I 1.40721E+05 I 2.32141E+05

d l -d I - d I d I

L I ' I ' I ' I ' I ' I ' 6.048390-01 I6.03925841 I6.0363OE-01~6.03469Wl I6.0332iE-01 16.03254E41 I6.032011~-01 1.02010E+04 3.05507E+04 5.08718E+04 7.1 1568E+04 1.01492E+05 1.21637E+05 1.41704E+05 2.30740E+05 6.91037E+05 1.15068E+06 1.60952E+06 2.29568E+06 2.75134E+06 3.20524E+06 9.99974E-01 I l I l l I l 9.99765E-01 9.99347E-01 9.98721E-01 9.97390E-01 9.96241E-01 9.94884E-01


A P I MPMS*L4.3-4 92 W 0732290 0506383 721 W


Table 4-C-5-Selected Round Robin Test Results Matrix-US Units (Dm = 14.31154 in, CS = 0.00000620 in/in-"F, dm = 7.62500 in, al = 0.00000925 in/in-"F)

Flow Conditions

T p O.OO°F, PJ= 14.696 psia, pf,p = 58.199 Ib/ft3, /.i = 1.8650E+03 cP, k = -1.0, pb = 56.861 Ib/ft3

Tf= 68.00°F, PJ= 14.696 psia, PLI> = 56.660 Ib/ft3, /.i = 2.1220E+02 cP, k = -1.0, pb = 56.861 Ib/ft3

T/= 176.00°F, PJ= 14.696 psia, pl,(> = 54.214 Ib/ft3, /.i = 1.7490E+01 cP, k = -1.0, Pb = 56.861 Ib/ft3

ïj= 60.OO0F, PJ= 14.696 psia, pf,, = 62.366 Ib/ft3, /.i = 1.1990 cP, k = -1.0, pb = 62.366 Ib/ft3

r f = 210.00°F, PJ= 14.696 psia, = 58.792 Ib/ft3, /.i = 2.8250E-01 cP,

k = -1.0, pb = 62.366 Ib/ft3

r f = 0.0û0F, PJ= 14.696 psia,

k = 1.3198, pb = 0.116198 Ib/ft3 = 0.13223 lb/f$, p = 1.3WOE-02 cP,

r f = 50.00°F, PJ= 100.00 psia, gl,p = 0.31 109 lb/ft3, /.i = 1.0670E-02 cP, = 1.3622, pb = 0.044210 Ib/ft3

rf= O.OO°F, PJ= 1000.00 psia,

c=-1.0,pb=0.1161981b/ft3 = 65.072 Ib/ft3, p = 1.543OE-O1 cP,

rf= O.OO"F, PJ= 200.00 psia,

:= 1.3198, pb = 0,116198 lb/ft3 = 2.0466 Ib/ft3, p = 1.3520E-02 cP,

?= 50.00"F, PJ= 500.00 psia, %p - - 1.6623 Ib/ft3, /.i = 1.1310E-02 cP, : = 1.3622, pb = 0.044210 lb/ft3

'f= 150.00°F, PJ= 1OOO.00 psia,

: = 1.3622, pb = 0.044210 Ib/ft3 = 2.7573 Ib/ft3, /.i = 1.3650E-02 cP,

i= 140.00"F, PJ= 2000.00 psia, = 32.465 Ib/ft3, /.i = 4.1710E-02 cP,

Z-1.0, pb = 0.116198 ib/ft3

- Cell

Valut

cd 9n1 Q v Y ICD

4111

Y ICD

41,l

Y ICD

-

- cd

Qv

- cd

Q v

Cd -

ICD

cd 4111

Q" Y [CD

cd 8,1 Q" Y rm cd 7111

Q v Y iCD G bn 2, Y [CD -d Ini

2, Y CD <d 7111

r'

-

-

-

-

- n

- - 2,

CD -d Li1

- r7

2,

CD ?i 'ni

-

2,

CD -

At' (inches H,O at 60°F)

2.2484 20.2360 56.2110 110.1736

1.42469E+OO 1.06100E+00 9.47960E-01 8.87985E-0 3.54371E+05 7.91731E+05 1.17896E+06 1.54612E+Oi

1.OOOOOE+OO 1.OOOOOE+00 l.OOOOOE+OO I.OOOOOE+Oi -5 -4 -4 -4 8.54888E-01 7.3124OE-O1 6.91137E-01 6.67583E-0 2.10082E+05 5.39094E+05 8.49215E+05 1.14838E+Oi 3.69466E+03 9.48091E+03 1.49349E+04 2.01963E+D l.O0000E+00 1.00000E+00 1.00000E+00 1.00000E+O( -4 -? -2 -2

6.23223~+03 i .39240~+04 2.07341~+04 2.7 19 i 3 ~ + a

I - I - I -

6.36316E-01~6.19881B01~6.15544E-01~6.13373E-0 1.53272E+05 4.47943E+05 7.41347E+05 1.03423E+0( 2.69555E+03 7.87786E+03 1.30379E+04 1.81887E+D 1.00000E+00 l.OOOOOE+OO l.OOOOOE+OO l.OOOOOE+CH -3 3 2 2 6.09680E-01 6.06737E-01 6.05855E-01 6.05387E-0. 1.57163E+05 4.69218E+05 7.80893E+05 l.O9240E+Oi 2.52001E+03 7.52362E+03 1.2521 1E+04 1.7516OE+O 1.00000E+00 l.OOOOOE+OO l.OOOOOE+00 l.OOOOOE+O( 2 2 2 2 6.06167E-01 6.04754E-01 6.04309E-01 6.04068E-01 1.52148E+05 4.55383E+05 7.58414E+05 1.06136E+O( 2.43959E+03 7.30 179E+03 1.21607E+04 1.701 82E+D 1.000OOE+00 1.00000E+00 1.00000E+00 l.OOOOOE+Ci 2 2 2 2 6.06 122E-0 1 6.04740E-O 1 6.0432 1 E-0 1 6.04 109E-0 1 7.17310E+03 2.1 1550E+04 3.41829E+04 4.56334E+ol 6.17317E+04 1.82060E+05 2.94178E+05 3.92721E+O! 9.98167E-01 9.83500E-01 9.54167&01 9.10168E-01

6.05231E-01 6.04198E-01 6.03870E-01 6.Ö3691Ero1 1.10139E+04 3.29169E+04 5.46020E+04 7.59383E+O~ 2.49128E+05 7.44557E+05 1.23506E+06 1.71767E+(x 9.99739E-01 9.97651E-01 9.93474E-O1 9.87209E-01 2 2 2 2 6.05229E-01 6.04195E-01 6.03865E-01 6.03684E-03 1.59182E+05 4.76737E+05 7.94126E+05 1.1 1144E+OC 1.36992E+06 4.10280E+06 6.83424E+06 9.56508E+OC l.OOOOOE+OO l.OOOOOE+OO l.OOOOOE+OO 1.00000E+O( 2 2 2 2 6.04507E-01 6.03758E-01 6.03515E-01 6.03381E-01 2.8 1928E+O4 8.43833E+04 1.40279E+05 1.957 10E+O2 2.42627E+05 7.26203E+05 1.20724E+06 1.68428E+OC 9.99865E-01 9.98788E-01 9.96632E-01 9.93399E-01 2 2 2 2 5.04445E-01 6.03720E-01 6.03483501 6.03354E-01 2.54320E+04 7.61734E+04 1.26800E+05 1.77259E+05 5.75255E+05 1.72299E+06 2.86813E+06 4.00948E+Of J.99948E-01 9.99530E-01 9.98695E-01 9.97442E-01 2 2 2 2 5.04394E-01 6.03689501 6.03459E-01 6.03332E-01 3.28148E+04 9.83099E+04 1.63719E+05 2.29015E+05 7.42248E+05 2.22370E+06 3.70321E+06 5.18015E+M >.99974E-01 9.99765E-01 9.99347E-01 9.98721E-01 1 2 2 2 5.04302E-01 6.03632501 6.03413E-01 6.03292E-01 L.I2564E+05 3.37319E+05 5.61994E+05 7.86634E+05 ).68722E+05 2.90297E+06 4.83652E+06 6.76978E+06 L.OOOOOE+OO 1.OOOOOE+00 l.OOOOOE+OO 1.00000E+00 ! 2 2 2

224.8440 I 323.7754 1 440.6943 1 8.34766E-01 8.11098E-01 7.92724E-01 2.07637E+06 2.42100E+06 2.76052E+06 3.65166E+04 4.25775E+04 4.85485E+04 l.OOOOOE+OO 1.00000E+00 I.OOOOOE+00 -4 4 -4 6.4339 1E-01 6.36079E-O 1 6.32963E-O 1 1.58109E+06 1.87575E+06 2.17766E+O6 2.78063E+04 3.29884E+04 3.82979E+04 l.OOOOOE+OO I.OOOOOE+00 1.OOOOOE+00 -3 -3 3 6.11517E-01 6.10712E-01 6.10096E-01 1.47300E+06 1.76527E+06 2.05740E+06 2.59052E+04 3.10453E+04 3.61830E+04 I.OOOOOE+OO 1.00000E+00 1.OOOOOE+00 2 2 2 6.04967E-01 6.04779E-01 6.04631E-01 1.55950E+06 1.87081E+06 2.18208E+06 2.50055E+04 2.99973E+04 3.49883E+04 1.OOOOOE+OO l.OooOOE+00 l.OOOOOE+OO 2 2 2 6.03848&01 6.03749E-01 6.03670E-01 1.5 1567E+06 1.81850E+06 2.12131E+06 2.43028E+04 2.91586E+04 3.40139E+04 1 .OOOOOE+00 l.OOOOOE+OO 1 .OOOOOE+00

6.03948E-0 1 6.0390 1E-0 1 6.03892E-01 5.84781E+04 6.32374E+04 6.42199E+W 5.03262E+05 5.44221E+05 5.52677E+02 8.16669E-01 7.36003E-01 6.40671E-01 2 2 2 6.03531E-01 6.03459E-01 6.03404E-01 1.06992E+05 1.26861E+05 1.45904E+05 2.42008E+06 2.8695 1E+06 3.30024E+OE 9.73895E-01 9.62409E-01 9.48835E-01 2 2 2 6.03518&01 6.03443E-01 6.03383Wl 1.58734E+06 1.90457E+06 2.22178E+06 1.36606E+07 1.63907E+07 1.9 1206E+07 l.OOOOOE+OO l.OOOOOE+NI 1.00000E+G€ 2 2 2 6.03260E-01 6.03205E-01 6.03162E-01 2.77596E+05 3.3 1083E+05 3.83477E+05 2.38899E+M 2.84930E+06 3.30021E+M 9.86529E-01 9.80602E-01 9.73597E-01


A P I MPMS*L4-3-4 92 m 0732290 0506384 668 m

5.26734E-01 5.49363E+06 1.14202E+05 I .00000E+00 3 5.08942E-01 5.18430E+O6 1.08762E+05 1 .OOOOOE+00

SECTION &CONCENTRIC. SQUARE-EDGED ORIFICE METERS, PART 4-BACKGROUND 97

6.24236E-01 6.22355E-01 7.76 I30E+06 9.027568+06 1.36496E+05 1.58765E+05 l.OOOOOE+ûO I .00000E+OO 3 3 6.084lOE-01 6.07999E-01 7.4 l466E+06 8.6446 lE+06 1.30400E+05 1.52030E+05 1.00000E+00 1.00000E+00

Table 4-C-&Selected Round Robin Test Results Matrix-US Units ( Dm = 29.37598 in, CS = 0.00000620 idin-OF, d, = 15.65626 in, al = 0.00000925 idin-OF)

5.04464E-01 5.56968E+06 1.05341E+05 l.OOOOOE+OO 2 6.03651E-01 6.38829E+06 1.02432E+05 1.00000E+00 2 6.03724E-01 2.46459E+05 2.12103E+06 8.16654E-O 1 2 6.03415E-01 4.51012E+05 i.O2016E+07 9.73893E-01 2 6.03406E-01 6.69130E+06 5.75853E+07 1.00000E+00 2 6.03212E-01 1.1703 1E+06 1 .O07 17E+07 9.86528E-01 2 6.03 194E-01 1.06452E+06 2.40788E+07 9.94779E-01 2 6.03180E-01 1.37720E+06 3.1 1513E+07 9.97389E-01 2 6.03153E-01 4.73692E+06 4.07660E+07 1 .000OOE+00 2

Flow Conditions

6.04328E-01 6.04222E-01 7.88185E+06 9.19387E+06 1.2638 1E+05 1.47418E+05 I.ooOOOE+00 1.00000E+00 2 2 6.03577E-01 6.03519E-01 7.66501E+06 8.94165E+06 1.22904E+05 1.43374E+05 1 .OoooOE+OO l.OOOOOE+OO 2 2 6.03689E-01 6.03682E-01 2.66520E+05 2.70657E+05 2.29367E+06 2.32928E+06 7.3598 IE-01 6.4064 1 E-0 1 2 2 6.03362E-01 6.03321E-01 5.34783E+05 6.15071E+05 1.20964E+07 1.39125E+07 9.62406E-01 9.48830E-01 2 2 6.03349E-01 6.03305E-01 8.02881E+06 9.36625E+06 6.90959E+07 8.06060E+07 1.00000E+00 l.OOOOOE+00 2 2 6.03171E-01 6.03139E-01 1.39583E+06 1.61675E+06 1.20125E+07 1.39 138E+07 9.80600E-01 9.73594E-01 2 2 6.03 153E-01 6.03 120E-01 1.27439E+06 1.48264E+06 2.88259E+07 3.35364E+07 9.92481E-01 9.89766E-01 2 2 6.03 140E-01 6.03108E-01 1.65063E+06 1.92301E+06 3.73361E+07 4.34971E+07 9.96240E-01 9.94883E-01 2 2 6.031 15E-01 6.03084E-01 5.68394E+06 6.63093Ert.06 4.89160E+07 5.70658E+07 l.OOOOOE+OO 1 .OOOOOE+00 2 2

r/=0.00OF, Pf= 14.696 psia, pf,p = 58.199 lb/ft3, j i = 1.8650E+03 cP, k = -1.0, pb = 56.86 I Ib/ft3

2 6.04300E-01 8.91285E+04 7.67040E+05 9.83499E-01 2 6.03907E-01 1.38717E+05 3.13769E+06 9.97650E-01

r/= 68.00"F. Pf= 14.696 psia, P,,~ = 56.660 lb/ft3, j i = 2.1220E+02 cP, k = -1.0, pb = 56.861 Ib/ft3

2 2 6.03996E-01 6.03842E-01 1.44044E+05 1.92313E+05 1.23964E+06 1.65504E+06 9.54163E-01 9.10160E-01 2 2 6.03666E-01 6.03535E-01 2.30135E+05 3.20088E+05 5.20551E+06 7.24017E+06 9.93473E-01 9.87208E-01

r/= 176.00'F, Pf= 14.696 psia, pf,p = 54.214 ib/ft3, j i = 1.7490E+01 cP, k=-1.0, pb = 56.861 Ib/ft3

6.04651E-01 6.70504E+05 5.77036E+06 l.OOOOOE+00 2 6.04132E-01 1.18793E+05 l.O2233E+O6 9.99865E-01 2 6.04087E-01 1.07163E+05 2.42395E+06 9.99948E-01 2 6.04050E-01 1.38275E+05 3.12769E+06

ïj= 60.00°F, P f = 14.696 psia. pf,p = 62.366 lb/ft3, p = 1.1990 cP, k =-1.o, pb = 62.366 Ib/ft3

6.03905E-01 6.03662E-01 6.03529E-01 2.00905E+06 3.34707E+06 4.68486E+05 1.72899E+07 2.88049E+07 4.03179E+07 l.OOOOOE+oO l.OOOOOE+oO 1.00000E+W 2 2 2 6.03583E-01 6.03403E-01 6.03303E-01 3.55674E+05 5.91334E+05 8.25045E+05 3.06093E+06 5.08902E+06 7.10034E+06 9.98787E-01 9.96632E-01 9.93399E-01 2 2 2 6.03555E-01 6.03380E-01 6.03283E-01 3.21075E+05 5.34522E+05 7.47272E+05 7.26250E+06 1.20905E+07 1.69028E-cO7 9.99530E-01 9.98695E-01 9.97442E-01 2 2 2 6.03533E-01 6.03362E-01 6.03267501 4.14387E+05 6.90161E+05 9.65467E+05 9.37316E+06 1.561 10E+07 2.18382E+07

Tf= 210.OOQF, Pf= 14.696 psia, P, ,~ = 58.792 Ib/ft3, j i = 2.825OE-O1 cP, k = -1 .O, pb = 62.366 Ib/ft3

Tf= O.OO'F,Pf= 14.696 psia, pf,p = 0.13223 Ib/ft3, p = 1.3070E-02 cP, k = 1.3198,pb=0.1161981b/ft3

TJ= 50.00'F, Pf= 100.00 psia, pf,p = 0.3 1109 Ib/ft3, p = 1.0670E-02 cP, k = 1.3622, pb = 0.044210 lb/ft3

Tf= O.OO'F, Pf= 1ooO.00 psia,

k= -1.0, pb = 0.1 16198 Ib/ft3 = 65.072 lb/ft3, j i = 1.5430E-01 cP,

TJ= O.OO"F, Pf= 200.00 psia, p,,,, = 2.0466 lb/ft3, j i = 1.3520E-02 cP, k = 1.3198,pb=O.l161981b/f~

T/= 50.û0°F, P f = 500.00 psia, pf.p = 1.6623 IblfG, j i = 1.131OE-02 cP, k 1.3622, pb = 0.044210 ib/ft3

ïj= 150.00°F, Pf= 1OOO.00 psia, p,,, = 2.7573 ib/f$, p = 1.3650E-02 cP, k 1 1.3622, pb = 0.044210 lb/ft3

Tf= 140.00"F. Pf= 2000.00 psia, pGp = 32.465 ib/ft3, j i = 4.1710E-02 cP, k=-1.0, pb = 0.116198 Ib/ft3

Cell Value

Cd

QI. 4111

Y ICD cd 4ni Q,. Y ICD Cd 4111

Qv Y ICD c,, %ia

Q, Y ICD ci 4 1

QI. Y ICD

cd 4811 Qv Y ICD Cd 4111

QI. Y ICD Cd 9111

Q, Y ICD cd 4111

Qv Y ICD cd 4111

Y ICD cd qn1

Y ICD cd 41n Qv Y ICD

-

-

-

-

-

-

-

-

-

Q"

-

Q"

-

-

Aí' (inches H,O at 60°F) I

7.67058E-01 6.76588E-01 7.94747E+05 2.10305E+06 1.39770E+04 3.69859E+04 1 .OOOOOE+00 I .00000E+W -3 6.2438 1E-0 1 6.143 1OE-01 6.34103E+05 1.87165E+06

6.41762E-0 1 3.32467E+06 5.8470 1E+O4 I.OOOOOE+OC -3 6.11559E-01 3.10543E+06

6.3265 1E-0 I 4.58846E+06 8 .O696 I E+04 i .OOOOOE+00 3 6.1 O 158E-O 1 4.33765E+06

1.1 1518E+04 3.29162E+W 5.461458+04 7.62851E+04 I .000WE+00 l I .0000013+00 I .00000E+W I I .OOOOOE+W 3 6.07720E-01 6.60501E+05 1.05907E+04 1 .OOOOOE+W 2 6.05316E-01 6.40584E+05

2 6.057 13E-0 1 1.97498E+O6 3.16675E+O4 1.00000E+OC 2 6.0431 IE-01 1.91858E+O6

1.027 14E+ü4 3.076338+04 5.124478+04 7.172178+04 I .00000E+00 I .00000E+00 I 1.000WE+Oü 1 .OO(MX)E+OO 2 6.05283E-01 3.020 14E+O4 2.59913E+05 9.98167E-01 2 6.04652E-01 4.63926E+O4 1.04937E+06 9.99739501

9.98721E-01 2 6.03237E-01 3.31631E+Ot 2.85401E+07 l.~OOE+OC 2

224.8440 323.7754 440.6943 7.52977E-01 7.36253E-01 7.23090E-01 7.89665E+06 9.26553E+06 I .O6 165E+Oï I .38876E+05 1.62950E+05 1.867 IOE+05 i i .OOOOOE+00 1.00000E+00 I .ooOOOE+OC



Table 4-C-5-Selected Round Robin Test Results Matrix-US Units ( Dm = 1.93945 in, CS = 0.00000620 in/in-OF, d, = 1.28126 in, al = 0.00000925 in/in-"F)

Flow Conditions ïj= 0.00"F, P f = 14.696 psia, prP = 58.199 Ib/ft3, /i = 1.8650E+03 cP, k = -1.0, pi> = 56.861 Ib/ft3

ïj= 68,00"F, P f = 14.696 psia, pf,p = 56.660 Ib/ft3, /.i = 2.1220E+02 cP, k = -1.0, pb = 56.861 Ib/ft3

T,== 176.00°F, P f = 14.696 psia, P,,~ = 54.214 Ib/ft3, /.i = 1.749OE+Ol cP, k = -1.0, pb = 56.861 Ib/ft3

ïj= 60.0O0F, P f = 14.696 psia, pIP = 62.366 Ib/ft3, /i = 1.1990 cP, k 2 -1.0, pb = 62.366 ib/ft3

r f = 210.00"F, Pf= 14.696 psia, pf,P = 58.792 lb/ft3, /.i = 2.8250E-01 cP, k = -1.0, pb = 62.366 Ib/ft3

T,== O.OO°F, P f = 14.696 psia, pbp = 0.13223 ib/ft3, /.i = 1.3070E-02 cP, k = 1.3198, pb = 0.116198 lb/ft3

ïj= 50.00"F, P/= 100.00 psia,

k = 1.3622, pb = 0.044210 Ib/ft3 = 0.31109 Ib/ft3, /.i = 1.0670E-02 CP,

T,== O.OO"F, P f = 1000.00 psia, pf,P = 65.072 Ib/ft3, p = 1.5430501 cP, k=-1.0,/3b = 0.1161981b/ft3

r f = O.OO"F, Pf= 200.00 psia, pf,p = 2,0466 Ib/ft3, /i = 1.352ûE-02 cP, k = 1.3198, pb = 0.116198 lb/ft3

Tj= 50.00"F, Pf= 500.00 psia, pfp = 1.6623 Ib/ft3, p = 1.1310E-02 cP, k 1,3622, pb = 0.044210 Ib/ft3

Tj= 150.00"F, Pf= 1000.00 psia, = 2.7573 lb/ft3, /.i = 1.3650E-02 cP,

k = 1.3622, pb = 0.044210 Ib/ft3

r f = 140.00"F, Pf= 2000.00 psia,

G=-1.0,pb=0.1161981b/ft3 = 32.465 Ib/ft3, /.i = 4.1710E-02 cP,

Cell Value

cd

-

4111

Y ICD

cd 4nr Qv Y ICD

4111

Y ICD

Q"

-

- cd

Qv

- cd 4ni Qv Y ICD cd 4rn Qv Y ICD Cd 4111

Qv Y ICD cd 9"l Qv Y ICD cd 4111

Qv Y ICD cd 4111

Y ICD cd 41n Qv Y [CD

cd 4111

Qv Y [CD

-

-

Q"

-

-

- cd Ym Qv Y [CD -

Aí' (inches H?O at 60°F)

I - I - l -

1.62622E+OO I 1.18494E+OO I l.O4463E+Oo I 9.6836 1E-01

-5

8.68359E-01 7.04472E-01 6.29459E+03 1.53199E+04 1.10701E+02 2.69428E+02 l.OOOOOE+OO l.OOOOOE+oO

6.33221E-O1 6.21185E-01 4.91 177E+03 1.44554E+04 7.87572E+01 2.31783E+02 1.00000E+00 1.00000E+W

6.18927E-01 6.13466501 6.1 1766E-01 4.67525E+03 1.39021E+04 2.31060E+04 7.49648E+01 2.22912E+02 3.70490E+02 1.00000E+00 1.00000E+00 1.00000E+0(1 2 2 2 6.18777E-01 6.13441E-01 6.1 1845E-01 2.20304E+02 6.44744E+02 1.03696E+03 1.89593E+03 5.54866E+03 8.92405E+03 9.98006E-01 9.82053E-01 9.50147E-01 2 2 2 6.15314E-01 6.11361E-01 6.10105E-01 3.36929E+02 1.00202E+03 1.65901E+03 7.621 11E+03 2.26650E+04 3.75257E+04 9.99716E-01 9.97444E-01 9.92901E-01 2 2 2 6.15312E-01 6.11354E-01 6.10090E-01 4.86947Et03 1.45146Et04 2.41409E+04

6.10844E-01 3.22997E+04 5.17905E+02 1.00000E+OC 2 6.1 1047E-01 1.37682E+01 1.18489E+04 9.02289E-01 2 6.09423E-01 2.30410E+03 5.21171E+04 9.86086E-01 2 6.09397E-01 3.37589Et04

4.190668+04 1.24912B+05 2.077578+05 2.905298+05 1.00000E+00 1 .OOoOOE+00 1 .OOOOOo+00 1 .wooE+oo 2 2 2 2 6.12545E-O1 6.09680501 6.08748501 6.08236I3-O1 8.595678+02 2.56366E+03 4.2562 lE+03 5.93266E+03 7.39743E+03 2.20628Et04 3.662898+04 5.10565Et04 9.99853E-01 9.98681E-01 9.96337E-01 9.92820E-01 2 2 2 2 6.12302E-01 6.09529501 6.08623501 6.08123501 7.75208E+02 2.3 1406E+03 3.84753E+03 5.37477E+03 1.753478+04 5.234248+04 8.702858+04 1.215748+05 9.99943E-01 9.99489E-01 9.98580EOl 9.97217E-01 2 2 2 2 6.12098E-01 6.09401E-01 6.085 1 8 M 1 6.08030E-01 1.00009E+03 2.98639E+03 4.967858+03 6.944678+03 2.26213E+04 6.75502B+04 1.123698+05 1.57084E+05 9.99972E-01 9.99744E-01 9.9929OE-O1 9.98608E-01 2 2 2 2 6.1 1747501 6.09183E-01 6.08341LFol 6.07874E-01 3.42910B+03 1.024438+04 1.70502E+04 2.38520E+04 2.95 l09E+04 8.816248+04 1.46734E+05 2.052708+05 1.00000E+00 l . r n E + 0 0 1 . r n E + 0 0 1.00000E+00 2 2 2 2

6.41117E-01 6.37613E-01 4.64739E+04 5.54639E+oL 8.17325E+02 9.75429E+O: l.OOOOOE+OO l.OOOOOE+O( 3 3 6.14300E-01 6.13578E-01 4.76504E+04 5.71133E+oL 7.64045E+02 9.15776E+O; 1.00000E+00 l.OOOOOE+O( 2 2 6.10005E-01 6.09623E-01 4.60790E+04 5.52602E+@ 7.38848E+02 8.86062E+O: l.OOOOOE+00 l.OOOOOE+O( 2 2 6.10456E-01 6.10301E-01 1.74350E+03 1.86243E+O: 1.5W6E+04 1.6028 1E+W 8.00589E-01 7.12849E-01 Ei 4.8 1767E+O4

2 6.08535E-01 3.83623E+O: 8.67729E+04 9.59110E-01 2 6.08471E-01 5.77845Et04

6.07767E-01 8.40496E+03 7.23331E+04 9.85347E-01 2 6.07663E-01 7.65015E+03 1.7304 1E+05 9.94321E-01 2

6.07555E-01 1.00165E+04 8.62017EtCv 9.78900E-01 2 6.07453E-01 9.15395E+01 2.07056E+05 9.9 1822E-01 2

6.07580E-01 6.07374E-01 9.899240+03 1.18602B+04 2.239 14E+05 2.68269B+05 9.97 1608-01 9.959 10E-01 2 2 k5.07443B-01 6.07245E-0 1 3.40501E+04 4.08468E+04 2.93035E+05 3.515288+05 i .00000E+00 1.00000E+W 2 2

440.6943

1.40605E+3+00 1.47326E+05 2.59098E+03 l.OOOOOE+OO -5 8.40876E-01 8.70522E+04 1.53097E+03 I.OOOOOE+OO -4 6.34968E-01 6.44395E+04 1.13328E+03 1.00000E+00 3 6.13014E-01 6.65710E+04 ï.O6742E+O3 1.00000E+00 2 6.09322E-01 6.44384E+04 1.03323E+03 1.00000E+00 2 6.10308E-01 1.85679E+03 1.59795E+04 6.09155E-01 2 6.08325E-01 4.40517E+03 9.96420E+04 9.44345E-01 2 6.08242E-01 6.73899E+04 5.79957Et05 1.0OOOOEi00 2 6.07389E-01 1.159 17EtO4 9;97586Et04 9.71281E-01 2 6.07288E-01 1.06449E+04 2.40780E+05 9.88869E-01 2 6.0721 1E-01 1.38126E+W 3.12433E+05 9.94434E-01 2 6.07089E-01 4.76423E+04 4.100 10E+05 l.OOOOOE+00 2


A P I MPMS*14-3e4 92 W 0732290 0506386 430 W

SECTION 3-CONCENTRIC. SQUARE-EDGED ORIFICE METERS, PART 4-BACKGROUND 99

440.6943 I .26025E+00 !.97536E+05 !.23269E+03 I .OOOOOE+OO -5 1.793 16E-01 1.81789E+O5 3.19707E+03 I .00000E+00 -4 5.27923E-01 I .43586E+05 2.525218+03 I .OOOOOE+OO 3 5.10183E-01 1.49307E+05 2.39404E+03 1.00000E+00 2 6.07046E-01 1.44652E+05 2.3 194 1 E+03 l.OOOOOE+00 2 6.07895E-01 4.16268E+03 3.58240E+04 6.08491E-01 2 6.06193E-01 9.89008E+03 2.23707E+05 9.44250E-O 1 2 6.06123E-O 1 1.5 13 15E+05 1.30222E+06 1.00000E+00 2 6.05387E-01 2.60314E+04 2.24026E+05 9.71232E-O 1 2 6.05298E-01 2.39064E+04 5.40745E+05 9.88850E-01 2 6.05230E-01 3.102 13E+04 7.01680E+05 9.94424E-01 2 6.05 124E-01 1.07002E+05 9.20857E+05 l.OOO00E+00 2

Table 4-C-&Selected Round Robin Test Results Matrix-US Units ( Dm = 2.90039 in, CS = 0.00000620 in/in-OF, d,,, = 1.921 89 in, al = 0.00000925 in/in-"F)

2.2484 I.O2096E+00 i.O9444E+04 1.95946E+02 1 .OOOOOE+00 -6 1.4447 1 E+OO '407 14E+O4 1.23338E+02 I .00000E+00 -5 1.04108E-01 1.3 1338E+04 !.30980E+02 I.ooO00E+00 4 5.26553E-01 I .09508E+3+04 1.75589E+02 I .OOOOOE+00 3 5.15093E-01 1.04692E+04 1.67867E+02 l.OOOOOE+00 2 5.14973E-01 4.93340E+02 4.24569E+03 9.98003E-01 2 6.121 lOE-01 7.55224E+02 1.70826E+04 9.99716E-01 2 6.12109E-01 1.09149E+04 9.39335E+04 l.OOOOOE+OO 2 6.09789E-01 1.92808E+03 1.6593 1E+04 9.99853E-01 2 6.09584E-01 1.73896E+03 3.93342E+04 9.99943501 2 6.09409E-01 2.24353E+03 5.07471E+04 9.99972E-01 2 6.09113E-01 7.69329E+03 6.62085E+04 l.OOOOOE+OO 2

?ow Conditions rf= O.OO"F, P/= 14.696 psia,

= 58.199 Ib/ft3, p = 1.8650E+03 cP, C = -1.0, pb = 56.861 Ib/ft3

20.2360 56.21 10 110.1736 224.8440 323.7754 2.031 17E+OO 1.71348E+00 1.54120E+00 1.38544E+00 1.31519E+00 l.O276OE+05 l.U79E+05 1.8 1933E+05 2.33638E+05 2.66 l49E+05 1.80721E+03 2.54091E+03 3.19962E+03 4.10892E+03 4.68070E+03 1.00000E+00 1 .OOOOOE+00 1.00000E+00 1 .ooOOOE+00 I .OOOOOE+00 -5 -5 -5 -5 -5 I.O7496E+OO 9.567 13E-01 8.91648E-01 8.30968E-01 8.02446E-O 1 5.37328E+04 7.97034E+04 I.O3996E+05 1.38455E+05 1.60443E+05 9.44985E+02 1.40172E+03 1.82895E+03 2.43498E+03 2.82168E+03 1.00000E+00 1 .OOOOOE+00 1 .OOOOOE+00 1 .OOOOOE+00 ~ 1.00000E+00 -4 -4 -4 4 -4 6.62435E-01 6.46722E-01 6.39093E-01 6.32713E-01 6.29989E-01 3.24596E+04 5.28161E+04 7.30703E+04 1.03344E+05 1.23479E+05 5.70859E+02 9.28863E+02 1.28507E+03 1.81748E+03 2.17 159E+03 1 .OOOOOE+00 1 .OOOOOE+00 1 .OOOOOE+00 1.00000E+00 1 .OOOOOE+OO 3 3 3 3 3 6.16940E-01 6. I41 1OE-01 6.12608E-01 6.1 1263E-01 6.10657E-O 1 3.23486E+04 5.36670E+04 7.49501 E+04 1.06836E+05 1.28077E+05 5.18690E+02 8.60517E+02 1.20178E+03 1.71306E+03 2.05363E+03 1.00000E+00 l.OOOOOE+OO 1 .OOOOOE+00 1.0OOOOE+00 1 .OOOOOE+00 2 2 2 2 2 6.10561E-01 6.09127E-01 6.08345E-01 6.07630E-01 6.07304E-01 3.1 1764E+O4 5.18387E+04 7.24810E+04 1.03423E+05 1.24040E+05 4.99895E+02 8.31201E+02 1.16219E+03 1.65832E+03 1.98891E+03 l.O0000E+00 1 .OOOOOE+00 l.OOOOOE+OO 1.00000E+00 l.OOOOOE+OO 2 2 2 2 2 6.10543E-01 6.09199E-01 6.08522E-01 6.08019E-01 6.07888E-O 1 1.44585E+03 2.32618E+03 3.08889E+03 3.91 1 16E+03 4.17702E+03 1.24430E+04 2.00191E+04 2.65830E+04 3.36594E+04 3.59475E+04 9.82022E-0í 9.50063E-01 9.02123E-01 8.00250E-01 7.12360E-01 2 2 2 2 2 6.08787E-01 6.07719E-01 6.07136E-01 6.06609E-01 6.06374E-01 2.24827E+03 3.72346E+03 5.17205E+03 7.27362E+03 8.61257E+03 5.08543E+04 8.42222E+04 1.16988E+05 1.64524E+05 1.9481 1E+05 9.97440E-01 9.92889E-01 9.86062E-01 9.71556E-01 9.59041E-01 2 2 2 2 2 6.08782E-01 6.07706E-01 6.071 14E-01 6.06570E-01 6.06320E-01 3.25670E+04 5.41824E+04 7.57815E+04 1.08162E+05 1.29741E+O: 2.80272E+05 4.66294E+05 6.52175E+05 9.30843E+05 1.1 l655E+M 1.OOOOOE+00 1.00000E+00 1.0OOOOE+00 1.00000E+00 1.00000E+OC 2 2 2 2 2 6.07357E-01 6.06558E-01 6.061 17E-01 6.057 13E-01 6.05530E-01 5.75447E+03 9.55564E+03 1.33209E+04 1.88738E+04 2.24933E+W 4.95230E+04 8.22358E+04 1.14640E+05 1.62428E+05 1.93577E+O( 9.98679E-01 9.96331E-01 9.92808E-01 9.85322E-01 9.78864E-01 2 2 2 2 2 6.07226E-01 6.06449E-01 6.06019E-01 6.05623E-01 6.05441E-01 5.19440E+03 8.63837E+03 1.20686E+04 1.71795E+04 2.05573E+@ 1.17494E+05 1.95394E+05 2.72984E+05 3.88588E+05 4.64992E+O: 9.99488E-01 9.98578E-01 9.97212E-01 9.9431 1E-01 9.91808E-01 2 2 2 2 2 6.07114E-01 6.06357E-01 6.05937E-01 6.05549E-01 6.05371E-03 6.70379E+03 1.1 1539E+04 1.55940E+04 2.22306E+04 2.66354E+@ 1.51635E+05 2.52295Er-O5 3.52727E+05 5.02841E+05 6.02474E+O: 9.99744E-01 9.99289E-01 9.98606E-01 9.97155E-01 9.95903E-01 2 2 2 2 2 6.06928E-01 6.06205E-01 6.05803E-01 6.0543 1E-01 6.0526OE-01 2.29973E+04 3.82832E+04 5.35609E+04 7.64686E+04 9.17363E+O~ 1.97915E+05 3.29465E+05 4.60945E+05 6.58089E+05 7.89483E+01 l.OOOOOE+OO l.OOOOOE+00 l.OOOOOE+OO 1.00000E+00 l.OOOOOE+O( 2 2 2 2 2

rf= 68.00"F. Pf= 14.696 psia, y f , p = 56.660 Ib/ft3, /i = 2.1220E+02 cP, ¿=-I.(), pb = 56.861 lb/ft3

r f = 176.00"F, P i = 14.696 psia, gf,p = 54.214 Ib/ft3, /i = 1.7490E+01 cP, k = -1 .o, pb = 56.86 1 Ib/ft3

r f = 60.00"F, P f = 14.696 psia, = 62.366 lb/ft3, /i = 1.1990 cP,

k = -1.0, Pb = 62.366 lb/ft3

r/= 210.0OoF, Pf= 14.696 psia, pf,p = 58.792 ib/ft3, /i = 2.8250501 cP, k = -1.0, pb = 62.366 ib/ft3

r/= 0.OOoF, Pf= 14.696 psia, pbp = 0.13223 lb/ft3, /i = 1.3070E-02 cP, k = 1.3198, pb = 0,116198 lb/ft3

Tf= 50.00"F, Pf= 100.00 psia, pf,p = 0.31 109 Ib/ft3, /i = 1.0670E-02 cP, k = 1.3622, pb = 0.044210 lb/ft3

TI= O.W°F, Pf= looO.00 psia, pf,p = 65.072 lb/ft3, p = 1.5430E-01 cP, k = -1.0, pb = 0.116198 lb/ft3

q= O.OOOF, P/= 200.00 psia, P , , ~ = 2.0466 lb/ft3, /i = 1.3520E-02 cP, k = 1.3198, pb = 0.116198 lb/ft3

ïj= 50.00"F, Pf= 500.00 psia, pf,p = 1.6623 ib/ft3, /i = 1.1310E-02 cP, k 1.3622, pb = 0.044210 Ib/ft3

Tf= 150.0O0F, Pf= 1ooO.00 psia, prp = 2.7573 lb/ft3, p = 1.3650E-02 cP, k A 1.3622, pb = 0.044210 lb/ft3

ïj= 140.0O0F, P f = 2000.00 psia, pf,p = 32.465 ib/ft3, /i = 4.1710E-02 cP, k=-l.O, pb = 0.116198 lb/ft3

- Cell falue

-d 1ni

2, Y [CD Cd 7111

Qv Y iCD cd 8 1

Qv Y [CD cd 4,n

Y ICD

- P

-

-

-

Q,

- cd 4ni

Qv Y ICD

cd 4111

Qv Y ICD

cd 4111

Qv Y ICD cd q,n

Y ICD cd 4lli

Qv Y ICE

cd 4ni

Y ICE cd %i

Y ICI

'd q1n Qv Y ICI

-

-

-

QV

-

-

Q"

-

Q"

-

-

AP (inches H,O at 60°F)


.___I_~ - - .~ -. __ A P I MPMS*L4.3.Y 72 H 0732270 0506387 377 =

1 O0 CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT

Table 4-C-5-Selected Round Robin Test Results Matrix-US Units ( Dm = 4.02638 in, a;! = 0.00000620 in/in-OF, dm = 2.66406 in, al = 0.00000925 idin-OF)

Flow Conditions T / = O.OO"F, Pf= 14.696 psia, pf,p = 58.199 Ib/ft3, /.i = 1.8650E+03 cP, k = -1.0, p,, = 56.861 Ib/ft3

T,-= 68.00"F, Pl= 14.696 psia, pl,p = 56.660 lb/ft3, /.i = 2.1220E+02 cP, k = -1.0, pb = 56.861 Ib/ft3

î j= 176.00°F, Pf= 14.696 psia, pfp = 54.214 Iblft', /.i = 1.749OE+Ol cP, k = -1.0, pb = 56.861 Ib/ft3

Tj= 60.00"F, Pf= 14.696 psia, pIp = 62.366 Ib/ft3, p = 1.1990 cP, k = -1.0, p,, = 62.366 Ib/ft3

TJ= 210.00°F, Pf= 14.696 pcia, P , , ~ = 58.792 lb/ft3, p = 2.8250E-01 CP, k = -1.0, pb = 62.366 lb/ft3

ï j= O.OO°F, Pf= 14.696 psia, pf,p = 0.13223 Ib/ft3, /.i = 1.3070502 cP, k = 1.3198,p,, = 0.116198 ib/ft3

ï)= 50.00"F. Pf= 100.00 psia,

k = 1.3622, pb = 0.044210 lb/ft3 = 0.31 109 Ib/ft3, /i = 1.0670E-02 cP,

ï)= O.OO°F, Pf= 1000.00 psia, r ~ ~ , ~ = 65.072 lb/ft3, /.i = 1.5430E-01 ci', t=-l.O,p~=O.l16198Ib/f?

r f = O.OO"F, P f = 200.00 psia,

E.= 1.3198,p~=0.1161981b/ft3 = 2.0466 ib/ft3, p = 1.3520E-02 cP,

r f = 50.00"F, Pf= 500.00 psia,

¿= 1.3622, pi, = 0.044210 ib/ft3 = 1.6623 lb/f?, /.i = 1.1310E-02 cP,

rf= 150.0O0F, Pf= 1000.00 psia, = 2.7573 lb/ft3, /.i = 1.3650E-02 cP,

¿ = 1.3622, p b = 0.044210 Ib/ft3

rf= 140.00°F, Pf= 2000.00 psia,

;=-l .O,pb = 0.1161981b/ft3 = 32.465 lb/ft3, /.i = 4.1710E-02 cP,

Cell Valui - Cd 411,

Qv Y ICD Cd 4111

Q" Y ICD Cd 411,

Qv Y ICD

cd 4111

Qv Y ICD Cd 4in Qv Y ICD cd 4111

Qv Y ICD

Cd 9ni Qv Y ICD

9111

Q" Y [CD

cd %Il

Qv Y [CD

Cd ?Il,

2, Y iCD

I l l ,

Y :CD -d ?ni

-

-

-

-

-

-

- cd

-

-

- cd

2,

- P

2" Y 'CD -

7.55677E-01 2.36993E+04 1.16793E+02 l.OOOOOE+W -3 6.22413E-O 1 2.08877E+04

6.51377E-O 6.12854E+D 1 .O778 1E+O: 1.00000E+O( 3 6.14376E-0 6.18547E+D

3.34022t?+02 9.9 1802B+O: 1 .O(JOOOE+00 I 1 .O(K)Oí)E+O(

5.12804&01 6.08915C-0i 2.00271E+04 5.97006E+& 3.21 122E+02 9.57262E+ü: 1.00000E+00 l.OOOOOE+O( 2 2 5.12707E-01 6.08906E-01 ).437778+02 2.76877EtO: 3.12214B+03 2.38281E+W 9.98004E-01 9.82037E-01 2. 2 5.10255E-O1 6.07381E-01 1.44572E+03 4.30695E+ü: 3.2701 1 E+04 9.74203E+oL 1.997 I6E-01 9.97442E-01 1 2 5.10255E431 6.073788431 1.08943E+04 6.23879E+oL 1.79816E+05 5.3691 IC+O' I .OOí)OoE+oO 1.00000E+O(

j.08253E-01 6.06136E-01 3.69280E+03 1.1027OE+W 3.17802E+04 9.48983E+Oi j.99853E-01 9.98680E-01

n I '

i.08073E-01 I 6.06020E-01

i.07919E-01 L29728E+03 1.720 15E+04 1.99972E-01

9.95399E+O? 2.25152E+05 9.99488E-01

6.05920E-01 1.28466E+04 2.90582E+05 9.99744E-01

.47367E+04 4.40720E+04

.26824E+05 3.79284E+05

.OOOOOE+OO l.OOOOOE+OO

Aí' (inches H,O at 60°F)

56.2110 110.1736 224.8440 ~ 323.1754 440.6943

1.54695E+00 1.39839E+OO 1.26419E+OO 1.20368E+00 1.15635E+OO 2.50453E+05 3.16963E+05 4.09347E+05 4.67705E+05 5.24201E+05 4.40466E+03 5.57434E+03 7.19909E+03 8.22542E+03 9.21898E+03 1.00000E+OO 1.00000E+00 l.OOOOOE+OO l.OOOOOE+OO 1.00000E+00 -5 -5 -5 -5 -4 8.93370E-01 8.35705E-01 7.80664E-01 7.54158E-01 7.32280E-01 1.42906E+05 1.87155E+05 2.49755E+05 2.89530E+05 3.27986E+05 2.51326E+03 3.29145E+03 4.39238E+03 5.09189E+03 5.76821E+03 1.00000E+00 1.00000E+OO 1 .OOOOOE+OO 1.0OOOOE+00 l.OOOOOE+íM -4 -4 -4 -3 -3 6.38819E-01 6.32665E-01 6.27474E-01 6.25242E-O1 6.23542E-01 1.00173E+05 1.38891E+05 1.96788E+05 2.35306E+05 2.73777E+05 1.76172E+03 2.44264E+03 3.46086E+03 4.13826E+03 4.81484E+03 l.OOOOOE+OO 1.00000E+00 1.OoooOE+00 l.OOOOOE+OO l.OOOOOE+OO 3 3 3 3 3 6.11969Eol 6.10683E-01 6.09525E-01 6.09003E-OI 6.08593E-01 1.02687E+05 1.43460E+05 2.04554E+05 2.45255E+05 2.85938E+05 1.64652E+03 2.30029E+03 3.27990E+03 3.93250E+03 4.58483E+03 1.OOOOOE+OO 1.00000E+00 l.OOOOOE+OO l.OOOOOE+OO l.OOOOOE+00 2 2 2 2 2 6.07673Eo1 6.06992501 6.06369E-01 6.06083E-01 6.05858E-01 9.92979E+04 1.38861E+05 1.98170E+05 2.37692E+05 2.77204E+05 1.59218E+03 2.22656E+03 3,17753E+03 3.81 124E+03 4.44479E+03 1.OoooOE+00 1.OoooOE+OO l.OOOOOE+OO l.OOOOOE+OO l.OOOOOE+OO 2 2 2 2 2 6.07740E-01 6.07152E-01 6.06714E-01 6.06599E-01 6.06605E-01 4.45602E+03 5.91818E+03 7.49528E+03 8.00602E+03 7.98010E+03 3.83485E+04 5.09319E+04 6.45044E+04 6.88998E+04 6.86767E+W 9.50104E-01 9.02204E-01 8.00417E-01 7.12600E-01 6.08817E-01

6.06450E-01 6.05941E-01 6.05480E-01 7.13457E+03 9.91 145E+03 1.39405E+04 1.6 1379E+05 2.24 190E+05 3,15324E+05 9.92895E-01 9.86074E-01 9.71580E-01 2 2 2 6.06441E-01 6.05923E-01 6.05447E-01 1.03819E+05 1.45223E+05 2.07298E+05 8.93469E+05 1.24979E+06 1.78401E+06 1.00000E+00 l.OOOOOE+OO 1.00000E+00

1.65076E+04 1.89572E+04 3.73391E+05 4.28798E+05 9.59075E-0 1 9.44296E-O 1

6.05228E-01 6.05055E-01 2.48668E+05 2.9OO30E+05 2.14004E+06 2.49600E+06 1.00000E+OO l.OOOOOE+OO

6.05436E-01 6.05050E-01 6.04695E-01 6.04534E-01 1.83140E+04 2.55327E+04 3.61792E+04 4.31 193E+O4 1.57610E+05 2.19734E+05 3.11358E+05 3.71084E+05 9.96334E-01 9.92814E-01 9.85335E-01 9.78882501 2 2 2 2 6.05340E-01 6.04962E-01 6.04614E-01 6.04454E-01 1.65563E+M 2.31327E+04 3.29316E+04 3.94082E+04 3.74491E+05 5.23245E+05 7.44891E+05 8.91386E+05 9.98579501 9.97215E-01 9.94316E-01 9.91815E-01 2 2 2 2

6.04408E-01 4.99035E+04 4.29469E+05 9.71256E-01 2 6.04328E-01 4.58296E+04 l.O3663E+O6 9.88859501 2

6.05256E-01

9.99289E-01

1 .OOOOOE+OO

6.04887E-01 6.04546E-01 6.04390E-01 6.04266E-01 2.98904E+04 4.26145E+W 5.10600E+04 5.94694E+04 6.761OOE+05 9.63911E+05 1.15494E+06 1.34516E+06 9.98607E-01 9.97157E-01 9.95907E-01 9.94429E-01 2 2 2 2 6.04770E-01 6.04443E-01 6.04292E-01 6.04173E-01 1.02667E+05 1.46588E+05 1.75862E+05 2.05132E+05 8.83553E+05 1.26154E+06 1.5 1347E+06 1.76536E+06 1.00000E+OO l.OOO00E+00 I.OOOOOE+OO 1.00000E+00


A P I f l P f l S * L 4 - 3 . 4 92 0732290 0506388 203

2.2484

SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 4-BACKGROUND 1 o1

20.2360 56.21 10 110.1736

Table 4-C-5-Selected Round Robin Test Results Matrix-US Units (Dm = 7.98146 in, q, = 0.00000620 in/in-"F, d, = 5.28906 in, al = 0.00000925 in/in-"F)

2.69562E+05 4.7407 1E+03 I .00000E+00 -5 I . 10290E+00 I .39 177E+05 2.44767E+03 l.W00E+00 -d

Flow Conditions

5.65561E+05 8.13372E+05 I.O4086E+06 9.94638E+03 1.43046E+04 1.83053E+04 1.00000E+00 1.00000E+00 I .OOOOOE+OO -5 -5 4 8.64632E-01 7.82848E-01 7.33853E-01 3.27333E+05 4.9395 IE+05 6.48252E+05 5.75672E+03 8.68699E+03 I. 14006E+04 1.00000E+00 I .OOOOOE+00 1.OOOOOE+00 L t d -?

T/= 0.00"F. PJ= 14.696 psia,

k = -1.0, PI, = 56.861 Ib/ft3 = 58.199 Ib/ft3, p = 1.8650E+03 cP,

6.65546E-01 8.233 I lE+04 1.44794E+03 1.00000E+00 -3 6.15735E-01 8.15067E+04 1.3069 1E+03 1.00000E+00

ïj=68.WoF, PJ= 14.696 psia,

k =-1.O, PI, = 56.861 Ib/ft' = 56.660 Ib/ft3, p = 2.1220E+02 cP,

6.34768E-01 6.26700E-01 6.22658E-Ö 2.35574E+05 3.87632E+05 5.39184E+05 4.14297E+03 6.8 17 19E+03 9.48250E+03 I .OOOOOE+00 I .00000E+00 1 .OOOOOE+OO 3 3 3 6.10062E-01 6.08307E-01 6.07358E-01 2.42269E+05 4.0262 1E+05 5.62790E+05 3.88464E+03 6.45577E+03 9.02398E+03 l.OOOOOE+ûO 1 .OOOOOE+OO I .00000E+Cû

T/= 176.00°F, PJ= 14.696 psia, pf,p = 54.2 14 lb/ft3, p = I .7490E+O 1 cP, k = -1 .o, pb = 56.861 Ib/ft'

6.08913E-01 7.84944E+04 1.25861E+03 1 .OOO00E+00 2 6.08852E-01 3.69924E+03 3.18357E+04 9.98002E-01 2 6.07041E-O 1 5.67252E+03 1.28308E+05 9.99716E-01

T/= 60.00"F, PJ= 14.696 psia, p,.p = 62.366 Ib/ft3, p = I. 1990 cP, k=-1.0, pl, = 62.366 Ib/ft"

6.06031E-01 6.05094E-01 6.04577E-01 2.3437 1E+05 3.90014E+05 5.45553E+05 3.75800E+03 6.25363E+03 8.74760E+03 l.O0000E+00 I .OOOOOE+OO 1 .OOOO0E+OO 2 2 2 6.06035E-01 6.05155E-01 6.04709E-01 1.08696E+04 1.75010E+04 2.32478E+04 9.35439E+04 1.50613E+05 2.00071E+05 9.82022E-01 9.50061E-01 9.02120E-01 2 2 2 6.0488 1E-01 6.04171E-01 6.03780E-01 1.69186E+04 2.80360E+04 3.89553E+04 3.82686E+05 6.34154E+05 8.81 142E+05 9.97440E-01 9.92889E-01 9.86062E-01

T/= 210.00"F, PJ= 14.696 p i a , pf.p = 58.792 lb/ft', p = 2.8250E-01 cP, k = -1 .o, p h = 62.366 Ib/ft3

9.34158E+05 I .49786E+04 I .00000E+00 2 6.04287E-01 3.14480E+04 2.70641E+05 7.12351E-01 2 6.03266E-01 6.4895 1E+04 1.46788E+06 9.59039E-01 2 6.03233E-01 9.77625E+05 8.41344E+06 1.0CWOE+00 2 6.02696E-01 1.69561E+05 1.45925E+06 9.78864E-01

Tf= O.OO'F, Pi= 14.696 psia, p,.r = 0.13223 lb/ft', p = 1.3070E-02 cP, k = 1.3198,p~=0.1161981b/ft3

1.08954E+06 1.7470 1 E+04 1 .00000E+00 2 6.04292E-01 3.13396E+04 2.69709E+05 6.08478E-01 2 6.03144E-01 7.45282E+04 1.68578E+06 9.44248E-01 2 6.03 1OOE-01 1.1403 1E+06 9.81351E+06 1 .OooOOE+00 2 6.02598E-01 1.96247E+05 1.68890E+06 9.71231E-01

TJ= 50.00"F, PJ= 100.00 psia, pf,p = 0.3 I 109 Ib/ft3, p = 1.0670E-02 cP, k = 1.3622, PI, = 0.044210 Ib/ft3

8.19826E+W 7.05542Et05 I .00(XK)E+W 2 6.05543E-01 I .45012E+04 I .24797E+05 9.99853E-01 2 6.054058-01 1.30802E+04 2.958658+05 9.999438-01 2 6.05283E-01 1.68769E+ü4 3.817448+05 9.999728-01 2 6.05089E-01 5.78822E+04 4.981358+05 1.00000E+00

?I

T/= 0.00"F. PJ= 1ooO.00 psia,

k=- l .O, pb = 0.1161981b/ft3 = 65.072 ib/fe, p = 1.5430E-01 cP, 2.450748+05 4.07974E+05 5.707888+05

2.1091 IE+06 3.51 102E+06 4.912208+06 I .00000E+00 1.00000E+W I .OOOOOli+OC 2 2 2 6.03932E-01 6.03394E-01 6.03096E-0 I 4.33372B+M 7. 19946E+M 1 .üü386E+05 3.729608+05 6.195858+05 8.63925E+05 9.98679E-O1 9.96330E41 9.92808E-01 2 2 2 6.03841E01 6.033178-01 6.03026E-01 3.912188+04 6.50871E+04 9.09533E+04 8.84908B+05 1.47222E+06 2.057308+06 9.99488E-01 9.98578E-01 9.97212E-01 2 2 2 6.03759E-01 6.03248E-O1 6.02963E-01 5.04922E+04 8.40441E+W 1.17526E+05 1.14210E+06 1.90102E+06 2.65835E+06 9.99744E-01 9.99289E-O I 9.986068-01 2 2 2 6.036348-01 6.031451i-01 6.02872E-01 1.7323 I E+05 2.88484E+05 4.036958+05 1.490838+06 2.482698+06 3.47420E+06 I .00000E+00 I .(XXXX)E+OO 1.00000E+ûC ?I e n

T/= 0.00"F, PJ= 200.00 psia, pf = 2.0466 Ib/ft3, /i = 1.3520E-02 cP, k = I.3l98,pb=0.116198 Ib/ft3

2 12 Ti= 50.00"F, PJ= 500.00 psia, pf,p = 1.6623 Ib/ft3, p = 1.131OE-02 cP, k = 1.3622, p,, = 0.044210 Ib/ft3

2

Tf= 150.00"F, PJ= 1OOO.00 psia,

k = 1.3622, PI, = 0.044210 lb/fe = 2.7573 lb/ft3, /i = 1.3650E-02 cP,

6.02698E-O I 1.67577E+05 3.79047E+06 9.97155E-01 -3

T/= 140.0û0F, PI= 2000.00 psia,

k=-1.0, pb = 0.116198 lb/ft3 = 32.465 Ib/ft3, p = 4.1710E-02 cP,

6.02577E-O 1 6.02480E-O 1 2.00799E+05 2.33880E+05 4.54194E+06 5.29021E+06 9.95903E-01 9.94424E-01 ,3 -3

Cell Value

( l n 1

Y QI.

ICD cd

-

%Il

Y ICD

cd 4,ll

Qv Y ICD cd

Q,.

-

_.

QI

Y Q" ICD

4 1

Y ICD

cd %I

Y ICD cd

- Cd

Q,

_.

Q V

-

4 1

Y Q" ICD

cd 4111

Y ICD

-

Q"

-

AP (inches H,O at 60°F) I

2 12 12 12 6.07044E-01 I 6.04881E-01 I 6.04166E-01 I 6.03769E-01

6.83450E-01 8.62469E+05 1.51680E+04 I .OOO00E+OC -3 6.19 I86E-01 7.65968E+05 1.34709E+04 1 .oOoOOE+W 3

;OCWOE+00I ;OOOOOE+COI ;.OOOE+001

6.04100E-01 6.03882E-01 6.03709E-01 7.78747E+05 1.24867E+04 I .OOOOOE+OC 2 6.04375E-01 2.94444E+04 2.53398E+05 8.00244E-01 2 6.03425E-0 1 5.47995E+04 1.23953E+M 9.71555E-01 2 6.03402E-O 1 8.149 16E+05 7.0 13 16E+O6 1.OOOOOE+OC 2 6.0282 1E-0 1 1.42263E+05 1.22431E+Of 9.85322E-01

1.29497E+05 2.929 14E+Of 9.9431 1E-01 n L

L I ' I L 6.02618E-01 I 6.02501E-01 I 6.02408E-O1


----_ __ - A P I MPMS*L4.3.4 92 m 0732290 0506389 L4T m


Table 4-C-5-Selected Round Robin Test Results Matrix-US Units ( Dm = 14.31 154 in, c+ = 0.00000620 in/in-"F, d, = 9.47657 in, al = 0.00000925 in/in-OF)

Flow Conditions

T/= O.OO"F, P f = 14.696 psia, pip = 58.199 lb/ft3, p = 1.8650E+03 ci', k = -1.0, p1, = 56.861 lb/ft3

Tf= 68.0û0F, P f = 14.696 psia, pi,p = 56.660 lb/ft3, p = 2.1220E+02 cP, k = -1.0, pb = 56.861 lb/ft3

T/= 176.0O0F, P f = 14.696 psia, pt,p = 54.214 lb/ft3, p = 1.749OE+Ol cP, k = -1.0, pb = 56.861 Ib/ft3

T/= 60.00"F, P f = 14.696 psia, pf,p = 62.366 Ib/ft3, p = 1.1990 cP, k = -1.0, pb = 62.366 lb/ft3

r/= 210.OO0F, P f = 14.696 psia, pi,p = 58.792 lb/ft3, p = 2.8250E-01 cP, k = -1.0, PI, = 62.366 lb/ft3

T/= O.OO"F, Pf= 14.696 psia, pf,p = 0,13223 lb/ft3, p = 1.3070E-02 cP, k = 1.3198,p,=o.1161981b/ft3

ïj= 50.00"F, Pj= 100.00 psia,

k = 1.3622, = 0.31 109 lb/ft3, p = 1.0670E-02 cP,

= 0.044210 lb/ft3

TJ-= 0.00OF, P f = 1OOO.00 psia, o , , ~ = 65.072 lb/ft3, p = 1.5430E-01 cP, k=-i.û,pb=0.1161981b/ft3

TJ-= 0.00'F, P f = 200.00 psia,

k = 1.3198,pb= 0.1161981b/ft3 = 2.0466 Ib/ft3, p = 1.3520E-02 cP,

Tj= 50.Cû°F, P f = 500.00 psia, gf,p = 1.6623 lb/f$, p = 1.1310E-02 cP, k = 1.3622, pb = 0.044210 lb/ft3

r f= 150.0O0F, P f = 1000.00 psia,

i = 1.3622, pb = 0.044210 lb/ft3 = 2.7573 lb/ft3, p = 1.3650E-02 cP,

r/= 140.00°F, Pj= 2000.00 psia,

c = -1.0, pb = 0.1 16198 lb/ft3 = 32.465 lb/ft3, p = 4.1710E-02 cP,

Cell Value

cd

Qv 4m

Y ICD cd 4"l Qv Y ICD cd 4,li

Y ICD cd 4111

QV Y ICD

4111

Y ICD cd 4.1 Qv Y ICD

cd 4tli

Y ICD

4111

Y ICD cd 4111

Qv Y ICD

411,

Y ICD

4111

Y ICD cd 9111

Qv Y ICD

-

-

Q"

-

- cd

Qv

-

-

Q,

- cd

Q"

-

- cd

Qv

- cd

Qv

-

-

AP (inches H20 at 60°F)

2.2484 1 20.2360 I 56.2110 I 110.1736 I 224.8440 I 323.7754 I 440.6943

1.73701E+00 1.24988E+00 1.09486E+00 1.01075E+W 7.1 1957E+05 1.53689E+06 2.24378E+06 2.89998E+06 1.25210E+04 2.70289E+04 3.94609E+04 5.10013E+04 l.OOOOOE+OO 1.00000E+00 l.OOOOOE+OO l.OOOOOE+OC -5 -5 4 4 9.63376E-01 7.72226E-01 6.99061E-01 6.63303E-01 3.90136E+05 9.38 188E+05 1.41550E+06 1.88033E+M 6.86122E+03 1.64997E+04 2.48940E+04 3.30689E+04 l.OOOOOE+OO 1.00000E+00 1.00000E+ûO l.OOOOOE+OO 4 d -? -?

9.34104E-01 3.82868E+06 6.73340E+04 l.OOOOOE+OC -4 6.50969E-01 2.63624E+06 4.63628E+04 l.OOOOOE+OC ?

I ' I - I - l -

6.46078E-01 6.25380E-01 6.19757E-01 6.16885E-O1 6.14382E-01 2.56482E+05 7.44804E+05 1.23018E+06 1.7 1427E+06 2.43902E+M

8.99056E-01 8.71263E-01 4.42204E+06 4.99956E+Of 7.77692E+04 8.79259E+OL 1.00000E+00 l.OOOOOE+O( -4 -4 6.45788E-01 6.41900E-01 3.13830E+06 3.63931E+Of 5.51925E+04 6.40037E+oL 1.00000E+00 l.OOOOOE+O( 3 3 6.13279E-01 6.12425E-01 2.92157E+06 3.40375E+Of 5.13809E+û4 5.98609E+oL l.OOMH)E+OO 1.OOO00E+O( 2 2 6.O454 1 E-0 1 6.04300E-0 1 3.08175E+06 3,59394E+N 4.94140E+04 5.76266E+OL l.OOOOOE+OO l.OOOOOE+O(

6.06716E-01 6.04479E-01 6.03742E-01 6.03333E-01 6.02955E-01 2.50990E+05 7.50201E+05 1.24881E+06 1.74715E+06 2.49436E+06 4.02447E+03 1.20290E+04 2.00239E+04 2.80144E+04 3.99955E+04 l.O0000E+00 1 .OOOOOE+OO 1 .OOOOOE+OO l.OOOOOE+OO 1 .OOOOOE+OC 2 2 2 2 2 6.06676E-01 6.04488E-01 6.03797E-01 6.03444E-01 6.03180E-01 1.18289E+04 3.47933E+04 5.60381E+04 7.44528E+04 9.43142E+04 1.01800E+05 2.99431E+05 4.82264E+05 6.40741E+05 8.11668E+05 9.98003E-01 9.82030E-01 9.50083E-01 9.02162E-01 8.00330E-01

6.02781E-01 2.99237E+M 4.79808E+04 l.OOOOOE+OC 2 6.03110E-01 l.O0742E+O5 8.66982E+05 7.12475E-01

2 6.02644E-01 3.49030E+Of 5.59648E+3+04 1 .OOOOOE+O( 2 6.03114E-01 l.O0405E+O~ 8.64082E+05 6.08647E-01

6.05273E-01 6.03578E-01 6.03016E-01 6.02706E-01 6.02423E-01 6.02296E-01 1.81508E+04 5.41770E+04 8.97994E+04 1.24791E+05 1.75569E+05 2.07926E+05 4.10559E+05 1.22545E+06 2.03120E+06 2.82269E+06 3.97124E+06 4.70314E+06 9.99716E-01 9.97441E-01 9.92892E-01 9.86068E-01 9.71567E-01 9.59057E-01 2 2 2 2 2 2 6.05277E-01 6.03580E-01 6.03014E-01 6.02698E-01 6.02406E-01 6.02271E-01 2.62327E+05 7.84784E+05 1.30674E+06 1.82849E+06 2.61085E+06 3.13232E+06 2.25759E+06 6.75385E+06 1.12458E+07 1.57359E+07 2.24690E+07 2.69568E+07 1.OOOOOE+00 1 .00000E+00 1.00000E+00 l.OOOOOE+OO 1 .OOOOOE+00 l.OOOOOE+W

4.1878 1E+04

9.99943E-01

6.02828501

9.98680E-01

9.99488E-01

9.96332E-01

6.02336E-01

9.98578E-01

6.02198E-01 2.38802E+05 5.40 153E+Ot 9.44272E-01 2 6.02 164E-0 1 3.65373E+M 3.14440E+05 l.OOOOOE+OC

6.02161E-01 6.01941E-01 6.01841E-01 6.01762E-01 3.21655E+05 4.55877E+05 5.43378E+05 6.28917E+05 2.76816E+06 3.92328E+06 4.67631E+06 5.41246E+Of 9.9281 lE-01 9.85328E-01 9.78873E-01 9.71243E-01 2 2 2 2 6.02103E-01 6.01887E-01 6.01787E-01 6.01709E-01 2.91435E+05 4.14976E+05 4.96636E+05 5.77605E+05 6.59206E+06 9.38647E+06 1.12336E+07 1.30650E+07 9.97214E-01 9.94313E-01 9.9181 1E-01 9.88854E-01

2 6.03740E-01 I 6.02586E-01 I 6.02196E-01 1.853378+05 5.549558+05 9.243268+05 1.59501 E+06 4.77595B+06 7.95475E+06

6.02049E-01 6.01838E-01 6.01740E-01 6.01663E-01 3.76585E+05 5.37008E+05 6.43496E+05 7.49535E+05 8.5 1809E+06 1.21467E+07 1.45554E+07 1.69540E+07 9.98607501 9.97156E-01 9.95905E-01 9.94426E-01 2 2 2 2 6.01977E-01 6.01774E-01 6.01680E-01 6.01605E-01 1.29359E+06 1.84736E+06 2.21648E+06 2.58557E+06 1.1 1326E+07 1.58983E+07 1.90750E+07 2.22514E+07

1.00000E+00 l.OOOOOE+OO 1.OOOOOE+OO l.OOOOOE+OO l.OOOOOE+ûO 1.00000E+00 1.00000E+00 2 2 2 2 2 2 2


SECTION %CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 4-BACKGROUND 103

2.2484 .39324E+00 !.40880E+ffi L23629E+04 .OOOOOE+OO -5 1.3 1308E-01 I .42OO6E+06 !.49742E+04 I .OOOOOE+OO 4 i.30862E-0 1 i.O5641E+ffi I .85788E+M I .OOOOOE+OO % 3.08688E-01 1.09070E+06 1.74887E+04 I .OOOOOE+00 1 3.04985E-01 I.O5570E+(M 1.69274E+04 1.00000E+00 i 5.04963E-01 3.97556E+04 $.28196E+05 3.98003E-01 L 5.03924E-01 7.63926E+04 1.72795E+06 9.99716E-01 2 5.03929E-01 1.10408E+06 9SOI67E+06 l.OOOOOE+00 2

Table 4-C-5-Selected Round Robin Test Results Matrix-US Units ( Dm = 29.37598 in, g = 0.00000620 in/in-"F, d, = 19.46094 in, al = 0.00000925 idin-OF)

20.2360 56.21 10 110.1736 224.8440

1.04244E+OO 9.29760E-01 8.67347E-01 8.0861 1E-01 5.40693E+06 8.03745E+06 1 .O497 I E+07 1.39803E+07 9.50903E+04 1.4 1353E+05 1.846 10E+05 2.45868E+05 1 .OOOOOE+OO 1 .OOOOOE+00 I .00000E+OO 1.00000E+00 4 -4 -4 -4 6.69662E-O 1 6.50267E-O 1 6.4 13 14E-0 1 6.33857E-O 1 3.43 182E+ffi 5.55405E+06 7.66861E+06 1.08278E+07 6.03546E+04 9.76776E+04 1.34866E+05 1.90425E+05 l.OM)OOE+OO 1 .OOMH)E+00 1 .OOOOOE+OO 1 .OOOOOE+OO -3 3 3 3 6.178 16E-0 1 6.14102E-0 1 6.12 163E-O 1 6.1 O445E-01 3.10371E+06 5.14176E+06 7.17573E+06 1.02223E+07 5.45842E+M 9.04268E+O4 1.261 98E+05 1.79777E+05 1 .OOOOOE+00 1 .OOOOOE+OO 1 .OOOOOE+OO 1.00000E+00 3 2 2 2 6.05638E-01 6.04651E-01 6.04107E-01 6.03607E-01 3.25573E+06 5.41737E+ffi 7.57750E+06 1.08160E+07 5.22037E+04 8.68642E+04 1.21501E+05 1.73428E+05 1 .OOOOOE+00 1 .OOOOOE+00 l.OOOOOE+OO 1.00000E+00 2 2 2 2 6.03326E-01 6.02772E-01 6.02463E-01 6.02177E-01 3.15844E+06 5.25922E+06 7.35914E+06 1 .O508 1E+07 5.06436E+04 8.43284E+04 1.17999E+05 1.68490E+05 l.O0000E+OO 1.OoooOE+00 l.OOOOOE+OO I.OOOOOE+OO 2 2 2 2 6.03340E-01~ 6.02821E-01 6.02555E-01 6.02354E-01 1.46484E+05 2.35993E+05 3.13582E+05 3.97262E+05 1.26065E+06 2.03095E+ffi 2.69869E+06 3.41884E+06 9.82025E-01 9.5OO69E-O 1 9.02 135E-0 1 8.OO276E-O 1 2 2 2 2 6.02654E-01 6.02229E-01 6.01993E-Ql 6.01777E-01 2.28178E+05 3.78294E+05 5.25764E+05 7.39778E+05 5.16123E+06 8.55674E+06 1.18924E+07 1.67333E+07 9.97440E-01 9.92890E-01 9.86064E-01 9.71560E-01 2 2 2 2 6.02657E-01 6.02229E-01 6.0 1989E-01 6.01766E-01 3.30529E+06 5.50489E+06 7.70377E+06 1.10013E+07 2.84453E+07 4.73751E+07 6.62987E+07 9.46773E+07 1.OOOOOE+00 1.00000E+00 1.OOOOOE+00 l.OOOOOE+OO 2 2 2 2

:low Conditions rf= O.ûO"F, PJ= 14.696 psia, J ~ , ~ = 58.199 lb/ft3, p = 1.8650E+03 cP, : = -i .o, pr> = 56.861 Ib/ft3

1 i.09679E-O 1 1.225 13E+07 3.15461E+05 I .00000E+00 3 j.03378E-01 I .29743E+07 !.08035E+05 I .00000E+00 ! 3.02045E-01 I .26069E+07 Z.O2144E+05 I .00000E+00

rf= 68.00°F, Pf= 14.696 psia, J,,p = 56.660 Ib/ft3, g = 2.1220E+02 cP, i = -1.0, pr> = 56.861 Ib/ft3

3 6.09082E-0 1 I .42792E+07 2.51 125E+05 1.00000E+OO 2 6.03197E-01 1.5 1322E+07 2.42635E+05 1.00000E+00 2 6.01940E-01 1.47055E+07 2.35793E+05 1.00000E+00

7j= 176.OOoF, Pf= 14.696 pia, 3,,p = 54.2141b/ft3, /i= 1.749OE+O1 cP, 'C=-l.O, ph = 56.861 Ib/ft3

1.243298+05 3.65 1788+06 7.123988431 2 5.0168OE-O1 3.76159E+05 1.98 I8 I8+07 J.59046E-ü I 2 5.016638-01 1.3 1993E+07

1.00000E+00 2

I . 13593~+08

i')= 60.00°F, PI= 14.696 psia, L + ~ = 62.366 Ib/ft3, p = 1.1990 cP, k = -1.0. pb = 62.366 ib/ft3

4.228828+05 3.639328+06 6.085428-01 2 6.OI605E-01 1.006308+06 2.276 I8E+07 9.442578-0 I 2 6.0 I58 I E 4 1 1.5397 I E+07

I .OoooOD+OC 2

I .3250w+oa

r/= 210.00"F, Pf= 14.696 psia, o , , ~ = 58.792 Ib/ft3, p = 2.8250E-01 cP, k = -1 .O, p,, = 62.366 Ib/ft3

r f = 0.00"F, P'= 14.696 psia, o , , ~ = 0.13223 Ib/ft3, p = 1.3070E-02 cP, k = 1.3198, pr> = 0.116198 ib/ft3

r/= 50.00°F, Pf= 100.00 psia, = 0.31109 lb/ft3, = 1.0670E-02 cP,

k = 1.3622, pr> = 0.044210 Ib/ft3

Tf= O.OO"F, Pf= 1000.00 psia,

k=-1.0, pr> = 0.116198 Ib/ft3 = 65.072 lb/ft3, p = 1.5430E-01 cP,

Tf= O.OO"F, Pf= 200.00 psia, pt,p = 2.0466 lb/ft3, p = 1.3520E-02 cP, k = i.3i98,p6 = 0.116198 Ib/ft3

Tf= 50.00"F, Pf= 500.00 psia, pr,p = 1.6623 lb/f$, p = 1.1310E-02cP, k = 1.3622, p,, = 0.044210 lb/f$

ïj= 15O.OO0F, Pf= 1000.00 psia, pCp = 2.7573 lb/f?, p = 1.3650E-02 cP, k = 1.3622, pr> = 0.044210 lb/ft3

ïj= 140.WQF, PJ= 2000.00 psia, P,,~ = 32.465 lb/ft3, /i = 4.1710E-02 cP, k=-1.0, pr> = 0.116198 ib/ft3

Cell lalue

-d

- "

Li 2, Y [CD c, b 2, Y [CD Cd 7tii

Qv Y [CD

c, B Qv Y [CD Cd "Is1

Qv Y ICD cd %li

Qv Y ICD cd e,, Q" Y ICD c, e,, Qv Y ICD c, en Qv Y ICD

cd 9tli

Y ICD cd %,i

Qv Y ICD cd 4rri Qv Y ICD

-

-

-

-

-

-

-

-

-

Q,

-

-

-

Aí' (inches H20 at 60°F)

6.0305 1E-0 1

9.99972E-01

6.01761E-01 6.01578E-01 6.01410E-01 9.7 1928E+05 1.35548E+O6 1.92 126E+ffi 8.36441E+06 1.16652E+07 1.65344E+07 9.96331E-01 9.92809E-01 9.85324E-01 2 2 2 6.01711E-01 6.01533E-01 6.01367E-01 8.78715E+05 1.22816E+06 1.74892E+06 1.98759E+O7 2.77800E+07 3.95594E+07 9.98578E-01 9.97213501 9.94312E-01 2 2 2 6.0 1663E-O 1 6.0 1488E-O 1 6.0 1326E-01 1.13469E+06 1.58702E+06 2.26326E+06 2.56658E+07 3.58972E+07 5.1 1934E+07 9.99289E-01 9.98606E-01 9.97155E-01

323.7754 1 440.6943 '.80737E-01 .6 198 1E+07 !.84872E+05

.29283E+O7 !.27367E+05

7.57973E-01 1.83468E+07 3.22660E+05 1 .OOOOOE+00 -3 6.28288E-01 1.50257E+07 2.64253E+05 1.00000E+00

6.01291E-01 2.093 16E+06

9.91809E-01

2.7 1217E+06

9.95904E-01

6.01230E-01 2.43449E+Of 5.50665E+O; 9.8885 1E-01 2 6.01191E-01 3.159 18E+OI 7.145 85E+O; 9.94425E-01



4.00107E+00 4.1871 lE+04 7.36376E+02 1.00000E+00 -6

Table 4-C-5-Selected Round Robin Test Results Matrix-US Units (Dm = 1.93945 in, g = 0.00000620 in/in-"F, d, = 1.45311 in, al = 0.00000925 in/in-"F)

2.63642E+00 2.19651E+oC 8.27710E+04 1.14933E+O: 1.45567E+03 2.02130E+O? 1.00000E+00 l.OOOOOE+OC 4 4

Flow Conditions

Tf= 0.00'F, Pf= 14.696 psia, P, ,~ = 58.199 lb/ft3, /.i = 1.8650E+03 cP, k = -1.0, pb = 56.861 lb/ft3

1.64096E+00 2.06072E+05 3.62414E+03 l.OOOOOE+IH) -5 9.02520E-01 1.1 1993E+05 1.96959E+03 1.00000E+00 -4 6.41953E-01 7.81003E+04 1.37353E+03 l.OoooOE+OO 3 6.13618E-01 7.98716E+04 1.28069E+03 l.OOOOOE+OO 2 . 6.08437E-01 7.71405E+04 1.23690E+03 l.OOOOOE+OO 2 6.09487E-01 2.50490E+03 2.15571E+04 6.86586E-01 2 6.06999E-01 5.33003E+03 1.20562E+05 9.55369E-01 2 6.06910E-01 8.059 1OE+04 6.93567E+05 1.OOOOOE+00 2 6.05653E-01 1.39343E+04 1.19919E+05 9.76970E-Ol 2 6.05502E-01 1.27498E+04 2.88392E+05 9.91074E-01 2 6.05377E-01 1.65264E+04 3.738 16E+05 9.95536E-01 2

Tf= 68.OO0F, Pf= 14.696 psia, P , ~ = 56.660 lb/ft3, p = 2.1220E+02 cP, k k -1.0, pb = 56.861 lb/ft3

1.56365E+00 2.29092E+05 4.02898E+03 l.OOOOOE+OC -5 8.67927E-01 1.25650E+05 2.20978E+03 1.00000E+OC -4 6.38957E-01 9.06917E+04 1.59497E+03 1.OOOOOE+OO 3 6.12898E-01 9.30743E+04 1.49239E+03 1.00000E+00 2 6.08033E-01 8.99375E+04 1.44209E+03 l.OOOM)E+OO 2 6.09568E-01 2.44098E+03 2.10070E+04 5.73409E-01 2 6.06714E-01 6.1 1060E+03 1.3821 8E+05 9.39252E-01 2 6.06597E-01 9.39743E+04 8.08743E+05 1.00000E+00 2 6.05423501 1.61 123E+04 1.38662E+05 9.68654E-01 2 6.05273E-01 1.48208E+04 3.35236E+05 9.87850E-01 2 6.05151E-01 1.92424E+04 4.35249E+05 9.93924E-01 2

r f = 176.0OoF, Pf= 14.696 psia, P,,~ = 54.214 ib/ft3, /.i = 1.7490E+01 cP, k = -1.0, pb = 56.861 lb/ft3

1.82233E+OO 1.88441E+04 3.31406E+02 1.00000E+00 -5 9.04948E-01 9.17462E+03 1.61352E+02 l.OOOOOE+OO -4 6.36984E-01 6.90936E+03 1.10787E+02 I.OOOOOE+ûû

Tf= 60.00'F, Pf= 14.696 psia, P , , ~ = 62.366 lb/ft3, /.i = 1.1990 cP, k = -1.0, p1, = 62.366 lb/ft3

1.30067E+00 1.13011E+O( 4.03498E+04 5.84306E+04 7.09622E+02 1.02760E+02 1.00000E+OO l.OOOOOE+OC -5 -4 6.89114E-01 6.66239E-01 2.09595E+04 3.37729E+04 3.68609E+02 5.93955E+02 1.OOOOOE+00 l.OOOOOE+OC 4 3 6.22975E-O1 6.18795E-01 2.02724E+04 3.35606E+04 3.25056E+02 5.38123E+02 1.OOOOOE+OO 1.00000E+OC

7j= 210.0OoF, Pf= 14.696 p i a , P , ~ = 58.792 Ib/ft3, /.i = 2.8250E-01 cP, k k -1.0, p1, = 62.366 lb/ft3

6.20084E-01 3.08638E+02 2.656 14E+03 9.97824E-01 3 6.15810E-01 4.71518E+02 1.06654E+04 3.99690E-01 2 5.15815E-01 5.81439E+03 5.86447E+04 l.OOOOOE+OO

Tf= 0.00'F, Pf= 14.696 p i a , P, ,~ = 0.13223 lb/ft3, /.i = 1.3070E-02 cP, k = 1,3198, pb = 0.116198 Ib/ft3

6.13460E-01 6.11418E-01 9.00047E+02 1.44198E+03 7.7458 1E+03 1.24097E+O4 9.80412E-01 9.45588E-01 2 2 6.10761E-01 6.09106E-01 1.39949E+03 2.31459E+03 3.16555E+04 5.23545E+04 9.97211E-01 9.92251E-01 2 2 6.10758E-01 6.09091E-01 2.02755E+04 3.37002E+04 1.74491E+05 2.90024E+05 1.00000E+00 l.O0000E+Oa .l .l

Tf= 50.00'F, Pf= 100.00 pia, P , , ~ = 0.31109 ib/ft3, /.i = 1.0670E-02 cP, k = 1.3622, pb = 0.044210 lb/ft3

1.20142E+03 1.03394E+04 3.99840E-01 2 5.11984E-01 1.08345E+03 1.45070E+04 3.99938E-01 1 5.1 1705E-01 1.39778E+03 3.16 168E+04 3.99969E-01 1 5.11251E-01 $.79185E+03 $.12386E+M l.OOOOOE+00 1

Tf= O.OO°F, Pf= 1000.00 psia, P , , ~ = 65.072 Ib/ft3, /.i = 1.5430E-01 cP, k = - l . O , p b = 0.1161981b/ft3

3.57758E+03 5.93506E+03 3.07886E+04 5.10771E+04 9.98561E-01 9.96002E-01 2 2 6.08334E-01 6.071 1OE-01 3.22941E+03 5.36618E+03 7.30470E+04 1.21379E+05 9.99442E-01 9.98450E-01 2 2 6.08147E-01 6.06952E-01 4.16795E+03 6.92949E+03 9.42763E+04 1.56740E+05 9.99721E-01 9.99225E-01 2 2 6.07855E-01 6.06711E-01 1.42958E+04 2.37815E+04 1.23030E+05 2.04664E+05 l.OOOOOE+OO 1.00000E+OO 2 2

lj= O.OO°F, Pf= 200.00 psia, pbp = 2.0466 lb/ft3, /.i = 1.3520E-02 cP, k = 1.3198, pb = 0.116198 lb/ft3

r f = 50.00'F, P f = 500.00 psia, P,,~ = 1.6623 lb/ft3, /.i = 1.1310E-02 cP, k = 1,3622, p1, = 0.044210 lb/ft3

r f = 150.00"F, P f = 1000.00 psia, P,,~ = 2.7573 lb/ft3, p = 1.3650E-02 cP, k = 1.3622, pb = 0.044210 Ib/ft3

ïj= 140.00°F, Pj= 2000.00 psia,

k = -1.0, pb = 0.116198 lb/ft3 = 32.465 lb/ft3, /.i = 4.1710E-02 cP,

- Cell

Value

cd 4111

Qv Y ICD cd %Il

Qv Y ICD cd 4111

Y ICD

cd 9,n Qv Y ICD

4n1

Y ICD cd %i

Qv Y ICD cd 4111

Qv Y ICD

cd 4 1

Qv Y ICD cd %Il

Qv Y ICD

'd %Il

Qv Y ICD cd 4111

Qv Y íCD

cd B Qv Y [CD

-

-

Q"

-

- cd

Q"

-

-

-

-

-

-

-

AP (inches H,O at 60°F)

2.2484 I 20.2360 I 56.2110

3 13 ( 2 G.20235E-01 ~6.134548-01~6.11266E41

L I ' I' 5.12304E-01 I6.085458-01 I 6.072888-01

110.1736

1.95699E+0( 1.4336OE+O' 2.52124E+O? l.OOOOOE+O( -5 1.03488E+O( 7.49101E+oL 1.3 1743E+O: l.OOOOOE+OC 4 6.55156501 4.64955E+oL; 8.17705E+Oi l.OOOOOE+O( 3 6.16557E-01 4.68 149E+04 7.50648E+Ol 1 .OOOOOE+O( 2 6.10059E-01 4.51186E+04 7.23449E+02 1 .OOOOOE+OC 2 6.10391E-01 1.90405E+01 1.63862E+M 8.93352E-01 2 6.08 196E-0 1 3.21133E+03 7.26381E+04 9.848 13E-01 2 6.08164E-01 4.71085E+3+04 4.05416E+05 l.OOOOOE+OC 2 6.06589E-01 8.26754E+03 7.11504E+3+04 9.92164E-01 2 6.06426E-01 7.49301E+03 1.69487E+05 9.96963E-01 2 6.06283E-01 9.68339E+03 2.19032E+05 9.98481E-01 2 6.06071E-01 3.32589E+04 2.86226E+05 l.OOOOOE+OO 2

224.8440 - 1.73948E+0( 1.82038E+O: 3 -20 145E+O: 1 .OOOOOE+O( -5 9.45054E-O I 9.77256E+& 1.71867E+O: l.OOOOOE+o( 4 6.45902E-01 6.54839E+& 1.15165E+O: I.OOOOOE+O( 3

6.14534E-01 6.66591E+oL I.O6884E+O: l.OOOOOE+O( 2 6.08947E-01 6.43377E+3+04 1 .O3 16 1 E+OT 1 .OOOOOE+O( 2 6.09649E-01 2.3792OE+O: 2.04754E+Of 7.82351E-01 2 6.07369E-01 4.50784E+O? 1.01964E+O! 9.69006E-01 2 6.07306E-01 6.72029E+04 5.78349E+O! 1.OOOOOE+OC 2 6.05946E-01 1.17013E+3+04 1 .OO701E+05 9.84007E-01 2 6.05793E-01 1.06592E+04 2.41104E+05 9.93801E-01 2 6.05663E-01 1.37974E+04 3.12087E+05 9.96900E-01 2 6.05475E-0 1 4.74660E+O4 4.08493E+05 1.00000E+OC 2

323.7754 I 440.6943 I


API MPMS*14-3-4 92 W 0732290 0506392 734 W

2.2484 3.44032E+00 8.03890E+04 1.41378E+03 1.00000E+00 4 1.60637E+00 3.70896E+04 6.52285E+02 1.00000E+00

SECTION %CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 4-BACKGROUND 105

20.2360 56.21 10 110.1736

2.29 147E+00 1.92130E+00 1.7 1974E+OC 1.60634E+05 2.24475E+05 2.81295E+05 2.82503E+03 3.94778E+03 4.94706E++63 1.00000E+00 1.00000E+00 1.00000E+OC -6 -5 -5 1.16515E+00 1.01822E+OO 9.34395E-01 8.07079E+04 1. 17550E+05 1.5 1022E+05 I .41939E+03 2.06732E+03 2.65598E+03 1.00000E+00 1.00000E+00 1.00000E+W

Table 4-C-5-Selected Round Robin Test Results Matrix-US Units ( Dm = 2.90039 in, Q = 0.00000620 in/in-"F, d, = 2.1 71 89 in, al = 0.00000925 in/in-"F)

6.3 I9 I7E-01 1.7 l660E+05 3.01893E+03 1.00000E+00

Flow Conditions T/= 0.00"F, Pf= 14.696 psia, pi,p = 58.199 Ib/ft3, j i = 1.8650E+03 cP, k = -1.0, pb 56.861 Ib/ft3

6.29522E-01 1.995 1 1 E+05 3.50874E+03 1 .OOOOOE+00

T/= 68.00"F, P'= 14.696 psia, = 56.660 Ib/ft3, p = 2.1220E+02 cP,

k=-l.O,Pb = 56.861 Ib/ft3

6.27946E-01 1.52087E+04 2.43861E+02 l.OOOOOE+OO 3 6.14197E-01 1.44843E+04 2.32328E+02 1.00000E+00 2 6.14089E-01 6.82480E+02 5.87342E+03 9.97825E-01 2 6.10484E-01 1.04372E+03 2.36083E+04 9.99690E-01 2 6.10492E-01 1.50840E+04 1.29813E+05 1.00000E+OO

~~

T/= i76.Oo0F, Pf= 14.696 psia, pf,,, = 54.214 Iblft', p = 1.749OE+Ol cP, k=-1.0, pb = 56.861 Ib/ft3

6.16496E-01 6.13002E-01 6.11115E-01 6 . 0 9 4 0 0 m 4.47945E+04 7.42343E+04 1.03608E+05 1.47596E+05 7.18252E+02 1.19030E+03 1.66129E+03 2.36661E+03 1.00000E+00 1.00000E+00 1 .OOO00E+00 1.00000E+OC 3 2 2 2 6.08468E-01 6.06599E-01 6.05564E-01 6.04609E-01 4.30630E+04 7.15511E+04 1.00001E+05 1.42633E+05 6.90488E+02 1.14728E+03 1.60345E+03 2.28703E+03 1 .OOO00E+00 1.00000E+00 1.00000E+00 1.00000E+OC 2 2 2 2 6.08492E-01 6.06748E-01 6.05868E-01 6.0523 1E-01 1.99341E+03 3.19522E+03 4.22019E+03 5.27458E+03 1.71553E+04 2.74980E+04 3.63189E+04 4.53930E+04 9.80421E-01 9.45613E-01 8.93402E-01 7.82452E-01 2 2 2 2 6.06181E-01 6.04760E-01 6.03976E-01 6.03264E-01 3.10142E+03 5.13 128E+03 7.12072E+03 9.99745E+03 7.01520E+04 1.16066E+05 1.61066E+05 2.26136E+05 9.97212E-01 9.92255E-01 9.84820E-01 9.69020E-01 2 2 2 2 6.06183E-01 6.04751E-01 6.03954E-01 6.03214E-01 4.4933 IE+04 7.471 15E+04 1 .O4458E+05 1.49043E+05 3.86694E+05 6.42967E+05 8.98967E+05 1.28267E+06 I.OOOOOE+OO 1.00000E+00 1.00000E+00 l.OOOOOE+OC

T/= 60.00"F, P/= 14.696 psia, pf,p = 62.366 Ib/ft3, p = 1.199OcP, k = -1.0, pb = 62.366 Ib/ft3

1.76889E+05 2.83631E+03 1.00000E+00 2 6.04170E-01 1.71035E+05 2.74244E+03 l.OOOOOE+OO 2 6.05091E-01 5.55390Et.03 4.77969E+04 6.86732E-01 2 6.02944E-01 1.18219E+M 2.67404E+05 9.55389E-01

T/= 210.00"F, Pf= 14.696 psia, p f p = 58.792 Ib/ft3, p = 2.8250E-01 cP, k L -1.0, pb = 62.366 Ib/ft3

2.06162E+05 3.30569E+03 1.00000E+00 2 6.03822E-01 1.99426E+05 3.19767E+03 I.OOOOOE+00 2 6.05 16 1E-01 5.41280E+03 4.65825E+04 5.73607E-01 2 6.02699E-O 1 1.35542E+O4 3.06586E+05 9.39280E-01

T/= 0.00"F, P/= 14.696 psia, = O. 13223 Ib/ft3, p = 1.3070E-02 cP,

k = 1.3198,~b=0.1161981b/ft3

2 6.0428 1E-01 7.93224E+03 6.82649E+04 9.98561E-01 2 6.04096E-01 7.16055E+03 1.61967E+05 9.99442E-01

TJ= 50.00"F.. Pf= 100.00 psia, pf,p = 0.31 IO9 lb/ft3, p = 1.0670E-02 cP, k = 1.3622, pb = 0.044210 Ib/ft3

2 2 2 6.03199E-01 6.02595E-01 6.02040E-01 1.31629E+04 1.83387E+04 2.59589E+04 1.13280E+05 1.57823E+05 2.23403E+05 9.96004E-01 9.92167E-01 9.84015E-01 2 2 2 6.03040E-01 6.02451E-01 6.01904E-01 1.19016E+04 1.66211E+04 2.36477E+04 2.69205E+05 3.75958E+05 5.34895E+05 9.98451E-01 9.96964E-01 9.93804E-01

T/= 0.00"F, P/= 1000.00 psia, P,,~ = 65.072 Ib/ft3, p = 1.5430E-01 cP, k=-í.û,pb = 0.i161981b/ft3

T/= O.OO"F, P/= 200.00 psia, pf,+ = 2.0466 Iblft', j i = 1.3520E-02 cP, k = I.3198,pb= 0.1161981b/ft3

Tf= 50.00"F, P'= 500.00 psia, pf,p = 1.6623 ib/ft3, p = 1.1310E-02 cP, k = 1.3622, pb = 0.044210 Ib/ft3

T/= 150.000F, Pf= 1000,00psia, pf,p = 2.7573 ib/ft3, p = 1.3650E-02 cP, k = 1.3622, pb = 0.044210 lb/ft3

ïj= 140.00"F, Pf= 2000.00 psia, pf,p = 32.465 lb/ft3, p = 4.1710E-02 cP, k=-í.O,pb= 0.116198 ib/ft3

Cell Value

cd

-

9111 Q, Y ICD Cd 4111

QV

Y ICD

4111

Y ICD

cd 4111

Y ICD

cd %,I

Qv Y ICD Cd 4111

Qv Y ICD cd 9111

Q" Y ICD Cd 4111

Qv Y ICD cd 4ili

Qv Y ICD cd 4m Qv Y ICD

4ltl

Y ICD

4 m

Y ICD

-

- cd

QV

-

QV

_.

-

-

-

-

-

- cd

Qv

- cd

Qv

-

A?' (inches H,O at 60°F)

-5 1-4 1-4 1-4 8.16003E-01 I6.68533E-01 16.50958E-01 16.42337E-01

224.8440

1.53657E+oC 3.59049E+05 6.3 1450E+OI i .OOOOOE+oC -5 8.53219E-01 1.97002E+05 3.46463E+01 I .OOOOOE+oC -4 6.35054E-01 1.43760E+05 2.52827E+01 1 .OOO00E+oC 3

9.99840E-01

9.99938E-01

6.06980E-01 2 12 12 12 6.03926E-01~6.02895E-01 I 6.02318E-01 I 6.01782E-01

3.096928+03 9.241 8 l8+03 I .53691 E+04 2.14801E+04 3.0610 lE+W 7.00502E+04 2.090438+05 I 3.476388+05 I 4.8586617+05 6.92379E+05

9.99721E-01 9.99225E-01 2 I2 6.03675E-01 6.02688E-01 6.02135E-01 6.01620E-01 3.17009E+04 5.27484E+04 7.37800E+04 1.05310E+05 2.72818E+05 4.53953E+05 6.34950E+05 9.06295E+05 1.00000E+00 l.OOOOOE+OO 1.00000E+00 l.OOOOOE+OO 2 l 2 11 /i

323.7754 I 440.6943 I

1.7875 1E+O5 1.53833E+M 1.OOOooEioC 2 6.0 1787E-01 3.0915 1E+O4 2.66055E+02 9.76981E-01 2 6.01652E-01 2.82876E+O4 6.39845E+05 9.91078E-01 2 6.01535E-01 3.66668E+04 8.29378E+05 9.95538E-01 ,I

2.08449E+05 1.79391E+06 I.OOOOOE+OO 2 6.01588E-01 3.57489E+04 3.07655E+05 9.68669E-01 2 6.0 1453E-O 1 3.28840E+04 7.43814E+05 9.87856E-01 2 6.01339E-01 4.26948E+04 9.65726E+05 9.93926E-01 0


_-- - - ~ . _ _ _ _

API M P M S * 1 4 * 3 - 4 72 W 0732270 0506373 670 W


Table 4-C-5-Selected Round Robin Test Results Matrix-US Units ( Q,, = 4.02638 in, a;! = 0.00000620 in/in-"F, ú,,, = 3.02343 in, al = 0.00000925 in/in-"F)

Flow Conditions

Tf= 0.OOoF, Pf= 14.696 psia, pf,p = 58.199 Ib/ft3, p = 1.8650E+03 cP, k = -1.0, pb = 56.861 Ib/ft3

Tf= 68.00°F, Pf= 14.696 psia, pbp = 56.660 Ib/ft3, p = 2.1220E+02 cP, k = -1.0, pb = 56.861 lb/ft3

Tf= 176.0O0F, P f = 14.696 psia, pbp = 54.214 lb/ft3, p = 1.7490E+01 CP, k = -1.0, pb = 56.861 Ib/ft3

Tf= 60.û0°F, P f = 14.696 psia, pf,p = 62.366 lb/ft3, p = 1.1990 cP, k = -1.0, pb = 62.366 lb/ft3

Tf= 210.OO0F, Pf= 14.696 psia, pf,p = 58.792 Ib/ft3, p = 2.8250E-01 cP, k = -1.0, pb = 62.366 lb/ft3

Tf= O.OO°F, P f = 14.696 psia, pf,p = 0.13223 lb/ft3, p = 1.3070E-02 cP, k = 1.3198, pb = 0.116198 lb/ft3

T,== 50.û0°F, Pf= 100.00 psia, pf,p = 0.31 109 lb/fG, p = 1.0670E-02 cP, k = 1.3622, pb = 0.044210 Ib/ft3

Tf= 0,00OF, Pf= 1000.00 psia, pf,p = 65.072 lb/ft3, p = 1.5430E-01 cP, k=-1.0,pb=0.1161981b/ft3

Tf= O.W°F, PI= 200.00 psia, pf,p = 2.0466 lb/ft3, p = 1.3520E-02 cP, k = 1.3198, pb = 0.116198 lb/ft3

Tf= 50.W°F, P f = 500.00 psia, pf,p = 1.6623 lb/ft3, p = 1.1310E-02 cP, k = 1.3622, pb = 0.044210 lb/ft3

Tf= 150.0O0F, Pf= 1ooO.00 psia, pf,p = 2.7573 lb/ft3, p = 1.3650E-02 cP, k = 1,3622, pb = 0.0442101b/f$

Tf= 140.00"F, P f = 2000.00 psia, pf,p = 32.465 ib/ft3, p = 4.1710E-02 cP, k=-1.0, pb = 0.116198 lb/fG

Cell Value

cd 9111 Q v Y ICD cd 9 m Q v Y ICD cd 9ni Q v Y ICD cd 4111 Q v Y ICD

-

-

- cd 9ni Q v Y ICD cd 9ni Q v Y ICD cd 4ni

Y ICD

cd 4111 Q v Y ICD cd 91" Q v Y ICD cd 4nr

Y ICD cd 4tn Q v Y ICD cd 4ni Q v Y ICD

-

-

Q"

-

Q"

-

-

2.2484

3.06062E+OC 1.38945E+05 2.44359E+03 1 .OOOOOE+OC

1.45976E+OC 6.54827E+W 1,15 163E+OI l.OOOOOE+OC -5 7.46086E-01 3.28134E+W 5.7708 1E+O2 l.OOOOOE+OC

6.2 1807E-01 2.92592E+W 4.69 153E+02 1.OOO00E+OC 3 6.09944E-01 2.79557E+W 4.48253E+02 1.00000E+OC 2 6.09868501 1.31683E+03 1,13326E+04 9.97819E-01 2 6.06696E-01 2.01520E+03 4.55825E+04 9.99689E-01

6.06708E-01 2.91241E+04 2.50642E+05 1 .OOOOOE+OC 2 6.04065E-01 5.14169E+03 4.42494E+04 9.99840E-01 2 6.03813E-01 4.63735E+03 l.O4894E+O5 9.99938E-01 2 6.03583E-01 5.98318E+03 1.35335E+05 9.99969E-01

6.03240E-01 2.05150E+04 1.76552E+05 1 .OOOOOE+OO 2

20.2360

2.05802E+OC 2.80291E+05 4.9294 1 E+OI 1.00000E+OC -5 1.07087E+OC 1.44115E+OI 2.53451E+0? l.OOOOOE+OC 4 6.55357E-01 8.64702E+W 1.52073E+O? 1.00000E+OC 3 6.1 1965E-01 8.63889E+04 1.38519E+01 l.OOOOOE+OC 2 6.04898E-01 8.31742E+04 1.33365E+03 l.OOOOOE+OC 2 6.04939E-01 3.85008E+Ol 3.3 1338E+M 9.80375E-01 2 6.02882E-01 5.99274E+Ol 1.35552E+05 9.97205E-01 2 6.02889E-01 8.68232E+W 7.47200E+05 l.OOOOOE+OC 2 6.01194E-01 1.53322E+W 1.3 1949E+05 9.98558E-01

6.01023E-01 1.38410E+O4 3.13075E+05 9.99441E-01 2 6.00862E-01 1.78643E+O4 4.04079E+05 9.99720E-01

6.00639E-01 6.12803E+04 5.27378E+05 l.OOOOOE+OO 2

AP (inches H20 at 60°F)

56.2110 110.1736 224.8440 323.7754 440.6943

1.73497E+00 1.55891E+OO 1.39866E+00 1.32581E+00 1.26848E+OC 3.93820E+05 4.95401E+05 6.34963E+05 7.22273E+05 8.06210E+05 6.92602E+03 8.71249E+03 1.1 1669E+04 1.27024E+04 1.41786E+04 l.OOOOOE+OO 1.00000E+00 l.OOOOOE+OO l.OOOOOE+OO l.OOOOOE+OC -5 -5 -5 -5 -5 9.37930E-01 8.60053E-01 7.82520E-01 7.43996E-01 7.11684E-01 2.10373E+05 2.70067E+05 3.51030E+05 4.00498E+05 4.46955E+05 3.69977E+03 4.74960E+03 6.17347E+03 7.04345E+03 7.86048E+03 1.00OOOE+00 1.00000E+00 1.00000E+00 1.OOOOOE+OO l.OOOOOE+OC -4 1-4 1-4 1-4 1-3 6.41001E-01 I 6.33877E-01 I 6.27798E-0116.25158E-01 I 6.23134E-01

6.08910E-01 6.07251E-01 6.05738E-01 6.05048E-01 6.04504E-01 1.43263E+05 2.00021E+05 2.85033E+05 3.41650E+05 3.98233E+05 2.29713E+03 3.20722E+03 4.57032E+03 5.47814E+03 6.38542E+03 l.OOOOOE+OO l.OOOOOE+OO l.OOOOOE+00 l.OOOOOE+00 l.OOOOOE+G€ 2 2 2 2 2 6.03239E-01 6.02318E-01 6.01467E-01 6.01075E-01 6.00764E-01 1.38243E+05 1.93245E+05 2.75674E+05 3.30594E+05 3.85493E+05 2.21665E+03 3.09857E+03 4.42027E+03 5.30086E+03 6.18 114E+03 1.OOOOOE+OO 1.OOOOOE+00 l.OOOOOE+OO l.ooOOOE+OO 1.OOOOOE+OC 2 2 2 2 2 6.03392E-01 6.02609E-01 6.02043E-01 6.01919E-01 6.01983E-01 6.17261E+03 8.15273E+03 1.01870E+04 1.07222E+04 1.04426E+04 5.31214E+04 7.01624E+04 8.76691E+04 9.22752E+04 8.98691E+04 9.45485E-01 8.93150E-01 7.81940E-01 6.85993E-01 5.72601E-01 2 2 2 2 2 6.01616E-01 6.00917E-01 6.00280E-01 5.99995E-01 5.99775E-01 9.91725E+03 1.37639E+04 1,93259E+04 2.28532E+04 2.62018E+04 2.24321E+05 3.1 1329E+05 4.37139E+05 5.16924E+05 5.92667E+05 9.92237E-01 9.84784E-01 9.68947E-01 9.55284E-01 9.39137E-01

6.01613E-01 6.00901E-01 6.00240E-01 5.99935E-01 5.99693E-01 1.44399E+05 2.019 19E+05 2.88 139E+05 3.4559 1E+05 4.03027E+05 1.24270E+06 1.73772E+06 2.47972E+06 2.97416E+06 3.46845E+06 l.OOOOOE+OO l.OOOOOE+OO l.OoooOE+00 l.OOOOOE+OO l.OOOOOE+OC n n n n ,l L I' I' I ' I ' 6.00227E-01 I5.99687E4115.99189E-01 I 5.98963E-01 I 5.98785E-01

6.00080E-01

9.99223E-01

2 2 2 2 5.99553E-01 5.99063E-01 5.98838E-01 5.98659E-01 3.21366E+04 4.57262E+04 5.46999E+04 6.35897E+04 7.26908E+05 1.03429E+06 1.23728E+06 1.43836E+06 9.96957E-01 9.93789E-01 9.91057E-01 9.87827E-01 2 2 2 2 5.99425E-01 5.98944E-01 5.98723E-01 5.98548E-01 4.15320E+04 5.91899E+04 7.09043E+04 8.25632E+04 9.39426E+05 1.33883E+06 1.60381E+06 1.86752E+06 9.98478E-01 9.96894E-01 9.95527E-01 9.93912E-01


A P I M P M S * L 4 - 3 . 4 92 0732290 O506394 507 =


2.39587E+00 4.2553 I E+05 7.4837 I E+03 I .00000E+00 -6 I .20140E+W 2.108478+05 3.7081 IE+03 I .00000EtUO -5

Table 4-Cd-Selected Round Robin Test Results Matrix-US Units ( D, = 7.98146 in, a;! = 0.00000620 in/in-"F, d, = 5.98437 in, al = 0.00000925 in/in-"F)

I .641)30E+OO I .40824E+W I .27622E+W 8.788 1OE+ü5 1.25060E+06 I S867 IE+(Ki I .54554E+04 2.199408+04 2.790508+04 I .00000E+00 I .00000E+OO I .00000E+00 -5 -5 -5 8.98192E-01 7.84948E-01 7.13884E-01 4.72905E+05 6.88801E+05 8.770198+05 8.316868+03 1.21 138EtW 1.542398+04 1 .OOoOOE+00 1 .OOOOE+OO I .00000E+íK1 4 -4 -?

Flow Conditions

2.05 153E+06 3.60798E+04 1.00000E+00 -4 6.78543E-01 1.19086E+06 2.09433E+04 I .oooOOE+00 3 6.15992E-01 1.05993E+06 1.86406E+04 1.00000E+00 3 5.99900E-01 I . 10439E+06 1.77082E+W 1 .OoooOE+OO

Value I 2.34324E+06 2.62389E+06 4.12100E+04 4.61457E+W 1.00000E+ûO 1 .OoooOE+OO 4 -4 6.69599E-01 6.62896E-01 1.41019E+06 1.62876E+06 2.48007E+04 2.86446E+04 1.00000E+ûO 1.00000E+ûO 3 3 6.14137E-01 6.12702E-01 1.26808E+06 1.47597E+06 2.23014E+04 2.59575E+04 1 .OOOOOE+00 1.00000E+00 3 3 5.99373E-01 5.98957E-01 1.3241 lE+06 1.54372E+06 2.123 12E+04 2.47526E+04 1.00000E+OO 1.00000E+W

ïj= 0.00'F, Pf= 14.696 psia, pf,p = 58.199 Ib/ft3, j i = 1.8650E+03 cP, k=-1.0, pb = 56.861 Ib/ft3

TJ= 68.û0°F, P'= 14.696 psia, P,,~ = 56.660 Ib/ft3, j i = 2.1220E+02 cP, k,= -1.0, pb = 56.861 Ib/ft3

TI= 176.OOoF, Pf= 14.696 psia, pf,p = 54.214 ib/ft3, j i = 1.7490E+Ol cP, k = -1.0, pb = 56.861 Iblft3

ICD cd qJ,:

Y ICD cd q,,,

Y

Q"

Q"

ïj= 60.00'F, Pf= 14.696 psia, pf,p = 62.366 lb/ft3, j i = 1.1990 cP, k= -1.0, pb = 62.366 lb/ft3

ICD

6.70077E-0 I I . 15298E+05 2.02771E+03 I .00000E+00

~ ~~ Tf= O.OO°F, Pi= 14.696 psia, pf,p = 0.13223 lb/ft3, j i = 1.3070E-02 CP,

cd 4":

Y ICD cd qrJI

Y

Q" k = 1.3198, pb = 0.116198 ib/ft3

Tf= 50.00"F, P'= 100.00 psia, pf,p = 0.31 109 lb/ft3, p = 1.0670E-02 CP, k = 1.3622, pb = 0.044210 ib/ft3 Q"

6.34574E-01 6.25047E-01 6.20204E-0 1 3.27570E+05 5.37753E+05 7.47021E+05 5.76089E+03 9.45732E+03 1.313778+04 1 .OOOOOE+OO 1.00000E+OO 1.00000E+W

1.12624E+05 1.80586E+03 1 .OOOOOE+OO 3 6.03062E-01 1.08137E+05 1.73391E+03 1 .OOOOE+OO ,-I

pf,p = 2.0466 lb/ft3, p = 1.3520Er02 cP, k = 1.3198, pb = 0.116198 Ib/ft3

3.33911E+05 5.5441 1E+05 7.74559E+05 5.35405E+03 8.88964E+03 1.24196E+04 I .OOOOOE+00 1.00000E+00 1 .OOOOOE+W 2 2 2 5.99236E-01 5.97963E-01 5.97253E-01 3.22357E+05 5.36120E+05 7.49677E+05 5.1688OE+O3 8.59635E+03 1.20206E+04 1.00000E+00 1.00000E+00 l.OOOOOE+OO ,-I " "

I ICD

2 5.9629 1E-01 1.28309E+06 2.05736E+04 1 .ooOOOE+OO 2 5.96975E-01 4.16284E+04 3.58254E+05 6.86392E-01 2 5.95477E-01 8.874 13E+O4 2.00727E+06 9.55341E-01

AP (inches H20 at 60'F) I

2 5.9605 1E-0 1 1.49634E+06 2.39928E+04 1 .OOOOOE+OO 2 5.97023E-01 4.05568E+04 3.49032E+05 5.73145E-01 2 5.95306E-01 1.01755E+05 2.30162E+06 9.39214E-01

2.2484 I 20.2360 I 56.2110 I 110.1736

5.094168+03 4.384WE+04 9.97822841 2 6.00632E-01 7.80532E+03 1.7655 1 E+05 9.9969OE-O1 2 6.00648E-01 1.12805E+05 9.70799E+05 1.00000E+OO 2 5.9862860 1 1.99350E+W 1.7156OE+O5 9.998408-01

1.492278+04 2.393978+04 3.16310E+O4 I .28425E+05 2.06025E+05 2.722 l6E+05 9.80399E-01 9.45554E-01 8.93286E-01 2 2 2 5.97712E-01 5.96734E-01 5.96193E-ol 2.324458+04 3.848508+04 5.34263E+04 5.25775E+05 8.70505E+05 1.208478+06 9.97209E-01 9.92247E-01 9.84804E-01 2 2 2 5.97724E-01 5.96739E-01 5.96188E-01 3.36771E+05 5.60359E+05 7.837788+05 2.898258+06 4.82245E+06 6.74520E+O(i I .00000E+00 l.OOOOOE+ûO 1.00000E+0(3 2 2 2 5.964 15E-01 5.95664E-01 5.95245E-o 1 5.95080E+04 9.88012E+04 1.37691 E+05 5.12126E+05 8.502838+05 1.184978+06 9,985608-O1 9.95999501 9.921 5 9 ~ 4 1

ïj= 0.00'F. Pf= 1ooO.00 psia, P,,~ = 65.072 ib/ft3, /i = 1.5430E-01 cP, k=-1.0, pb = 0.116198 Ib/ft3

3 13 13 13 6.1 1774E-01 I 6.04594E-01 I 6.02306E-01 I6.01052E-01

cd 9":

Y Q"

1.11872E+06 9.62770E+06 1.00000E+00 2 5.94858E-01 1.94957E+05 1.67780E+06 9.83997E-01 2 5.94752E-01 1.77610E+05 4.01741E+06 9.93797501 2 5.94645E-01 2.29908E+05 5.20036E+06 9.96898E-01 2 5.94534E-O 1 7.91035E+05 6.80765E+06 1.OOOOOE+00 2

L I ' I' I' 6.03036E41 I 5.992998-01 I 5.981 11E-01 I 5.975088-01

1.34193E+06 1.56509E+06 1.15486E+07 1.34692E+07 1.00000E+OO 1.OOOOOE+OO 2 2 5.94681E-01 5.94543E-01 2.32205E+05 2.68536E+05 1.99836E+06 2.31 102E+06 9.76956-1 9.68635E-01 2 2 5.94576E-01 5.94438E-01 2.12484E+05 2.47033E+05 4.80623E+06 5.58772E+M 9.91068E-01 9.87843E-01 2 2 5.94473E-01 5.94336E-01 2.75432E+05 3.20743E+05 6.23008E+06 7.25498E+06 9.95533E-01 9.93920E-01 2 2 5.94368E-O 1 5.94236E-O 1 9.48976E+05 1.10689E+06 8.16689E+06 9.52592E+06 1.00000E+OO 1.00000E+Cû 2 2

5.98428E-01 1.798 1OE+04 4.06718E+05 9.99938E-01 2 5.98237E-01 2.32007E+04 5.24784E+05 9.99969E-01

5.96275E-01 5.95543E-01 5.95133E-01 5.37228E+04 8.93392E+04 1.24802E+05 1.21517E+06 2.02079E+06 2.82295E+M 9.99442E-01 9.98449501 9.96961E-01 2 2 2 5.96136E-01 5.95420E-01 5.95019E-01 6.93412E+04 1.15373E+05 1.61292E+05 1.56845E+06 2.60965E+06 3.64832E+06 9.99721E-01 9.99224E-01 9.98480E-01

5.97974E-01 7.95605E+04 6.84697E+05 l.OOOOOE+OO ,-I

224.8440 I 323.7754 I 440.6943 I

5.95964E-01 5.95279E-01 5.94894E-01 2.37882E+05 3.96013E+05 5.54059E+05 2.04721E+06 3.40809E+06 4.76824E+M 1.OOO00E+OO l.OOOOOE+00 1.00000E+OC " " n

I 1

I . 155068+001 I .09942E+001 1.05522E+00

5.96595E-01 1.06979E+Ot 1.71534E+04 1.00000E+OC 2 5.97070E-01 3.95396E+04 3.40278E+05 7.82217E-01 2 5.95699E-01 7.50353E+04 1.69725E+Ot 9.68987E-01 2 12 12 5.95675841 I 5.95438F-01 I 5.95250E-01


-- - I_

A P I NPMS*L4#3*4 72 0732290 050b39.5 4 4 3


Table 4-C-5-Selected Round Robin Test Results Matrix-US Units ( Dm = 14.31 154 in, q, = 0.00000620 in/in-"F, d,,, = 10.73437 in, al = 0.00000925 in/in-"F)

Flow Conditions

Tf= O.OO°F, Pf= 14.696 psia, pLP = 58.199 lb/ft3, p = 1.8650E+03 cP, k = -1.0, pb = 56.861 lb/ft3-

Tf= 68.00"F, Pf= 14.696 psia, pfp = 56.660 Ib/ft3, p = 2.1220E+02 cP, k ; -1.0, pb = 56.861 Ib/ft3

Tf= 176.00'F, Pf= 14.696 psia, pfp = 54.214 lb/f$, p = 1.749OE+Ol cP, k -1.0, pb = 56.861 lb/ft3

Tf= 60.00"F, Pf= 14.696 psia, pf,p = 62.366 lb/ft3, p = 1.1990 cP, k = -1.0, pb = 62.366 lb/ft3

Tf= 210.0O0F, Pf= 14.696 psia, pf,p = 58.792 Ib/ft3, /i = 2.8250E-01 cP, k = -1.0, pb = 62,366 Ib/ft3

Tf= O.OO°F, Pf= 14.696 psia, pf,p = 0.13223 Ib/ft3, p = 1.3070E-02 cP, k = 1,3198, pb = 0.116198 1b/ft3

Tf= 50.00'F, Pf= 100.00 psia, pf,p = 0.31109 Ib/ft3, p = 1.0670E-02 cP, k = 1.3622, pb = 0.044210 lb/f?

Tf= O.OO"F, Pf= 1000.00 psia, pf,p = 65.072 lb/ft3, /i = 1.5430E-01 cP, k=-1.0, pb = 0.116198 Ib/ft3

~ f = O.OOOF, pf= 200.0öpsia, pf,p = 2.0466 lb/ft3, p = 1.3520E-02 cP, k = 1.3198, pb = 0.116198 Ib/ft3

Tf= 50.00'F, P'= 500.00 psia, &, = 1.6623 Ib/ft3, p = 1.1310E-02 cP, k = 1.3622, pb = 0.044210 lb/ft3

Tf= 15O.0O0F, Pf= 1000.00 psia, prP = 2.7573 Ib/ft3, p = 1.3650E-02 cP, k L 1.3622, Pb = 0.044210 1b/ft3

ï j= l4O.0OoF, Pf= 2000.00 psia, = 32.465 lb/ft3, /.i = 4.1710E-02 cP,

k=-1.0,pb=0.11619S1b/ft3

Cell ValUf

cd 9111

Q v Y ICD cd 4111

Qv Y ICD

cd 9m Q v Y ICD

cd 4m Q v Y ICD

cd 4ni Q v Y ICD cd 4111

Q v Y ICD

9"l

Y ICD cd 9"1 Q v Y ICD

4 m

Y ICD

cd 4111

Q v Y ICD cd 41"

Q v Y ICD cd 4"l

Q v Y [CD

-

-

-

-

- cd

Q"

-

- cd

Q v

-

-

-

AP íinches H,O at 60°F)

2.2484

1.96155E+O( 1.12 13 1E+Of 1.97202E+oL l.OOOOOE+O( -5 1.02805E+3+0( 5.80702E+O! l.O2127E+m l.OOOOOE+O( -4

6.47068E-01 3.58348E+O: 6.3021 8E+O? 1.OOOOOE+OC 3 6.05944E-01 3.59031E+O: 5.75684E+O? 1.00000E+OC 2 5.99188E-01 3.45809E+05 5.54483E+Ol l.OOOOOE+OC 2 5.99192E-01 1.629 12E+04 1.40202E+05 9.97822E-01 2 5.972843-01 2.498 17E+O4 5.65069E+05 9.99690E-01 2 5.97302E-01 3.6 1 045E+05 3.10715E+06 1.00000E+íM 2 5.95691E-01 6.38466E+04 5.49464E+05 9.99840E-01 2 5.95525E-01 5.75918E+04 1.30269E+06 J.99938E-01 2 5.95361E-01 7.43135E+04 I .68092E+06 9.99969E-01 2 5.95 15 1E-01 2.54860E+05 1.19332E+06 I.OOOOOE+00 1

20.2360 I 56.2110 I 110.1736 I 224.8440

1.38180Et00 1.19299E+00 1.08827E+00 9.90379E-0; 2.36973E+06 3.40988E+06 4.35477E+06 5.66152E+Oi 4.16759E+04 5.99687E+04 7.65862E+04 9.95676E+O 1.00000E+00 1.00000E+00 l.OOOOOE+00 l.OOOOOE+o( -5 -5 -4 -4 7.69481E-01 6.84268E-01 6.67053E-01 6.52787E-01 1.30395E+06 1.93258E+06 2.63755E+06 3.68734E+0( 2.29323E+04 3.39879E+04 4.63858E+04 6.48484E+@ l.O0000E+00 1.00000E+00 1.00000E+00 1.00000E+O( 4 4 3 3 6.22607E-01 6.15779E-O1 6.12237E-01 6.09111E-01 1.03441E+06 1.70512E+06 2.37343E+06 3.37330E+0( 1.81920E+04 2.99874E+û4 4.17410E+04 5.93255E+@ 1.00000E+00 l.o0000E+00 1.00000E+00 1.00000E+O( 3 3 3 3 6.00408E-01 5.98610E-01 5.97616E-01 5.96701E-01 1.06726E+06 1.77344E+06 2.47870E+06 3.53557E+ûI 1.71 129E+04 2.84361E+04 3.97444E+04 5.66907E+@ 1.00000E+00 l.OoooOE+00 l.OOOOOE+OO 1.00000E+O(

5.96154E-01 1.03218E+Ot 1.65504E+M l.OOOOOE+OC 2 5.96228E-01 4.77829E+04 4.1 1220E+05 9.80394E-0 1 2 5.94951E-01 7.44678E+04 1.68441E+06 9.97208E-01 2 5.94966E-01 1.07891E+06

2 2 2 5.95135E-01 5.94565E-01 5.94035E-01 1.71736E+06 2.40201E+06 3.42838E+06 2.75369E+04 3.85147E+04 5.49719E+@ l.OOOOOE+OO 1.00000E+00 1.OOOOOE+O( 2 2 2 5.95277E-01 5.94793E-01 5.94441E-01 7.66843E+04 1.01339E+05 1.26689E+O: 6.59945E+05 8.72125E+05 1.09028E+(x 9.45538E-01 8.93254E-01 7.82151E-01 2 12 ( 2 5.94164E-01 I 5.93728E-01 15.93329E-01

9.28509E+06 1.54545E+07 2.16201E+07 3.08644E+Oi 1.00000Et00 1.00000E+00 I 1.00000E+00 1 .OoooOE++oC 2 ( 2 - 12 12 5.93912E-ûlI5.93306E-01I5.92967E-01~ 5.92654E-01 1.907258+05 3.16736E+05 4.41468E+05 6.25148E+05 1.64138E+06 2.72583E+06 3.79927E+M 5.380028+06 9.98559E-01 9.95998E-01 9.92156E-01 9.83992E-01 2 2 2 2 5.93794E-01 5.93203501 5.92871E-01 5.92562E-01 1.72189E+05 2.864128+05 4.00154E+05 5.69538E+05 3.8948 1 E+06 6.478448+06 9.05 122E+O6 1.28826E+Oï 9.99442Ml 9.98449E-01 9.96960Eol 9.93795E-01

5.93671E-01 5.93093E-01 5.92768E-01 5,924650-01 2.222558+05 3.69880E+05 5.17162E+05 7.37255E+05 5.02725E+06 8.36642E+06 1.169798+07 1.66762B+07 9.99721E-01 9.99224E-01 9.98479E-01 9.96897841 2 2 2 2 5.93534E-01 5.92980E-01 5.92668E-01 5.92376E-01 7.625098+05 1.26966E+06 1.77659E+06 2.53674E+06 3.56215E+06 1.092678+07 1.528938+07 2.18312E+07 I .00000E+00 1.00000E+00 1.00000E+00 1.00000E+ûü

323.7754 1 440.6943 I 9.44490E-01 9.07450E-01 6.47903E+06 7.26243E+06 1.13945E+05 1.27723E+05 l.OOOOOE+OO 1.OoooOE+00 -4 -4 6.46757E-01 6.42214E-01 4.38394E+06 5.07866E+06 7.70992E+û4.8.93172E+04 l.OOOOOE+OO 1.00000E+00 3 3 6.07719E-01 6.06635E-01 4.03871E+06 4.70343E+06 7.10278E+04 8.2718 1E+04 1 .OOOOOE+00 1.00000E+00 2 2 5.96280E-01 5.95947E-01 4.23970E+06 4.94356E+06 6.79809E+04 7.92668E+04 1.00000E+00 1.00000E+00 2 2 5.93790E-01 5.93596E-01 4.1 1236E+06 4.79618E+06 6.59391E+04 7.69038E+04 1.00000E+00 1.00000E+00 2 2 5.94364E-01 5.94403E-01 1.33378E+05 1.29931E+05 1.14785E+06 1.11819E+06 6.86298E-01 5.73016E-01

7.44628E+05 8.61 168E+05 6.40827E+06 7.41 121E+M 9.76949E-01 9.68625E-01 2 2 5.92420E-01 5.92308501 6.81404E+05 7.92233m.05 1.54129Et.07 1.79 198E+07 9.91065E-01 9.87839E-01 2 2 5.92325E-01 5.92214E-01 8.83286m.05 1.02864E+06 1.99793E+07 2.32671E+07 9.95532E-01 9.93918E-01 2 2 5.92241E-01 5.92134E-01 3.04339E+06 3.54998E+M 2.61914E+07 3.0551 1E+07 1.00000E+00 1.00000E+00 2 2


A P I MPMS*14*3=4 92 = 0732290 0506396 38T

1.55369E+00 3.74090E+06 6.57903E+04 I .00000E+00 -5

SECTION &CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 4-BACKGROUND 1 o9

1.12772E+00 9.8G29E-01 9.01873ECol 8.14595E+06 1.18514E+07 1.52006E+07 1.4326 1E+05 2.08428E+05 2.67329E705 I .00000E+00 1 .OOOOOE+00 1.00000E+ûC 4 ~ - 4 -4

Table 4-Cd-Selected Round Robin Test Results Matrix-US Units ( Dm = 29.37598 in, q, = 0.00000620 in/in°F, d, = 22.03126 in, al = 0.00000925 in/in-"F)

8.52642E-01 2.02857E+3+06 3.56759E+04 1.00000E+00 -4 6.28736E-01 I .46659E+06 2.57926E+04 1 .OOOOOE+00 3 6.01355E-01 1.50078E+06 2.40640E+04 1.00000E+00 2 5.96367E-01

I Flow Conditions

6.73057E-01 6.51622E-01 6.41 140E-01 4.80398E+06 7.75 163E+06 1.06777E+Oi 8.44864E+04 1.36326E+05 1.87786E705 i .00000E+00 I .00000E+00 1 .OOOOOE+OC 3 3 3 6.12914E-01 6.08275E-01 6.058 15E-01 4.28909E+06 7.09438E-1-O6 9.89 I97E+06 7.543 12E+Q4 1.24767E+05 1.73968Et05 I.OOCOOE+00 1 .OOOOOE+OO 1 .OOOOOE+OC 3 3 2 5.97295E-01 5.95951E-O 1 5.952O4E-0 I 4.47 i98E+06 7.43652E+O6 1 .O398 1E+O7 7.17054E+04 1.19240E+05 1.66727E+05 1 .OOOOOE+OO 1.00000Et00 1.00000E+OC 2 2 2 5.94080E-01 5.93304E-01 5.92869E-01

Value I

6.32329E-01 1.5O443E+07 2.64580E+05 I .ooOOOE+00

6.28554E-01 6.25683E-01 I .79453E+07 2.08406E+07 3.15600E+05 3.665 18E+05 I .ooOOOE+OO 1.00000E+00

~

ïj= 176.0O0F, PJ= 14.696 psia,

k = -1.0, pb = 56.861 Ib/ft"

pf,p = 62.366 ib/ft3, p = I. 1990 cP,

pf,p = 54.2 14 Ib/ft', p = 1.749OE+O I cP,

TJ= 60.0O0F, PI= 14.696 psia,

k -1 .o, pb = 62.366 Ib/ft3

TJ= 210.00"F. PI= 14.696 psia, pf,p = 58.792 ib/ft3, p = 2.8250E-01 cP, k = -1.0, pb = 62.366 lb/ft3

TJ= 0.00"F, PJ= 14.696 psia,

k s 1.3198, pb = 0.1 16198 Ib/ft' pf,p = 0.13223 Ib/ft', p = 1.3070E-02 cP,

I IY

Cd

QI. qff,

Y ICD

4,f

Y ICD cd qfff

Y ICD

cd

Q,.

Q,.

Cd

Q,* qJff

Y

1.40799E+07 2.47620E+05 1.00000E+00 2 5.94512E-01 1.4837 1 E+07 2.37904E+05 1.00000E+00 .-l

TJ= 140.00"F, PI= 2000.00 psia, I pf,p = 32.465 lb/ft3, p = 4.1710E-02 cP, I i k = -1 .o, pb = o. 1 16198 lb/ft3

1 0

1.68681E+07 1.96541E+07 2.96655E+05 3.4565 1E+05 1.00000E+00 1 .OOOOOE+00 2 2 5.94193E-01 5.93940E-01 I .77950E+07 2.07520E+07 2.85332E+05 3.32745E+05 1.00000E+00 1 .ooOOOE+00 'I 'I

AP (inches H?O at 60°F) I

1 .OOOOOE+OO 2

2.2484 I 20.2360 1 56.2110 I 110.1736 1

1 .ooOOOE+00 1.00000E+00 2 2

5.92798E-0 1 5.32147E+05 4.57966E+06 7.82170E-01 2 5.91939E-01 1.01078E+06 2.28632E+07 9.68980E-01 2 5.91935E-01 1.50706E+07 1.29697E+08 l.OOOOOE+OO

5.92739E-0 i 5.92769E-O 1 5.60271E+05 5.45798E+05 4.82170E+06 4.69714E+06 6.86324E-01 5.73052E-01 2 2 5.91802E-01 5.91695E-01 1.19557E+O6 1.37104E+06 2.70431E+07 3.10120E+07 9.55331E-01 9.39201E-01 2 2 5.91787E-01 5.91670E-01 1.80802E+07 2.10894E+07 1.55598E+08 1.81495E+08 l.OOOOOE+00 1.00000E+00

T/= 50.0O0F, PJ= 100.00 psia,

k = 1.3622, pb = 0.044210 Ib/ft3 pf,p = 0.3 1109 Iblft', p = 1.067OE-02 cP,

î j= 0.00"F. PJ= 1ooO.00 psia, pf,p = 65.072 Ib/ft3, p = 1.5430E-01 cP, k=-l.O,pb = 0.116198 Ib/ft3

T/= O.OO"F, PJ= 200.00 psia, pf,p = 2.0466 lb/ft3, p = 1.3520E-02 cP, k = 1.3198, pb = 0.116198 Ib/ft3

3 13 13 6.03609E-01 I6.02616E-01 I6.01838E-01

ICD Cd

QV qfa

Y ICD cd qJJf Qv Y ICD Cd qia Qv

5.94954E-0 1 I.O4812E+O5 2.37077E+06 9.99690E-01 2 5.94974E-01 1.51478E+06 1.30362E+07 1.00000E+00 2 5.93753E-01 2.68045E+05 2.30680E+06 9.99840E-01

' I ' I ' 5.92463E-01 15.92275E-01 I 5.92126E-01

5.93 182E-01 5.9258 1E-01 5.92246E-01 ~ 3.12724E+05 5.18086EIO5 7.19472E+05 7.0736OE+M 1.17 188E+07 1.62740E+07 9.97208E-01 9.92245E-01 9.84800E-01 2 2 2 5.93200E-01 5.92594E-01 5.92253E-01 4.53084E+06 7.54368E+06 1.05551E+Oi 3.89924E+07 6.49209W07 9.08370E+07 I.OOCOOE+IX! 1.OOOOOE+00 i.ooOOOE+OC 2 2 2 5.92393E-01 5.91928E-01 5.91667E-01 8.01275E+05 1.33099E+06 1.85537E+06 6.89577E+06 1.14545E+07 1.59674E+07 9.98559E-01 9.95998E-01 9.92157E-01

I I .449688+06 4.33240E+O6 7.2 I I24E+06 1.008838+07 I .44020E+07 I .7277üE+07 2.015 l4E+07 2.324478+04 6.946748+04 I I . 15628E+05 I 1.617608+05 I 2.309288+05 I 2.770258+05 I 3.231 15E+05

5.91426E-01 2.62765E+06 2.26136E+07 9.83994E-01

5.91315E-01 5.91229E-01 3.13003E+06 3.62006E+O6 2.69371E+07 3.1 1543E+07 9.76951E-01 9.68628E-01

TJ= 50.00"F, PJ= 500.00 psia, pf,p = 1.66231b/ft3, p = 1.1310E-02 cP, k = 1.3622, pb = 0.044210 Ib/ft3

T/= 150.00"F, PJ= 1ooO.00 psia, pf,p = 2.7573 Ib/ft3, p = 1.3650E-02 cP, k = 1.3622, pb = 0.044210 ib/ft3

cd qJJf Qv Y ICD cd qJJi

Y Q"

2.41799E+05 5.46933E46 9.99938E-01 2 5.93483E-01 3.12019E+05 7.05766E+06 9.99969E-01

2 12 12 12 12 12 12 5.93620E-01 I 5.92297E-01 I5.91843E-01I5.91588E-01 I 5.91350E-01 I5.91240E-01 I 5.91153E-01

7.23429E+05 1.20359E+06 1.68179E+06 í.63635E+07 2.72244E+07 3.80410E+07 9.99442E-01 9.98449E-01 9.96960E-01 2 2 2 5.92191E-01 5.91747E-01 5.91497E-01 9.33796E+05 1.55439E+06 2.17360E+M 2.11218E+07 3.51592E+07 4.91654E+07 9.99721E-01 9.99224E-01 9.98480E-01

5.91263E-01 3.09900E+O6 7.00972E+07 9.96897E-01

2 5.91 155E-01 5.91070E-01 3.7 1303E+O6 4.32422E+06 8.39862E+07 9.78109E+07 9.95532E-01 9.93919E-01

1.07017E+06 9.20987E+M 1.00000E+00 2

2 12 12 12 12 12 12 5.93325E-01~5.92087E-01~5.91661E-01~ 5.91420E-0lI5.91196E-01 I 5.91092E-01 I 5.91009E-01

3.20384E+06 5.33588E+06 7.467208+06 1.066348+07 1.27938E+07 1.49240E+07 2.75722E+07 4.59206E+07 6.426278+07 9.176908+07 1.l0103E+08 i .28436E+08 1.00000E+00 1.00000E+00 1.00(X)OE+OO I .oOOOOE+00 1.00000E+00 1 .OOOOOC+OO 2 2 2 2 2 2


A P I M P M S * L 4 . 3 - 4 92 = 0732290 0506397 2Lb

SECTION +CONCENTRIC, SQUARE-EDGED ORIFICE METERS. PART 4-BACKGROUND

559.5 1.43078E+W 2.47361E-01 2.71578- 1.00000E+00 -5 1.03233E+00 1.76320E-01 1.93581E-04 l.OooOOE+00 4 6.97291E-01 1.1673 1 E-01 1.28159E-04 1 .OOOOOE+OO -3 6.12716E-01 1.09778E-01 1.09887E-04 l.OOOM)E+00 -3 6.02411E-01 1.05084E-01 1 .O5 1 88E-04 I.OOOOOE+00

111

5035.6 1.35697E+OO 7.03806E-01 7.72708- l.OOOOOE+OO -5 8.30723E-01 4.25662E-01 4.67335- 1.OOOOOE+00 4 6.45881E-01 3.24377E-01 3.56133E-04 1.00000E+00 -3 6.03868E-01 3.24582E-01 3.24904E-04 l.OOOOOE+OO 2 5.99259E-01 3.13607E-01 3.139 17E-04 l.OooOOE+~

Table 4-C-&Selected Round Robin Test Results Matrix-SI Units (D, = 0.073670 m, CS = 0.00001 11 6 m/m-K, d, = 0.01 4684 m, al = 0.01 000665 m/m-K)

6.18538E-01 1.03548E+00 1.13685E-03 1.00OOOE+00 -7

Flow Conditions Tf= 255.37 K, Pf= I.OI325E+O5 Pa,

= 932.26 kg/m3, p = 1.8650 Pa-s, k = -1.0, pb = 910.83 kg/m3

6.15959E-01 6.14002E-01 1.23739B+OO 1.43904E+00 1.35853E-03 1.57992E-03 1.00000E+00 1.000OOE+00 -? -7

Tf= 293.15 K, Pf = 1.01325E+05 Pa, = 907.60 kg/m3, p= 2.1220E-01 Pa-s,

k=-l.O,Pb= 910.83 kg/m3

1.07447E+00 1.07553E-03 l.OOOOOE+OO 2 5.97692E-01 1.04262E+00 1.04365E-03 l.OOOOOE+OO 2 5.97837E-01 4.08036-2 2.19220E-02 8.28229E-01 2 5.97264E-01 7.37152E-02 1.04092E-01 9.75542E-01

r f = 353.15 K, Pf= 1.01325E+05Pa, pf,p = 868.43 kg/m3, p = 1.7490E-02 Pa-s, k=-1.0, Pb=910.83 kg/m3

1.28854E+00 1.50258E+ûû 1.28982E-03 1.50407E-03 1.oooOOE+00 l.OOOOOE+OO 2 2 5.97549E-0 1 5.97441E-O 1 1.25084E+00 1.45905E+W 1.25208E-03 1.46050E-03 1.00000E+00 1.00000E+Oû 2 2 5.97758E-01 5.97734E-01 4.44903E-02 4.57436E-02 2.39027E-02 2.45760E-02 7.52650E-01 6.63329E-01 2 2 5.97176E-01 5.9711 1E-01 8.74695E-02 1.00692E-01 1.235 15E-01 1.42186E-01 9.6478 1E-0 i 9.52063E-0 i

r /= 288.71 K, Pf= i.O1325E+O5 Pa, pf,p = 999.01 kg/m3, p = 1.1990E-03 Pa-s, k = -1.0, pb = 999.01 kg/m3

6.00256E-01 1.09732E-01 5.8954 1E-02 1.000OOE+OO n

Tf= 372.04 K, Pf = 1.01325E+05 Pa, pf,p = 941.75 kg/m3, p = 2.8250E-04 Pa-s, k =-].o, pb = 999.01 kg/m3

5.98249E-01 3.28098E-01 1.76273E-01 l.OOOOOE+Oû a

r f = 255.37 K, Pf= 1.01325E+05 Pa, pf,p =2.1181 kg/m3, p = 1.3070E-05 Pa-s, k = 1.3198, pb= 1.86131 kg/m3

5.96876E-01 2.07994E-01 2.93707E-01 9.92956E-01 2 5.96858E-01 2.69322E-01 3.80308E-01 9.96478E-01 2 5.96828E-01 9.271 85E-01 4.98136E-01

~ 1.OOOOOE+00 2

Tf = 283.15 K, Pj = 6.89476E+05 Pa, pf,p = 4.9831 kg/m3, p = 1.0670E-05 Pas, k = 1.3622, pb = 0.70817 kg/m3

5.96836E-01 2.42022E-01 3.41757E-01 9.90413E-01 2 5.96820E-01 3.13788E-01 4.43097E-01 9.95206E-01 2 5.96792E-01 1.08 165E+OC 5.81 i24E-01 1.00000E+OC 2

Tf = 255.37 K, Pf = 6.89476E+06 Pa, pf,p = 1042.35 kg/m3, p = 1.5430E-04 Pa-s k=-1.0, Pb= 1.86131 kglm3

ï j = 255.37 K, Pf = 1.37895E+06 Pa, P,,~ = 32.783 kg/m3, p = 1.3520E-05 Pa-s, k = 1.3198, pb= 1.86131 kg/m3

ï j = 283.15 K, Pf = 3.44738E+06 Pa, pf,p = 26.627 kg/m3, p= 1.1310E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

~~

Tf = 338.71 K, Pf = 6.89476E+06 Pa, pf,p = 44.168 kg/m3, p = 1.3650E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

Tf = 333.15 K, Pf = 1.37895E+07 Pa,

k=-1.0, pb= 1.86131 kg/m3 = 520.04 kg/m3, p = 4.1710E-05 Pa-s,

Cell Value

cd “in1

Q v Y ICD cd 4111

Q v Y ICD

-

cd 4m Q v Y ICD cd 4”l

Q v Y ICD cd 9ni Q v Y ICD

91n

Y ICD cd 9 m Q v Y ICD cd 9111

Y ICD

-

-

- cd

Q v

-

-

Qv

- cd 9 m Q v Y ICD cd 9m Q v Y ICD cd ‘lin Q v Y ICD cd 9 m Q v Y ICD

-

-

-

-

L I L

5.98801E-01 I 5.97568E-01

L

5.98588E-01 I 5.97468E-01

~~~~~

4.16222E-02 1.24652E-01

13987.7 1.18122E+00 l.O2109E+OO 1.12105E-03 l.OOOOOE+Oû -4 7.69 144E-01 5.56847E-01 7.21152E-04 l.OOOOOE+OO -4 6.31661E-01 5.28724E-01 5.80486E-04 1.00000E+Oa -7

6.01673E-01 5.39002E-01 5.39537E-04 1.oO000E+oa 2 5.98434E-01 5.21957E-01 5.22474E-04 I.OOOOOE+C-C 2 5.98461E-01 2.35999E-02 1.26792E-02 9.57057E-01 2 5.97729E-01 3.75799E-02 5.30662E-02 9.93886E-01 2 5.97724E-O 1 5.46349E-01 2.93529E-01 1.00000E+OC 2 5.9724-1 9.65089E-02 5.18500E-02 9.96845E-01 2 5.97206E-0 1 8.72206E-02 1.23 163E-01 9.987773-01 2 5.97174E-O I 1.12605E-01 1.59009E-01 9.99389E-01 2 5.97121E-01 3.86517E-01 2.07659E-01 l.OOOOOE+OC 2

Pa

27415.

1.08585E+W 1.31410E+OO 1 A4275E-03 1.00000E+OO 4 7.36966E-O1 8.81 114E-01 9.67375E-04 l.OOOOOE+OO -3 6.24554E-01 7.31885E-01 8.03536E-04 l.OOOOOE+OC -3 6.00597E-01 7.53254E-01 7.54000E-04 1.00000E+OC 2 5.98030E-01 7.30246E-O 1 7.30969E4 1 .OOOOOE+OC

5.98099E-01 3.15975E-02 1.69760E-02 9.15832E-01 2 5.97474E-0 1 5.22788E-02 7.38224E-02 9.88016E-01

5.97466E-01 7.64558E-01 4.10764E-01 1.00000E+OC 2 5.97088E-01 1.34666E-01 7.23503E-02 9.93815E-01 2 5.97056E-01 1.2 1934E-01 1.72182E-01 9.97603E-01 2 5.97030E-01 1.575 16E-O I 2.22427E-01 9.98802E-01

5.96987E-01 5.4 1OO3E-01 2.90657E-01 1.00000E+OC 2

7.08901E-01 I 6.96641E-01 I 6.87257E-01

-3

I I - I I

5.99699E-01 I5.99318E-01 15.99032E-01

5.97250E-O i

1.9 1092E-01 1.02665E-01 9.87378E-01

5.96930E-01 1.73720E-03 2.45308E-03 9.95108E-01 2 5.969 10E-01 2.24697E-01 3. i7292E-01 9.97554E-03 2 5.96875E-01 7.727 16E-01 4.15146E-03 1.00000E+O( 2


. - - -

A P I


Table 4-C-&Selected Round Robin Test Results Matrix-SI Units (Dm = 0.1 02270 m, % = 0.0000111 6 m/m-KI dm = 0.020439 m, al = 0.00001 665 m/m-K)

- Cell

Value

cd 9m Qv Y ICD Cd 4m Qv Y ICD

4111

Y ICD

9111

Y ICD

-

-

- cd

Qv

-

Q"

Pa

Flow Conditions

rJ. = 255.37 K, Pf = 1.01325E+05 Pa, pf,/, = 932.26 kg/m3, p = 1.8650 Pa-s, k=-1.0, pb=910.83 kg/m3

559.5

4.78798E-01 5.25673E-04 1.00000E+Oû -S

I .42942~+oa

5035.6

1.23678E+oC 1.24282E+oC I .36449E-03 I .OOOOOE+OC -5

13987.7

1.08598E+OC 1.8 1881E+OC 1.99687E-03 I .00000E+OC -4

27415.

1.00447E+OC 2.35522B+OC 2.58580E-03 1.000OOE+OC -4

55950.8

9.31233E-01 3.1 1928E+OI 3.42465E-03 1.00000E+O( -4

80569. I 8.98444E-01 3.61 133E+O( 3.96488E-0- 1.00000E+O( -4 6.77452E-0 1 2.6901 8E+O( 2.95354E-02 I .00000E+O( -3 6.12122E-01 2.3 8247E+0( 2.6 1572E-O: I .00000E+O( -3 5.98911E-01 2.4948 1 E+O( 2.49128E-02 1 .OOOOOE+O( 2

109663.5

8.72954E-01 4.09369E+Gí 4.49446E-0: 1 .OOOOOE+O( -4 6.69788E-01 3.10303E+Oi 3.40682E-0: 1 .OOOOOE+O( -3 6.10537E-03 2.77235E+Oi 3.04377E-0: I .00000E+O( -2 5.98683E-03 2.9095 1E+O( 2.9 I239E-O: 1.00000E+O( 2

Tf = 293.15 K, Pf = 1 .O 1325E+05 Pa, pf,/> = 907.60 kg/m3, p = 2.1220E-01 Pa-s, k = -1 .O, pb = 910.83 kg/m3

9.58873E-O1 3. i 7306E-O I 3.4837 1 E-O4 1 .00000E+OC 4 6.77984E-01 2.19900E-01 2.41428E-04 1 .OOOOOE+OO -3 6.0949 1 E-0 1 2.1 1572E-01 2.1 1782E-04 1.00000E+00 -2 6.0 1365E-O 1 2.03244E-01 2.03445E-O4 I .00000E+ûû 2 6.01295E-O1 9.58381E-03 5.14896E-03 9.98282E-01 2 5.99655E-01 1.46950E-O2 2.07507E-02 9.99755E-O1 2 5.99655E-01 2.12389E-01 1.14107E-01 1.00000E+00 2 5.98500E-01 3.75887E-02 2.0 1948E-02 9.99874E-01 2

7.88535E-01 7.82825E-01 8.59463E-04 I.OOOOOE+Oû 4 6.36219E-01 6.19067E-O1 6.79674E-04 1.00000E+OC -3 6.02522E-O1 6.27466E-O 1 6.28087E-04 1.00000E+OC 2 5.98864E-O1 6.07202E-01 6.07803E-04 I.OOOOOE+Oû 2 5.98851501 2.82407E-02 1.51725E-02 9.84540E-01 2 5.98064E-01 4.3 8 825E-02 6. I9661 E 4 2 9.97799E-01 2 5.98062E-O 1 5.35480E-01 3.41416E-01 1.00000E+OO 2 5.97520E-01 1.12469E-01 5.04246E-O2 9.98864E-01 2

7.37203E-01 1.2 1977E+OC 1.339 18E-03 1.00000E+OC -3 6.24766E-0 1 l.O132OE+OC I . I 1239E-O3 1 .OOO00E+OC -3 6.0078OE-O 1 1.04275E+OC 1.04378E-03 1 .OOOOOE+OC 2

7.1 0578E-3-01 I .64600E+OC 1.80715E-O3 1 .OOOOOE+OC -3 6.1905OE-01 1.40550E+oC 1.5431OE-O3 1 .OOOOOE+OC -3 5.99926E-01 1.45777E+OC 1.45922E-03 1 .OOOOOE+OC 2

6.87492E-O1 2.27504E+OC 2.49776E-O3 I .00000E+O( -3 6.14205E-O1 1.99215E+O( 2.187 I8E-03 1 .OOOOOE+O( -3 5.99213E-01 2.08006E+O( 2.082 I2E-03 1 .OOOOOE+O( 2

Tf = 353.15 K, Pf = l.O1325E+O5 Pa, pL,, = 868.43 kg/m3, p = 1.7490E-02 Pa-s, k = -1 .O, p6 = 910.83 kg/m3

T/ = 288.71 K, Pf = 1.01325E+05 Pa, pf,,, = 999.0 1 kg/m3, p = 1. I990E-03 Pas , k=-1.0, pb=999.01 kg/m3

cd

Qv 4111

Y ICD

9111

Q" Y ICD cd 4m Q" Y ICD

cd 9lll

Y ICD

%Il

Y ICD

cd 4lll

Q" Y ICD

Cd %li

Q" Y iCD

%Il

Q" Y iCD

- cd

-

-

Q"

-

Q"

-

-

- cd

-

5.98209E-01

1 .O1 189E-03 l.OOOOOE+Oû

i,oi089~+0a 5.97888E-01 1.41449E+OC 1.41589E-03 1.00000E+OC

Tf = 372.04 K, Pf = 1.01325E+05 Pa, pf,p = 941 -75 kg/m3, p = 2.8250E-04 Pa-s, k = -1.0, pi> = 999.01 kg/m"

5.9761 9E-01 2.01979E+OC 2.021 79E-03 1.00000E+OC 2 5.97734E-01 7.90418E-02 4.24657E-O2 8.28227E-O I 2 5.97278L01 1.42824E-01 2.0 1680E-0 I 9.75542E-01

5.97505E-01 2.42329E+O( 2.42569E-01 1 .OOOOOE+O( 2 5.9767 1 E-0 1 8.61856E-02 4.63037E-O2 7.52646E-O1 2 5.97208E-O1 1.69478E-01 2.39319E-01 9.64780E-01

5.974 19E-0 1 2.82676E+ûí 2.82956E-07 1 .OOOOOE+O( 2 5.97652E-O 1 8.8614OE-02 4.76084E-02 6.63324E-01 2 5.97 l57E-01 i .95 101E-01 2.75501E-01 9.52062E-0 1

Tj = 255.37 K, Pf = 1.01325E+05 Pa, pf,,=2.1181 kg/m3,p= 1.3070E=o5 Pa-s, k = 1.3198, p b = 1.86131 kg/m3

5.98230E-01 4.57063E-02 2.4556OE-O2 9.57057E-0 1 2 5.97648E-01 7.27999E-02 1.02800E-01 9.93885E-Ol 2 5.97644E-01 1.05839EtOO 5.68627E-01 1 .O~OE+OO 2 5.97264E-0 1 1.86988E-01 1.0046 1E-01 3.96845E-01

5.97942E-O 1 6.12030E-O2 3.288 17E-O2 9.15831E-O1 2 5.97446501 I .01284E-01 1.43022E-01 9.88016E-01 2 5.97439E-01 1.48124E+Oo 7.95804E-01 l.OOOOOE+Oû 2 5.97138E-01 2.60933E-01 1.40188E-01 9.93815E-01 2 5.97 1 12E-0 1 2.36266E-01 3.33629E-01 3.97603E-01 2 5.97092E-O1 3.05215E-01 4.3099OE-O1 5.98802E-01

Tf = 283.15 K, Pf = 6.89476E+05 Pa, pLP = 4.9831 kg/m3, p = 1.0670E-05 Pa-s, k = 1.3622, p h = 0.70817 kg/m3

Tf = 255.37 K, Pf = 6.89476E+06 Pa, = 1042.35 kg/m3, p = 1.5430E-04 Pa-s

pb= 1.86131 kg/m3

5.97267E-01 2.1 1545E+OC 1.13654E+OC 1 .O0000E+OC 2 5.97033E-01 3.70282E-01 1.98936E-O 1 9.87378E-O1

5.97 194E-01 2.53823B+OC 1.36368E+OC 1.00000E+OC 2 5.96989E-01 4.4 1807E-O 1 2.37363E-01 9.81825E-01

5.97 14OE-01 2.96099E+O( 1.59081E+3+0( 1 .OOOOOE+O( 2 5.96956E-01 5.1 1967E-01 2.75057E-01 9.7526 1 E-0 1

lj = 255.37 K, Pf = 1.37895E+06 Pa, pfp = 32.783 kg/m3, p = 1.352OE-O5 Pa-s, k L 1.3198, p),'1.86131 kg/rn3

ï j = 283.15 K, Pf = 3.44738E+06 Pa, pf,p = 26.627 kg/m3, p = 1.1310E-05 Pa-s, k = 1.3622, p,, = 0.70817 kg/m3

5.98408E-01 3.39049E-02 4.78768E-02 9.99951E-01 2 5.98331E-01 4.37436E-02 6.17698E-02 9.99976E-01 2

5.97477501 1.01518E-01 1.43352E-01 3.99560E-01 2 7.9744 1E-O1 1.3101 1E-01 1.85000E-01 >.99780E-01 ?

5.97232E-01 1.68994E-O1 2.38635E-01 3.98777E-01 2 3.97207E-01 1. 18 180E-01 3.0809 1E-O1 ).99389E-01 1 5.97 164E-01 7.489 18E-O1 L02361E-01 i .OOOOOE+OO 1

5.970 12E-0 1 3.36623E-01 4.75342E-01 9.95108E-01 2 S.96996E-O 1 4.35406E-01 6.14833501 9.97554E-01 2 5.96969E-01 1.49735E+00 9.04458E-O1 I .00000E+00 2

5.96969E-01 4.03045E-01 5.69136E-O1 9.92956E-01 2 5.96955E-01 5.21888E-01 7.36952E-01 9.96478E-01

5.96937E-01 4.68989E-01 6.62255E-01 9.90412E-01 2 5.96924E-O 1 6.08060E-01 8.58636E-01 9.95206E-01

ï j = 338.71 K, Pf = 6.89476E+06 Pa, of, = 44.168 kg/rn3, p = 1.3650E-05 Pa-s, k 1.3622, p b = 0.70817 kg/m3

rf = 333.15 K, Pf = 1.37895E+07 Pa, of,p = 520.04 kg/m3, ,u = 4.1710E-05 Pa-s, k = -1.0, pb = 1.86131 kg/m3

5.96902E-01 2.09605E+OC 1.126 12E+OC 1.00000E+OC 2

5.98202E-01

8.06114E-02 1.00000E+00 2

1.50043E-01 5.9738OE-O1 L49515E-01 L41505E-01 l.OOOOOE+OO l

5.97058E-O1 l.O483OE+OO 5.63205E-01 1.00000E+00 1

5.96931E-01 1.79670E+OC 9.65288E-O1 1 .OOOOOE+OC 2


A P I MPMS*14.3e4 92 W 0732290 0506399 O99 W

80569.1 109663.5 7.9838 1E-01 7.80599E-01 1.25883E+01 1.435938+01 1.38207E-O2 1.5765 1E-O2 I .00000E+00 1.00000E+00 4 4 6.48378E-01 6.43399E-01 1.00998E+01 1.16926E+Ol 1.10885E-02 1.28373E-02 1.00000E+00 1.00000E+00 -3 -3 6.06292E-01 6.05308E-01 9.25665E+00 1.07819E+01 1.01629E-02 1.18374E-02 1.00000E+00 1.00000E+00 -2 -2 5.983 19E-01 5.98 178E-01 9.77665E+00 1.14034E+OI 9.78634E-03 1.14147E-02 I.OOOOOE+OO 1.00000E+00 2 2 5.97444E-01 5.97390E-01 9.50479E+00 1.10879E+01 9.51421E-03 1.10989E-02 1 .00000E+OO 1 .00000E+OO 2 2 5.97547E-01 5.97535E-01 3.38008E-01 3.47536E-01 I .8 1597E-Ol 1.867 16E-01 7.52648E-01 6.63326E-01 2 2 5.97258E-01 5.97225E-01 6.64863E-01 7.65407E-01 9.38847E-01 1.08082E+OO 9.64781E-01 9.52063E-01 2 2 5.97249E-01 5.97214E-01 9.95754E+00 1.16165E+01 5.34975E+00 6.24 10 1E+OO l.OOOOOE+00 1.00000E+OO 2 2 5.97120E-01 5.97099501 1.73344E+00 2.00876E+00 9.31303E-01 1.07922E+00 9.8 1825E-01 9.7526 1 E 4 1 2 2 5.97 108E-O 1 5.97088E-0 1 1.58138E+00 1.84015E+OO 2.23305E+OO 2.59846E+OO

SECTION SCONCENTRIC. SQUARE-EDGED ORIFICE METERS. PART 4-BACKGROUND 113

8.40869E-O1 1.09151E+00 1.19837E-03 l.OOOOOE+OO 4 6.48724E-01 8.25368E-01 9.06172E-04 1.OOOOOE+OO -3 6.04694E-01 8.23396E-01 8.24212E-04 l.OOOOOE+OO

Table 4-C-&Selected Round Robin Test Results Matrix-SI Units (O, = 0.202729 m, % = 0.00001 11 6 m/m-K, d, = 0.040481 m, al = 0.00001 665 m/m-K)

7.22461E-01 6.87816E-01 2.8 1346E+OO 4.46421E+00 3.08889E-03 4.90126E-03 l.OOOOOE+ûO I.OOOOOE+OO -3 -3 6.21815E-01 6.14499E-01 2.37342E+00 3.90915E+OO 2.60578E-03 .4.29185E-03 1.OOOOOE+00 1.00000E+00 -3 -3 6.00563E-01 5.99481E-01 2.45334E+00 4.08151E+00 2.45577E-03 4.08556E-O3 1.00000E+OO 1.00000E+OO

Flow Conditions Tf = 255.37 K, Pf = 1.01325E+05 Pa, pl,p = 932.26 kg/m3, p = 1.8650 Pa-s, k = -1.0, pb = 910.83 kg/m3

5.99801E-01 3.75007E-02 2.01475E-O2 9.98282E-01 2 5.98782E-01 5.75599E-02 8.12798E-O2 9.99755E-01 2 5.98781E-01 8.3 19 18E-0 I

1.OOOOOE+00 2 5.98063E-01 1.47341E-01 7.91596E-02 9.99874E-01 2

4.46953~-01

Tf = 293.15 K, Pf = 1.01325E+05 Pa, pl,p = 907.60 kg/m3, p = 2.1220E-01 Pa-s, k = -1.0, pb = 910.83 kg/m3

5.98282E-01 5.97895E-01 1.10674E-01 1.79190E-01 5.94600E-02 9.6271 1E-O2 9.84540E-01 9.57057E-01 2 2 5.97792E-01 5.97533E-01 1.72059E-01 2.85515E-01 2.42962E-01 4.03173E-O1 9.97799E-O1 9.93886E-01 2 2 5.97790E-01 5.97530E-01 2.49 165E+OO 4.15093E+W

l.OOOOOE+OO l.OOOOOE+Oû 2 2 5.97453E-01 5.97292E-01 4.41 129E-01 7.33529E-01 2.36999E-01 3.94093E-01 9.98864E-01 9.96845E-01 2 2

1,33865~+00 2.2301i~+oa

ïj = 353.15 K, Pf = 1.01325E+05 Pa, pIp = 868.43 kg/m3, p = 1.7490E-02Pa-s, k = -1.0, pb = 910.83 kg/m3

5.98006E-01 1.32909E-01 1.87679E-01 9.99951E-O1 2 5.97958E-01 1.7 1485E-O 1 2.42152E-01 9.99976E-01 2 5.97878E-01 5.88250E-01 3.16041E-01 1 .OOOOOE+OO 2

Tf = 288.71 K, Pf = 1.01325E+05 Pa, pl,p =999.01 kg/m3, p = 1.1990E-03 Pa-s, k=-1.0, pb = 999.01 kg/m3

5.97426E-01 3.98 187E-01 5.62276E-01 9.99560E-01 2 5.97404E-01 5.13882E-0 I 7.25647E-01 9.99780E-01 2 5.97366E-01 1.76326E+OC 9.47320E-01 1.00000E+OC 2

Tf = 372.04 K, Pf = 1.01325E+05 Pa, pl,p = 941.75 kg/m3, p= 2.8250E-04 Pa-s, k = -1.0, pb = 999.01 kg/m3

Tf = 255.37 K, Pf = l.OI325E+05 Pa, pl,p = 2.1181 kg/m3, p= 1.3070E-05 Pa-s, k = 1.3198, pb= 1.86131 kg/m3

Tf = 283.15 K, Pf = 6.89476E+05 Pa, pl,p = 4.9831 kg/m3, p = 1,0670E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

Tf = 255.37 K, Pl = 6.89476E+06 Pa, plSp = 1042.35 kg/m3, p = 1.5430E-04 Pa-s k=-1.0, pb=1.86131 kg/m3

Tf = 255.37 K, Pf = 1.37895E+06 Pa, pl,p = 32.783 kg/m3, p = 1.3520E-05 Pa-s, k = 1.3198, pb= 1.86131 kg/m3

Tf = 283.15 K, Pf = 3.44738E+06 Pa, pl,p = 26.627 kg/m3, p = 1.1310E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

Tf = 338.71 K, Pf = 6.89476E+06 Pa, pl,p =44.168 kg/m3, p= 1.3650E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

ïj = 333.15 K, Pf = 1.37895E+07 Pa, pl,p = 520.04 kg/m3, p = 4.1710E-05 Pa-s, k = -1.0, pb = 1.86131 kg/m3

Cell ?alue

cd ?ni

Q v Y [CD

cd ?ni

Q v Y [CD cd ?lit

Q v Y ICD

cd 4ni

Q v Y [CD cd 4ni Q v Y ìCD cd 4in Q v Y ICD

4ni

Y ICD

-

-

-

-

-

-

- cd

Q v

- cd 4in Q v Y ICD cd Q I

Y ICD

_.

Q"

- cd 4ni Q v Y ICD cd 4111

Q v Y ICD

-

- cd 4ni Qv Y ICD -

2 12 12 5.99845E-01 I 5.98290E-01 I 5.97883E-01 7.95243E-01 2.37957E+00 3.96324E+00 7.96031E-04 2.38193E-03 3.96717E-03 1 .OOOOOE+OO I I 1.OOOOOE+00 1 .OOOOOE+Oa

5.97273E-01 6.62954E-01 9.36151E-01 9.98777E-01 2 5.97257E-01 8.55922E-O 1 1.20864E+OC 9.99389E-01 2 5.97230E-01 2.93809E+oC 1.57850E+oC 1.00000E+OC 2

Pa

27415. 5.73195E-01 8.0313 lE+OO 8.81757E-03 1.00000E+00 4 5.701 11E-01 5.08902E+OO 5.68514E-03 1.00000E+Oû -3 6.10828E-01 5.4401 lE+Oû 5.97270E-03 1.00000E+OC -2 5.98950E-01 5.70906B+OC 5.71472E-03 I.OOOOOE+OC 2 5.97682E-01 5.54668E+OC 5.55217E-03 l.OOOOOE+OC

5.97716E-01 2.39989E-01 1.28935E-01 9.1583 1E-01 2 5.97406E-O 1 3.97276E-0 1 5.60990E-01 9.880 16E-û 1 2 5.97402E-01 5.8 1005E+OC 3.12149E+OC I .OOO00E+OC 2 5.97213E-01 1.02369E+OC 5.4998 1E-01 9.938 15E-01 2 5.97197E-01 9.26928E-01 1.30891E+o( 9.97603E-01 2 5.97185E-01 1.19744E+O( 1.69090E+oC 9.98802E-01 2 5.97 1 ó4E-01 4.11286E+o( 2.20966E+O( 1.00000E+O( 2

55950.8 8.21381E-01 1.07925E+01 1.1849 1E-02 1.OOOOOE+OC 4 6.54928E-01

9.33381E-03 l.OOOOOE+OC -3 6.07674E-01 7.73146E+OC 8.48837E-03 1.00000E+OC -2 5.98507E-01 8.14977E+OC 8.15785E-03 I.OOOOOE+OC 2 5.97515E-01 7.92 160E+oC 7.92945E-03 l.OOOOOE+OC 2 5.97586E-01 3.09979E-01 1.66538E-01 8.28227E-01 2 5.9730 1 E-O 1 5.60274E-0 1 7.91157E-01 9.75542E-O 1 2 5.97294E-01 8.29859E+O( 4.45846E+O( 1 .00000E+O( 2 5.97 147E-01 1.45277B+O( 7.80512E-01 9.87378E-01 2 5.97 134E.g 1.32073E+Gí 1.86499E+O( 9.95108E-01 2 5.97 125E-01 1.70832E+M 2.4 123 1 E+O( 9.97554E-01 2

8.5015 i ~ + o a

5.97108E-01 5.87496E+N 3.15636E+Gí l.OOO00E+CM 2

9.96478E-01 2 5.97084E-01 7.04967E+Oa 3.78748E+OC l.OOOOOE+OC 2



7.54610E-01 3. I9158E+OI 3.50404E-02 1.00000E+00 -3 6.36388E-O1 2.65908E+Ol

I . O ~ O E + O O 2.91940E-02

Table 4-C-&Selected Round Robin Test Results Matrix-SI Units (Dm = 0.36351 3 m, a;! = 0.0000111 6 m/m-K, d,,, = 0.072628 m, al = 0.00001 665 m/m-K)

7.37907E-O1 7.25060E-01 3.745 i 3E+Oi 4.29325E+Ol 4. I 1 177E-O2 4.71355E-02 1 .OOOOOE+ûû I .0000ûE+Oû -3 -3 6.3 1890E-01 6.28479E-01 3.16834E+01 3.67645E+01

1 .OOOOOE+00 1.00000E+Oû 3.47852E-02 4.03637E-O2

Flow Conditions

2.4741 iE+01 2.71632E-02 1.00000E+00 2 5.98 12 1 E-0 1 2.62 163E+O 1

1.00000E+00 2.62423E-O2

î j = 255.37 K, Pf = 1.01325E+05 Pa, P,,]~ = 932.26 kg/m', p = 1.8650 Pa-s, k=-1 .0 , p,,=910.83 kglm'

2.96483E+01 3.45537E+01 3.25509E-02 3.79365E-O2 1.00000E+00 i .00000E+00 2 2 5.97995E-01 5.97901E-O 1 3.14530E+O 1 3.66893E+O 1

1 .OOOOOE+00 1.00000E+00 3.14841E-02 3.67257E-02

7 j =293,15K, P f = 1.01325E+05Pa, p , = 907.60 kg/m3, p = 2. i 22OE-O I Pa-s k=-1.0, plJ=910.83 kglm"

'/'

2 5.97977E-0 1 7.65557E+00 7.66315E-03 1.00000E+00 2 5.9797OE-O1 3.5606 1 E-0 1 1.9 1296E-01 9.84540801 2 5.97643E-01 5.53700E-01 7.8 1874E-01 9.97799E-01 2 5.97642E-O1 8.0 1836E+OO 4.30791E+00 1 .00000E+00 2 5.97416E-01 1.41986E+00 7.62827E-01 9.98864E-01 2 5.97397E-01 1.28166E+00 1.80982E+00 9.99560E-01

ïj =353.15 K, Pf = 1.01325E+05 Pa, pi,/, = 868.43 kg/rn3, p = 1.749OE-O2 Pa-s k = -1.0, pl, = 910.83 kg/m'

2 2 5.977O4E-O 1 5.9757OE-O I i .27534E+Ol i .78508E+01 1.27661E-02 1.78685E-02 1 .OOOOOE+OO 1.00000E+Oû 2 2 5.97712E-01 5.97592E-01 5.766 18E-0 1 7.72337E-O 1 3.09791E-01 4.14943E-01 9.57057E-01 9.15831E-01 2 2 5.97469E-01 5.97384E-01 9.18944E-01 1.27874E+00 1.29763E+Oû 1.80570E+00 9.93886E-01 9.88016E-01 2 2 5.97467E-01 5.97381E-01 1.33600E+01 1.8701 3E+O 1 7.17774E+00 1.00474E+Ol 1 .OOOOOE+OO 1.00000E+00 2 2 5.97308E-01 5.97254E-01 2.36121E+00 3.29536E+00 1.26858E+00 1.77045E+00 9.96845E-01 9.93815E-01 2 2 5.97295E-01 5.97244E-01 2.13406E+00 2.98391E+00 3.01348E+00 4.21355E+00 9.98777E-O1 9.97603E-O1

ïj = 288.71 K, Pf = 1.01325E+05 Pa, p,,+ = 999.01 kg/m3, p = I . 199OE-O3 Pa-s k = -1 .O, plJ = 999.01 kg/m'

2 5.97314E-01 1.80350E+00

Tj = 372.04 K, Pf = 1.01325E+05 Pa, pl,/> = 941.75 kgltn', p = 2.8250E-04 Pa-s k = -1.0, plJ = 999.01 kg/m3

2 2 5.97285E-01 5.97263E-O1 2.14022E+OO 2.46392E+00

Tf = 255.37 K, Pj = 1.01325E+05 Pa, pl.p = 2. i 18 i kg/rn3, p = 1.3070E-05 Pa-s k = 1.3198, pl>= 1.86131 kg/m3

5.972 10E-01 4.67682E+00 1.51265B+00 9.873788-01 1 3.972018-01 1.25 177E+00 i.00388E+00

Tj = 283.15 K, Pf = 6.89476E+05 Pa, pl , / , = 4.983 1 kg/m3, p = 1.0670E-05 Pa-s k = 1.3622, p,, = 0.708 17 kg/m3

5.971918-01 5.97 177E-01 5.580448+00 6.46683E+00 2.998128+00 3.474358+00 9.81825E-01 9.75261E-01 2 2 5.97 183E-01 5.97170B-01 5.090938+00 5.924078+00 7. I88861!+00 8.365328+00

Tf = 255.37 K, Pf = 6.89476E+06 Pa, P , , ~ = 1042.35 kg/m3, p = 1.5430E-04 Pa-: k = - l . O , PI>= 1.86131 kg/m3

ij = 255.37 K, Pf = 1.37895E+06 Pa,

B = 1.3198, p,,= 1.86131 kg/m3 = 32.783 kg/m3, p = 1.352OE-O5 Pa-s.

r/ = 283.15 K, P' = 3.44738E+06 Pa, g,,,, = 26.627 kg/m3, p = 1. I3 IOE-05 Pa-s, r( = 1.3622, p,, = 0.708 i 7 kg/m3

rJ = 338.71 K, Pf = 6.89476E+06 Pa, ?,,+ = 44.168 kg/m3, p = 1.3650E-05 Pa-s, i = 1.3622, p,, = 0.70817 kg/m3

rf = 333.15 K, Pf = 1.37895E+07 Pa, ?,,p = 520.04 kg/m3, p = 4.1710E-05 Pa-s, : = -1.0, pb = 1.86131 kg/m3

Cell Value

cd 4111

Qin Y ICD - cd qlJ1

Q,, Y ICD

cd

Qv Y [CD cd

-

q J J 1

-

Y I J I

Q" Y [CD cd bi

Y [CD

-d ?in

-

2,

- r-

2, Y CD -d 1111

Y CD

- "

2,

-

559.5

1.17826E+O 4.98335E+OI 5.47 122E-0: I .00000E+Oi 4 7.6883 1E-O 3.2 I246E+oi 3.52695E-O: I .00000E+Oi -4

6.321 28E-O 2.58880E+M 2.84225E-O: 1 .OOOOOE+O( -3 6.02246E-O1 2.63970E+M 2.6423 1 E-O: 1 .OOOOOE+O( 2 5.990 14E-01 2.55626E+O( 2.55879E-0: 1 .00000E+O( 2 5.98984E-01 1.20546E-03 5.47642E-3-02 3.98282E-01 2 5.98304E-01 1.85131E-O1 2.6 1422E-0 1 >.99755E-01 1 3.98304E-01 2.67572E+Oí 1.43755E+OC I .00000E+OC 1 L97824E-O 1 1.74084E-O1 L54705E-01 1.99874E-01 ! i.97786E-01 1.2766 1E-0 1 i.03896E-01 j.99951E-O1 ! i.97755E-01 i.51803E-O1 l.79 196E-01 1.99976E-01

1.97701E-01 .89295E+OO .01700E+00 .00000E+00

,

Pa

5035.6 I 13987.7 I 27415.

6.13732E-01

8.27868E-03

7.89076E-03

6.08682E-O1 1.24640E+O i 1.36842E-O2 1 .OOOOOE+OC -2 5.98771E-01 1.3 i 224E+0 1

1.00000E+OC 1.3 1354E-02

7.92546E-01 2.34642E+Ol 2.57614E-0î I .00000E+O( -4 6.46865E-01 1.89200E+OI 2.07723E-02 1.00000E+O( -3 6.06089E-O 1 1.73753E+Ol 1.90763E-O2 1.00000E+OC -2 5.98417E-01 1.83605E+01 1.83787E-02 1.00000E+OC

L I ' I ' 5.973578-01 ~5.972668-01 I5.97221E41

55950.8 I 80569.1 I 109663.5 I

-3 1-3 1-3 6.041 17E-O1 I6.03284E-01 I 6.02656E-01

3.06235E-02

5.97479E-0 1

5.84473E-O1 7.52647E-01

5.9747 1 E-O 1 1.1 1856E+OO 6.00953E-01 6.63325E-01

2.54670E+00 3.02218E+OO 3.47927E+OC 9.75542E-0 1 9.6478 1E-01 9.52062E-O 1

2.67129E+01 3.20538E+01 3.73947E+01 1.43517E+01 1.7221 1E+01 2.00905E+01 Y 1 .OOOOOE+OO 1.00000E+00 1 .OOOOOE+OC

5.97309E-01 5.97278E-O1 5.97255E-01

j.95108E-01

L97195E-01

i.97183E-O1 ' .89133E+01 .01613E+01 .OOOOOE+OO

5.97167E-01

9.95206E-O1

5.97155501


A P I MPMS*L4-3e4 92 0732290 0506403 577

5.975 16E-01 1.245428+02 1.36734E-O1 1.00000E+00

SECTION 3---CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 4-BACKGROUND 115

6.86507E-01 6.78091E-01 1.4709 1E+02 i .69503E+02 1.61491E-01 1.86097E-01 1.00000E+00 1.00000E+00

Table 4-C-6-Selected Round Robin Test Results Matrix-SI Units (Dm= 0.746150 m, Q = 0.00001116 m/m-K, d, = 0.149225 m, al = 0.00001665 m/m-K)

-3

:low Conditions

~~

-2 12

ïj = 255.37 K, Pf = 1.01325E+05 Pa, >,,p = 932.26 kg/m3, p = 1.8650 Pa-s, :=-].o, pb=910.83 k g h 3

1.1 1081E+01 1.1 1191E-02 1.OOOOOE+00 2 5.98357E-01 1.07796E+01 1.07903E-02 1 .OOOOOE+00 2 5.98338E-01 5.08348E-01 2.731 13E-01 9.98282E-01 2 5.97924E-O 1 7.81053~-01 i.i0292~+00 9.99755E-01 2 5.97924E-01 1.12886E+01 6.06488E+OO 1 .OOOOOE+OO 2 5.97631E-01 2.00074E+00

9.99874E-01 2 5.97608E-01 1.80487E+OO 2.54864E+00 9.99951E-01 2 5.97589E-01 2.32884E+OO 3.28853E+00

I . O ~ ~ ~ I E + O O

ïj = 293.15 K, PJ = 1.01325E+05 Pa, J , , ~ = 907.60 kg/m3, p = 2.1220E-01 Pa-s, :=-].o, pbZ910.83 kg/m3

3.32317E+01 5.53454E+01 3.32646E-O2 5.54002E-02 1.OOOOOE+OO 1.OOOOOE+OO 2 2 5.97725E-01 5.97558E-01 3.23051E+01 5.38266E+01 3.23371E-O2 5.38800E-02 l.OOOOOE+OO l.OOOOOE+OO 2 2 5.97720E-01 5.97562E-01 1.50251E+00 2.43364E+OO 8.07235501 1.30749E+3+0(1 9.84540E-01 9.57056E-01 2 2 5.97520E-01 5.97414E-O 1 2.33701~+00 3.87905~+00 3.30~08~+00 5.47756~+00 9.97799E-01 9.93885E-01 2 2 5.975 19E-01 5.97412E-01 3.38433E+01 5.63952E+01 1.81825E+01 3.02987E+01 1 .OOOOOE+00 1 .00000E+OO 2 2 5.97380E-01 5.97314E-01 5.9937 1E+00 9.968 18E+OC

9.98864E-01 9.96845E-01 2 2 5.97369E-01 5.97306E-01 5.41040E+00 9.00929E+OC 7.63997E+OO 1.27219E+OI 9.99560E-01 9.98777E-01 2 2 5.97361E-01 5.97300E-01 6.98256E+00 1.16318E+01 9.86001E+00 i .64252E+01

3.22016~+00 5.35547~+00

fj = 353.15 K, Pl = 1.01325E+05 Pa, ?,,p = 868.43 kg/m3, p = 1.7490E-02 Pa-s, ¿ = -1.0, Pb = 910.83 kg/m3

1.10618E+02 I . 10727EíIl 1.00000E+00 2 5.97407E-01 1.07626E+02 1.07733E-01 1.00000E+00 -

9 =288.71 K, Pf = 1.01325E+05 Pa, g,,p = 999.01 kg/m3, p = 1.1990E-03 Pa-s, k =-].o, pb = 999.01 k g h 3

1.32724E+02 1.54830E+02 1.32855E-01 i ,54983E-01 1.00000E+00 i .00000E+00 2 2 5.97378E-01 5.97355E-01 1.29 145E+02 1.50663E+02 1.29273E-01 1.50813E-01 l.OOOOOE+OO 1.00000E+00

*

r/ = 372.04 K, Pf = 1.01325E+05 Pa, %,p = 941.75 kg/m3, p = 2.8250E-44 Pa-s, k=-1.0, pb=999.01 kg/m3

4.21 119E+00

8.28226E-01 2 5.973 18E-01 7.61369E+00 1.075 12E+01 9.75542E-01

2.26249~+00

9 = 255.31 K, Pf = 1.01325E+05 Pa, o , , ~ = 2. I 18 1 kg/m3, p = 1.3070E-05 Pa-s, k = 1.3198, pb= 1.86131 kg/m3

4.59215E+00 4.72165E+00

7.52645E-01 6.63323E-01 2 2 5.97300E-01 5.97286E-01 9.03536E+00 1.04021E+OI 1.27587E+0 i 1.46886E+Oi 9.64780E-01 9.52062E-01

2.467 16~+00 2.53673~+00

r/ = 283.15 K, Pf = 6.89476E+05 Pa,

k = 1.3622, pb = 0.70817 k g h 3 = 4.9831 kg/m3, p = 1.0670E-05 Pa-s,

2 5.97248E-01 1.79507E+OI 2.53479E+Ol 9.95 108E-01 2 5.97245E-01 2.32188E+01 3.2787 i E+O 1 9.97554E-01 2 5.97237E-01 7.98514E+01 4.29006E+01 1 .OOOOOE+00 2

Tf = 255.37 K, Pf = 6.89476E+06 Pa,

k=-l.O, pb= 1.86131 kg/m3 = 1042.35 kg/m3, p = 1.5430E-04 Pa-s

2 2 5.97237E-01 5.97229E-01 2.14938E+O 1 2.50 1 15E+O 1 3.035 12E+01 3.53185E+O1 9.92956E-01 9.9O412E-O 1 2 2 5.97234E-01 5.97226E-01 2.78320E+OI 3.24288E+01 3.930 13E+O 1 4.57924E+O 1 9.96478E-O 1 9.95206E-01 2 2 5.97227E-01 5.97220E-01 9.58200E+01 1.1 1789E+02 5.14799E+Oi 6.00591E+01 1 .OOOOOE+00 1.00000E+OC 2 2

Tj = 255.37 K, Pf = 1.37895E+06 Pa, P,,~ = 32.783 kg/m3, p = 1.3520E-05 Pa-s, k = 1.3198, pb=1.86131 kg/m3

i'/ = 283.15 K, Pf = 3.44738E+06 Pa, P,,~ =26.627 kg/m3, p = 1.1310E-05 Pa-s, k = 1.3622, Pb = 0.70817 kg/m3

ï j = 338.71 K, Pf = 6.89476E+06 Pa, P,,~ = 44.168 kg/m3, p = 1.3650E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

TJ = 333.15 K, Pf = 1.37895E+07 Pa, P , , ~ = 520.04 kg/m3, p = 4.1710E-05 Pa-s, k = - l . O , pb= 1.86131 kg/m3

- Cell lalue

cd

_.

LI

Y [CD

cd b i

Y [CD cd Il"

Qv Y íCD

2,

-

2,

_.

- cd ?ni Q" Y iCD

cd L Qv Y ICD cd PlIl

Qv Y ICD cd 4n1 Qv Y ICD cd 4ni Qv Y ICD cd 4m Qv Y ICD

-

-

-

-

-

- cd 9m Qv Y ICD - cd 9ni Qv Y ICD

cd 9m Qv Y ICD

-

-

559s

1.94347E-02

1.36909E-02

5035.6

4.32590E+01 4.74941E-02 l.OOOOOE+OC -4 6.51218E-01 3.446€5E+01 3.78353E-02 1.00000E+O( -3

8.07596801 13987.7

7.51815E-01 6.7 1 183E+O i 7.36892E-02 1.00OOOE+OO -3 6.35725E-01 5.60693E+Oi 6.15585E-02 1.OOOOOE+00 -3

6.18734E-01 6.07105E-O1 6.04084E-01 i.O6973E+Oi 3.14891E+01 5.22205E+01 1.17446E-02 3.45718E-02 5.73329E-02 1.00000E+00 I l 1.00000E+00 1.OOOOOE+OO

y 9 7 6 E - 0 1 I92.99780E-01 9.99389E-4 1 2 5.97289E-01 3.99291E+OI 2.14522E+OI 1.00000E+OC n

Pa

27415. 7.22773E-01 9.03359E+O 1 9.91797E-42 1.00OOOE+OO -3 3.27969E-01 7.75394E+01 3.51305l502 1.00000E+00 -3

5.02653E-01 7.29355E+01 3.00758E-02 i .00000E+00 2 5.97992E-01 7.74556E+Ol 7.75324E-02 1.00000E+00 2 5.97476E-0 1 7.53469E+01 7.54216E-02 l.O0000E+OG 2 5.97489E-01

1.75142E+OC 9.15831E-01 2 5.97361E-01 5.39812E+(H: 7.62263E+Oí 9.88016E-01 2 5.97359E-01 7.89464E+01 4.24 144E+O 1 1 .OOOOOE+OC 2 5.9728 1E-01 1.39123E+Ol 7.47446E+oC 9.93815E-01 2 5.97275E-O 1 1 .25975E+O1 1.77888E+O1 9.97603E-01 2 5.97270E-01 1.62742E+Ol 2.29806E+OI 9.98802E-01 2 5.97261E-01 5.58982E+O i 3.003 16E+O 1 1.00000E+O( 2

3 . 2 m 3 ~ + 0 0

55950.8 I 80569.1 I 109663.5

-3 I -3 1-3 6.21400E-01 I6.18585E-01 I6.16449E-01 1.09612E+02 1.20343E-01 1.00000E+00

6.0 1458E-O 1 1.03987E+02 1.14167E-01 i l.OOOOOE+OO L I ' 5.97812lHl~ 5.97736E-0115.97678E-01

L I ' 5.97435E-01 I 5.97419E-01 I 5.97414E-01

1 .O608 i E+O 1 9.87378E-01

1.35322E+02 1.57872E+02 7.27027E+01 8.48178E+01 l.OOOOOE+00 1.00000E+OC

5.97242E-O 1 5.97233E-O 1 2.35603E+Ol 2.73029E+01 1.26579E+0 1 1.46686E+01 9.8 1824E-O1 9.75261 E-01


A P I M P M S * 1 4 = 3 - 4 92 m 0732290 0506402 403 m


Table 4-C-&Selected Round Robin Test Results Matrix-SI Units ( Dm = 0.049262 m, Q = 0.00001 11 6 m/m-K, d,,, = 0.020042 m, al = 0.00001 665 m/m-K)

- Cell Valut - c, 4111

QV Y ICD c, 4111

Qv Y ICD

c, 4lli

Qv Y ICD c, %Il

Qv Y ICD

c, 7lll

Qv Y ICD c, ?ni Qv Y [CD

7111

Q" Y [CD

111,

Y [CD

-

-

-

-

-

-

cd

2,

-d

2,

-

Irir

Y CD

L i

Y CD

-d 7111

- " d

2,

- ,7

2, f CD -d Ill1

- r 7

3"

CD -

Pa

Flow Conditions Tf = 255.37 K, Pf = 1.01325E+05 Pa,

k = - I .O, pIl = 9 10.83 kg/m3 = 932.26 kg/m3, p = I .8650 Pa-s,

559.5

2.28720E+CM 7.46344E-O I 8.194 1 1 E-O4 1.00000E+O( -6 1. I6527E+0( 3.75659E-01 4.12436E-O4 1.000OOE+O( -4 7.35864E-0 1 2.32520E-01 2.55283W i .00000E+O( -3 6.17849E-O1 2.0894OE-O 1 2.09 147E-04 I .OOOOOE+oE 3

5035.6

I .58276E+O( I .54944E+O( I -70 I I3E-0: 1.00000E+CM -5

13987.7

1.35635E+0( 2.21300E+O( 2.42966E-O: I .00000E+O( -5 8.28083E-03 1.33479E+Oí 1.46547E-0: 1.00000E+O( -4 6.48324E-O1 1.02430E+Oí I . I2458E-OC 1 .OOOOOE+O( -3 6.0687 1 E 4 i i .O26 15E+O( 1 .O27 16E-02 1.00000E+O( 2

27415.

¡.23382E+Oi 2.8 I83 1E+@ 3.09422E-O: 1 .OOOOOE+O( -5 7.86823E-03 I .77560E+0( 1.94943E-0: i .00000E+O( -4 6.37253E-O1 I .40953E+CM 1 S4752E-O: 1 .OOOOOE+O( -3 6.05725E-01 1.43389E+0( 1.43531E-0? i .00000E+O( 2

55950.8

I . 12345E+Oi 3.66601 E+O( 4.0249 I E-0: 1 .OOOOOE+O( 4 7.50763E-O i 2.42032E+Oi 2.65727E-0: I .00000E+O( -3 6.26545E-01 1.97978E+N 2.37360E-O: 1 .OOOOOE+O( -3 6.04753E-01 2.045 13E+O( 2.047 I5E-O: 1.00000E+Oí 2

80569.1

i .O739 1 E+Oi 4.20523E+Oi 4.6 I692E-0: 1.000ûOE+Oi -4 7.34967E-0 2.84327E+O( 3.12163E-O: 1 .OOOOOE+O( -3

109663.5

1.03533E+O( 4.72983E+O( 5. 19287E-03 I .OOOOOE+O( -4 7.22844E-01 3.26243E+OC 3.58182E-03 1.00000E+OC -3

= 293. I 5 K, PJ = I .O I325E+05 Pa, p = 907.60 kg/m3, I( = 2.1220E-O I Pa-s, k=-1.0, pl>=9i0.83 kg/m3

9.06957E-O1 8.771 6 0 M I 9.63033E-04 1 .OOOOOE+O( -4 6.68419E-O1 6.33631E-O1 6.95663E-O4 1.00000E+O( -3 6.09 l74E-01 6.18025E-0 1 6.18637E-04 1.00000E+OC 2

Tj = 353.15 K, Pf = l.O1325E+O5 Pa, p = 868.43 kg/m3, p = 1.749OE-02 Pa-s, k=-1.0, p,,=910.83 kg/m3

6.2 1233E-O 2.35559E+Oi 2.5862 1 E-0: I .00000E+O( -3 6.04334E-0 2.45245E+0( 2.45488E-O: 1 .OOOOOE+O( 2

6. I9 144E-0 1 2.73895E+0(: 3.00709E-03 i .OOOOOE+OC 3 6.040 1 6E-0 1 2.85969B+OC 2.86252E-03 1.000OOE+OC 2

ï'' = 288.7 i K, PJ = 1 .O i 325E+05 Pa,

k = -1.0, p,, = 999.01 kg/m3 = 999.0 I kg/m3, p = I . 1990E-03 Pa-s,

TJ = 372.04 K, Pf = 1.01325E+05 Pa, o/,/, = 941.75 kg/m3, p = 2.825OE-3-04 Pa-s, I. = -1.0, pi, = 999.01 kg/m3

6.07653Ml 2.00075E-01 2.00273E-04 1 .00000E+OC 2 6.07555E-O1 9.43329E-O3 5.06809E-03 9.98245E-01 2 6.05358E-01 1.44520E-02 2.04075E-O2 9.99750E-01 2 6.05357E-O1 2.08875E-01 1.122 I9E-O 1 1.00000E+00 2 6.03756E-01 3.69400E-02 1.98462E-O2 9.99871E-O1 2 6.03624E-01 3.33 180E-O2 4.70480E-02 3.99950E-01 2 5.03515E-01 4.29848E-02 5.06984E-O2 3.99975E-O1 2 5.03329E-O1 1.47426E-01 7.92057E-02 I .00000E+00 1

6.04271E-01 5.96891E-01 5.97483E-O4 1 .OOOOOE+oE 2 6.04251E-01 2.77503E-02 1.49090E-02 9.84201 E-O1 2 6.03127E-O1 4.31101E-O2 6.08753E-02 9.97750E-01

6.03340E-03 9.93282E-O 1 9.94267E-04 1 .OOOOOE+O( 2 6.03369E-01 4.48649E-02 2.41 039E-02 9.561 13E-O1 2 6.02504E-01 7.14880E-02 i.OO948E-01 9.9375 1E-01 2 6.02496E-O1 1.03945E+OC 5.58448E-O1 1 .OOooOE+OC 2 6.0 1890E-O 1 1.83561E-01 9.8619OE-O2 9,96775501 2 6.01838E-O1 1.65899E-01 2.34265E-01 9.98750E-01 2 6.01796E-01 2.14185E-01 3.02448E-O 1 9.99375E-01 2 6.01723E-01 7.35175E-O1 3.94977E-01 1.00000E+00 2

6.02867E-O I 1.38951E+ûí 1.39088E-O? l.OOOOOE+O( 2 6.02949E-0 1 6.OOO12Mi 3.22360E-02 9.13981E-O1 2 6.021 87E-01 9.94267E-O2 1.40400E-01 9.87752E-01 2 6.02 175E-O 1 1.45445E+0( 7.8141 1E-01 1.00000E+OC 2 6.01677E-O 1 2.56096E-01 1.37589E-01 9.93679E-01 2 6.0 1633E-O 1 2.3 1900E-01 3.27464E-01 9.97550E-01 2 6.01597E-01 2.99580E-01 k23034E-0 I 9.98775E-01 2 6.01536E-01 1.02893E+ûC 5.52796E-O 1 1 .OOOOOE+00 2

6.02460E-03 1.98367E+O( 1.98563E-O: 1.00000E+O( 2 6.02639E-01 7.72798E-02 4.15 i 90E-0; 8.2445 1 E-01 2 6.01915E-03 1.40 142E-O 1 1.97893E-03 9.75004F!-OI 2 6.01896E-01 2.07682E+0( I . 1 1578E+0( 1 .OOOOOE+O( 2 6.01491E-01 3.63317E-01 1 -9.5 194E-01 9.87 1 O 1 E-O 1 2 6.01453E-01 3.30341E-01 4.6647 IBO1 9.95001E-01 2 6.01423E-O1 4.27301M1 6.03388E-01 9.97500E-01 2 6.01 372E-O 1 1.46949E+OC 7.89494E-01 I.OOOOOE+OC 2

6.02282E-01 2.37970E+Oi 2.38205E-0: 1.00000E+O( 2 6.02546E-01 8.40345E-3-02 4.51481E-0: 7.4721OE-O1 2 6.01798E-03 1.6624 1 E-03 2.34747E-03 9.64006E-03 2 6.01774E-O3 2.49168E+CM 1.33867E+ûí 1.00000E+O( 2 6.0141OE-01 4.334 15E-O i 2.32855E-O1 9.81425E-03 2 6.01373E-03 3.95480E-01 5.58454E-01 9.92801E-01 2 6.01 346E-O 1 5.121 30E-0 1 7.23 174E-O 1 9.96400E-01 2 6.01299E-01 1.76318E+OC 9.47278E-0 I 1 .OOOOOE+OC 2

6.02146E-01 2.77568E+OC 2.77844E-03 1.00000E+OC 2 6.02521 E-01 8.60592E-02 4.62358E-02 6.55925E-01 2 6.01710E-01 1.9 1305E-01 2.70 140E-O 1 9.51008E-O1

r/ = 255.37 K, Pf = l.Ö1325E+05 Pa, ol,,=2.1181 kg/m3,p= 1.3070E-05 Pa-s, k = 1.3198, p 6 = 1.86131 kg/m3

ïj = 283.15 K, Pf = 6.89476E+05 Pa, glp = 4.9831 kg/m3, p = 1.0670E-05 Pa-s, G 1.3622, p,, = 0.708 i7 kg/m3

Q = 255.37 K, Pf = 6.89476E+06 Pa, 31,p = 1042.35 kg/m3, p = 1.5430E104 Pa-s t = -1.0, pi, = 1.86131 kg/m3

6.03 123E-01

3.35418E-01 1 .OOOOOE+OC 2 6.02305E-01 1.1044 1E-0 1 5.93349E-O2 9.98839E-01 2 6.02236E-01 9.96853E-02 1.40765E-01 9.99550E-01 2 6.021 80E-O 1 1.28645E-01 1.81658E-O1 9.99775E-01 2 5.02082E-O1 4.41370E-01 2.37 129E-O 1 1.00000E+00 2

6.243 18E-O1 6.01680E-01 2.90650E+W 1.56154E+00 l.OOOOOE+OO 2 6.0 1348E-O 1 5.02143E-01 2.69779E-01 9.74717E-01

rf = 255.37 K, Pj = 1.37895E+06 Pa,

i = 1.3198, pi, = 1.86131 kg/m3 = 32.783 kg/m3, p = 1.352OE-O5 Pa-s,

Q = 283.15 K, Pf = 3.44738E+06 Pa, ),,p = 26.627 kg/m3, p = 1.1310E-05 Pa-s, : = 1.3622, p,, = 0.70817 kg/m3

6.01312E-01 4.601 39E-0 1 6.49758E-O1 9.90202E-01 2 6.01287E-01 5.96647E-01 8.425 19E-O I 9.95101E-01

!j = 338.71 K, Pf = 6.89476E+06 Pa, + p = 44.168 kg/m3, p = 1.3650E-05 Pa-s, : = 1.3622, p,, = 0.70817 kg/m3

9 = 333.15 K, Pf = 1.37895E+07 Pa, J ~ , ~ = 520.04 kg/m3, p = 4.171OE-O5 Pa-s, : = -1.0, p,, = 1.86131 kg/m3

6.01243E-01 2.05685E+00 I. 10505E+00 i.OOOOOE+OO 2


6.050 19E-0 1 4.45264E-01 4.45705E-04 1.000M)E+00 2 6.04938E-01 2.09942E-O2 1.12793E-02 9.98245E-01 2 6.03248E-01 3.21900E-02 4.54552E-02 9.99750E-01

6.02409E-O 1 1.33004E+OO 1.33136E-03 1.00000E+OO 2 6.02388E-01 6.18353E-02 3.322 14E-02 9.8420 lE-0 1 2 6.01510E-01 9.61 002E-02 1.35702E=Ol 9.97750E-01

A P I M P M S * L 4 - 3 * 4 72 0732290 0506403 3 4 T

SECTION &CONCENTRIC, SQUAREEDGED ORIFICE METERS, PART &BACKGROUND 117

Table 4-C-&Selected Round Robin Test Results Matrix-SI Units (D, = 0.073670 m, q = 0.00001 11 6 m/rn-K, d, = 0.029964 m, al = 0.00001 665 m/m-K) -

Cell Value

Pa

Flow Conditions 559.5 5035.6 1.98290E+00 1.39637E+00 1.44626E+00 3.05544E+00 1.58785E-03 3.35456E-03 1.00000E+00 1.OOOOOE+OO

1.051550+00 8.41232E-01 7.577 16E-01 1.81852E+00 8.31896E-04 1.99656E-03 i I.OOOOOE+OO 1.00000E+00

13987.7 27415. 55950.8

7.41964E+W B.14602E-03 l.OooOoE+OO 4 7.16547E-01 5.16327E+OC 5.66875E-O3 l.OOOOOE+OC -3 6.17209E-01

4.78597E-03 1.00000E+OC 3 6.02779E-01 4.55629E+OC 4.56080E-03 l.OOOOOE+OC 2 6.00989E-01 4.42301E+oC 4.42739E-03 1.00000E+OC 2 6.01125E-01 1.72301E-01 9.25695E-02 8.24456E-O 1 2 6.00552E-01 3.12532E-01 4.41323E-01 9.75005E-01 2 6.00536E-01 4.63 156E+OC 2.48833E+OC l.OOOOOE+oC 2 6.00210E-01 8.10346E-01 4.35364E-01 9.87101E-01 2 6.00181E-01 7.36807E-01 1.04044E+O[ 9.95001E-01 2 6.00160E-01 9.53084E-01 1.34584E+O( 9.97500E-03 2 6.001 18E-01 3.27772E+O( 1.76097E+O( 1.00000E+O( 2

i.o1726~+0a

~ .3592i~+oa

80569. I 9.76749E-01 8.54897E+OC 9.38591E-03 1.00000E+OC 4 7.04057E-01 6.08792E+OC 6.68393E-O3 l.OOOOOE+OC -3 6.15227E-01 5.21426E+OC 5.72473E-03 l.OooOoE+O( 3 6.02454E-01 5.46459E+oC 5.47001E-03 l.ooOoOE+O( 2 6.00848E-01 5.30636E+O( 5.31 162E-01 1.OOOOOE+O( 2 6.0 1052E-O 1 1.87367E-01 1.00664E-O3 7.472 16E-01 2 6.00459E-O1 3.70750E-01 5.23532E-03 9.64007E-01 2 6.00438E-01

109663.5 9.45276E-01 9.65242E+OO 1.05974E-02 1 .000oOE+00 4 6.94472E-01 7.00588E+00 7.69176E-03 1.00000E+00 -3 6.13737E-O1 6.06856E+OO 6.66267E-03 1.00000E+00 2 6.02206E-O I 6.37273E+00 6.37905E-03 1.00000E+00 2 6.00740E-01 6.18964E+00 6.19578E-03 l.OOOOOE+OO 2 6.01032E-01 1.9 1884E-01 1.03091E-01 6.55933E-01 2 6.00388E-01 4.26660E-01 6.02482E-0 1 9.5 1OO9E-O1

12 6.00363E-01

Tf= 255.37 K, P f = 1.01325E+05 Pa, pf,p = 932.26 kg/m3, p = 1.8650 Pa-s, k=-1.0, pb=910.83 kg/m3

cd 4111

Q v Y ICD cd 4111

Q v Y ICD

G 4111

Q" Y ICD

cd 4m Q v Y ICD cd 4111

Q v Y ICD cd 9111

Q v Y ICD

-

-

-

-

-

i .20890E+00 +.40871E+00 1.84032E-03 I.OMXX)E+OO -5 7.77967E-01 L.80293E+00 3.07733E-03 L.OOOOOE+OO -4 5.34050E-01 2.23908E+00 1.45828E-03 1.00000E+OO -3 5.04415E-01 2.28433E+00 2.28659E-03 l.o0000E+OO

1.10787E+OO 5.65637E+00 5.210 i 3E-03 I .000ûOE+00 4 7.45 12OE-0 1 3.7584lE+OO t. 12636E-03 1.00000E+00 -3 5.24074E-01

3.38745E-03 1.00000E+OO -3 5.03532E-01 3.19338E+OO 3.19655E-03 1 .OOMH)E+OO 2

3.08539~+00

Tf= 293.15 K, Pf= 1.01325E+05 Pa, pf,p = 907.60 kg/m3, p = 2.1220E-01 Pa-s, k = -1.0, pb = 910.83 kg/m3

q= 353.15 K, Pf= 1.01325E+05 Pa, pf,p = 868.43 kg/m3, p = 1.7490E-02 Pas, k = -1.0, pb = 910.83 kg/m3

7.04769E-O 1 4.97759E-01 5.4649OE-3-04 1.00000E+O( -3 6.12758E-01 4.63168E-01 4.63627E44 l.OooOoE+O( 2

6.50983E-01 1.37933E+00 1.51436E-03 1.00000E+00 -3 6.06179E-01 1.37460E+00 1.37596503 1.00000E+00 2

Tf= 288.71 K, P f = 1.01325E+05 Pa, pf,p = 999.01 kg/m3, p= 1.199OE-O3 Pa-s, k = -1 .o, pb = 999.01 kg/m3

Tf = 372.04 K, P f = 1.01325E+05 Pa, pf,p = 941.75 kg/m3, p = 2.8250E-04 Pa-s, k = -1.0, pb = 999.01 kg/m3

5.01682E-01 2.21405E+00 2.21625E-03 1.OOOOOE+00 2 5.0 1699E-O 1 1.00003E-01 5.37273E-02 3.56114E-01 2 5.01019E-01 1.59394E-01 2.25079E-01 3.93751E-01 2 6.01012E-01 2.31762E+W 1.24515E+OO l.OOOOOE+W 2 6.00531E-01 4.09363E-01 2.19933E-01 9.96775E-01 2 6.00491E-O1 3.69982E-01 5.22449E-01 9.98750E-01 2 6.00459E-01 4.77676E-01 6.74522E-0 1 9.99375E-01 2 6.00400E-01 1.63963E+oC 8.80901E-01 1.00000E+OC 2

6.01 3 1OE-0 1 3.09776E+OC 3.10083E-03 1.000OOE+00 2 6.0 1370E-O 1 1.33762E-01 7.18644E-02 9.13983E-01 2 6.00768E-O1 2.21712E-01 3.13078E-01 9.87752E-O 1 2 6.00758E-01 3.24329E+OC 1.74248E-M 1.00000E+OC 2 6.00360E-01 5.7 1165E-01 3.06862E-01 9.93680E-01 2 6.00326E-01 5.17211E-01 7.30349E-01 9.97550E-01 2 6.00300E-01 6.68168E-01 9.43514E-01 9.98775E-01 2 6.00250E-01 2.29491E+O( 1.23295E+O( 1.00000E+OC 2

Tf = 255.37 K, Pf = 1.01325E+05 Pa, p -2.1181 kg/m3, p= 1.3070E-05 Pa-s, bp - k = 1.3198, & = 1.86131 kg/m3

cd 4111

Q v Y ICD Gf Q I

Q v Y ICD cd 9ni Q v Y ICD cd 4ni Q v Y ICD cd 4 m Q v Y ICD

_.

-

-

-

- cd 9ni Q v Y ICD

T - 283.15 K, Pf = 6.89476E+05 Pa, di= 4.983 1 kg/m3, p = 1.0670E-05 Pa-s, k = 1.3622, p b = 0.70817 kg/m3

2 6.03245E-01 4.65242E-01 2.49954E-01 l.O0000E+O( 2 6.02001E-01 8.23273E-0;

2 6.01506E-01 1.39172E+00 7.47708E-01 l.OOOOOE+OO 2

Tf = 255.37 K, Pf = 6.89476E+06 Pa, P,,~ = 1042.35 kg/m3, p = 1 S430E-04 Pa-s k=-1.0, p b = 1.86131 kg/m3

Tf= 255.37 K, Pf = 1.37895E+06 Pa, pf,p = 32.783 kg/m3, p = 1.3520E-05 Pa-s, k = 1.3198, pb= 1.86131 kg/m3

I ' 6.00117E-0l I6.00067E-01 Tf =283.15 K, Pf = 3.44738E+06 Pa,

p,,=26.627 kg/m3,p= 1.1310E-05Pa-s, k = 1.3622, & = 0.70817 kg/m3

8.821 19E-01 1.02636E+OC i .24563~+00 I .4493 i ~ + o a 9.9280 1E-0 1 9.90202E-01

6.00097E-01 6.00049E-01

1.61306E+00 1.87930B+OC t 9.96401E-01 9.95101E-01

i.i4232~+o0 1.33086~+oa Tf = 338.71 K, Pf = 6.89476E+06 Pa, pf,p = 44.168 kg/m3, p= 1.3650E-05 Pa-s, k = 1.3622, &, =0.70817 k g h 3

L I ' 6.Ml059E-01 I6.00013E-01 Tf = 333.15 K, Pf = 1.37895E+07 Pa,

pfP = 520.04 kg/m3, p = 4.1710E-05 Pa-s, k=-1.0, pb= 1.86131 kg/m3


A P I M P M S * L 4 - 3 - 4 92 W 0732290 050b404 286 W


Table 4-C-6-Selected Round Robin Test Results Matrix-SI Units (D, = 0.1 02270 m, c+ = 0.000011 16 m/m-K, d, = 0.041 672 m, al = 0.00001 665 m/m-K)

Pa Cell Value ~

Cd

Q,. 9111

Y ICD

9/11

Y ICD

-

Q,.

13987.7 I 27415. I 55950.8 I 80569.1 109663.5

8.86185E-01 I .75039E+O I I .92 I76E-O2 I .00000E+00 -4 6.76935E-01 I .32096E+0 1 1.45028E-O2 1 .OOOOOE+00 -3 . 6.1 132OE-O I 1.16925E+OI 1.2837 1 E 4 2 I .o0o00E+00 2 6.02039E-O 1 1.23236E+01 1.23359E-02 I .00000E+00 2 6.00828E-01 I . 19747E+0 1 I . I9865E-O2 1 .OOOOOE+00 2 6.0 1070E-0 1 3.71161E-01 I .99409E-01 6.55876E-01 2 6.00533E-01 8.25498E-01 1.16568E+00 9.51001E-01 2 6.00511E-01 I .25421E+01 6.73832E+00 1 .00OOOE+OO 2 6.00285E-01 2.16721E+00 1.16435E+00 9.74714E-01 2 6.00262E-01 1.98597E+00 2.80437E+00 9.90200E-01 2 6.00247E-01 2.57519E+00 3.63640E+00 9.95100E-01 2 6.002 16E-0 1 8.87777E+00 6.76964E+00 1 .OOOOOE+00 2

Flow Conditions Ti= 255.37 K, P/ = I .O l325E+05 Pa, pl,/, = 932.26 kglm?, p = 1.8650 Pas, k = - I . O , p,,=910.83 kg/m3

559.5

1.77644E+O( 2.50628E+0( 2.75 165E-O: I .00000E+O( -5

5035.6

I .2709 I E+O( 5.37924E+O( 5.90586E-0: I .OOOOOE+O( -5 7.98803E-0 I 3.34023E+O( 3.66723E-0: 1.00000E+O( 4 6.4002 I E-0 i 2.623 17E+O( 2.87998E-0: 1.00000E+O(

I , I 1027E+OO I .02406E+ûC 7.83214E+00 1.01 136E+OI 8.59890E-03 I . I 1037E-02 I ,00000E-cOO I .OOOOOE+OO

-4

9.47065E-0 I 9. I2766E-O I I .33617E+01 I .54534E+Oi I .46699E-02 I .69663E-O2 I .00000E+00 I .00000E+OC -4 -4

q=293.15K, Pf= 1.01325E+05Pa, pl,,J = 907.60 kg/m3, p = 2.122OE-O1 Pa-s, k=-1.0, p,>=910.83 kglm'

7.461 IOE-01 7.18886E-01 5.19980E+00 7.01410E+Oû 5.70886E-O3 7.70078E-03 1.000ûOE+00 1.00000E+00 -3 6.24525E-0 I 6.17802E-0 I 4.26608E+00 5.90822E+00

I .OOOOOE+OO I .00000E+00 4.68373E-O3 6.48664E-03

6.9524 I E-O I 9.69056E+OC I ,06393E-02 1.00000E+OC -3 6.14082E-01 8.38949E+OC 9.2 1082E-03 I .00000E+Oa

6.84894E-03 I . 14556E+01 1.2577 1E-02 1.00000E+OC -3 6. I2507E-O I 1.004 16E+O I

1 .OOOOOE+OC 1.10246E-02

9.76 I59E-O I 1.36060E+O( 1.4938 1 E-O? I .OOMH)E+O( -4 6.85485E-01 9.36492E-O 1 1.028 17E-02 I .00000E+O(

Tf=353.15K,Pf= 1.01325E+05Pa, pl,ll = 868.43 kglm', p = 1.749OE-02 Pa-s, k = - I .O, p,, = 9 10.83 kg/m3

c, Q,. Y ICD c,, qiri

QI. Y ICD

G 9111

QI. Y ICD Cd 4111

Q,. Y [CD Cd Lh QI. Y ICD c, 7111

QI. Y [CD Cd ?,il

QI.

Y [CD

qJ11

-

-

-

-

T f = 288.71 K, Pf = 1.01325E+05 Pa, i ,,,, = 999.0 I kg/m3, p = I . 1990E-03 Pa-s, k=-1.0, pIJ=999.O1 kglm"

6.0384OE-O1 6.03 122E-01 6.02508E-01 4.41447E+00 6.1729IE+00 8.80947E+00 4.41884E-03 6.17903E-O3 8.81820E-03 I.OOOOOE+OO I.OOOOOE+OO 1 .OOOOOE+o(1 2 2 2 6.01609E-01 6.01302E-01 6.01035E-01 4.28222E+00 5.99205E+OO 8.55628E+ûC

1.00000E+00 1.00000E+00 1 .OOOOOE+W 4.28647E-03 5.99799E-03 8.56476E-03

6.02242E-O I 1.05667E+01 1.05772E-02 I.OOOOOE+OC 2 6.009 18E-01 1.02655E+01 1.02757E-02 1.00000E+OC

6.10538E-01 8.92681E-01 8.93565E-04 1 .OOOOOE+(H 2 6.04330E-01 8.603 12E-O1 8.6 I 165E-O4 1.00000E+O(

6.05266E-01 2.65494E+O( 2.65758E-O? I .OOOOOE+O( 2 6.02206E-01 2.57 189E+O( 2.57444E-02 1.00000E+O( 2 6.02188E-01 I . I957 I E-01 6.4240 1 E-O2 9.84 198E-O 1 2 6.01466E-O 1 1.85877E-3-01 2.62475E-O1 9.9775OE-O1 2 6.01463E-01 2.69186E+OC 1.44622E+OC 1 .OOOOOE+OC 2 6.00928E-01 4.76408E-01 2.55953E-01 9.98839E-01 2 6.00883E-01 4.30030E-O 1 6.07241E-O I 9.99550E-01 2 6.00849E-01 5.54977E-01 7.83678E-O1 9.99775E-01 2 6.00784E-01 1.90419E+OO 1.02303E+OC I .00000E+Oa 2

Tr= 372.04 K, PJ = 1.01325E+05 Pa, &, = 94 I .75 kg/m3. p = 2.8250E-04 Pa-s, k = -1 .O, p,, = 999.01 kglm'

6.0 135OE-O 1 6.0 1 147E-01 6.0 1087E-O 1 2.58729E-O1 3.33289E-01 3.62433E-O1 1.39004E-O1 1.79062EXI 1.94719E-O1 9.13969E-O1 8.24427E-O 1 7.47 174E-01 2 2 2 6.0085 1E-01 6.0067OE-O1 6.00592E-01 4.28926E-01 6.04660E-01 7.17312E-01 6.05682E-01 8.53834E-01 1.01291E+OC 9.87750E-01 9.75001E-01 9.64001E-01 2 2 2 6.00842E-01 6.00656E-01 6.00574E-01 6.27451E+00 8.96082E+00 l.O7515E+Ol 3 -37 102E+ûO 4.8 1425E+00 5.7763 1 E+ OC 1.00000E+00 1 .OOOOOE+00 l.OOOOOE+OO 2 2 2 6.00509E-01 6.00383E-O1 6.00327E-01

5.93723E-01 8.42382E-01 1.00495E+00 9.93678E-01 9.87099E-01 9.81422E-01 2 2 2 6.00480E-01 6.00358E-01 6.00304E-01 1.00072E+00 1.42566E+00 1.70685E+00 1.413 11E+OO 2.01316E+00 2.41023E+OO 9.97550E-01 9.95000E-01 9.92800E-01

1.105 IOE+OO i.56793~+00 1.87053~+oa

6.04264E-O1 4.05647E-O2 2.17936E-02 9.98244E-O1 2 6.02891E-01 6.22296E-O2 8.78739E-O2 9.99750E-01 2

6.0 1622E-01 1.934 14E-0 I 1.03913E-01 9.56107E-O1 2 6.01060E-0I 3.08344E-O1 4.35409E-O1 9.9375OE-O I 2

i"f= 255.37 K, PJ, = 1.01325E+05 Pa, p,,,> = 2.1 18 I kg/m', p = I ,307OE-05 Pa-s, k = 1.3198, p,,= 1.86131 kg/m3

T / = 283.15 K, P l = 6.89476E+05 Pa,

k = I .3622, p/> = 0.708 17 kglm" of,/,,, = 4.983 I kg/m', p = 1.0670E-05 Pa-s,

TJ= 255.37 K, P/ = 6.89476E+06 Pa,

k=-i .û, pi,'1.86131 kg/m3 = 1042.35 kg/m3, p = 1 S43OE-O4 Pa-s

6.02889KOI 8.99406E-01 4.8321 1E-O1 1.00000E+OC 2 6.0 187 1E-O1 1.59215E-01 8.55391E-02 9.99871E-O1 2 6.0 1788E-O 1 1.43615E-01 2.02797E-01 9.99950E-01 2 6.0 172OE-O 1 I ,85296E-O1 2.6 1654E-01 9.99975E-01 2 6.0 1 600E-O 1 6.35584M1 3.41471E-01 1.00000E+OC

6.0 1054E-O 1 4.48337E+O( 2.40872E+O( l.OOOOOE+O( 2 6.00652E-01 7.92007E-01 4.2551 IE-01 9.96775E-O1 2 6.006 19E-0 1 7.15826E-01

9.98750E-01 1.01081E+OC

ïj= 255.37 K, PJ = 1.37895E+06 Pa,

k = 1.3198, pi,= 1.86131 kg/m3 = 32.783 kg/m3, p = 1.352OE-O5 Pa-s,

r / = 283.15 K, Pf = 3.44738E+06 Pa, o,+ = 26.627 kg/m3, p = 1.131OE-05 Pas, k = 1.3622, pr, = 0.70817 kg/m3

ïj= 338.71 K, Pf = 6.89476E+06 Pa, of./, = 44.168 kg/m3, p = 1.365OE-05 Pa-s, i = 1.3622, pr, = 0.708 17 kg/m3

I ' I ' I ' 6.005438-01 I 6.00417E-01 I 6.00305E-01 I 6.00255E-O1 r f= 333.15 K, Pf = 1.37895E+07 Pa,

31,1> = 520.04 kg/m3, p = 4.371OE-O5 Pa-s, ¿=-leo, pb= 1.86131 kg/m3


A P I MPMS*14 .3 .4 92 0732290 0506405 112

8.53630E-01 4.66884E+OO 5.12592E-03 1.00000E+00 d


7.31434E-01 6.95889E-01 6.77546E-01 1.20016E+01 1.90306E+Ol 2.59405E+Ol 1.31766E-02 2.08937E-02 2.84801E-02 1 .OOOOOE+OO 1 .00000E+00 l.O0000E+OO -2 -2 -?

Table 4-C-6-Selected Round Robin Test Results Matrix-SI Units (O, = 0.202729 m, a2 = 0.00001 11 6 m/m-K, d, = 0.082550 m, al = 0.00001 665 m/m-K)

9.97402E+00 1.09505E-02 l.O0000E+OO -3 6.03831E-01 l.O3933E+Ol 1.04036E-02 l.OOOOOE+OO 2 6.01828E-01 I.O0858E+Ol 1.00958E-02 1 .OOOOOE+OO 2 6.01814E-01 4.68904E-01 2.51922E-01 9.84199E-01 2 6.0 l329E-O 1 7.29215E-01 l.O2972E+m 9.97750E-01 2 6.01326E-O1 l.O5605E+Ol

Flow Conditions Tf = 255.37 K, Pf = 1.01325E+05 Pa,

= 932.26 kg/m3, y = 1.8650 Pa-s, k=-1.0, pb=910.83 kg/m3

1.64717E+Ol 2.29565E+01 1.80843E-02 2.52039E42 1 .OOOOOE+OO 1.OOOOOE+OO 2 2 6.02905E-01 6.02434E-01 1.72955E+01 2.41948E+OI 1.73127E-02 2.42188E-02 1.00000E+00 l.OOOOOE+OO 2 2 6.01427E-01 6.01219E-01 1.67983E+Ol 2.35096E+OI 1.68 150E-02 2.35329E-02 l.OOOOOE+OO 1.00000E+00 2 2 6.01434E-01 6.01250E-01 7.58722E-01 I.O1509E+OO 4.07628E-01 5.45362E-01 9.56109E-01 9.13974E-01 2 2 6.01052E-0 1 6.00908E-O 1 1.20993E+00 1.68327E+OC 1.70852E+00 2.37692E+O€ 9.9375 1E-01 9.8775 1E-01 2 2 6.01048E-01 6.00902E-01 1.75926E+OI 2.46236E+01

Tf = 293.15 K, Pf = 1.01325E+05 Pa, pf,p = 907.60 kg/m3, y = 2.1220E-01 Pa-s, k =-1.0, p,, = 910.83 kg/m3

3.9141 1E+O1 4.29730E-02 l.O0000E+00 2 6.0185 1E-01 4.14367E+01 4.14778E-02 1.00000E+OO 2 6.00956E-01 4.02844E+01 4.03244E-02 1 .oooOOE+00 2 6.01070E-01 1.42218E+00 7.64074E-01 7.47 190E-0 1 2 6.00728E-01 2.81538E+00 3.97557E+00 9.64003E-O1 2 6.007 l6E-O 1 4.21988E+01 2.26716E+01 1 .00000E+00

Tf=353.15 K, P f = I.O1325E+05 Pa, pf,p = 868.43 kg/m3, y = 1.7490E-02 Pa-s, k = -1.0, p,, = 910.83 kg/m3

4.56086E+01 5.00737E-O2 l.OOOOOE+OO 2 6.01715E-01 4.83319E+OI 4.83798E-02 1.00000E+00 2 6.00893E-01 4.69936E+O 1 4.70402E-02 1.00000E+00 2 6.01059E-01 1.45646E+00 7.82490E-01 6.55898E-O 1 2 6.00687E-01 3.24009E+W 4.57530E+00 9.51004E-01 2 6.0067 IE-01 4.92283E+01 2.64482E+01 1.00000E+OO

Tf = 288.71 K, Pf = 1.01325E+05 Pa, pf.p = 999.01 kg/m3, y = 1.199OE-O3 Pa-s, k=-1.0, pb=999.01 kg/m3

6.01602E-01 6.24479E-01 3.35505E-01 9.99871E-01 2 6.01546E-01 5.63319E-01 7.95457E-01 9.99950E-01 2 6.01501E-01 7.26836E-01 l.O2636E+OO 9.99975E-01 i! 6.01420E-01 2.49329E+00 1.33953E+00 I.OOOOOE+00 2

T - 372.04 K, Pf = 1.01325E+05 Pa, di= 941.75 kg/m3, y = 2.8250E-04 Pa-s. k = -1 .O, pb = 999.01 kgím3

6.00961E-01 6.00770E-01 1.86953E+00 ~ 3.10845E+OO 1.00442E+00 1.67003E+OO 9.98839E-01 9.96775E-01 2 2 6.00931E-01 6.00747E-01 1.68757E+OO 2.80950E+OC 2.38300E+00 3.96727E+OC 9.99550E-01 9.98750E-01 2 2 6.00908E-01 6.00730E-01 2.17794E+OO 3.62737E+OC 3.07545E+OO 5.12217E+OC 9.99775E-01 9.99375E-01 2 2 6.00863E-01 6.00695E-01 7.47300E+00 1.245 l5E+01 4.01491E+00 6.68964E+M 1.00000E+00 1.00000E+OC 2 2

Tf = 255.37 K, Pf = 1.01325E+05 Pa, pf,p = 2.1 18 1 kg/m3, y = I ,307OE-05 Pa-s. k = 1.3198, pb = 1.86131 kg/m3

Tf = 283.15 K, Pf = 6.89476E+05 Pa, pf,p = 4.983 I kg/rn3, y = 1.0670E-05 Pa-s. k = 1.3622, pb = 0.70817 kg/m3

Tf = 255.37 K, Pf = 6.89476E+06 Pa, pf,p = 1042.35 kg/m3, y = 1.5430E-04 Pa-! k=-1.0, pb= 1.86131 kg/m3

Tf = 255.37 K, Pf = 1.37895E+06 Pa, pf,p = 32.783 kg/m3, p= 1.3520E-05 Pa-s k = 1.3198, pb= 1.86131 kg/m3

Tf = 283.15 K, Pf = 3.44738E+06 Pa, pf,p = 26.627 kg/m3, y = 1.13IOE-05 Pa-s k = 1.3622, pb = 0.708 17 kg/m3

Tf = 338.71 K, Pf = 6.89476E+06 Pa, pf,p = 44.168 kg/m3, y = 1.3650E-05 Pa-s k = 1.3622, pb = 0.70817 kg/m3

Tf = 333.15 K, Pf = 1.37895E+07 Pa, pf,p = 520.04 kg/m3, p=4.171OE-05 Pa-s k = -1.0, pb = 1.86131 kg/m3

- Cell lalue - r- "d

liir

2, Y iCD cd ?Il,

Y [CD cd Ill1

Y [CD cd BI Q v Y [CD cd 7111

Y [CD cd BI Qv Y iCD cd 9111

Y ICD cd &Il

Qv Y ICD cd 4"l

Y ICD cd 4111

Qv Y ICD

4111

Y ICD

-

Q V

-

QV

-

-

Q V

-

-

Q,

-

-

Q,

-

- cd

Qv

- cd 4m Q" Y ICD -

Pa

5035.6 13987.7 27415. 8.87250E-01 3.4384OE+Ol 3.77502E-02 1.00000E+00 -4

I - l - I -

6.54698E-O1 I6.20169E-01 I6.14514E-01 I 6.11743E-01 3.50975E+OC 3.85335E-03 l.OOOOOE+OC -3 6.07194E-01 3.48369B+OC 3.48714E-03 l.OOOOOE+OC 2 6.03226E-01 3.36970E+oC 3.37303E-03 l.OOOOOE+OC 2 6.03 I8OE-O 1 1.58890E-01 8.53648E-02 9.98244E-01 2 6.0228 lE-01 2.43942E-01 3.44468E-01 9.99750E-01 2 6.02279E-01 3.52570E+o( 1.894208+00 5.673U7E+OO 9.45 I7 I E+OO I .32292E+OI l.OOOOOE+OO I I.OOOOOE+OO I 1.00000E+00 I I.OOOOOE+O(:

6.00670E-01 4.33758E+OC 2.33039E+OC 9.93679E-01 2 6.00650E-01 3.92794E+OC 5.54660E+OC 9.97550E-01 2 6.00636E-01 5.07447E+OC 7.16561E+OC 9.98775E-01 2 6.00606E-O1 1.74295E+03 9.3641 1E+O( 1.00000E+O( 2

55950.8 5.333 18E-01 g.6 1342E+0 1 5.06507E-02 l.OOOOOE+OO 4 6.61455E-01 3.6 1778E+0 1 3.97196E-02 1 .00000E+OO -3 6.09423E-01 3.26706E+OI 3.58690E-02 1.00000E+C€ 2 6.02028E-01 3.45408E+01 3.45750E-02 1.00000E+OC 2 6.0 1036E-O 1 3.35749E+O 1 3.36082E-02 1.00000E+OC 2 6.01 112E-01 1.30777E+OC 7.02605E-01 8.24438E-01 2 6.00783E-01 2.373 13E+OC 3.35108E+OC 9.75002E-01 2 6.00773E-O1 3.5 169 1E+01 1.88948E+OI I .00000E+OC 2 6.0058 1E-01 6.1546 1 E+O( 3.30660E+0( 9.87100E-01 2 6.00564E-01 5.59619E+O( 7.90233E+O( 9.95000E-01 2 6.00552E-01 7.23898E+O( 1.02221E+03 9.97500E-03 2 6.00526E-01 2.4896OE+Ol 1.33755E+OI 1.00OOOE+01

80569.1

5.90433E-02

4.7 147 1 E 4 2 1 .00000E+OO

109663.5 7.91133E-01 6.13 182E+01 6.73213E-02 1.00000E+00 4 6.48679E-01 4.96707E+O 1 5.45335E-02 1 .OOOOOE+00 -? - I -

6.08435E-01 I 6.07688E-01

2 12


- -- __ __ A P I MPMS*LY.3 .Y 7 2 W 0732290 0506406 057 W


Table 4-C-6-Selected Round Robin Test Results Matrix-SI Units (Dm = 0.363513 m, CS = 0.00001116 m/m-K, dm= 0.148034 m, al = 0.00001665 m/m-K)

Flow Conditions

Tf = 255.37 K, Pf = 1 .O1 325E+05 Pa, prp = 932.26 kg/m3, p = 1.8650 Pa-s, k = -1.0, p,, = 910.83 kg/m3

Tf= 293.15 K, Pf = i.O1325E+O5 Pa, pf,,> = 907.60 kg/m3, p = 2. I220E-0 I Pa-s, k = - 1 . 0 , pb=9i0.83 kg/m3

Tf=353.15K,P/= 1.01325E+05Pa, pf,/, = 868.43 kg/m3, p = I ,749OE-02 Pa-s, k = - 1 . 0 , pb=910.83 kg/m3

Tf = 288.71 K, Pf = 1.01325E+05 Pa, P,,~ = 999.01 kg/m3, p = 1.1990E-03 Pa-s, k = - 1 . 0 , pb=999.01 kg/m3

Tf= 372.04 K, Pf = 1.01325E+05 Pa, pf,p = 941.75 kg/m3, p = 2.8250E-04 Pa-s, k = -1 .O, pb = 999.01 kg/m3

Tf = 255.37 K, Pf = 1.01325E+05 Pa, p,+ = 2.1 181 kg/m3, p = 1.307OE-O5 Pa-s, k = 1.3198, pb= 1.86131 kg/m3

Tf = 283.15 K, Pf = 6.89476E+05 Pa, pf,p = 4.983 1 kg/m3, p = 1.0670E-05 Pa-s, k = 1.3622, pb= 0.70817 kg/m3

Tf = 255.37 K, Pf = 6.89476E+06 Pa, P,,~ = 1042.35 kg/m3, p = 1.5430E-04 Pa-s, k=-1 .0 , pb= 1.86131 kg/m3

T p 255.37 K, Pf = 1.37895E+06 Pa, pf,p = 32.783 kg/m3, p = 1.3520E-05 Pa-s, k = 1.3198, p,,= 1.86131 kg/m3

Tf = 283.15 K, Pf = 3.44738E+06 Pa, pf,p = 26.627 kg/m3, p = 1.1310E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

T p 338.71 K, Pf = 6.89476E+06 Pa, pf,,, = 44.168 kg/m3, p = 1.365OE-O5 Pa-s, k= 1.3622, pb = 0.70817 kg/m3

Tf= 333.15 K, Pf = 1.37895E+07 Pa, of,p = 520.04 kg/m3, p = 4.1710E-05 Pa-s, k=-l.O, pb= 1.86131 kg/m3

Cell Valui - Cd

QV

9nr

Y ICD

cd 9nr Qv Y ICD

%Il

Y ICD

cd 4111 Qv Y ICD cd 9r>i Qv Y ' ICD cd 4m

Y ICD

cd gin Qv Y ICD cd 4n1 Qv Y ICD cd 4ni

Qv Y ICD

-

cd

Qv

-

-

-

Q"

-

-

-

-

4m Qv Y ICD

cd 41n Qv Y ICD

cd 7rn Qv Y ICD

-

-

-

559.5 I 5035.6 7 2. I5677E+O I 4.98779E+O 1 2.36792E-O2 1 .OOOOOE+OC -5 7.79472E-01 1.37098E+01 1.50520E-02 1.00000E+00

5.47609E-02 I .OOOOOE+OC -4 6.9171 IE-O1 3.64989E+O 1 4.00722E-02 I .00OOOE+W

6.35173E-O1 6.14068E-01 1 .O950 1E+01 3.1759 1 E+O1

1.00000E+00 i .OOOOOE+OO 1.20221E-O2 3.48683E-02

1.1 1688E+Oi 3.33783E+01

1 .OOOOOE+00 1 .OûOOOE+OC 1.1 1799E-02 3.341 14E-02

6.02603E-01 6.0161 IE-O1 3.08251E+01 3.24222E+01 1.08358E-02 3.24544E-02 1.00000E+00 l.OOOOOE+OO 2 - 2 6.02569E-O 1 6.01 599E-01 5.10444E-O1 1.50737E+00 2.74239E-01 8.09845E-01 9.98244E-01 9.84199E-O1 2 2 6.0 1933E-Ol 6.0 1249E-0 1 7.84020E-01 2.34471E+00 1.107 1 lE+OO 3.3 lO94E+OO 9.99750E-ûl 9.97750E-01 2 2 6.01932E-01 6.01247E-01 lL13315E+01 3.39560E+01 6.08789E+00 1.82431E+01 1.00OOOE+00 l.OOOOOE+OO 2 2 6.01446E-01 6.00979E-01 2.00769E+00 6.01224E+ûO 1.07864E+00 3.2301 1E+00 9.99871E-O1 9.98839E-01 2 2 6.01407E-01 6.00957E-01 1.81111E+00 5.42715E+00 2.55745E+00 7.66363E+00 9.99950E-01 9.9955OELol 2 2 6.01375E-01 6.00941E-01 2.33688E+00 7.00425E+OO 3.29989E+OO 9.89063E+00 9.99975E-0 1 9.99775E-0 1 2 2 6.01316E-01 6.00908E41 8.0 1656E+OO 2.40336E+O 1 4.30695E+00 1.29122E+Ol 1.00000E+00 l.OOOOOE+00 2 2

13987.7

7.55438E+Ol 8.29395E-02 I .OOOOOE+OC 4 6.6621 1E-01 5.85889E+Oi 6.43247E-02 l.O0000E+Oû -3 6.10294E-01 5.26063E+01 5.77565E-02 1.00000E+OC 2 6.02375E-01 5.55704E+01 5.56255E-û2 i .OOOOOE+C€ 2 6.01321E-03 5.40 Iû9E+O1 5.40644E-02 1 .OOOOOE+OO 2 6.01 325E-01 2.43947E+00 1.3 1062E+OC 9.56109E-01 2 6.01047E-O1 3.89086E+OO 5.49425E+Oû P.9375OE-O1 2 5.0 1043E-O 1 5.65740E+01 3.03947E+01 l.OOOOOEtO0 L 5.00838E-01 3.99732E+OO 5.37112E+3+00 3.96775E-01 2 5.00821E-01 3.03594E+00 1.27596E+01 3.98750E-01 2 5.00809E-01 I. 16665E+01 1.6474 1E+01 2.99375E-01 1 5.00783E-O1 L00475E+01 1.15 158E+Ol i .OOOOOE+OO 1

8.48644E-O1 I .O0 I 89E+02 i ,09997E-01 I .OOOOOE+OO

6.52776E-01

8.82386E-02

55950.8

7.64763E-O I 1.36 154E+O: i .49483E-01 1 .OOOOOE+OE -3 6.40547E-01 I . 12664E+Oî I .23694E-0 1 i .00000E+OC -3

6.08432E-0 1 7.34242E+01 8.06 i 24E-O2 I .000OOE+00

7.77555E+Ol i i .OOOOOE+00

6.02042E-01

7.78326E-02

6.01 170E-01 7.55963Et.01 7.567 12E-02 1.00000E+OC 2 6.0 1 19 lE-0 1 3.26402E+00 1.75361E+OC 9.13974E-O1 2 6.0094 1E-O 1 5.4 1337E+OC 7.64416E+OO 9.8775 1 5 0 1 2 6.00936E-01

6.06863E-01 i .O462 1 E+Oî i. 14864E-3-01 I.OOOOOE+OC 2 6.01753E-01 I . 1 1026E+O2 1.1 I 136E-01 i .OOOOOE+OC 2 6.01036E-O1 1 .O797 iE+O2 1.08078E-01 1 .OOOOOE+OC 2 6.01090E-01 4.20537E+OC 2.25936E+OC 8.24436E-0 1 2 6.00848E-01 7.63238E+M l.O7776E+Oi 9.75002E-01 2 6.00840E-01

5.00716E-01 6.00656E-01 5.60603E+01 8.00782E+01 3.01 187E+01 4.30225E+Ol 1.00000E+00 1.00000E+00 1 l 2

80569.1

1.59714E+O: 1.7535OE-O1 1 .OOOOOE+O( -3 6.34849E-01 1.33994E+O; 1.47112E-01 1.00000E+O( -3 6.06192E-01 1.25407E+0; 1.37684E-0 1 i .00000E+O( 2 6.0 1626E-0 I 1.33203E+O; 1.33335E-03 i .00000E+O( 2 6.00977E-01 I .29552E+O; i .29680E-01 I .OOOOOE+OC 2 6.01060E-01 4.57337E+oE 2.45707E+OC 7.47188E-01 2 6.00807E-01 9.05492E+OC i .27864E+OI 9.64003E-01 2 6.00797E-O1 1.35722EtO2 7.29 i75E+OI i .OOOOOE+OC 2 6.00666E-01 2.36173E+Ol 1.26885E+01 9.8 1423E-01 2 6.00654E-01 2.15511E+Ol 3.04321E+Oi 9.92801E-01 2 6.00647E-O1 2.79087E+Ol 3.94095E+O 1

7.47581E-O1

9.964WE-0 1

6.00629E-01 9.60894E+O 1 5.16246E+Oi 1 .OOOOOE+OO

109663.5

7.34386E-01 i .83044E+0: 2.00964E-0 i 1.00000E+O( -3 6.3022280 I i .55 187E+O: 1.70379E-01 1 .OOOOOE+Gí -3 6.05684E-01 1.46 185E+O: 1.60497E-01 1 .OOOOOE+ûí 2 6.01528E-01 I .55378E+O: 1.55532E-01 l.OOOOOE+O( 2 6.0093 i E X I 1.5 1 132E+O: i .5 1282E-01 I .00000E+O( 2 6.0105 1E-O1 4.68362B+O( 2.5 1630E4 6.55895E-3-01 2 6.00776E-01 1.04211E+OI 1.47155E+Oi 9.5 1OO4E-01 2 6.00764E-01 1.58334E+Oí 8.50657E+03 1.00000E+O( 2 6.00643E-01 2.73641E+03 1.47015E+Oi 9.74715E-01

6.00632E-01 2.50761E+OI 3.54098E+OI 9.90201E-01 2 6.00624E-01 3.25 164E+OI 4.59 I6 1 E+01 9.95 IOOE-01 2 6.00608E-01 1.12100E+02 6.02266E+OI 1 .OOOOOE+OC 2


A P I MPMS*L4-3-4 92 0732290 050bY07 T95

559.5 1.0 1286E+00 7.5949OE+Ol 8.33844E-02 l.OOOOOE+OO 4 7.16018E-01 5.30428E+01 5.82356E-02 l.O0000E+00 -3 6.18033E-01 4.48755E+Ol 4.92688E-02 l.OOOOOE+OO 3 6.03849E-01 4.69249E+01 4.69714E-02 1.00000E+00 2 6.0208 1E-01 4.55542E+01 4.55994E-O2 1 .OOOOOE+OO 2 6.02057E-01 2.14808E+OO

9.98244E-01 2 6.01636E-O1 3.30053E+00 4.66065E+00 9.99750E-01 2 6.01635E-01 4.77027E+01 2.56286E+Oi 1.00000E+00 2

i. I ~ ~ O ~ E + O O


5035.6 13987.7 8.19828E-0 1 7.62126E-O 1 1.84425E+02 2.85740E+02 2.02480E-01 3.13714E-01 l.OOOOOE+OO l.OOOOOE+Oa -4 -3 6.57743E-01 6.39850E-01 1.46179E+02 2.37003E+02 1.60489E-01 2.60205E-01 1.00000E+00 l.OOOOOE+Oû -3 -3 6.09276E-01 6.06951E-01 1.32720E+02 2.20356E+02 1.45713E-O1 2.41928E-01 l.WOOOE+ûO 1.00000E+Oû 2 2 6.02357E-01 ~ 6.0193OE-O1 1.40428E+02 2.33880E+02 1.40567E-01 2.341 12E-01 1.00000E+OO 1.00000E+ûC 2 2 6.01421 E-01 6.01224E-O 1 1.36514E+02 2.27448E+02 1.36649E-01 2.27674E-O 1 1 .OOOOOE+00 l.OOOOOE+OC 2 2 6.0141 1E-01 6.01225E-01 6.34683E+00 i .02729E+01

9.84199E-01 9.561 IOE-01 2 2 6.01 174E-01 6.01034E-01 9.87429E+00 1.63873E+01 1.39434E+Ol 2.31404E+01 9.97750E-01 9.9375 1E-01 2 2 6.01171E-01 6.01031E-01 1.42999E+02 2.38276E+02 7.68272E+01 1.28015E+02 l.OOOOOE+00 l.OOOOOE+OC 2 2

3.40987~+00 5.51919~+00

Table 4-C-6-Selected Round Robin Test Results Matrix-SI Units (Dm = 0.746150 m, CS = 0.00001116 m/m-K, d, = 0.303808 m, al = 0.00001665 m/m-K)

4.39157E+02 4.82 150E-01 1 .OOOOOE+00 2 6.015 15E-01 4.67439E+02 4.67902E-0 1 I.OOOOOE+OO

Flow Conditions

5.26620E+02 6.14062E+02 5.78 176E-O 1 6.74 179E-0 1 1 .OOOOOE+00 1 .OOOoOE+Oû 2 2 6.01430E-01 6.01364E-01 5.60847E+02 6.54249E+02 5.61403E-O 1 6.54898E-O 1 1.OOOOOE+00 1.00000E+OC 'I 'I

Tf= 255.37 K, Pf = I.O1325E+O5 Pa, pf,p = 932.26 kg/m3, p = 1.8650 Pa-s, k = -1.0, pb = 910.83 kg/m3

Tf= 293.15 K, Pf = 1.01325E+05 Pa, pt,p = 907.60 kg/m3, p = 2.1220E-01 Pa-s, k = -1.0, pb = 910.83 kg/m3

4.54748E+02 4.55 199E-0 1 1 .OOOOOE+00 2 6.01064E-01 1.771 16E+OI 9.51567E+00 8.24439E-01 2 6.00895E-01 3.21489E+OI 4.5397 1 E+O 1 9.75002E-01 2 6.00889E-01 4.76439E+02 2.55970E+02 l.OOOOOE+OO

Tf= 353.15 K, Pf = 1.01325E+05 Pa, pf,p = 868.43 kg/m3, p = 1.7490E-02 Pa-s, k = -1.0, pb = 910.83 kg/m3

Tf=288.71 K, Pj = l.O1325E+O5 Pa, pf,p = 999.01 kg/m3, p = 1.1990E-03 Pa-s, k = -1.0, pb = 999.01 kg/m3

5.45660E+02 6.36569E+02 5.46201 E-0 1 6.37200E-01 1 .OOOOOE+00 1.00000E+OC 2 2 6.0 1042E-0 1 6.01036E-01 1.92618E+Oi 1.97263E+Ol I.O3485E+Ol 1.05981E+01 7.47192E-O1 6.55900E-01 2 2 6.00866E-01 6.00844E-01 3.81416E+01 4.38969E+01 5.38594E+O 1 6. I9864E+0 1 9.64003E-01 9.51005E-01 2 2 6.00858E-01 6.00835E-01 5.71698E+02 6.66954E+02 3.07148E+02 3.58325E+02 I.OOOOOE+00 l.OOOOOE+OC

Tf= 372.04 K, Pf = 1.01325E+05 Pa, pf,p = 941.75 kg/m3, p = 2.8250E-04 Pas, k = -1.0, pb = 999.01 kg/m3

6.01308E-01 8.45412E+OO 4.54203E+00 9.99871E-01 2 6.0 128 1E-01 7.62651E+OO 1.07693E+OI 9.99950E-01 2 6.01261E-01 9.84068E+OO 1.38959E+01 9.99975E-01 'I

pf,p = 2.1181 kg/m3, p = 1.3070E-05 Pa-s, k = 1.3198, p b = 1.86131 kg/m3

6.00986E-01 2.53229E+Ol 1.36049E+OI 9.98839E-01 2 6.00972E-O 1 2.28588E+Ol 3.22787E+Ol 9.9955OE-O1 2 6.00961E-01 2.95017E+Ol 4.16591E+OI 9.99775E-01 'I

Tf = 283.1.5 K, Pf = 6.89476E+05 Pa, ptSp = 4.983 1 kg/m3, p = 1.0670E-05 Pa-s, k = 1.3622, pb = 0.708 I7 kg/m3

Tf = 255.37 K, Pf = 6.89476E+06 Pa, pf,p = 1042.35 kg/m3, p = 1.5430E-04 Pa-s. k=-1.0, p b = 1.86131 kg/m3

Tf = 255.37 K, Pf = 1.37895E+06 Pa, pf,p = 32.783 kg/m3, p = 1.3520E-05 Pa-s, k = 1.3198, p b = 1.86131 kg/m3

6.00786E-01 8.33896E+Ol 4.48015E+01 9.87 1OOE-0 1 rl

Tf= 283.15 K, Pf = 3.44738E+06 Pa, pf,p = 26.627 kg/m3, y = 1.131OE-O5 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

Tf= 338.71 K, Pf = 6.89476E+06 Pa, = 44.168 kg/m3, p = 1.3650E-05 Pa-s,

k = 1.3622, pb = 0.70817 kg/m3

6.00765E-01 6.00749E-01 9.94885E+01 1.15273E+02 5.34508E+O 1 6. i 93 13E+01 9.8 1424E-O 1 9.747 16E-0 1 'I m

T / = 333.15 K, Pl = 1.37895E+07 Pa, P,,~ = 520.04 kg/m3, p = 4.1710E-05 Pa-s, k=-1.0, p b = 1.86131 kg/m3

6.00772E-01 9.80843E+Ol 1.38504E+02 9.97500E-01 'I

Cell Value

6.00752E-01 6.00736E-01 1.17567E+02 1.36979E+02 1.66016E+02 1.93427E+02 9.96400E-01 9.95100E-01 'I m

cd

Qv 4111

Y ICD cd q111

Qv Y ICD

Cd 4111 Qv Y ICD

-

-

cd %r Qv Y ICD

cd 4in Qv Y ICD cd B.

Y ICD

cd %Il

Qv Y ICD

cd 4m

Y ICD

q111

Y ICD

4111

Y ICD cd 4111 Qv Y ICD

cd 4ni QV Y ICD

-

-

Q"

-

-

Q"

c, Qv

Cd

Q"

-

-

-

-

-

6.01220E-01 I 6.00937E-01

6.00887E-01 4.21 105E+Oi 2.26241 E-FO 1 9.96775E-01 2 6.00876E-01 3.80614E+01 5.3746 1 E+O 1 9.98750E-01 2 6.00868E-01 4.91421E+01 6.93931E+01 9.99375E-01 2 6.00849E-01

3.375918+01 1.012318+02 1.686928+02 1.81373E+Ol 5.438678+01 9.06310E+01 1*00000E+00 I .OOOOOE+00 I .OOOooE+OC 2 l 2 l 2

Pa 27415.

7.32247E-O 1 3.84353E+02 4.21981E-01 1.OOOOOE+OC -3 6.29603E-01 3.26490E+02 3.58454E-01 I .OOOOOE+OC -3 6.05793E-01 3.07909E+02 3.38054E-01 1 .OOOOOE+OC 2 6.01709E-01 3.273 13E+02 3.27637E-O 1 1 .OOOOOE+OC 2 6.01120E-01 3.18373E+02 3.18688E-01 l.OOOOOE+OC 2 6.01133E-01 1.37462E+Oi 7.38523E+OC 9.13975E-01

6.00960E-01 2.28009E+OI 3.21 97OE+OI 9.87751E-O1 2 6.00956E-01 3.33544E+O: 1.79199E+02 1.00000E+OC 2 6.00834E-01 5.87664E+OI 3.15726E+Ol 9.93679E-01 2 6.00824E-O 1 5.32173E+O 1 7.5 1477E+O i 9.97550E-01 2 6.008 18E-01 6.875 l9E+Ol 9.70839E+OI 9.98775E-01 2 6.00802E-01 2.36151E+O; 1.26873E+0; 1.00000E+O( 2

55950.8

5.81458E-01

5.04349E-01

-3 6.04810E-01 I 6.04387E-01 I 6.04065E-01

I' I' 6.01028E-01 I 6.00986E-01 I 6.00954E-01

L I' I' 6.00778E-01 I 6.00757E-01~6.00740E-01 7.58246E+Ol 9.07851E+01 1.05636E+02 1.07071E+02 1.28197E+02 1.49167E+O2 9.95OOOE-O 1 I I 9.9280 1 E-O 1 9.90201E-01

L I L I ' 6.00759E-01 I 6.00739E-01 I 6.00724E-01 3.37334E+02 4.04787E+02 4.72240E+02 1.81235E+02 2.17474E+02 2.53714E+02 1 .OoooOE+00 1.00000E+00 I .OOOOOE+OC 2 l 2 l 2



Table 4-C-6-Selected Round Robin Test Results Matrix-SI Units ( D,,, = 0.049262 m, % = 0.0000111 6 m/m-K, d,,, = 0.0261 94 m, ai = 0.00001 665 m/m-K)

Cell Value

Pa

13987.7

1.5967 1 E+O( 4.57515E+N 5.02306E-O? I .OOOOOE+0( -5 9.15217E-01 2.59086E+O( 2.84451502 1 .0000OE+O( -4 6.58288E-O1 1.82662E+0( 2.00545E-0? I .00000E+M -3 6.1 I855E-O1 1.8 1694E+0( 1.8 1874E-03 1 .OOOOOE+O( 2

27415.

I .4396 1 E+O( 5.77499E+O( 6.34036E-02 1 .OOOOOE+O( -5 8.60580E-01 3.4 1067E+O( 3.74457E-0: 1.00000E+O( 4 6.37689E-01 2.47725E+O( 2.7 1977E-0: I .00000E+O( -3 6.10500E-OI 2.53808E+ûí 2.54060E-02 1.00000E+O( 2 6.06928E-01 2.45685E+0( 2.45928E-02 1 .00000E+0( 2 6.07039E-3-03 1.05651E-O1 5.676 15E-02 9.102 14E-0 1 2 6.0599 1 E-0 1 1.75623E-01 2.47995E-01 9.87215E-01 2 6.05973E-O1 2.57039E+oC 1.38096E+OC 1.00000E+OC 2 6.05246E-01 4.52294E-01 2.42998E-01 9.93403E-01

Flow Conditions

Tf = 255.37 K, Pf = 1.01325E+05 Pa, pv = 932.26 kg/m', y = 1.8650 Pa-s, k=-1.0, p/,=910.83 kg/mJ

559.5

2.790 I6E+o( 1.59895E+o( 1.75549E-01 1 .00000E+O( -6 I .35 I72E+O( 7.65306E-01 8.40229E-3-04 I .00000E+O( -5

5035.6

I .88676E+0( 3.24375E+O( 3.56131E-02 1.00000E+O( -5 1 .O1 838E+0( 1.72975E+N I .89909E-01 I .00000E+O( -4 6.93474E-01 1,15456E+0( 1.26759E-03 1.00000E+O( -3 6. I45 l4E-0 1 I .09490E+O( 1.09599E-O3 I .00000E+OE 2

55950.8 80569.1

I .29789E+OO I .234 17E+OC 7.43785E+00 8.48719E+OC 8.16601E-O3 9.31808E-O3 I .OOOOOE+00 I .00000E+OC -5 -5 8.121 17E-01 7.90546E-O1 4.59800E+00 5.37104E+OC 5.048 14E-03 5.89686E-O3 I .00000E+00 1 .OOOOOE+OC 4 -4 6.30764E-01 6.27849E-01 3.50049E+00 4.18 1 18E+Oû

1.00000E+00 1.00000E+Oû 3.84319E-03 4.59051E-03

109663.5

I . I8446E+oC 9.50290E+oC 1.04332E-02 1 .OOOOOE+oC -4 7.73776E-01 6.13329E+OC 6.73374E-03 I .00000E+OC -4 6.25659E-O1 4.86103E+OC

l.OOOOOE+OC 5.33692E-03

G/ (1111

8,. Y ICD G/ (1ru

Q I .

Y ICD

~

Tf=293.15 K, Pj = 1.01325EtO5 Pa, p,+ = 907.60 kg/m3, y = 2.1220E-01 Pa-s, k=-1.0, p/,=910.83 k g / d

TI= 353.15 K, Pj = 1.01325E+05 Pa, p,+ = 868.43 kglm", y = 1.749OE-O2 Pa-s, k=-1.0, p/,=910.83 kg/mJ

G/

QI.

Cd

QI.

Cd

QI.

Cd

QI.

(1111

Y ICD

411,

Y ICD

4lii

Y ICD

-

-

-

4,ll

Y ICD

cd G,lll

Y ICD

4rn

Y ICD

-

QV

- cd

QI,

7.9 I82 1 E-O 1 4.39427E-O1 4.82447E-O4 1 .00000E+0( 4 6.242 17E-O1 3.70727E-01 3.71095E-04 1.00000E+OC

3 3 3 6.09323B-01 I 6.08806E-01 I 6.08408E-O1 Tf= 288.71 K, Pf = l.O1325E+O5 Pa,

p,+ = 999.01 kg/mJ, p = 1.1990E-03 Pa-s, k = -1 .O, pl1 = 999.01 kg/m'

3.618841k00 4.3389313+00 5.05877EtOC 3.622438-03 4.343238-03 5.06378E-03 I .00000E+00 I .OOOOOE+00 I .00OOOE+OC 2 2 2 6,063748-01 6,061278-01 6.05935E41 3.50659E+00 4.20619E+ûO 4.905660+00 3.51006E-03 4.21036E43 4.91052E-03 I .OOOWE+OO I .mooEtoo I .ooooo~+oa .-I .-I .-,

ïj= 372.04 K, P j = l.O1325E+O5 Pa, pl,/l = 94 I .75 kg/&, p = 2.8250E-04 Pa-s, k=-1.0, p,,=999.01 kg/m3

6.12772E-01 3.54356E-01 3.54707E-04 1 .00000E+OC 2 6.12650E-01 1.67043E-O2 8.97446E-03 9.98168E-01 2 6.10059E-01 2.55776E-02 3.61 178E-02 9.99739E-O1 2 6.10055E-01 3.69670E-0 1 1.98607E-01 1.00000E+OC 2 6.08078E-01 6.53376E-O2 3.51030E-02 9.99865E-01 2 6.07912E-01 5.89292E-92 8.32133E-02 9.99948E-01 2 6.07775E-01 7.60261E-O2 1.07356E-01 9.99974E-01

6.08733E-01 1.05607E+Oc I .O57 12E-03 1.00000E+OC 2 6.08703E-01 4.90592E-02 2.63573E-02 9.83509E-01 2 6.07268E-01 7.62229E-O2 1.07634E-O1 9.97652E-01 2 6.07261E-O1 1.10394E+OC 5.93098E-01 1.00000E+OC 2 6.06 155E-O I 1.95184E-01 1.04864E-01 9.98788S01 2 6.0606OE-O1 1.76177E-41 2.48778E-01 9.9953OE-O1 2 6.05982E-01 2.27360E-01 3.21053E-O1 9.99765E-01

6.07550E-O1 1.75669E+OC 1.75843E-03 1.00000E+O( 2 6.07587E-O1 7.91 822E-O2 4.2541 1E-O2 9.54191E-01 2 6.06432E-01 1.26332E-01 1.78393E-01 9.93477E-01 2 6.0642 1 E-O 1 1.83735E+OC 9.87127E-01 l.OOOOOE+OC 2 6.05563E-O1 3.24288E-01 1.74225E-01 9.96634E-01

L I L I L 6.0663OE-0116.065 I IE-O1 I 6.OCA88E-OI Tf = 255.37 K, Pf = 1.01325E+05 Pa,

Q ~ , ~ ~ = 2.1 18 1 kg/m", p = 1.3070E-05 Pa-s, i<= 1.3198, pb= 1.86131 kg/m3

1.35343E-O1 1.46350E-01 1.48636El-01 7.27136E-02 7.86277E-02 7.98558E-02 8.16764E-01 7.36140E-01 6.40857E-01 2 2 2 6.05601E-01 6.05430E-01 6.05299E-01 2.47348E-01 2.93236E-01 3.37214E-01 3.49278E-01 4.14076E-01 4.76176E-01 9.73909E-01 9.62429E-01 9.48861E-01

Tf= 283.15 K, Pf = 6.89476E+05 Pa, of,/> = 4.983 1 kg/m3, p = 1.0670E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

6.05572E-O 1

9.86536E-O 1

r,= 255.37 K, Pf = 6.89476E+06 Pa, o,,/, = 1042.35 kg/m3, p = 1.5430E-04 Pa-s i<=-l,O, p,,= 1.86131 kg/m3

4.40215E+00 5.13465E+Oû 2.36508E+OO 2.75862E+Oû l.O0000E+OO I.OOOOOE+OO

6.04834E-01 6.04735E-01 7.64856E-O1 8.85816E-01 4.10923E-O1 4.7591OE-01 i- 9.80612E-01 9.73610E-01

rr= 255.37 K, Pf = 1.37895E+06 Pa, ol,p = 32.783 kg/m3, y = 1.3520E-05 Pa-s, k = 1.3198, p,,= 1.86131 kg/m3

cd 4111

Q v Y ICD Cd (1m Qv Y ICD

cd 41n Q v Y ICD Cd 4111

Qv Y ICD

-

-

6.04777E-01 6.04679E-01 6.98258E-01 8.12276E-01 9.86003E-01 I. 14701E+00 9.92486E-O1 9.89772E-01 i- 9.96243E-01 9.94886E-01

6.04735E-01 6.04639E-01 9.04369E-01 1.05349E+00 1.27705E+00 1.48763E+OO

6.05488E-01 2.93 105E-O1 4.13891E-O1 9.98695E-O1 2 6.05427E-O1 3.78428E-O 1 5.34374E-0 1 9.99348E-O1 2 6.05317E-01

6.97832E-01 1.00000E+Oû 2

6.05 18OE-01 4.09625E-01 5.78427E-01 9.97443E-01 2 6.05128E-O1 5.29205E-O 1 7.47285E-01 9.98721E-01

6.04902E-01 5.83349E-O1 8.23741E-01 9.94782E-01

7.54662E-01

9.9739 1E-0 1

rf = 283.15 K, pf = 3.44738E+06 Pa, o,+ = 26.627 kg/m3, y = 1.13 10E-05 Pa-s, k = 1.3622, pi, = 0.70817 kg/m3

7j.= 338.71 K, Pj = 6.89476Et06 Pa, grsp = 44.168 kg/m3, y = 1.3650E-05 Pa-s, '(= 1.3622, pb=0.70817 kg/m3

r/= 333.15 K, Pi.= 1.37895E+07 Pa, 3r,p = 520.04 kg/m3, /.I = 4.1710E-05 Pa-s, k=-l.O, pb= 1.86131 kg/m3

6.07534E-O1 2.60726E-01 1.4OO76E-01 1.00000E+00 2

6.05843E-01 7.80008E-01 4.19064E-O1 I.OOOOOE+OO 2

6.05033E-01 1.8 1758E+OC 9.76506E-01 1.00000EtOû 2

6.04776E-01 6.04659E-O1 6.04567E-01 2.59544E+OO 3.1 1392E+W 3.63236E+00 1.39441E+OO 1.67297E+W 1.95 15 1E+00 1.00000E+00 I.OOOOOE+00 l.OOOOOE+OO 2 l 2 II


A P I f lPf lS*L4.3=4 92 = 0732290 050b409 8b8

SECTION %CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 4-BACKGROUND

109663.5 1.0725 1E+00 1.937 10E+01 2.12674E-02 1 .OOOOOE+OO 4 7.352 12E-01 1.31191E+01 1.44034E-02 I.OOOOOE+OO -3 6.2OO98E-01 1.08458E+01 1.19076E-02 I.OOOOOE+OO 3 6.06617E-01 1.13547E+O I 1.13660E-02 l.OOOOOE+OO 2 6.04589E-01 1.1 O 1 9 1E+O 1 1.10300E-02 I.OOOOOE+OO 2 6.05044E-01 3.33667E-01 1.79265E-01 6.40578E-01 2 6.04055E-01 7.57540E-01 1.06971E+OO 9.48822E-01 2 6.040 14E-O 1 1.15354E+01 6.19748E+OO 1 .OOOOOE+OO 2 6.03579E-01 1.99029E+OO 1.06929E+OO 9.73590E-01 2 6.03533E-01 1.825 1 OE+OO 2.5772 1E+OO 9.89764E-01 2 6.03500E-01 2.367 14E+OO 3.3426 1E+OO 9.94882E-01 2 6.03439E-01 8.16188E+OO 4.38502E+OO 1.00000E+OO 2

~

123

8.51475E-O1 5.42631E+OO 5.95754E-03 1.OOOOOEfOO d

Table 4-C-6-Selected Round Robin Test Results Matrix-SI Units ( D, = 0.073670 m, % = 0.00001116 m/m-K, d, = 0.039291 m, q = 0.00001665 m/m-K)

8.06808E-01 7.67033E-01 7.19832E+00 9.77634E+C€ 7.90303E-03 1.07334E-02 I.OOOOOE+OO I.OOOOOE+W d -2

Flow Conditions

3.96977E+OO 4.35841E-03 l.OOOOOE+OO -3 6.09384E-01 4.07376E+00 4.07779E-03 l.OOOOOE+OO_

Tf= 255.37 K, PJ= 1.01325E+05Pa, p , =932.26 kg/m3, F = 1.8650Pa-s, k=-1.0, pbZ910.83 kg/m3 ' P

5.50258E+00 7.79552E+Oo 6.04128E-03 8.55870E-03 l.OOOOOE+OO I.OOOOOE+OC 3 3 6.08303E-01 6.07357E-01 5.63314E+OO 8.12042E+OC 5.69878E-03 8.12846E-03 1.OOOOOE+00 l.OOOOOE+OC

T,r=293.15 K, Pf= 1.01325E+05 Pa,

k=-I.0, pb=910.83kg/m3 = 907.60 kg/m3, p = 2.1220E-01 Pa-s,

3.94405E+00 3.94795E-03 1.00000E+OO 2 6.05947E-01 1.77766E-O 1 9.55060E-02 9.54155E-01 2 6.04998E-0 1 2.83724E-01 4.OO6ME-O 1 9.93472501 2 6.04988E-01 4.12645E+OO

I .OOOOOE+OO 2 6.04275E-01 7.28478E-01 3.9 1379E-01 9.96631E-01

2.21696~+00

9

Tf= 353.15 K, Pl= 1.01325E+05 Pa, pf,p = 868.43 kg/m3, p = 1.7490E-02 Pas, k=-l.O, pbZ910.83 kg/m3

5.51701E+OO 7.87550E+OC 5.52248E-03 7.88331E-03 I.OooOoE+OO l.OOOOOE+OC 2 2 6.05498E-01 6.05 161E-01 2.37218E-01 3.0389 lE-01 1.27447E-01 1.63267E-01 9.10144E-01 8.16621E-01 2 2 6.04633E-0 1 6.04308E-O 1 3.94469E-01 5.55628E-01 5.57026E-O 1 7.84596E-O 1 9.87205E-01 9.73889E-01 2 2 6.04617E-01 6.04283E-01 5.77348E+OO 8.24327E+OC

l.OOOOOE+OO 1 .OOOOoE+W 2 2 6.040IOE-01 6.03770E-01 1.0161 lE+OO 1.44098E+OC 5.459 13E-01 7.74174E-01 9.93397E-01 9.86525E-01

3.10184~+00 4.42875~+00

,7 .-.

TJ= 288.71 K, PJ= 1.01325E+05 Pa, P,,~ = 999.01 kg/m3, p = 1.1990E-03 Pa-s, k = -1.0, pb = 999.01 kg/m3

6.58446E-O1 9.29785E-01 9.98694E-01 2 6.04164E-01 8.50135E-01 1.20047E+OO 9.99347E-01 .-I

Tf= 372.04 K, Pf= 1.01325E+05 Pa, P,,~ = 941.75 kg/m3, p = 2.8250E34 Pa-s, k = -1.0, pb = 999.01 kg/m3

9.20274E-01 1.31066E+G€ 1.29951E+OO 1.85077E+OC 9.9744 1E-0 1 9.94778E-O 1 2 2 6.03913E-01 6.03685E-01 1.18895E+OO 1.69559E+OC 1.67890E+OO 2.39433E+OC 9.98720E-01 9.97389E-01 .-.

T/= 255.37 K, PJ= 1.0132?E+05 Pa, p,,,=2.1181 kg/m3, F = 1.3070E-05 Pa-s, k = 1.3198, pb= 1.86131 kg/m3

Tf= 283.15 K, PJ= 6.89476E+05 Pa, P,,~ = 4.9831 kg/m3, p = 1.0670E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

Tf= 255.37 K, PJ= 6.89476E+06 Pa, pf,p = 1042.35 kg/m3, p = 1.5430E4Pa-s k=-1.0, pb= 1.86131 kg/m3

TJ= 255.37 K, Pl= 1.37895E+06 Pa, P,,~ = 32.783 kg/m3, p = 1.3520E-05 Pa-s, k = 1.3198, pb= 1.86131 kg/m3

ïj=283.15 K, Pf=3.44738E+O6 Pa,

k = 1.3622, pb = 0.70817 kg/m3 = 26.627 kg/m3, p = 1.1310E-05 Pa-s,

TJ= 338.71 K, P'= 6.89476E+06 Pa, P, ,~ = 44.168 kg/m3, p = 1.3650E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

Tf= 333.15 K, Pf= 1.37895E+07 Pa, p, = 520.04 kg/m3, p = 4.1710E-05 Pa-s, I P k = -1.0, pb = 1.86131 kg/m3

Cell Value

cd e 1

Q v Y ICD cd 9ni Q v Y ICD cd qn, Q v Y IC33 cd 4111

Q v Y ICD

cd 4 1

Q v Y ICD cd

Q v

-

-

-

-

-

Y ICD cd %I

Q v Y ICD cd 9111

Q v Y ICD cd e l l

Q v Y ICD cd 4ni Q v Y ICD cd "ni

Q v Y ICD cd 4111

Q v Y ICD

-

-

-

-

-

-

-

559.5 2.41408E+OC 3.11437E+oC 3.41927E-03 1.00000E+OC -6 1.21094E+OC 1.5434 1E+K 1.6945 1E-03 l.OOOOOE+OC -5 7.50247E-0 I 9.37294E-01 1.02906E-03 l.OOOOOE+OC -3 6.18993E-01 8.27593E-01 8.28413E-04 1.00000E+OC 3 6.101 14E-01 7.94262E-O 1 7.95049504 1 .OOOOOE+OC 2 6.10013E-01 3.74425E-02 2.01 162E-02 9.98166E-01 2 6.07949E-0 1 5.73808E-02 8.10269E-02 9.99739E-01 2 6.07945E-01 8.293 18E-01 4.45556E-01 1 .OOOOOE+OC 2 6.06348E-01 1.46669E-01 7.87986E-02 9.99865E-01

6.06213E-01 1.32290E-01 1.86805E-01 9.99948E-01 2 6.06103E-01 1.70678E-O 1 2.41013E-01 9.99974E-01 2 6.05906E-01 5.85371E-01 3,14494E-01 1.00000E+K 2

5035.6 1.65682E+oE 6.41239E+oC 7.04016E-03 I.OOOOOE+CK -5 9.35895E-01 3.57859E+OC 3.92893E-03 1.00000E+OE 4 6.64836E-01 2.49179E+OC 2.73574E-03 l.OOOOOE+oC -3 6.11483E-01 2.45268E+OE 2.4551 1E-03 1 .OOOOOE+OC 2 6.06883E-01 2.37019E+íX 2.37254E-03 I .OOOOOE+CK 2 6.06855E-01 1.10105E-01 5.91544E-02 9.83496E-O 1 2 6.05686E-01 1.71145E-01 2.41672E-01 9.97650E-01 2 6.05680E-01 2.47871E+OC 1.33 170E+oC l.OOOOOE+O( 2 6.04768E-01 4.38391E-01 2.35528E-01 9.98787E-01 2 6.04690E-01 3.9571 1E-01 5.58780E-01 9.99530E-01 2 6.04627E-01 5.10687E-01 7.21 136E-01 9.99765E-01 2 6.045 11E-01 1.75209E+oC 9.41319E-01 1.00000E+Oí 2

I ' I - ,

6.35507E-01 I 6.29207E-01 I 6.23979E-01

2 12 12 6.05921E-01~6.05410E-01 I 6.04954E-01

L I L I' 6.04213E-01~6.03955E-01 I 6.03721E-01

L I L 6.04072E-01 I 6.03833E-01 I6.03616E-01 2.91801E+00 4.08360E+OO 5.83162E+OC 1.56772B+OO 2.19394E+OO 3.13307E+G€ l.OOOOOE+OO l.OooOoE+OO 1.00000E+OC 2 l 2 l 2

80569.1 1.11358E+OC 1.72394E+OI 1.89272E-02 1 .OOOOOE+OC 4 7.49192E-01 1.14587E+O1 1.25805E-02 l.OOOOOE+OC -3 6.21766E-01 9.32145E+OC 1.02340E-02 l.OOOOOE+OC 3

6.06940E-0 1 9.73780E+OC 9.74745E-03 1 .OOOOOE+OC 2 6,04749E-01 9.44740E+OC 9.45676E-03 1 .OOOOOE+OC 2 6.05063E-01 3.28585E-01 1.76534E-01 7.35935E-01 2 6.04165E-01 6.58731E-01 9.30188E-01 9.624OOE-O 1 2 6.04 132E-O 1 9.88945E+OC 5.31317E+OC 1.00000E+OC 2 6.03663E-01 1.7 1847E+K 9.2326 1E-01 9.80597E-01 2 6.036 15E-01 1.56888E+OC 2.2 1540E+oC 9.92480E-01 2 6.03581E-01 2.03202E+OC 2.86939E+K 9.96240E-O 1 2 6.035 17E-01 6.99680E+OC 3.75907E+OC I.OOOOOE+OC 2


- _ - A P I MPMS*L4.3-4 92 = 0732290 05064LO 5 8 T


Table 4-C-6-Selected Round Robin Test Results Matrix-SI Units ( Dm = 0.1 02270 m, Q = 0.00001 11 6 m/m-K, d, = 0.054570 m, ai = 0.00001 665 m/m-K)

Flow Conditions

T/= 255.37 K, PJ= I.O1325E+O5 Pa, pf,/) = 932.26 kg/m3, p = 1.8650 Pa-s, k=-1.0, p/)=910.83 kg/m"

?=293.15 K, PJ= 1.01325E+05 Pa, pie = 907.60 kg/m3, p = 2.1220E-01 Pa-s, k=-l..O, p,,=910.83 kg/m3

T/= 353.15 K, PJ= 1.01325E+05 Pa, pbP = 868.43 kg/m3, p = 1.7490E-02 Pa-s, k=-1.0, p,,=910.83 k g / d

T/= 288.71 K, Pi= 1.01325E+05 Pa, pf,/, = 999.01 kg/m3, p = 1.1990E-03 Pa-s, k = -I .O, p,, = 999.01 kg/m3

Tj= 372.04 K, Pf= I.O1325E+05 Pa, pbp = 941.75 kg/m3, p = 2.8250E-04 Pa-s, k = -1.0, pi, = 999.01 kg/m3

T/= 255.37 K, Pf= 1.01325E+05 Pa, pn> = 2.1 181 kg/m3, p = 1.3070E-05 Pas , k = 1.3198, ph= 1.86131 kg/m3

TI= 283.15 K, Pf= 6.89476E+05 Pa, pbp = 4.983 I kg/m3, p = 1.0670E-05 Pa-s, k = 1.3622, p,, = 0.70817 kg/m3

Tf= 255.37 K, Pj= 6.89476E+06 Pa,

k=-1.0, pb= 1.86131 kg/m3 = 1042.35 kg/m3, p = 1.5430E4 Pa-s

Tj= 255.37 K, Pf= 1.37895E+06 Pa,

k = 1.3198, ph= 1.86131 kg/m3 = 32.783 kg/m3, p = 1.3520E-05 Pa-s,

T/= 283.15 K, PJ= 3.44738E+06 Pa, pf,p = 26.627 kg/m3, p = 1.1310E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

Tf= 338.71 K, Pf= 6.89476E+06 Pa, pl,p = 44.168 kg/m3, p = 1.3650E-05 Pa-s, k = 1.3622, p,, = 0.70817 kg/m3

Tf= 333.15 K, PJ= 1,37895E+07 Pa,

k=-1.0, ph= 1.86131 kg/m3 = 520.04 kg/m3, p = 4.1710E-05 Pa-s,

Cell Va'ue

C,, 2.35099E+00 1.49685E+0(1

5035.6 559.5

9,,, 5.35321E+00 1.1 l758E+01 Q,, 5.87728E-03 1.22699E-02 Y 1.00000E+00 I .0000OE+W ICD -6 -5 C, 1.1 1396E+00 8.79898E-01 9,,, 2.73897~+00 6.49045~+0a Q, 3.00712E-O3 7.12586E-03 Y 1.00000E+00 1 .OMH1OE+Oû ICD -4 -4

C, 7.2175OE-01 6.42738E-01 9,,, 1.73947E+00 4.647 17E+OO Q,, 1.9O976E-03 5. I02 I3E-03 Y I .00000E+OO 1 .OoooOE+Oû ICD -3 -3

C, 6.16303E-0 1 6.1017 I E-01 9,,, 1.58958E+W 4.72 134E+OC Q, 1.59 1 16E-03 4.72602E-03 Y 1.00000E+00 1 .OoooOE+Oû ICD 2 2

Cd 6.09037E-01 6.06333E-01 9,,, 1.52952E+00 4.56822E+C€ Q, 1.53103E-O3 4.57275E-03 Y 1.00000E+00 l.OOOOOE+OC ICD 2 2

Cd 6.08953E-01 6.06309E-01 91f1 7.21053E-02 2.1221 3E-01 Q, 3.87390E-02 1.14013E-01 Y 9.98166E-01 9.83494E-01 ICD 12 12 CA I6.07230E-01 I6.05317E-01 qrir 1.10563E-01 3.29957E-01 Q, 1.56125E-01 4.65929E-01 Y 9.99739E-O1 9.97650E-01 ICD 2 2

Cd 6.07227E-01 6.053 11E01 9,ri 1.59796E+OO 4.77879E+ûC Q, 8.58511E-01 2.56744E+OC Y l.OOOM)E+OO l.OoooOE+OO ICD 2 2 Cd 6.05879E-O1 6.04531E-01 9111 2.82721E-01 8.45373E-01 Q, 1.51894E-01 4.54182E-01 Y 9.99865E-01 9.98787E-01 ICD 2 2 Cd 6.05765E-01 6.04464E-01 9,11 2.55014E-01 7.63086E-01

Y 9.99948E-O1 9.99530E-01 ICD 2 2 Cd 6.05671E-01 6.04410E-01 qrri 3.29024E-01 9.84818E-01

Q, 3.60102~-01 1.07755~+00

Q, 4.64611E-O1 1.39065E+C€ Y 9.99974E-O1 9.99765E-01 ICD 12 12 CA I 6.05504E-O1 I 6.04310E-01

13987.7

1.28854E+OC 1.6034 1 E+O I 1.76039E-02 1.000OOE+0(1 -5 8.08397E-O1 9.93836E+C€ 1 .O9 1 I3E-O2 1.00000E+W -4 6.295 12E-O 1 7.58589E+OC 8.32855E-03 1.00000E+OC 3 6.08430E-01

7.85420E-03 1 .OOOOOE+Oû 2 6.05516E-01 7.60343E+OC 7.61097E-03 1 .OOOOOE+OO 2 6.05539E-01 3.42698E-01 1.841 17E-01 9.54150E-01 2 6.04729E-01 5.4709 1E-01 7.72542E-01 9.93471 E-01 2 6.04720E-01 7.95685E+oC 4.27487E+oC 1 .OOOOOE+OO

7.84643~+oa

6.04 I07E-0 1 1.40492E+OC 7.54803E-O1 9.96631E-O1 2 6.04053E-01 i.26988~+oa 1.793 18E+OC 9.98694E-01 2 6.04010E-01 1.63959E+OC 2.31525E+OC 9.99347E-01 2 6.0393 1 M 1 5.62786E+OC 3.02360E+OC 1 .0000OE+OC 2

Pa

274 15.

I . I7639E+Oc 2.0494lE+Ol 2.25005E-02 I .00000E+OC -4 7.70446E-O1 1.32605E+Ol I .45587E-02 1.000M)E+OC -3 6.24502E-01 1.05357E+01 1,15672E-02 1.00000E+OC 3 6.07527E-03 1.09687E+01 1.09796E-02 1.00000E+OC 2 6.05081E-01 1.06372E+01 1.06477E-02 1 .OOOOOE+OC 2 6.05156E-01 4.57356E-01 2.457 17E-01 9.10134E-01 2 6.04415E-01 7.607OOE-O 1 1.07418E+oC 9.87204E-01 2 6.0440 1 E 4 1 1.11337E+OI 5.98166E+OC 1.OOOOOE+OC 2 6.03877E-01 1.95976E+OC 1.05289E+CK 9.93397E-01 2 6.03829E-01 1.77494E+OC 2.50638E+OC 9.97441E-01

6.03793E-01 2.29316E+OC 3.238 i 5E+OC 9.98720E-O 1 2 6.03723E-01 7.87630E+oC 4.23159E+oC 1 .OOOOOE+OC 2

55950.8 I 80569.1 I 109663.5 I l.O7584E+OO 1.03085E+oO 9.95884E-01 2.67747E+OI 3.07863E+Ol 3.46989E+01 2.93959E-02 3.38002E-02 3.80959E-02 I .OoooOE+00 I .00000E+00 1 .OOOOOE+OO -4 -4 -4 7.36338E-01 7.20837E-01 7.08548E-01 1.81049E+Ol 2.32686E+01 2.43903E+OI I ,98774E-02 2.33508E-02 2.67781E-02 I .00000E+00 1 .OOOOOE+ûO 1 .OOOOOE+00 -3 6.20321E-01 1.49503E+01 1 .641 39E-02 1 .OOOOOE+OO 3 6.06732E-01 1.5649 1 E+Ol 1.56646E-02 1 .OOOOOE+00 2 6.04690E-03 1.51861E+O1 I .520 12E-02 1.00000E+00 2 6.04868E-01 5.85940E-01 3.148OOE-0 1 8.16599E-01

6.04784E-01 6.33557501 3.40382E-O 1 7.35903501

1 .OOOOOE+OO

6.04768E-03 6.43343E-01 3.45640E-0 1 6.40535E-01

6.04135E-O1 6.0401 IE-01 6.03916E-01 1.07156E+Gû 1.27044E+OO 1.46103E+00 1.51314E+00 1.79397E+00 2.0631 1E+OO 9.73885E-01 9.62395E-01 9.48815E-01 2 2 2 6.041 13501 6.03982E-01 6.03880E-01 1.58977E+01 1.90732E+OI 2.22482E+01 8.54115E+íM 1.02472E+Ol 1.19530E+01 1 .OoooOE+00 1.00000E+00 1 .OoooOE+00 2 2 2 6.03669E-O1 6.03576E-01 6.03503E-01 2.77934E+OO 3.31464E+00 3.83899E+00 1.49322E+00 1.78081E+00 2.06252E+00 9.86524E-01 9.80594E-01 9.73587E-01 2 ' 2 2 6.03626E-01 6.03534E-01 6.03462E-01 2.52801E+00 3.02614E+00 3.52042E+3+00 3.56978E+00 4.273 19E+00 4.971 15E+00 9.94777E-O1 9.92479E-01 9.89763E-01 2 2 2 6.03594E-0 1 6.035O4E-O 1 6.03434E-O I 3.27050E+00 3.91949E+00 4.56597E+00 4.61824E+ûO 5.53467E+00 6.44756E+Oû 9.97388E-01 9.96239E-01 9.94881E-01 2 2 2 6.03534E-01 6.03448E-01 6.03381E-O1 1.12483E+01 1.34961E+Ol 1.57436E+Ol 6.04324E+00 7.25085E+00 8.45837E+00 l.OOOOOE+00 l.OoooOE+OO l.OOOOOE+OO 2 2 2


A P I MPMSE14-3.4 92 W 0732290 050641iL 4Lb =

Ceil

cd q,,L Q, Y ICD

q,,, Q, Y

cd

SECTION &CONCENTRIC, SQUARE-EDGED ORIFICE METERS. PART &BACKGROUND 125

559.5 5035.6 13987.7

1.66182E+OI 3.58929E+O 1 5.24964E+Ol I.82452E-02 3.94068E-02 5.76358E-02 1.00000E+00 l.OOOOOE+OO l.OOOOOE+OO -5 -5 -4

9.17169E+00 2.2742OE+Ol 3.54543E+Ol 1.00696E-02 2.49684E-02 3.89253E-02 1.00000Et00 1.00000E+00 1.00000E+OC

1.70699E+00 1.22893E+00 1.07845E+W

9.53571E-01 7.88145E-01 7.37224E-01

Table 4-C-&Selected Round Robin Test Results Matrix-SI Units ( Dm = 0.202729 m, a;! = 0.00001 11 6 m/m-KI d, = 0.1 07950 m, al = 0.00001 665 m/m-K)

8.94613E-01 1.04514E+02 1.14746E-01 1.00000E+OO d

T/= 255.37 K, Pf= 1.01325E+05 Pa, pf,p = 932.26 kg/m3, p = 1.8650 Pa-s, k = -1.0, p b = 910.83 kg/m3

8.69903E-01 1.18565E+O2 1.30173E-01 i .OOOOOE+00 d

T/= 293.15 K, PI= 1.01325E+05 Pa, pf,p = 907.60 kg/m3, p = 2.1220Ë-01 Pa-s, k = -1.0, p b = 910.83 kg/m3

6.57002E+Ol 7.21323E-02 1 .OOOOOE+00 -3 6.14663E-01 5.79494E+Ol 6.36227E-02 1.00000E+00 2 6.05594E-01 6.11016E+Ol 6.1 1621E-02 1.00000E+00 2 6.04130E-01 5.93504E+Ol 5.94092E-02 1.00000E+00 2 6.04259E-01 2.29006E+00 1.23035E+00 8.16697E-01 2 6.03722E-01 4.18894E+00 5.91517E+00 9.73899E-01 2 6.03706E-01 6.21473E+01 3.3389OE+Ol 1.00000E+00 2 6.03377E-01 l.O8671E+Ol

T f = 288.71 K, Pf= 1.01325E+05 Pa, pf,p = 999.01 kg/m3, p = 1.1990E-03 Pa-s, k = -1.0, pb = 999.01 kg/m3

Tf= 372.04 K, Pf= 1.01325E+05 Pa, pf,p = 941.75 kg/m3, p =2.8250E-O4 Pa-s, k = -1.0, pb = 999.01 kg/m3

T/= 255.37 K, Pf= 1.01325E+05 Pa, pf*p =2.1181 kg/m3, p= 1.3070E-05 Pa-s, k = 1.3198, pb= 1.86131 kg/m3

7.73817E+OI 8.88693E+01 8.49574E-02 9.75696E-02 1 .OOOOOE+00 1.OOOOOE+00 -3 -3 6.13516E-01 6.12643E-01 6.94095E+Ol 8.08625E+O1 7.62047E-02 8.87789E-02 1.00000E+00 1.00000E+OO 2 2 6.05345E-O 1 6.05 15 1E-01 7.32917E+Ol 8.54796E+01 7.33644E-02 8.55643E-02 1 .OOOOOE+00 1 .OOOOOE+00 2 2 6.04001E-01 6.0390 1E-0 1 7.12053E+01 8.30589E+01 7.12758E-02 8.3 1413E-02 1.00000E+00 1.00000E+00 2 2 6.04198E-01 6.04186E-01 2.47644E+00 2.5 1498E+00 1.33048E+ûO 1.351 19E+OO 7.36044E-01 6.40726E-01 2 2 6.03631E-01 6.03561E-01 4.96670E+00 5.7121 1E+00 7.01343E+OO 8.06601E+00 9.62415E-01 9.48843E-01 2 2 6.03610E-01 6.03534E-01 7.45648E+01 8.69814E+OI 4.00604E+01 4.67313E+01 1.00000E+00 1.00000E+00 2 2 6.03307E-01 6.03253E-01 1.29607E+01 1.501 14E+01

~~~~

T/= 283.15 K, Pf= 6.89476E+05 Pa, pf,p = 4.9831 kg/m3, p = 1.0670E-05 Pa-s, k = 1.3622, p b = 0.70817 kg/m3

T/= 255.37 K, Pf= 6.89476E+06 Pa, pf,p = 1042.35 kg/m3, p = 1.5430- Pa-s k=-1.0, pb= 1.86131 kg/m3

qlli Q, Y ICD Cd q,,l Qu Y

Tf=255.37 K, Pf= 1.37895E+06 Pa, pf.p = 32.783 kg/m3, p = 1.3520E-05 Pa-s, k = 1.3198, pb= 1.86131 k g h 3

Tf= 283.15 K, Pf=3.44738E+06 Pa, pf,p = 26.627 kg/m3, p = 1.1310E-05 Pa-s, k = 1.3622, p b = 0.70817 kg/m3

6.32758E+00 1.77306E+Ol 2.92493E+Ol 6.94705E-03 1.94665E-02 3.21 128E-02 l.OOOOOE+00 1.00000E+00 1.00000E+W -3 3 3 6.12058E-01 6.07974E-01 6.06780E-01 6.17534E+00 1.84026E+01 3.06106E+01 6.18146E-03 1.84208E-02 3.06410E-02 l.OOOOOE+00 l.OOOOOE+00 l.OOOOOE+OC

T f = 338.71 K, Pf= 6.89476E+06 Pa, = 44.168 kg/m3, p = 1.3650E-05 Pa-s,

k = 1.3622, pb = 0.70817 kg/m3

Tf= 333.15 K, Pf= 1.37895E+07 Pa, pf,p = 520.04 kg/m3, p = 4,1710E-05 Pa-s, k =-LO, pb= 1.86131 kg/m3

Y ICD Cd

9.98167E-01 9.83503E-01 9.54174E-01 2 2 2 6.05944E-01 6.04584E-01 6.04158E-01

ICD 1-4 1-4 1-3 Cd I 6.71164E-01 I 6.26888E-01 I 6.20488E-01

qm Q, Y ICD

qnl Q, Y ICD

qm Q, Y ICD

qni Qu Y ICD

qni Qu Y ICD

qm Qv Y ICD

cd

cd

cd

cd

cd

4.31588E-01 1.28917E+00 2.13811E+00 6.09441E-01 1.82043E+00 3.01921E+C€ 9.99739E-01 9.97651E-01 9.93475E-01 2 2 2

6.23770E+Oo 1.86712E+Ol 3.10966E+01 3.35124E+W 1.00312E+Ol 1.67068E+Ol l.O0000E+00 l.O¿M00E+OO l.OOOOOE+ûC 2 2 2

1.10433E+OO 3.30413E+00 5.49214E+OC 5.93308E-01 1.77516E+00 2.95069E+OC 9.99865E-01 9.98788E-01 9.96633E-01 2 2 2

9.96155E-01 2.98259E+00 4.96433E+OC 1.40666E+00 4.21 169E+00 7.01009E+OC 9.99948E-01 9.99530E-01 9.98695E-01 2 2 2

1.28531E+00 3.84935E+OO 6.40975E+ûC 1.81498E+00 5.43562E+OO 9.05115E+C€ 9.99974E-01 9.99765E-01 9.99347E-01 2 2 2

4.40876E+00 1.32074E+Ol 2.20021E+01 2.36863E+00 7.09577E+00 1.18208E+01 l.OOOOOE+00 1.00000E+00 l.oOoM1E+OC 2 2 2

6.05942E-01 6.04580E-01 6.04151E-01

6.04988E-01 6.04014E-01 6.03702E-01

6.04906E-01 6.03964E-01 6.03662E-01

6.04839E-01 6.03925E-01 6.03630E-01

6.04719Hl 6.03852Eol 6.03571E-01

ICD 12 12 12 Cd I6.072OOE-01 I6.05311E-01 I6.04728E-01

6.03345E-01 9.88456E+00 1.39579E+Ol 9.94780E-01 2 6.03321E-01 1.27878E+01 1.80576E+01 9.97390E-01 2 6.03276E-01 4.39827E+O1 2.36300E+01 1.00000E+00 2

ZD 1 :_6515E+CQ~~8400E+Ol~ 5.97106E-03 1.78577E-02 7 1 2.97340E-02

1.00000E+00 1.00000E+OO l.OOOOOE+OC

qnl 2.81224501 8.28757E-01 1.33885E+OO Q, 1.51089E-01 4.45255E-01 7.19306E-01

cd 6.07141E-01 6.05294E-01 6.04744E-01

6.03276E-01 6.03222E-01 1.18327E+Ol 1.37659E+01 1.67089E+Ol 1.94386E+01 9.92483-1 9.89769E-01 2 2 6.03254E-01 6.03201E-01 1.5326OE+Ol 1.78544E+Ol 2.16417E+01 2.52121E+Ol 9.96241E-01 9.94884E-01 2 2 6.03212E-01 6.03161!&01 527736E+Ol 6.15639E+Ol 2.83529E+01 3.30756E+Ol l.OOOOOE+00 1.00000E+00 2 2

Pa

274I5. 9.98074E-01 6.80173E+Ol 7.46762E-02 1.00000E+OC -4 7.09365E-01 4.77603E+01 5.2436 1E-02 1.00000E+OC -3 6.17332E-01 4.07407E+Oi 4.47292E-02 1 .O0000E+OC 2 6.06152E-01 4.28105E+Oi 4.28530E-02 1.00000E+OC 2 6.04414E-01 4.15648E+Ol 4.16060E-02 1.00000E+OC 2 6.04468E-01 1.787 16E+OC 9.60 16 1E-0 1 9.10182E-01 2 6.03928E-01 2.97335E+OC 4.19864E+OC 9.8721 1E-01 2

6.03918E-01 4.35 184E+01 2.33805E+Oi 1.00000E+CK 2 6.03531E-01 7.66 190E+OC 4. I 1640E+OC 9.93400E-01 2 6.03496M1 6.93945E+M 9.79913E+OC 9.97442E-O 1 2 6.03469EMl 8.96563E+OC 1.26603E+Oi 9.98721E-01 2 6.03417E-01 3.0795 lE+Ol 1.65448E+Oi 1.00000E+OC 2

55950.8

9.90278E-02

80569.1 I 109663.5 I

I ' I '

6.83074E-01 I 6.70437E-01 I 6.59971E-01


A P I MPMS*L4-3-4 72 0732270 O506432 352 W


Table 4-C-6-Selected. Round Robin Test Results Matrix-SI Units ( Dm = 0.36351 3 m, % = 0.00001 11 6 m/m-K, d,,, = 0.1 93675 m, al = 0.00001665 m/m-K)

Pa Cell Value - c/ 4111

QI* Y ICD

c/ 4111 QI* Y ICD

c/ 4111 QI.

Y ICD c, 41'1 QI. Y ICD

-

-

-

80569. I 109663.5

8.1 1098E-01 7.92724E-01 3.0504 I E+02 3.478 I9E-tO2 3.34904E-01 3.8187 IE-01 + 1.00000E+00 1 .OOOOOE+OC

Flow Conditions

T/= 255.37 K, PJ= 1.01325E+05 Pa, pt,p = 932.26 kg/m3, p = 1.8650 Pa-s, k = -1.0, pll = 910.83 kg/m3

559.5 5035.6 13987.7 27415.

1.42469E+OO 1.06100E+OO 9.47960E-01 8.87985E-01 4.465OOE+OI 9.97565E+01 I .48547E+02 I .94808E+O; 4.90212E-02 1.09523E-01 1.6309OE-01 2.13880E-01 1 .OOOOOE+OO I .OOOOOE+00 1.00000E+00 I .OoooOE+O( -5 4 4 -4 8.54889E-01 7.31240E-01 6.91 138E-01 6.67583E-01 2.64698E+01 6.79246E+OI 1.06999E+02 1.44693E+0; 2.90612E-02 7.45744E-02 1.17474E-O1 1.58859E-01 1 .OOOOOE+OO I .OoooOE+OO i .00000E+00 I .00000E+O( 4 -3 -3 -3

55950.8

8.34766E-01 2.6 I6 I8E+O: 2.8723 1 E-0 i I .00000E+ûí -4

6.43391E-01 1.99214E+K 2.187 17E-01 I .000OOE+O( -3

T/=293.15 K, Pf= I.O1325E+O5 Pa, pt,p = 907.60 kg/m7, p = 2.1220E-0 I Pa-s k=-1.0, p/l=910.83 kg/m7

6.36079E-01 6.32963E-01 2.36340E+02 2.74379E+02 2.59477E-O I 3.0 l240E-O I 1 .OOOOOE+OO 1 .OOOOOE+OC -3 3 6. IO7 12E-01 6.10096E-0I 2.22420E+02 2.592298+02 2.44195E-01 2.84607E-O1 i .oooOOE+OO I .00000E+W 2 2 6.04779E-01 6.04631E-01 2.357 18E+02 2.74938E+02 2.35952E-O I 2.752 1OE-0 1 1 .O~OE+OO I .OOOOOE+OG 2 2 6.03749E-01 6.03670E-01 2.29127E+02 2.67280E+02 2.29354E-01 2.67544E-01 1.000ûOE+OO 1.0@00E+00 2 2 6.03901E-01 6.03892E-01 7.96775E+00 8.09156E+ûC 4.28072E+OO 4.34724E+00 7.36005E-01 6.40674E-01 2 2 6.03459E-01 6.03404E-01 1.59841E+Ol 1.83834E+Ol 2.25709E+01 2.5959OE+Oi 9.62410E-01 9.48835E-01

T/= 353.15 K, PJ= I.O1325E+O5 Pa, = 868.43 kg/m7, p = 1.7490E-02 Pa-s

k=-1.0, ~ / ~ = 9 1 0 . 8 3 kg/m3

6.363 16E-O I 1.93120E+01 2.12026E-02 I .00000E+OC

6.19881E-01 6.15544E-01 6.13373E-01 5.644OIE+Ol 9.34084E+01 1.3031 lE+O; 6.19656E-02 1.02553E-0 1 1.43068E-0 1 I .OoooOE+00 1.00000E+OO 1.00000E+O(

6.1 1517E-01 1.85595E+0: 2.03764E-0 I 1.00000E+O( 2 6.04967E-01 1.96493E+O: I .96688E-01 i .OOOOOE+O( 2 6.03848E-01 1.9097OE+O; 1.91 160EOI 1 .OOOOOE+O( 2 6.03948E-01 7.36808E+O( 3.95855E+O( 8.16670E-O I 2 6.03531E-01 1.34806B+Oi 1.90359E+03 9.73896E-01 2 6.03518E-01 2.0000 1E+Oí 1.07452E+0; 1.00000E+OC 2 6.03260E-01 3.49763E+03 1.879 12E+01 9.86529E-01

-3 13 12 12 6.0968OE-O1 I 6.06737E-01 I 6.05855E-ûl~6.05387E-01 Tf= 288.7 i K, Pf= I .O1 325E+05 Pa,

i,,,, = 999.0 I kg/m3? p = I . 1990E-03 Pa-s k = -1 .O, pl] = 999.01 kg/m7

I .98023E+01 1.982 I9E-02 1.00000E+OC

5.9 I206E+O I 5.91792E-02 I .00000E+OC 2 n 2 L

Tj= 372.04 K, Pf= 1.01325E+05 Pa, p ,./, = 94 1.75 kg/m7, p = 2.8250E-04 Pa-s. k = -1.0, pb = 999.01 kg/m'

6.06 I67E-O 1 1.91702E+Ol I .9 1892E-02 1.00000E+OC 2 6.06 122E-01 9.03792E-01 4.85568E-01 9.98167E-01 2 6.05231E-01 1.38772E+OC 1.95959E+OC 9.99739E-01

6.04309E-01 6.04068E-01 9.55581E+01 1.33728E+O; 9.56528E-O2 I .33860E-01 I .00000E+OO I .OoooOE+O( 2 2 6.04321E-01 6.04109E-01 4.30695E+00 5.74968E+O( 2.3 1394E+OO 3.08905E+M 9.54168E-01 9.10168E-01 2 2 6.03870E-01 6.03691E-01 6.87968E+OO 9.56798E+3+0( 9.71472E+OO 1.35109E+03 9.93474E-û 1 9,8720950 1

6.04754E-0 I 5.73772E+03 5.74340E-02 1.00000E+OC 2 6.04740E-0 I 2.66547E+M 1.43204E+OC 9.83500E-01 2 6.04 198E-O 1 4.14743E+oC 5.85654E+OC 9.97651E-01

T y = 255.37 K, PJ= 1.01325E+05 Pa, p. -2.1181 kg/m3, p = 1.3070E-05Pa-s, k = 1.3198, p b = 1.86131 kdm' t P -

T/= 283.15 K, PJ= 6.89476E+05 Pa, pl,p = 4.983 1 kg/&, p = 1.0670E-05 Pa-s, k = 1.3622, p b = 0.708 17 kg/m7

2 6.03865E-01 1.00058E+02 5.37567E+O 1 1.00000E+OC 2 6.035 15E-01 1.76747E+Ol 9.49584E+W 9.96632E-01

~~

Tj= 255.37 K, Pf= 6.89476E+06 Pa, P , , ~ = 1042.35 kg/m3, p = 1.5430E-04 Pa-s k=-1.0, pb= 1.86131 kg/m3

6.03443Eol 6.03383E-01 2.39971E+02 2.79939E+02 1.28926E+02 1.50399E+3+02 l.OOOOOE+Oo l.OooOoE+OO

6.03205E-01 6.03162E-01 4.17 155E+01 4.83 17OE+OI 2.241 19E+01 2.59586E+01 i- 9.80602E-01 9.73597E-01

6.03684E-01 1.40039E+02 7.52368E+O I 1.00000E+OC 2 6.03381E-01 2.46589E+OI 1.32481E+01 9.93399E-01

Tj= 255.37 K, PJ= 1.37895E+06 Pa, pl,p = 32.783 kg/m3, p = 1.3520E-05 Pa-s, k = 1.3198, p,,= 1.86131 kg/m3

2 2 2 2 6.03720E-01 6.03483E-01 6,03354501 9.5976 1E+00 1.59764E+O 1 2.2334OE+O I 1.35527E+01 2.25601E+Ol 3.15377E+01 9.99530E-01 9.98695E-01 9.97442E-01 2 2 2

5.04394E-01 6.03689E-01 6.03459E-01 6.03332E-01 4.13461E+OO 1.23869E+Ol 2.06283E+Ol 2.88554E+Ol 5.83844E+00 1.749 14E+01 2.9129OE+Ol 4.07465E+Ol 9.99974E-01 9.99765E-01 9.99347E-01 9.98721E-01 2 2 2 2 5.04302E-01 6.03632E-01 6.03413501 6.03292E-01 1.41828E+Ol 4.25016E+01 7.08101E+01 9.91142E+01 7.61979E+00 2.28342E+Ol 3.80431E+O1 5.32497E+01 l.OOOOOE+OO l.OOOOOE+OO l.W00E+00 1.00000E+00 z 2 2 2

Tj= 283.15 K, PJ= 3.44738E+06 Pa, P, ,~ = 26.627 kg/m3, p = I . 13 10E-05 Pa-s, k = 1.3622, pb=0.70817 kg/m3

6.03234E-01 3.18 143E+01 4.49247E+Ol 9.94779E-01 2 6.03216E-01 4.11591E+Oi 5.81204E+01 9.97389E-01 2 6.03 18OE-01 1.4 1566E+02 7.6057OE+Ol 1 .OOOOOE+OC 2

T/= 338.71 K, PJ= 6.89476E+06 Pa, p,,+, = 44.168 kg/m3, p = 1.3650E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

T/= 333.15 K, PJ= 1.37895E+07 Pa, pl,p = 520.04 kg/m3, p = 4.1710E-05 Pa-s, k=-1.0, pb= 1.86131 kg/m3


A P I M P N S b 3 4 . 3 . 4 92 W 0732290 O 5 0 6 4 3 3 299 W

6.41762E-01 4.18899E+02 4.59909E-01 1.00000E+OO

SECTION 3-CONCENTRIC. SQUARE-EDGED ORIFICE METERS, PART 4-BACKGROUND 127

6.3265 1E-01 6.26734E-01 6.24236E-01 5.78134E+02 8.18 181E+02 9.77902E+02 6.34733E-01 8.98280E-01 1.07364E+ûû l.OOOOOE+OO I.OOOOOE+OO 1.00000E+OC

Table 4-C-6-Selected Round Robin Test Results Matrix-SI Units ( Dm = 0.746150 m, = 0.00001116 m/m-K, d,,, = 0.397669 m, ai = 0.00001665 m/m-K)

5.63585E+02 5.64 144E-0 1 l.OOOOOE+OO 2 6.03842E-01 2.42309E+Ol 1.301 82E+01 9.10161E-01 2 6.03535E-01 4.033OOE+01 5.69496E+01 9.87208E-01 2 6.03529E-01 5.90281E+02 3.17132E+02 1 .OOOOOE+OO

How Conditions Tf= 255.37 K, Pf= 1.01325E+05 Pa, pf,p = 932.26 kg/m3, p = 1.8650 Pa-s, k=-1.0, pb=910.83 kglm3

8.04907E+02 9.65770E+02 8.05704E-O 1 9.66727E-O 1 1.00000E+OO l.OOOOOE+OC 2 2 6.03724E-01 6.03689E-01 3.10532E+Ol 3.35808E+Ol 1.66835E+Ol 1.804 15E+O 1 8.16655E-01 7.35983E-01 2 2 6.03415E-01 6.03362E-01 5.6826OE+Ol 6.73809E+01 8.02435E+O1 9.5 l480E+01 9.73893E-01 9.62406E-01 2 2 6.03406501 6.03349E-01 8.43087E+02 1.01 161E+03 4.52954E+02 5.43493E+02 1.00000E+OO 1 .("3OE+OC

Tf=293.15 K, Pf= I.O1325E+05 Pa, pf+ = 907.60 kg/m3, p = 2.1220E-01 Pas , k=-1.0, pb=910.83 kg/m3

6.03303E-01 1.03953E+02 5.58495E+Ol 9.93399E-0 1 2 6.03283E-01 9.4 1537E+O 1 1.32954E+02 9.97442E-01

Tfz353.15 K, Pf= 1.01325E+05 Pa, pf,p = 868.43 kg/m3, p = 1.7490E-02 Pa-s, k = -1 .O, pb = 9 10.83 kg/m3

6.032 12E-01 6.03 I7 IE-01 1.47455E+02 1.75871E+02 7.92212E+OI 9.44877E+01 9.86528E-O 1 9.80600E-O 1 2 2 6.03 l94E-01 6.03 153E-01 1.34 126E+02 1.60569E+02 1.89398E+02 2.26738E+02 9.94779E-01 9.92481E-01


6.03362E-01 8.6959OE+Ol 1.22794E+02 9.99347E-01 a

ïj= 372.04 K, Pf= 1.01325E+05 Pa, pf,p = 941.75 kg/m3, p = 2.8250E-04 Pa-s, k = -1.0, pb = 999.01 kg/m3

6.03267E-01 6.03180E-01 6.03140E-01 1.21647E+02 1.73525E+02 2.07976E+02 1.71777E+02 2.45033E+02 2.93681E+02 9.9872 1E-0 1 9.97389E-O 1 9.96240E-O 1 a a a

Tf= 255.37 K, Pf= 1.01325E+05 Pa, pf,p = 2.1 181 kg/m3, p = 1.3070E-05 Pa-s, k = 1.3198, pb= 1.86131 kg/m3

Tj= 283.15 K, Pf= 6.89476Et05 Pa, pf,p = 4.9831 kg/m3, p = 1.0670E-05 Pa-s, k = 1.3622, pb = 0.708 I7 kg/m3

Tf= 255.37 K, Pj= 6.89476E+06 Pa, pf,p = 1042.35 kg/m3, p = 1.5430E-04 Pa-s k=-1.0, pb= 1.86131 kg/m3

ïj= 255.37 K, PI= 1.37895E+06 Pa, pf,p = 32.783 kg/m3, p = 1.3520E-05 Pa-s, k = 1.3198, pb= 1.86131 kg/m3

Tf= 283.15 K, Pf= 3.44738E+06 Pa, pf,p = 26.627 kg/m3, p = 1.131OE-05 Pa-s, k = 1.3622, &=0.70817 kg/m3

Tf= 338.71 K, Pf= 6.89476E+06 Pa, p , - 4 . 1 6 8 kg/m3, p = 1.3650E-05 Pa-s,

I P - k = 1.3622, pb = 0.70817 kg/m3

~~~

Tf= 333.15 K, Pf= 1.37895E+07 Pa, p,2p = 520.04 kg/m3, p = 4.1710E-05 Pa-s, k=-1.0, p b = 1.86131 kg/m3

Cell Value

cd

-

4ni Q" Y ICD Cd 4111

Q v Y ICD

cd 4n1 Q v Y ICD cd 4m Q v Y ICD cd 411,

Q v Y ICD cd %Il

Q v Y ICD

cd 4n1 Q v Y ICD cd 4nr Q v Y ICD

4n1

Y ICD cd 'In1 Q v Y ICD cd 4nr Q v Y ICD cd 4nr Q v Y ICD

-

-

-

-

-

-

-

- cd

Q v

-

-

-

-

559.5 1.16623E+W 1.54101E+02 1.69188E-01 1.00000E+0(1 -4 7.67058E-01 l.OO136EtO2 1.09939E-01 1.00000E+0(1 -3 6.24381E-01 7.98959E+OI 8.77177E-02 l.OOOOOE+OC x3 6.07720E-01 8.32219E+01 8.33044E-02 1 .OOOOOE+~ 2 6.05316E-01 8.0712OE+Ol 8.07920E-02 l.OOOOOE+OC 2 6.05283E-01 3.80529E+C€ 2.04442E+OC 9.98167E-01

6.04652E-01 5.84533E+OC 8.254 13E+OC 9.99739E-01 2 6.0465 1E-01 8.4482OE+Ol 4.53885E+Ol 1.00000E+OC 2 6.04132E-01 1.49675E+O1 8.04140E+oC 9.99865E-01 2 6.04087E-01 1.35022E+OI 1.90663E+OI 9.99948E-01 2 6.04050E-01 1.74224E+Ol 2.46020E+01 9.99974E-01 2 6.03983E-01 5.97660E+01 3.2 1096E+01 1.00000E+OC 2

5035.6 9.1OO39E-01 3.6075 1E+02 3.96068E-01 l.OOOOOE+OC -4 6.76588E-01 2.64980E+02 2.90921E-01 I.OOOOOE+oC -3 6.14310E-01 2.35 824E+02 2.58911E-01 l.OooOoE+oC 2 6.05713E-01 2.48844E+02 2.49090E-01 1 .OOOOOE+OC 2 6.04311E-01 2.41737E+02 2.41976E-01 1 .OOOOOE+OC 2 6.04300E-01 1.123OOE+01 6.03336E+OC 9.83499E-O I 2 6.03907E-01 1.7478OE+Ol 2.46805E+01 9.97650E-01 2 6.03905E-01 2.53136E+02 1.35999E+02 1 .OOOOOE+OC

6.03583E-01 4.48 140E+OI 2.40766E+O 1 9.98787E-01 2 6.03555E-01 4.64544E+01 5.71253E+Ol 9.99530E-01

6.03533E-01 5.22 121 E+O 1 7.37283E+OI 9.99765E-01 2 6.03491E-01 1.79 l53E+oi 9.62512E+OI 1.00000E+OC 2

13987.7

6.03220E-01 l.OOOOOE+OO

-3 13 13 13 6.11559E-01 I 6.10158E-01 I 6.08942E-01 I 6.08410E-01 3.91279E+02 5.46536E+02 7.79210E+02 9.34233E+02 4.29585E-01 6.00041E-01 8.55494E-01 1.02569E+OC 1.00000E+OO I I I 1.00000E+00 I.OOOOOE+OO I.OOOOOE+OC

6.05095E-01 6.04763E-01 6.04464E-01 6.04328E-01 4.143 l6E+02 5.79724E+02 8.27766E+02 9.93096E+02 4.14726E-01 5.80298E-01 8.28586E-01 9.94080E-01 I.OOOOOE+OO I l l 1.00000E+OO l.OOOOOE+OO l.OOOOOE+OC 2 12 12 12 6.03989501 I 6.03812E-01 I6.03651E-01 16.03577E-01 4.02678E+02 4.03077E-01 l.OOOOOE+O( 2 6.03996E-01 1.81492E+OJ 9.75075E+Oí 9.541 64E-0 1 2 6.03666E-01 2.89963E+Oi 4.09454E+OI 9.93473E-01 2 6.03662E-0 1 4.21723E+O; 2.26573E+O; I .00000E+OC

6.03403E-01

9.96632E-01

9.51014EtOl 9.98695E-01

d I ' I ' I ' 6.03327E-01 I 6.03237E-01 I 6.03153E-01 I 6.03115E-01 2.98507E+02 4.17848E+02 5.96842E+02 7.161 64E+02 1.603758+02 2.24491E+02 3.206578+02 3.84764E+02 1 .OoooOE+OO I .OOOOOE+00 I .00(KX)E+OO I .00000E+OC 2 l 2 l 2 l 2

109663.5 7.23090E-01 1.33766E+O3 1.46861E+OO l.OoM3OE+OO -3 6.22355E-01 1.13745E+03 1.2488OE+OO 1 .OooOoE+OO 3 6.07999E-01 1.08920E+O3 1.19584E+OO 1 .OOOOOE+OO 2 6.04222E-0 1 1.1584 1 E+03 1.15956E+OO 1.00000E+OO 2 6.03519E-01 1.12662E+03 1.12774E+OO l.OOOOOE+OO 2 6.03682E-01 3.4 1022E+O 1 1.83216E+Ol 6.40644E-0 1 2 6.03321E-01 7.74969E+01 l.O9433E+O2 9.4883 1E-01 2 6.03305E-01 1.18012E+03 6.34029E+02 1 .OOOOOE+OO 2 6.03 139E-0 1 2.03706E+02 1.094428+02 9.73595E-01 2 6.03120E-01 1.86808E+02 2.63790E+02 9.89766E-01 2 6.03108E-01 2.42295E+02 3.42 143E+02 9.94883E-01 2 6.03084E-01 8.35483E+02 4.48868E+02 1.00000E+OO 2


I __ ~ __ ___--

A P I N P M S * 3 4 - 3 = 4 92 m 0732290 0506434 125 W


Table 4-C-6-Selected Round Robin Test Results Matrix-SI Units ( ûm = 0.049262 m, cl2 = 0.00001116 m/m-KI dm = 0.032544 m, al = 0.00001665 m/m-K)

Cell Value - c, 9111

Q v Y ICD

Cd q11i

Q v Y ICD

Cd (7r>i Q v Y ICD

Cd 9111

Q v Y ICD

-

-

-

Pa

5035.6 13987.7 27415. 55950.8 I 80569.1 I 109663.5 559.5

3.49997E+M 3.30046B+O( 3.62358E-03 I .OOOOOE+O( 4

Flow Conditions

Tj= 255.37 K, Pl= 1.01325E+05 Pa, pf,p = 932.26 kg/m’, p = 1.8650 Pa-s, k=-1.0, p,,=910.83 kg/m3

I .94657E+O( 9.178 13E+O( 1.00767E-02 1 .OOO00E+O( -S

I .55550E+OO 1.47 165E+OO 1.40605E+OC 1.46685E+01 1.66533E+01 I .85627E+01 I ,61045E-02 I .82836E-02 2.03800E-02 1 .OOOOOE+OO I .OOOOOE+OO 1 .OOOOOE+o(1 -5 -5 -5

1.74 130E+o( I . 14944E+Ol 1.26 197E-02 I .OOOOOE+O( -5 9.68362E-01 6.31564E+O( 6.93394E-02 I .OOOOOE+O( -4 6.49397E-01 4.15 188E+O( 4.55835E-03 I .OOOOOE+O(

2.32459E+o( 6.5763 1 E+O( 7.2201 3E-01 I .OOOOOE+o(

Tj=293.15 K, Pf= 1.01325E+05 Pa, pAp = 907.60 kg/m’, p = 2. I220E-0 I Pa-s k=-1.0, ph=910.83 kg/m3

8.98564E-01 8.66463E-01 8.40876E-01 8.37202E+OO 9.68751E+00 1.09684E+01 9.19 I64E-03 1.06359E-02 1.20422E-02 1 .OOOOOE+00 1 .OOOOOE+00 1 .OOOOOE+OC -4 -4 -4 6.41 i 17E-01 6.37613E-01 6.34968E-01 5.85563E+OO 6.98834E+00 8.1 1925E+OC 6.42889E-03 7.67250E-03 8.91412E-03 1 .OoooOE+00 1 .OoooOE+OO 1.00000E+OC

1.62622E+N I .5 15 15E+O( 1.66349E-03 1.00000E+O( -5 8.68359E-01 7.93108E-01 8.70753E-04 1.00000E+O(

I . 18494E+O( 3.3 1208E+O( 3.63634E-01 1 .OOOOOE+O( -4 7.0447 1 E-0 1 1.93029B+O( 2.11926E-03 I .00000E+O(

1.04463E+O( 4.86647E+O( 5.34290E-03 1.00000E+O( -4 6.59396E-01 3.01 129E+O( 3.30609E-01 1.00000E+O( 3 6.17728E-01 3.01 868E+O( 3.021 67E-03 1 .OOOOOE+O( 2 6.1 1766E-01 2.91 129E+O( 2.91418E-01 1 .OOOOOE+O(

Tj= 353.15 K, Pf= 1.01325E+05 Pa, pf,+ = 868.43 kg/m3, p = 1.7490E-02 Pa-s k=-1.0, pb=910.83 kg/m3

6.33221E-01 6.18874E-01 6.19487E-04 1.00000E+O( 3

6.14300E-01 6.13578E-01 6.13014501 6.00386E+00 7.19616E+00 8.38780E+OC 6.00981E-03 7.20329E-03 8.3961 1E-03 1 .OoooOE+00 1 .OoooOE+00 1 .OoooOE+OC 2 2 2 6.10005E-01 6.09623E-01 6.09322E-01 5.80582E+00 6.96263E+00 8.1 1906E+OC 5.81 158E-03 6.96953E-03 8.32710E-03 1 . O ~ E + O O I.OOOOOE+OO I .OoooOE+OC 2 2 2 6.10456E-01 6.10301 E-01 6.10308E-01 2.19676E-01 2.34662E-01 2.33951E-01 1.18022E-01 1.26073E-01 1.25692E-01 8.00591E-01 7.12851E-01 6.09158E-01 .l .-, .-,

6.21 185E-01 1.82135E+O( 1.82315E-03 1 .OOOOOE+O( 2 6.13466E-01 I .75 I63E+O( 1.75337E-03 1.00000E+O( 2 6.13441E-01 8.12360E-02 4.36445E-02 9.82053E-O 1 2 6.1 1361E-01 1.26252E-01 1.78279E-01 9.97444E-01 2 6.11354E-01 1.82880E+OC 9.82536E-01 1.00000E+OC 2 6.09680E-01 3.23014E-01 1.73541E-01 9.9868 1E-01 2 6.09529E-01 2.91564E-01 4.11715E-01 9.99489E-01

6.159 14E-01 4.21374E+O( 4.21792E-02 1 .OOOOOE+O( 2 6.10844E-03 4.06967E+M 4.07370E-W 1 .OOOOOE+O( 2 6.1 1047E-01 1.73475E-01 9.32006E-02 9.02289E-01 2 6.09423E-0 1 2.90309E-01 4.09942E-01 9.86086E-01 2 6.09397501 4.25354E+o( 2.28524B+O( 1.00000E+O( 2 6.08236E-01 7.47498E-01 4.01598E-O1 9.92820E-01 2 6.08123E-01 6.77203E-01 9.5627 1E-0 1 9.97217E-01

ïj=288.71 K, P’= 1.01325E+05 Pa, pf,p = 999.01 kg/m3. p = 1.1990E-03 Pa-s k = - I .O, p,, = 999.01 kg/m3

Tf= 372.04 K, Pf= 1.01325E+05 Pa, pf,p = 941.75 kg/m3, p= 2.8250504 Pa-s k = -1.0, pb = 999.01 kg/m3

6.18927E-01 5.89070E-O I 5.89654E-04 1 .OOOOOE+OC 2 6.18777E-01 2.77577502 1.49 130E-02 9.98006E-01 2 6.15314E-01 4.24521-2 5.99461 E-02 9.99716501 2 6.153 12E-0 1 6.13542E-0 1 3.29629E-0 1 1 .0000OE+OC 2 6.12545E-01 1.08303E-01 5.8 1865E-02 9.99853E-01 2 6.12302E-01 9.76737E-02 1.37924E-01 9.99943E-01 2 6.12098JCOl 1.26009E-01 1.77937E-01 9.99972E-01 2 6.11747E-01 4.32060E-01 2.32127E-01 1.00000E+OC

cd q111

Q v Y ICD cd 9111

Q v Y ICD Cd 4111

Q v Y ICD cd 4111

Q v Y ICD

cd %Il

Q v Y ICD

-

-

-

Tf= 255.37 K, Pf= 1.01325E+05 Pa, pf,p = 2.1 18 1 kg/m3, p = 1.3070E-05 Pa-s k = 1.3198, pb- 1.86131 kg/m3

6.1 1845E-01 1.30654E-01 7.0 1944E-02 9.50148E-01 2 6.10105E-01 2.09030E-01 2.95169501 9.92901 E 4 1 2 6.1OO90E-01 3 .O4 1 69E+O( 1.63417E+OC 1 .OOOOOE+CK 2 6.08748E-01 5.36270E-0 1 2.881 14E-01 9.96337E-01 2 6.08623E-01 4.84775E-01 6.84547E-01 9.98580E-01 2 6.085 18E-01 6.25940E-01 8.83883E-01 9.99290E-01 2 6.08341E-01 2.14829E+OC 1.1541 8E+OC 1.OOOOOE+OC

L I ‘ I ‘ 6.08809E-01 I 6.08535E-01 I 6.083258-01 Tf= 283.15 K, Pf= 6.89476E+05 Pa,

php = 4.9831 kg/m3, p = 1.0670E-05 Pa-s k = 1.3622, pb=0.70817 kg/m3

4.08224E-01 4.83352E-01 5.55038E-01 5.76449E-01 6.82537E-01 7.83763E-01 9.71605E-01 9.591 11E-01 9.44345E-01 2 2 2 6.08762E-01 6.08471E-01 6.08242E-01 6.07015E+00 7.28070E+00 8.49095E+W 3.26122E+OO 3.91 160E+OO 4.56182E+OO 1.00000E+OO 1.00000E+00 1 .OOOOOE+Oa 2 2 2 6.07767E-O I 6.07555E-O 1 6.07389E-0 1 1.05900E+00 1.26204E+OO 1.46053E+W 5.68954E-O 1 6.7804 1 E-0 1 7.84676E-O 1 9.85347E-01 9.78900E-01 9.71281E-01 2 2 2 6.07663E-01 6.07453E-01 6.07288E-01 9.63893E-01 lb15337E+O0 1.34122E+OO 1.361 10E+00 1.62866E+00 1.89393E+00 9.94321E-01 9.91822E-01 9.88869E-01

Tf= 255.37 K, Pf= 6.89476E+06 Pa, pl,p = 1042.35 kg/m3, p = 1.5430E-04 Pa-s k=-1.0, pb= 1.86131 kg/m3

ïj= 255.37 K, Pf= 1.37895E+06 Pa, pt,p = 32.783 kg/m3, p = 1.3520E-05 Pa-s k = 1.3198, pb= 1.86131 kg/m3

ïj= 283.15 K, Pf= 3.44738E+06 Pa, pl,p = 26.627 kg/m3, p = 1.1310E-05 Pa-s. k = 1.3622, pb = 0.70817 kg/m3

cd 4m Q v Y ICD cd e1 Q v Y ICD

cd (ln1

Q v Y ICD

-

-

-

6.07580E-01 6.07374E-01 6.0721 1E-01 1.24729E+W 1.49436E+W 1.74037E+OO 1.76128E+00 2.1 1017E+OO 2.45756E+00 9.97160E-01 9.95910E-01 9.94434E-01 “ .-, .-,

6.08030E-01 8.75016E-01 1.23560E+O( 9.98608E-01 2 6.07874E-01 3.00530E+O( 1.61461E+OC 1.00000E+OC

ïj= 338.71 K, Pf= 6.89476E+06 Pa, p I p = 44.168 kg/m3, p = 1.3650E-05 Pa-s. k 1.3622, pb = 0.70817 kg/m3

6.09401E-01 3.7628 1E-01 5.3 1342E-0 1 9.99744E-01 2 6.09183E-01 1.29076E+OC 6.93469E-01 1.OOOOOE+OC

L I ’ I ‘ 6.07443M1 I 6.07245E-01 I 6.07089Eol ïj= 333.15 K, Pl= 1.37895E+07 Pa,

Pf,, = 520.04 kg/m3, p = 4.1710E-05 Pa-s, k = -1.0, p,, = 1.86131 kg/m3

4.29024E+OO 5.14661E+00 6.00283E+00 2.30496E+00 2.76505E+00 3.22505E+00 1.00000E+OO I I 1.OOOOOE+00 1 .OOOOOE+OO


SECTION SCONCENTRIC, SQUARE-EDGED ORIFICE METERS. PART &BACKGROUND 129

13987.7 1.7 1348E+W 1.82040E+01 1.99861E-02 l.OOOOOE+OO -5 9.56713E-01 1 .00424E+Ol 1.1O256E-02 l.OOOOOE+OO -4 6.467220-01 6.65472E+00 7.3062 1 E-03 1.OOOOOE+00 3 6.14109E-01 6.76193E+OO 6.76863E-03 l.OOOOOE+OO 2 6.09 127E-O 1 6.53153E+00 6.53800E-03 l.OOOOOE+00

Table 4-C-6-Selected Round Robin Test Results Matrix-SI Units ( Dm = 0.073670 m, CS = 0.00001116 m/m-K, d, = 0.048816 m, al = 0.00001665 m/m-K)

Pa

27415. 55950.8 80569.1 I.54120E+00 1.38544E+00 1.3 15 19E+C€ 2.29232E+Ol 2.94377E+01 3.35341E+01 2.5I673E-02 3.23197E-02 3.68171E-02 1.00000E+00 1.OOOOOE+00 l.OOOOOE+Oc -5 -5 -5 8.91648E-01 8.30968E-01 8.02446E-01 1.3 1032E+01 1.74450E+01 2.02154E+01 1.43860E-02 1.9 1528E-02 2.21945E-02 1.00000E+00 1.00000E+00 l.OOOOOE+OC 4 -4 4 6.39093E-O 1 6.327 13E-0 1 6.29989E-O 1 9.20670E+00 1.3021 1E+O1 1.55581E+Ol 1 .O 1080E-02 1.42959E-02 1.708 12E-02 l.OOOOOE+OO l.OOOOOE+OO 1.00000E+OC 3 3 3 6.12608E-41 6.1 1263E-01 6.10657E-01 9.44355E+00 1.34612E+O 1 1.6 1374E+Ol 9.45291E-03 1.34745E-02 1.61534E-02 1.OoooOE+00 I.OOOOOE+OO I.Mx)OOE+OC 2 2 2 6.08345E-0 1 6.07630E-0 1 6.07304E-O 1 9.13240E+00 1.30309E+OI 1.56287E+OI 9.14145E-03 1.30439E-02 1.56442E-02 1.OoooOE+00 I.OOOOOE+OO I.OOOOOE+OC

Flow Conditions

Tf= 255.37 K, Pf= 1.01325E+05 Pa, P,,~ = 932.26 kg/m3, p = 1.8650 Pa-s, k = -1.0, pb = 910.83 kg/m3

Tf= 293.15 K, Pf= 1.01325E+05 Pa, pCp = 907.60 kg/m3, p = 2.1220E-01 Pa-s, k = -1.0, pb = 910.83 kg/m3

Tf= 353.15 K, Pf= 1.01325EM5 Pa, P,,~ = 868.43 kg/m3, p = 1.7490E-02 Pas, k = -1.0. p6 = 910.83 kg/m3

Tf= 288.71 K, Pf= 1.01325E+05 Pa, P,,~ = 999.01 kg/m3, p = 1.1990E-03 Pa-s, k= -1.0, ph = 999.01 kg/m3

Tf=372.04 K, Pf= 1.01325E+05 Pa, P,,~ = 941.75 kg/m3, p = 2.8250E44 Pa-s, k = -1.0, pb = 999.01 kg/m3

Tf- 255.37 K, Pf= 1.01325E+05 Pa, p,,,=2.1181 kg/m3,p= I.3070E-05 Pa-s, k = 1.3198, pb= 1,86131 kp/m3

$= 283.15 K, Pf= 6.89476E+05 Pa, P, ,~ = 4.983 1 kg/m’, p = 1.0670E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

Tf= 255.37 K, Pf= 6.89476E+06 Pa, P, ,~ = 1042.35 kg/m3, p = 1 . 5 4 3 0 ~ 4 Pa-: k=-1.0, pb= 1.86131 kg/m3

Tf= 255.37 K, Pf= 1.37895E+06 Pa, P, ,~ = 32.783 kg/m3, p= 1.3520E-05 Pa-s, k = 1.3198, pb = 1.86131 kg/m3

Tf=283.15 K, Pf= 3.44738E+06Pa, p,,, = 26.627 kg/m3, p = 1.1310E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

Tf= 338.71 K, Pf= 6.89476Et.06 Pa, P,,~ = 44.168 kg/m3, p = 1.3650E-05 Pa-s, k = 1.3622, pb = 0.708 17 kg/m3

Tf= 333.15 K, Pf= 1.37895E+07 Pa, p,,p = 520.04 kg/m3, B= 4.1710E-05 Pa-s, k = -1.0, pb = 1.86131 kg/m3

Cell Value

cd 4111

Qv Y ICD cd 4ni

Y ICD

4111

Y ICD cd 4111

Qv Y ICD cd 4 1

Qv Y ICD Cd 4111

Qv Y ICD

Cd 9ni Q” Y ICD cd 4ni

Y ICD cd 4111

Qv Y ICD

-

-

Q”

- cd

Qv

7

-

-

-

-

Q,

-

-

4ni

Qv Y ICD cd clni Qv Y ICD cd 9nz Qv Y ICD

-

-

-

559.5

3.02095E+OC 6.41 887E+OC 7.04727E-03 1.00000E+OC -6 €.44471E+OC 3.03293E+ûC 3.32986E-03 1.00000E+OC -5 8.04107E-01 1.65483E+OC 1.8 1683E-03 1.00000E+00 4 6.26553E-01 1.37978E+OC 1.381 14E-03 l.OOOOOE+OC 3 6.15093E-01 1.31909E+OC 1.32040E-03 1.OOOOOE+OC 2 6.14973E-01 6.21595E-02 3.33956E-02 9.98003E-01

6.121 1OE-01 9.51558E-02 1.34369E-01 9.997 16E-01 2 6.12109E-01 1.37525E+00 7.38861E-01 1.00000E+00 2 6.09789E-01 2.42933E-01 1.30517EM1 9.99853E-01 2 6.09584E-01 2.19104E-01 3.09394E-01 9.99943E-01 2 6.09409E-01 2.82681E-01 3.99171E-ûl 9.99972E-01 2 6.091 13E-01 9.69339E-01 5.20783E-01 1.00000E+ûC 2

5035.6 2.03 116E+oC 1.29475E+03 1.42150E-02 1.00000EHK -5

1.07496E+oC 6.770 19E+OC 7.43299E-03 l.OOOOOE+OC 4 6.62434E-O 1 4.08985E+OC 4.49024E-03 l.oooOOE+OC 3

6.16940E-01 4.07587E+oC 4.0799 1E-03 1.00000E+OC 2 6.10561E-01 3.92815E+oC 3.93204E-03 1.00000E+OC 2 6.10543E-01 1.82173E-01 9.78733E-02 9.82023E-01 2 6.08787E-01 2.83274E-01 4.oooO9E-01 9.97440E-01 2 6.08782E-01 4.10337E+OC 2.20456E+OC 1.00000E+OC

6.07357E-01 7.25047Eco1 3.89536E-01 9.98679E-01 2 6.07226E-01 6.54477E-01 9.24181E-01 9.99488E-01

6.071 14E-01 8.44666E-01 I. 14275E+OC 9.99744E-01 2 6.06928E-01 2.89762E+oC 1.55676E+oC 1.00000E+OC 2

9.50063E-01

6.07719E-01 4.69 144E-0 1 6.62474E-01 9.92889E-01

2 2 2 6.08522E-01 6.08019E-01 6.07888E-01 3.89191E-01 4.92795E-01 5.26294E-01 2.09095E-01 2.64757E-01 2.82755E-01 9.02123E-01 8.00252E-01 7.12363E-01 2 2 2 6.07136E-01 6.06609E-01 6.06374E-01 6.51660E-01 9.16452E-01 ~ 1.08516E+OC 9.20203E-01 1.2941 1E+00 1.53234E+OC 9.86063E-01 9.71556E-01 9.59041E-01 2 . 2 2

6.06558E-01 1.20398E+N 6.46846E-01 9.9633 1E-01 2 6.06449E-01 1.08840E+(x 1.53693E+0( 9.98578E-01

6.06357E-01 1.40538E+OC 1.98452E+0( 9.99289E-01 2 6.06205E-01 4.82359E+0( 2.59150E+0( 1,00000E+O( 2

2 2 2 6.061 17E-01 6.05713E-01 6.05530E-01 1.67839E+00 2.37804E+00 2.83409E+OC 9.01727E-01 1.27762E+W 1.52263E+OC 9.92808E-01 9.85323E-01 9.78864E-01 2 2 2 6.06019E-01 6.05623E-01 6.05441E-01 1.52060E+00 2.16455E+00 2.59015E+OC 2.14723E+00 3.05655E+00 3.65752E+Qï 9.97213E-01 9.9431 1E-01 9.91808E-01 2 2 2 6.05937E-01 6.05549E-01 6.05371E-01 1.96482Em 2.80101E+00 3.35601EM 2.77450E+00 3.95528E+00 4.73899E+OC 9.98606E-01 9.97155E-01 9.95903E-01 2 2 2 6.05803E-01 6.05431E-01 6.05260E-01 6.74855E+00 9.63487E+00 1.15586E+01 3.62570E+00 5.17639E+00 6.20991E+OC 1.OOOOOE+00 1.OOOOOE+00 1.00000E+OC 2 2 2

109663.5 1.26025E+00 3.74888E+01 4.1 1589E-02 l.OOOOOE+OO -5 7.793 16E-O 1 2.29049E+Ol 2.5 1473E-02 1.00000E+OO -4 6.27923E-01 1.809 l6E+O I 1.98627E-02 1.00000E+00 3 6.10183E-01 1.88 123E+O 1 1.88310E-02 1.00000E+00 2 6.07046E-01 1.82258E+O 1 1.82439E-02 1.00000E+00 2 6.07895E-01 5.24487E-01 2.81784E-01 6.08494E-01 2 6.06193E-01 1.246 12E+00 1.75963E+00 9.4425 1E-01 2 6.06123E-01 1.90653E+01 1.02430E+01 1.00000E+00 2 6.05387E-01 3.27988E+00 1.762 13E+00 9.7 1232E-01 2 6.05298501 3.012 12E+00 4.25338E+00 9.88850E-01 2 6.05230E-01 3.90862E+ûO 5.51932E+00 9.94424E-01 2 6.05 124E-01 1.3482OE+Ol 7.24327E+00 1.00000E+00 2



Table 4-C-&Selected Round Robin Test Results Matrix-SI Units ( Dm = 0.102270 m, a;! = 0.00001116 m/m-K, d, = 0.067667 m, al = 0.00001665 m/m-K)

- Cell

Valu - c, 4111

Q,. Y ICE c/ 4111

QI. Y ICE c, 4111

Qin Y ICD cd 9111

Qin Y ICD Cd 4111

Qi? Y ICD Cd 4111 e,. Y ICD

cd 9in

Y ICD

4lil

Y ICD

4111

Y ICD

411,

Y ICD

%Il

Y [CD cd 4111

Qv Y iCD

-

-

-

-

-

-

Q,,

Cd

QV

Cd

QV

Cd

Qv

-

-

-

- cd

Q"

-

-

Pa

559.5 27415. I 55950.8 I 80569.1 I 109663.5 Flow Conditions 5035.6 13987.7

ïj= 255.37 K, Pf= 1.013258+05 Pa, pf,p = 932.26 kg/m3, p = 1.8650 Pa-s, k = - I .O, pb = 910.83 kg/m3

2.67749E+O l.O9236E+O 1 I 19930E-0: 1.00000E+Oi -6

1.39839E+00 1.26419E+00 1.20368E+00 1.15635E+o( 3.99364E+Ol 5.15766E+OI 5.89295E+Ol 6.604788+0 4.38461E-02 5.66260E-02 6.46987E-02 7.25 138E-0: I .00000E+OO 1.00000E+00 1.00000E+00 1 .OoooOE+o( -S -S -5 -4

r/= 293.15 K, Pf= 1.01325E+05 Pa, pf.p = 907.60 kg/m', p = 2.1220E-01 Pa-s. k = - I .O, ph = 910.83 kg/m3

7.80665E-01 7.54158E-01 7.32280E-01 3.14684E+OI 3.64799E+Ol 4.13252E+0 3.45491E-02 4.00513E-02 4.53709E-0; 1 .OOOOOE+00 1 .OOOOOE+00 I .OOOOOE+O( -4 -3 -3 6.27474E-01 6.25242l501 6.23542E-01 2.47948E+OI 2.96479E+01 3.44952E+O 2.72222E-02 3.25505E-02 3.78723E-02 1 .OoooOE+00 1 .OoooOE+00 I .OOOOOE+o( 3 3 3 6.09525E-01 6.09003E-01 6.08593E-01 2.57733E+01 3.09014E+01 3.60274E+OI 2.57988E-02 3.09320E-02 3.6063 1 E-02 I .OOOOOE+OO I .OOO00E+00 1 .OOOOOE+Oí 2 2 2 6.06369E-01 6.06083E-01 6.05858E-01 2.49687E+01 2.99484E+01 3.49268E+OI 2.49935E-02 2.99780E-02 3.49614E-01 l.OOOOOE+00 1 .OOOOOE+OO 1 .OoooOE+O( 2 2 2

I .3 1525E+01 5.301688+01 5.8207 1 E-O: I .OOOOOE+Oi -5 7.5567650 2.98605E+CH 3.27839E-0: I .00000E+O( -3

8.35705E-01 2.35809E+OI 2.58895E-02 1 .OOOOOE+O( -4 6.32664E-û I 1.74999E+01 1.92 132E-02 1 .OOOOOE+OC 3

r/=353.15 K, Pf= 1.01325E+05 Pa, pf.p = 868.43 kg/m7, p = 1.7490E-02 Pa-s, k = -1.0, ph = 910.83 kg/mg

3 6.14376E-0 I 7.79355E+3+0(: 7.80 127E-03 1 .00000E+Oa 2 6.089 15E-01 7.522 lOE+OC 7.52955E-03 1 .OOOOOE+OC 2

ïj=288.71 K, Pf= 1.01325E+05 Pa, pf,p = 999.01 kg/m3, p = 1.1990E-03 Pa-s, k = -1.0, pb = 999.01 kg/m7

6.224 I3E-0 2.63 180E+Oi 2.6344 I E-0: I .OOOOOE+Oi 3 6.12804E-01 2.52336E+3+0( 2.52586E-0: 1.00000E+Oí 2

6.10683E-01 1.80756E+OI I .80935E-02 I .00000E+OC 2 6.06992E-01 1.7496 1E+OI 1.75 134E-02 1 .00000E+OC

6.1 1969E-01 1.29383E+O1 1.295 1 1E-02 1.00000E+OC 2 6.07673E-01 1.251 12E+OI I .25236E-02 1 .OOOOOE+OC 2

ïj= 372.04 K, Pf= 1.01325E+05 Pa, pf,p = 941.75 kg/m', p = 2.8250E-04 Pa-s, k = -1.0, pb = 999.01 kg/m3

r /= 255.37 K, Pf= 1.01325E+05 Pa, prp = 2.1 I8 1 kg/m', p = 1.3070E-05 Pa-s, k = 1.3198,pb= 1.86131 kg/m3

6.12707E-0 i 1.189 13E-01 6.38867E-02 9.98OO4E-O I 2 6.10255E-01 1.82155Eol 2.572 19E-01 5.997 16E-01 2

6.08906E-01 6.07740E-01 3.48857E-01 5.61443E-01 1.87425E-01 3.01639E-01 9.82038E-01 9.50105E-01 2 2 6.0738 1E-01 6.06450E-01 5.42660E-0 1 8.98928E-0 1 7.66285501 1.26937E+OO 9.97442E-01 9.92895E-01 2 2 6.07378E-0 1 6.0644 lE-0 1 7.8607 1E+OO 1.30809E+01 4.22321E+00 7.02781E+OO 1.00000E+OO l.OOOOOE+00 2 2 6.06136E-01 6.05436E-01 1.38936E+00 2.3075OE+OO 7.46445E-01 1.23972E+00 9.98680E-01 9.96334E-01 2 2 6.06020E-01 6.05340E-01 1.254 17E+OO 2.08602E+OO 1.77 lOoE+OO 2.94565E+00 9.99488E-01 9.98579E-01 2 2 6.05920E-01 6.05256501 1.61865E+ûO 2.69356E+00 2.28568E+OO 3.80355E+00 9.99744E-01 9.99289E-01 2 2 6.05757E-01 6.05123E-01 5.55297E+OO 9.24524E+00 2.98337E+M 4.96706E+00 l.OOOOOE+OO 1.OOOOOE+00 2 2

6.07 152E-01 6.067 14E-01 7.4567 IE-01 9.4438 IE-01 4.006 16E-0 1 5.07375E-O 1 9.02205E-01 8.0041 8E-01

6.06599E-01

6.05228E-01

6.06605E-01 1.00547E+O( 5.40195E-01 6.08820E-03 2 6.05115E-01 2.38853E+o( 3.37282E+3+0( 9.44297E-01 2 6.05055E-01 3.65429E+O 1 1.96329E+Ol 1.00000E+OC

Ti= 283.15 K, Pl= 6.89476E+05 Pa, pf,p = 4.983 1 kg/m7, p = 1.0670E-05 Pa-s, k=-1.3622,pb=0.70817 kg/m3

1.24880E+OC I .76342E+OC 9.86074E-0 1 2

1.75645E+OC 2.48026E+oC 9.71580E-01 2

r /= 255.37 K, Pf= 6.89476E+06 Pa, pbp = 1042.35 kg/m3, p = 1.5430E-04 Pa-' k=-l.O,pb= 1.86131 kg/m3

6.10255E-03 2.63262E+3+0( 1.4 1439E+O( l.OOOOOE+O(

6.05924E-01 1.82977E+O1

6.05447E-01 2.61 190E+01

I 1.000M)E+OO I I .00000E+OO 9.830548+00 I .40326E+01

r /= 255.37 K, Pf= 1.37895E+06 Pa, pf,p = 32.783 kg/m3, p = 1.3520E-05 Pa-s, k = 1.3198,pb= 1.86131 kg/m3

5.08253E-01 t.65281E-01 2.49975E-03 3.99853E-01 2 3.08073E-03 L19658E-01 3.92596E-01 2.99943E-01

6.04408E-01 6.28766E+M 3.37809E+OC 9.7 1256E-01 2 6.04329E-01 5.77435E+OC

ïj= 283.15 K, Pf= 3.44738E+06 Pa, pf,p = 26.627 kg/m3, p = 1.1310E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3 1.1 15728+00 5.85913E+00 7.01 141E+00 8.15391E+OC

3.97215E-01 9.943 16E-O1 9.91 81 5E-01 9.88859E-O1 2 2 2 2 5.04887E-01 6.04546E-01 6.04390E-01 6.042668431 3.76612E+00 5.36933E+(K) 6.433448+00 7.49301 E+OC 5.31810E+00 7.58197E+Oo 9.084608+00 1.058088+01 >.98607E-01 9.97 158E-01 9.959078-01 9.94429E-01 1 2 2 2 5.04770&01 6.04443E-O1 6.04292E-01 6.04173E-01 I .29358E+01 1.846978+01 2.2 158 1 E+01 2.58460E+01 ;.94983E+OO 9.92295E+3+00 1.190468t01 1.388598+01 I .00000E+OO 1 .OOOOOC+00 1.00000E+OO I .OoooOE+OO

ïj= 338.71 K, Pf= 6.89476E+06 Pa, pf,p = 44.168 kg/m3, p = 1.3650E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

5.07919E-01 3.41448E-01 1.64573E-01 3.99972E-01 l j.07662E-01 l.85679E+OC 3.97573E-01 l.OOOOOE+OC l

Ti= 333.15 K, Pi= 1.37895E+07 Pa, pf,+, = 520.04 kg/m3, p = 4.1710E-05 Pa-s, k = -1 .o, pb = 1.8613 1 kg/m3

1 12 12 12


API M P M S * 1 4 - 3 m 4 92 m 0732290 0506417 934 m

1.10290E+OO 1.75359E+Ol 1.92527E-02 l.OOOOOE+OO d


8.64632E-01 7.82848E-01 7.33854E-01 4.12430E+Ol 6.22364E+Ol 8.16779E+01 4.52807E-02 6.83294502 8.96742E-02 l.OOOOOE+00 1.00000E+00 1.00000E+00 d d -2

Table 4-C-6-Selected Round Robin Test Results Matrix-SI Units ( D,,, = 0.202729 m, % = 0.00001 11 6 m/m-K, d,,, = 0.1 34342 m, ai = 0.00001 665 m/m-K)

6.65106E-01 1.26902E+02 1.39326E-01 1 .OoooOE+00

Row Conditions Tf= 255.37 K, Pf= 1.01325E+05 Pa, pf,p = 932.26 kg/m3, p = 1.8650 Pa-s, k=-1.0, pb=910.83 kg/m3

6.59243E-01 1.46747E+02 1.6 1 1 14E-01 1.0oooOE+00

Ti= 293.15 K, PJ= 1.01325E+05 Pa, pi,p = 907.60 kg/m3, p = 2.1220E-01 Pa-s, k = -1.0, pb = 910.83 kg/m3

1.03736E+OI 1.13891E-02 1.00000E+00 -3 6.15735E-01 1.02697E+01 1.02798E-02 1.00000E+00


2.96818E+Ol 4.88408E+01 6.79361E+Ol 3.25877E-02 5.36223E-02 7.45870E-02 1.00000E+00 1.00000E+00 l.OOOOOE+OO 3 3 3 6.10062E-01 6.08308E-01 6.07358E-01 3.05254E+OI 5.07293E+OI 7.09102E+Ol 3.05557E-02 5.07796E-02 7.09805E-02 l.OOOOOE+OO 1.00000E+00 l.OOOOOE+OO


2 6.07041E-01 7.14718E-01 1.00925E+00 9.997 16E-0 1 2 6.07044E-01 1.03296E+Ol 5.54964E+00 1.00000E+OO

Tf= 372.04 K, Pf= 1.01325E+05 Pa, pf,p = 941.75 kg/m3, p = 2.8250E-04 Pa-s, k=-1.0, pb = 999.01 kg/m3

2 2 2 6.04881E-01 6.04171E-01 6.03780E-01 2.13168E+00 3.53243B+OO 4.90823E+OC 3.01013E+00 4.9881 1E+00 6.93086E+W 9.97440E-O 1 9.92889501 9.86062E-0 1 2 2 2 6.04881501 6.04166E-01 6.03769E-01 3.08787E+Ol 5.14036E+Ol 7.19177E+Ol 1.65898E+Ol 2.76169E+Ol 3.86382E+Ol 1.00000E+00 l.ooOOOE+00 1.00000E+Oû

Tf= 255.37 K, Pf= 1.01325E+05 Pa, pf,,=2.1181 kg/m3,p= 1.3070E-05 Pa-s, k = 1.3198,pb= 1.86131 kg/m3

6.05543E-01 1.82710E+00 9.81622E-01 9.99853E-01 2 6.05405E-01 1.64806E+00 2.3272 1E+00 9.99943E-01 2

Tf= 283.15 K, Pf= 6.89476E+05 Pa, P,,~ = 4.9831 kg/m3, p = 1.0670E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

6.03932E-01 6.03394E-01 6.03096E-01 5.46036E+00 9.07108E+OO 1.26484E+01 2.93361E+00 4.87349E+00 6.79541E+OC 9.98679E-01 9.96331E-01 9.92808E-01 2 2 2 6.03841E-01 6.03317E-01 6.03026E-01 4.92921E+OO 8.20073E+00 1.14598E+Ol 6.96049E+00 1.158O2E+01 1.6 1823E+O 1 9.99488E-01 9.985783-01 9.97212E-01 2 2 2

T/= 255.37 K, Pf= 6.89476E+06 Pa, pf,p = 1042.35 kg/m3, p = I.5430E-04 Pa-s k=-l.o,Pb= 1.86131 kg/m3

6.05283E-01 2.12646E+00 3.00276E+ûû 9.99972E-01 2 6.05089E-01 7.29304E+00 3.9 1823E+OO 1.00000E+00 2

T/= 255.37 K, Pf= 1.37895E+06 Pa, pf,p = 32.783 kg/m3, p = 1.3520E-05 Pa-s, k = 1.3198,pb= 1.86131 kg/m3

6.03759E-01 6.03248E-01 6.36193E+00 l.O5894E+Ol 8.98362E+OO 1.49532E+Ol 9.99744E-01 9.99289E-01 2 2 6.03634E-01 6.03145E-01 2.18267E+01 3.63483E+O1 l.l7265E+O I 1.95283E+O1 l.OOOOOE+OO 1.00000E+C€ 2 2

Tf= 283.15 K, Pf= 3.44738E+06 Pa, pfp = 26.627 kg/m3, p = 1.1310E-05 Pa-s, k k 1.3622, pb = 0.70817 kg/m3

Tf= 338.71 K, Pf= 6.89476E+06 Pa, pf,p = 44.168 kg/m3, p = 1.3650E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

T/=333.15 K, Pf= 1.37895E+07 Pa, pi,,, = 520.04 kg/m3, p = 4.1710E-05 Pa-s, k = -1.0, p b = 1.86131 k g / d

Cell falue

cd ?ni

Y [CD cd lnr Q v Y iCD

-

Q"

-

- cd 4in Q v Y [CD cd 4nr Q v Y [CD

-

_.

cd 9nr Q v Y ICD cd qn, Q v Y ICD cd 9in Q v Y ICD cd 4ni Q v Y ICD cd 4m Q v Y ICD

-

-

_.

-

- cd 4nr Q v Y ICD

4m

Y ICD

4m

Y ICD

- cd

Q v

- cd

Q v

-

Pa

I ' I r I d

6.65546E-01 I 6.34768E-01 I 6.26700E-01 I 6.22658501

2 12 12 12 6.08913E-01 I 6.06031E-01 I 6.05094E-01 I 6.04577E-01 9.89008E+00 2.95301E+01 4.91406E+01 6.8738OE+Ol 9.899888-03 l 2.95594E-02 I 4.91893E-02 6.88062E-02

4.66094E-01 2.50412E-01 9.98002E-01

6.02963E-0 1 1.4808OE+Ol 2.09103E+01 9.98606E-01 2 6.02872E-01 5.08646E+Ol 2.73273E+OI 1.00000E+OC 2

55950.8 1.06521E+GU 1.71422E+02 1.88204E-01 1 .OOOOOE+OO -4 6.83451E-01 l.O8669E+O2 1.19307E-01 I.OOOOOE+Oa -3 6.19 186E-01 9.65103E+Ol 1.05959E-01 1.00000E+OC 3 6.06496E-0 1 1 .O1 156E+02 1 .O 1257E-01 1.00000E+OC 2 6.04100E-01 9.81198E+Ol 9.82170E-02 1.00000E+OC 2 6.04375E-01 3.7099 1E+OC 1.993 17E+OC 8.00245E-O 1 2 6.03425E-01 6.90454E+OC 9.74984E+OC 9.71555E-01 2 6.03402E-O 1 l.O2677E+O2 5.5 1639E+O1 1.00000E+OC

6.02821E-01 1.79247E+Ol 9.63014E+oC 9.85322E-0 1 2 6.02756E-01 1.63162E+OI 2.30399E+Ol 9.94311E-01

6.02698E-01 2.1 1143E+OI 2.98 153E+O1 9.97155E-01 2 6.026 18E-0 1 7.26331E+OI 3.90226E+O 1 1.00000E+CX

1.26839E-01 l.OOOOOE+OO

1.21430E-01

1.4770 1 E-0 1

1.41596E-01

I ' 6.03882E-01 I 6.03709E-01

6.04287E-01 3.96236E+Oí 2.12880E+Oí 7.12354E-01 2 6.03266E-01 8.17656E+Oí l.l546OE+O I 9.59040E-01 2 6.03233E-01 1.23178E+Oí 6.6 1782E+0 1 1.00000E+O( 2 6.02696E-01 2.13642E+OI 1.14780E+Ol 9.78864E-01 2 6.02632E-01 1.9526 1E+O1 2.75726E+OI 9.91808E-01

8.7 1427E+01

6.04292E-01 3.94871E+00 2.12147E+00 6.08481E-01 2 6.03 144E-0 1 9.39029E+00 1.32599E+O 1 9.44249E-01 2 6.03 100E-01 1.43676E+02 7.7 1908E+01 1.00000E+OO 2 6.02598E-01 2.47265E+Ol 1.32845E+O1 9.7123 1E-01 2 6.02534E-01 2.27088E+Ol 3.20669E+01 9.88850E-01 2 6.02480E-01 2.94684E+01 4.16 120E+01 9.94424E-0 1 2 6.02408E-01 1 .O 165 1E+02

4.68 180E+OI 5.461258+01 1.00000E+00 I 1.00000E+00



Table 4-C-&Selected Round Robin Test Results Matrix-SI Units ( Dm = 0.36351 3 m, % = 0.00001 11 6 m/m-K, d,,, = 0.240705 m, al = 0.00001 665 m/m-K)

Flow Conditions

Tf= 255.37 K, PJ= 1.01325E+05 Pa, prSp = 932.26 kg/rn3, /.I = 1.8650 Pa-s, k=-l.O,pb=910.83 kglrn’

T/=293.15 K, Pf= I.O1325E+O5 Pa, p,,,) = 907.60 kg/m3, /.I = 2.1220E-01 Pa-s, k.=-I.O,pb=910.83 kg/m3

T/= 353.15 K, Pf= 1.01325E+05 Pa, = 868.43 kglrn3, p = 1.7490E-02 Pa-s,

k = -1 .O, pb = 9 10.83 kg/m3

ïj= 288.7 I K, Pf= 1 .O1 325E+05 Pa, = 999.01 kg/m3, p = I . 1990E-03 Pa-s,

k = -1 .o, pb = 999.0 1 kg/rn3

Tj= 372.04 K, Pf= 1.01325E+05 Pa,

k = -1.0, pb = 999.01 kg/rn3 = 941.75 kg/rn3, p = 2.8250E-04 Pa-s,

TI= 255.37 K, Pf= 1.01325E+05 Pa, pr,p=2.1181 kg/m3,p= 1.3070505 Pa-s, k = 1.3198,pb= 1.86131 kg/m3

ïj= 283.15 K, Pf= 6.89476E+05 Pa, pip = 4.9831 kg/m3, p = 1.0670E-05 Pa-s, k A 1,3622, pb = 0.70817 kg/m3

Tf= 255.37 K, Pf= 6.89476E+06 Pa,

k=-i.û,pb= 1.86131 kg/m3 = 1042.35 kg/m3, p = 1.5430E-04 Pa-s

ïj= 255.37 K, Pf= 1.37895E+06 Pa, pf,p = 32.783 kg/m3, p = 1.3520E-05 Pa-s, k = 1.3198,pb= 1.86131 kg/rn3

ïj= 283.15 K, Pf= 3.44738E+06 Pa, pf,p = 26.627 kg/rn3, p = 1.131OE-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

ïj= 338.71 K, PJ= 6.89476E+06 Pa, pbp = 44.168 kg/m3, p = 1.3650E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/rn3

TJ= 333.15 K, PJ= 1.37895E+O7 Pa, pf ,p = 520.04 kg/m3, p = 4.1710E-05 Pa-s, k=-1.0, pb = 1.86131 kg/rn3

Cell Value - c, 9nr Q” Y ICD

Cd 9nr Qv Y ICD cd 9111

Qv Y ICD

cd 9ni Qv Y ICD

Cd 9m Q” Y ICD Cd qni Qv Y ICD

-

-

-

-

-

Cd 9ni Qv Y ICD - cd ‘?ni

Qv Y ICD

9111

Y ICD

- cd

Qv

cd cini Qv Y ICD cd cirri

Qv Y ICD cd 4ni Qv Y ICD

-

-

-

Pa

9.63377E-01 7.72226E-01 6.99061E-01 4.91563E+OI 1.1821OE+O2 1.78349E+02 5.39687E-02 1.29782E-01 1.95809E-01 I .OOOOOE+OO I .OOOOOE+W 1 .OOOOOE+W -4 4 -3 6.46078E-01 6.25379E-01 6.19757E-01 3.23164E+OI 9.38442E+Ol 1.55000E+02 3.54802E-02 1.03032E-01 3.70175E-01 I .OOOOOE+00 1.00000E+W I .00000E+W 3 3 3 6.1 3859E-01 6.07601E-01 6.06255E-01 3.27494E+01 9.75654E+01 1.62248E+02 3.278 18E-02 9.76620E-02 I ,624O9E-01 I .OOOOOE+OO 1.00000E+OO 1.00000E+W 2 2 2 6.06716E-01 6.04479E-01 6.03742E-01 3.16241E+01 9.45235E+Ol 1.57347E+02 3.16555E-02 9.46172E-02 1.57503E-01 1.00000E+00 1 .OOOOOE+OO 1 .OoooOE+Oû 2 2 2 6.06676E-01 6.04488E-01 6.03797E-01 1.49042E+OO 4.38387E+00 7.06065E+00 8.00736E-01 2.35526E+OO 3.79338E+00 9.98003E-01 9.82030E-01 9.50083E-01 2 2 2 6.05273E-01 6.03578E-01 6.03016E-01 2.28695E+OO 6.82615E+00 1.13144E+01

6.63304E-0 1 2.36917E+02 2.601 11E-0l 1.00000E+W -3 6.16885E-01 2. I5995E+02 2.37 141E-01 I.OOOOOE+OC

6.055 19E-01 2.26872E+02 2.27097E-0 1 l.OOOOOE+OC 2 6.03333E-01 2.20136E+02 2.20354E-0 1 1 .OOOOOE+OC 2 6.03444E-0 1 9.38085E+W 5.03992E+íX 9.021 62501 2 6.02706E-01 1.57233E+01

3.229388+00 9.63914E+00 3.59770E+OI 2.220278+01 9.99716E-01 9.97441E-01 I 9.92892E-01 I 9.86068E-01

6.05277E-0 I 6.0358OE-01 6.030 l4E-O 1 6.02698E-0 1 3.30527E+Ol 9.88811E+Ol 1.64647E+02 2.30385E+02 1.77578E+Ol 5.31245E+01 8.84575E+01 1.23776E+02 I.OOOOOE+OO 1 .OOOOOE+OO I .OoooOE+OO 1 .OOOOOE+W 2 2 2 2 6.04102E-01 6.02828E-01 6.02399E-01 6.02161E-01 5.84948E+OO 1.74910E+01 2.90625E+Ol 4.05276E+Ol 3.14267E+OO 9.39717B+OO 1.56140E+01 2.17737E+01 9.99853E-01 9.98680E-01 9.96332E-01 9.9281 1E-01 2 2 2 2 6.03992E-01 6.02754E-01 6.02336E-01 6.02103E-01 5.27652E+OO 1.57901E+01 2.62745E+01 3.67199E+Ol 7.45092E+ûO 2.2297OE+Ol 3.7102OE+Ol 5.18518E+01 9.99943E-01 9.99488E-01 9.98578E-01 9.97214E-01 2 12 12 12 6.03893501 I 6.02685E-01~6.02278E-01 I 6.02049E-01 6.80844E+00 2.038OOE+01 3.39282E+O1 4.74491E+O1 9.61413E+OO 2.87784E+Ol 4.79097E+Ol 6.70024E+01 9.99972E-Ol 9.99744E-01 9.99289E-01 9.98607E-O1 2 2 2 2 6.0374OE-01 6.0258650 1 6.02 196E-O1 6.0 1977E-0 1 2.33522Et01 6.99234E+01 1.16463E+O2 1.62989E+02 1.25461E+O1 3.75668E+O1 6.25706E+OI 8.7567OE+O1 1.OOOOOE+OO l.OOOOOE+OO 1.OOOOOE+OO l.OOOOOE+W

55950.8

9.34104E-01 4.82406E+02 5.29634E-O 1 I .OOOOOE+OC -4

6.50969E-O 1 3.32159E+02 3.64678E-01 I .00000E+OC 3 6.14382E-O1 3.073 13E+02

1.000OOE+OC 3.37398E-01

6.04848E-û 1 3.23743E+02 3.24064E-01 1.00000E+OC 2 6.02955E-0 1 3.14283E+02 3.14595E-01 1 .OOOOOE+OC 2 6.03179E-01 1.18833E+OI 6.38440E+OC 8.00331E-01 2 6.02423E-01 2.2121 1E+01 3.12370E+01 9.71568E-01 2 6.02406E-01 3.28962E+02 1.76737E+02 I .OOOOOE+OC 2 6.01941E-01 5.74392E+OI 3.08596E+01 9.85328E-01 2 6.01 887E-01 5.22856E+01 7.3832OE+Ol 9.943 14E-01 2 6.01838E-01 6.76621E+01 9.55450E+01 9.97 156E-01 2 6.01774E-01 2.32763E+02 1.25053E+02 1.OOOOOE+OC 2

80569.1

8.99057E-01 5.57168E+02 6.11714E-01 1.00000E+OC -4

6.45788E-01 3.954 18E+02 4.34 1 30E-O 1 I .00000E+O( 3 6.13279E-01 3.681 13E+02 4.041 5 1 E-0 I I .00000E+OC

6.04541E-01 3.88295E+Oi 3.88679E-0 1 1.00000E+OC 2 6.0278 I E N 1 3.7703 lE+Oi 3.77405E-0 1 1.00000E+OC

6.031 1OE-01 1.26932E+01 6.8 1950E+OC 7.12477E-01 2 6.02296E-01 2.6 1980E+OI 3.69939E+01 9.59058E-O1

6.02271E-01 3.94665E+Oi 2.12036E+Oi l.OOOOOE+OC 2 6.01841E-01 6.8464OE+O I 3.67827E+O I 9.78873E-01 2 6.0 1787E-0 1 6.25745E+OI 8.83608E+OI 9.918 12E-01 2 6.0 174OE-01 8.10795E+01 1. I4492E+02 9.95905E-01 2 6.0 1680E-0 1 2.79272E+02 1.5004 1E+02

109663.5

8.7 1263E-O 1 6.29934E+Oi 6.9 1604E-01 1.00000E+O( -4

6.419OOE-01 4.58544E+01 5.03436E-01 I .00000E+O( 3 6.12425E-01 4.28867E+01 4.70853E-03 I .00000E+O(

6.04299E-03 4.52829E+Oí 4.53278E-01 1.00000E+O( 2 6.02644E-0 1 4.39769E+Oí 4.40205E-01 I .OOOOOE+O(

6.03 1 13E-01 I .26508E+OI 6.79670B+O( 6.0865OE-01 2 6.02198E-01 3.00883E+01 4.24873E+01 9.44273E-O 1 2 6.02 1 64E-0 1 4.60361E+0; 2.47332E+01 1.000OOE+OC 2 6.01762E-01 7.9241 8E+OI 4.25731E+03 9.7 1244E-01 2 6.0 1709E-0 I 7.27764E+03 1.02767E+0: 9.88855E-01 2 6.0 l663E-01 9.44401E+OI 1.33358E+O1 9.94426E-O1 2 6.01605E-01 3.25777E+02 1.75026E+01


API MPMS*L4-3-4 92 0732290 05064117 707

109663.5 I.57973E-01 !.31165E+03 !.53796E+OO .OOOOOE+OO -3 t.28288E-01 .8932OE+O3 !.07854E+OO .oooOOE+OO

I i.09082E-01 1.79916E+03 1.97529E+W I .00000E+ûO ! i03197E-01 1.90662E+03 1.9085 1E+OO I .OOOOOE+OO ! i.01940E-01 i.85285E+03 i .85469E+00 I .ooOOoE+OO i 5.02304E-01 5.32822E+01 2.86262E+Ol 5.08545E-01 2 5.01605E-01 1.2679OE+O2 I .79039E+02 3.44258E-01 2 5.01581E-01 1.94000E+03 1.04228E+03 1.00000E+OO 2 6.01273E-01 3.33980E+02 1.79433E+02 9.71236E-01 2 6.01230E-01 3.06738E+02 4.33141E+02 9.88852E-01 2 6.01191E-01 3.9805 1E+02 5.62084E+02 9.94425E-01 2 6.01148E-01 1.373 14E+03 7.37725E+02 1.00000E+OO 2

x

i.08688E-01 1.37426E+02 1.37562E-01 I.OOOOOE+OO


6.05638E-01 6.04651E-01 6.04107E-01 6.03607E-01 4.10217E+02 6.82578E+02 9.54750E+02 1.36280E+03 4.10623E-01 6.83255E-01 9.55696E-01 1.36415E+ûû 1.00000E+OO 1.OoooOE+oO l.OOOOOE+OO l.OOOOOE+OO

Table 4-C-6-Selected Round Robin Test Results Matrix-SI Units ( Dm = 0.7461 50 m, + = 0.00001 11 6 m/m-K, d,,, = 0.494308 m, ai = 0.00001 665 m/m-K)

1.33015E+02 1.33 147E-01 1.00000E+íM L i.04963E-0I L26907E+OO 3.36810E+Oo 2.98OO3E-O 1

ilow Conditions

3.97955E+02 6.62648E+02 9.27232E+02 1.32399E+03 3.98350E-01 6.63305E-01 9.28 15 1E-01 1.32530E+ûC l.OOOC€IE+OO l.OOOOOE+OO l.OOOOOE+OO 1.OOOOOE+o(1 2 2 2 2 6.03340E-01 6.02821E-01 6.02555E-01 6.02354E-01 1.84567E+Ol 2.97344E+Ol 3.95105E+OI 5.054OE+Ol 9.91595E+OO 1.5975OE+Ol 2.12272E+OI 2.689 18E+01 9.82025E-01 9.5OO69E-O 1 9.02 136E-O 1 8.OO278E-O 1 n o .7 '>

!j= 255.37 K, Pf= 1.01325E+05 Pa, J , , ~ = 932.26 kg/m3, p = 1.8650 Pa-s, :=-1.o, pb = 910.83 kg/m3

).62524E+OO l.35917E+01 >.99716E-01 2 5.03929E-01 1.391 11E+02 7.47383E+Ol I .00000E+OO

r/= 293.15 K, Pf= 1.01325E+05 Pa, >,*p = 907.60 kg/m3, p = 2.122UE-01 Pas, := -1.0, pb = 910.83 k g h 3

2.87497E+01 4.76638E+Ol 6.62446E+Ol 4.05972E+Ol 6.73055E+Ol 9.35433E+Ol 9.97440E-01 9.92890E-01 9.86064E-01 2 2 2 6.02657E-01 6.02229E-01 6.01989E-01 4.16459E+02 6.93603E+02 9.70657E+02 2.23745E+02 3.72642E+02 5.21491E+02 1.00000E+OO 1 .OOOOOE+OO 1 .OOOOOE+OO

rf= 353.15 K, Pf= 1.01325E+05 Pa, 3,,p = 868.43 kg/m3, p = 1.7490E-02 Pa-s, C=-I.o, pb=910.83 kg/m3

6.01663E-01 1.42969E+02 2.01885E+02 9.99289E-01 n

rf= 288.71 K, Pl= 1.01325E+05 Pa, ?,,p = 999.01 kg/m3, p = 1.1990E-03 Pa-s, ¿ = -1.0, pb = 999.01 kg/m3

6.01488E-01 6.01326E-01 1.99961E+02 2.85167E+3+0: 2.82363E+02 4.02681E+O: 9.98606E-01 9.97156E-01 o CI

r/= 372.04 K, Pf= 1.01325E+05 Pa, g,,p = 941.75 kg/m3, p = 2.8250E-04 Pa-s, k = -1.0, pb = 999.01 kg/m3

r/= 255.37 K, Pf= 1.01325E+05 Pa, D ~ , ~ = 2.1181 kg/m3, p = 1.3070E-05 Pa-s, C = 1.3198, pb = 1.86131 k g h 3

r/= 283.15 K, Pf= 6.89476E+05 Pa, = 4.9831 kg/m3, p = 1.0670E-05 Pa-s,

k = 1.3622, pb = 0.70817 kg/m3

r/= 255.37 K. Pf=6.89476E+06 Pa, o,,~ = 1042.35 kg/m3, p = 1.5430E-04 Pa-s k=-l.O,pb= 1.86131 kg/m3

r/= 255.37 K, Pf= 1.37895E+06 Pa, P,,~ = 32.783 kg/m3, p = 1.3520E-05 Pa-s, k = 1.3198,pb= 1.86131 kg/m3

Tf= 283.15 K, Pf= 3.44738E+06 Pa, P,,~ = 26.627 kg/m3, p = 1.1310E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

T/= 338.71 K, Pf= 6.89476E+06 Pa, pf,p = 44.168 kg/m3. p = 1.3650E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

TI= 333.15 K, Pf= 1.37895E+07 Pa, P,,~ = 520.04 kg/m3, p = 4.1710E-05 Pa-s, k=-l.O,pb= 1.86131 kg/m3

- Cell lalue

-d ?ln

- "

2" Y CD -d b

Y [CD -d 7111

- n

2,

- "

2, Y [(SD

cd ?Ili

2 V Y iCD

cd Il l ,

Q v Y [CD

8 1

Q v Y iCD

-

-

-

4ni Q v Y ICD cd 4nI Q v Y ICD cd %i

Q" Y ICD

cd 9ni Q v Y ICD

-

-

-

- cd 4ni Q v Y ICD cd 41n

Q v Y ICD

-

-

1.31308E-01 6.69662E-01 .78924E+02 4.32402E+02 .9644OE-01 4.74734E-01 .00000E+ûû l.OOOOOE+o(1

i.30862E-01 6.17816E-01 .33106E+O2 3.9 1063E+O2 .46137E-01 4.29348E-01 .00000E+OO l.OOOOOE+OC

6.41314E-01 6.33857E-01 9.66225E+02 1.36427E+03 1.06082E+OO 1.49783E+OO l.OooOoE+OO 1.OOOOOE+OO

9.04129E+02 1.28799E+03 9.92643E-01 1.4 1408E+OO l.OOOOOE+OO l.OOOOOE+OO

I 13 12 12 2

6.50267E-01

7.68306E-01

7.11276E-01

! 12 1.2 12 12 3.04985E-01~ 6.03326E-01 I 6.02772E-01 I 6.02463E-01~6.02177E-01

I' I ' I A I L 5.03924E-01 I 6.02654E-01 I 6.02229E-01 16.01993E-01 I 6.01777E-01

2 6.01578E-01 1.70786E+02 9.17560E+01 9.92809E-01 m

9.32097E+01 1.3 162 1E+02 9.7 1560E-01 2 6.01766E-01 1.386 14E+O? 7.44712E+Oî 1.OOOOOE+OC 2 6.01410E-01 2.42073E+O; 1.30055E+O; 9.85324E-O 1 CI L I ' I ' I' I '

5.02966E-01 I 6.02029E-01 I6.01711E-01 I 6.01533E-01 I6.01367E-01 2.22194E+Ol 6.6525OE+Ol 1.10715E+02 1.54743E+02 2.20358E+O: 3.13758E+01 9.39393E+Ol 1.56340E+02 2.18512E+02 3.11 166E+O; 9.99943E-01 1 / 1 1 9.99488E-01 9.98578E-01 9.97213E-01 9.94312E-03 2 6.02888E-01 2.86713E+Ol 4.04865E+Ol 9.99972E-01 2 6.02773E-01

2 6.0 1974E-0 I 8.58648E+Ol í.2í249E+02 9.99744E-01 2 6.01899E-01

L I ' I ' 6.01601E41 I 6.01433E-O1 I 6.01277E-O1

9.83457E+01 2.94612E+02 4.90775E+02 6.86894E+02 9.81023E+O: 5.28368E+Ol 1.58282E+02 2.63672E+02 3.69038E+02 5.2706OE+O: I.OOOOOE+OO / I I I l.OOOOOE+OO 1.00000E+OO 1.00000E+00 l.OOOOOE+O(

80569.1

5.30686E-01

1.54364E+03 1.69477E+OO 1 .OOOOOE+OO 2 6.03378E-01 1.63474E+03 1.63636E+OO 1.00000E+OO 2 6.02045E-01 1.58844E+03 1,59OOIE+OO 1.00000E+00 2 6.02302E-01 5.34644E+01 2.8724 1E+O1 7.12400E-01

6.01680E-01 1.10393E+02 1.55885E+02 9.59047E-01 2 6.01663E-01 1.66308E+03 8.93501E+02 l.OOOOOE+OO 2 6.01333E-01 2.88547E+02 1.55024E+02 9.78867E-01 2 6.01291E-01 2.6373 1E+02 3.724 12E+02 9.9 1809E-0 1 2 6.01251E-01 3.41728E+02 4.8255 1E+02 9.95904E-01 2 6.01205E-01 1.17709E+Ol 6.32396E+02 1.OOOOOE+OC 2


II_ . -

A P I MPMS*14 .3 .4 92 m 0732290 050b420 429 m


Table 4-C-6-Selected Round Robin Test Results Matrix-SI Units ( Dm = 0.049262 m, = 0.00001 11 6 m/m-K, d, = 0.036909 m, al = 0.00001 665 m/m-K)

Pa

5035.6 2.63642E+Oi l.O4290E+O 1.14500E-0: I .OOOOOE+Ct -6 1.30068E+Oi 5.08399E+Oi 5.58 I7 1 E-0: 1.00000E+Oi -5 6.891 13E-O 2.64086B+Oi 2.89940E-û: 1 .OOOOOE+O( -4 6.22975E-0 2.55429E+Oi 2.55682E-O: 1.00000E+@ 3 6.13454E-01 2.44992E+O( 2.45235E-0: 1.00000E+O(

80569. I 1.64096E+O( 2.59647EtO 2.85066E-O; 1.00000E+O( -5

Flow Conditions

TJ= 255.37 K, P,== 3.01325E+05 Pa, pt.p = 932.26 kg/m3, p = 1.8650 Pa-s, k =-1.0, p/, = 910.83 kg/m7

559.5

4.00 107E+Oi 5.27568E+01 5.792 17E-0: 1 .OOOOOE+Oi -6 3.82233E+Oi 2.3743 IE+Oi 2.60676E-0: I .OOOOOE+O( -5 9.04948E-0 1,15599E+o( 1.269 16E-O: I .OOOOOE+Oi 4 6.36984E-O 8.70567E-0, 8.7 1430E-01 1 .00OOOE+O( 3 6.20235E-O1 8.25659E-01 8.26477E-3-01

13987.7 274 i 5. 55950.8 2.1965 IE+OO 1.95699E+00 1.73948E+O( 1.44813E+OI 1.80631E+01 2.29364E+01 1.58990E-02 1.98315E-O2 2.51819E-0; 1 .OOO00E+OO 1 .00OOOE+00 1 .00OOOE+O( -6 -5. -5 1.1301 IE+00 I.O3488E+OO 9.45055E-01 7.36212E+00 9.4385OE+OO 1.23132E+01 8.08287E-03 1.03625E-02 1.35186E-Oî I .00000E+Cû 1.00000Et00 1.00000EtO( -4 -4 -4 6.66239E-01 6.55156E-O1 6.45902E-01 4.25532E+OO 5.85835E+OO 8.25085E+N 4.67192E-03 6.43188E-03 9.05861E-01 I .OOOOOE+OO I .00000E+00 1.00000E+O(

109663.5

I .563658+00 2.88651E+Ol 3. I69 I OE42 1 .OOOOOE+00 -5 8.67928E-01 1.58316E+OI 1.738 15E-02 1 .OOOOOE+OO -4 6.38957E-01 I. 14270E+0 1 I ,25457E-02 I .000OOE+OO 3 6.12898E-01 I. 17272E+01 1.17388E-02 1.00000E+00 2 6.08033E-01 I. I33 19E+OI 1.1343 1E-02 1 .OOOOOE+OO 2 6.09568E-01 3.07558E-01 1.65237E-01 5.7341 1E-01 2 6.067 14E-01 7.699 16E-01 1.087 19E+OO 9.39252E-01 2 6.06597E-01 1.18405E+Ol 6.36140E+00 l.OOOOOE+OO 2 6.05423E-01 2.030 lOE+OO 1.09068E+00 9.68654E-01 2 6.05273E-01 1.86737E+m 2.63690E+00 9.87850E-01 2 6.05151E-01 2.42450E+00 3.42362E+OO 3.93924E-0 1 2 5.04980E-01 3.36603E+OO $.49470E+00 l,OOOOOE+OO 2

T/= 293.15 K, PJ= 1.01325E+05 Pa, p . = 907.60 kg/m7, p = 2.1220E-0 I Pa-s. r / J k = -1.0, pl, = 910.83 k g h '

9.0252 I E 4 I 1.4 1 IO8E+O I 1.54923E-0; 1 . ~ O O E t O ( -4 6.4 195380 I 9.84049E+N 1.08039E-02 1 .OOOOOE+O( 3 6.136 I8E-01 1.00637E+03 1.00736E-02 1 .OOOOOE+O( 2

ïj= 353.15 K, Pl= 1.01325E+05 Pa, p/.p = 868.43 kg/m', p = 1.7490E-02 Pa-s, k = -1.0, p/, = 910.83 kg/m'

ïj= 288.7 I K, PJ= I .O1 325E+05 Pa, p /,/, = 999.0 I kg/m3, p = I . I990E-03 Pa-s, k = -1.0, p/, = 999.01 kg/m7

5.89859E+OO 8.3989 IE+oC

1 .OOOOOE+OO I .OOOOOE+O(

6.10059E-01 6.08947E-01 5.68483B+OO 8.10638E+oC + I .OOOOOE+00 I .OOOOOE+OC

5.90443E-03 8.40724E-03

5.69046E-O3 8.11441E-O3

4.22857E+00 4.23276503

6.1 1266E-0 1 4.06862E+00 4. O 7 2 6 5 E-0 3 1 .00000E+00

ïj= 372.04 K, i'/= I .O1 325E+05 Pa, pi,/, = 94 1.75 kg/m3, p = 2.8250E-04 Pa-s, k=-l.O,p,,=999.01 kg/m7

6.08437E-01 9.7 195OE+O( 9.729 13E-03 1 .OOOOOE+O(

ïj= 255.37 K, PI= 1.01325E+05 Pa, p = 2.1 I8 1 kg/m7, p = I ,307OE-05 Pa-s, k = 1.3198,p6= 1.86131 kg/m7

5.20084E-03 3.88876E-0; 2.08926E-O; 3.97824E-01 3 5.158 IOE-01 5.94099E-3-02 3.38921E-01 3.99690E-01 2

6.1346OE-01 i , I3404E-0 I 6.09268E-0; 9.8041 2E-û I 2 6. IO76 1 E-01 1.76332E-01 2.48996503 9.97211E-01 2

6.09649E-0 1 2.99773E-01 1.6 lO55E-O1 7.82353E-01 2 6.07369E-01 5.67974E-01 8.02030E-O 1 9.69006E-01

6.09487E-01 3.1561 IE-01 1.69564E-01 6.86588E-01 2 6.06999E-01 6.71567E-01 9.483 13E-01 9.55369E-01 2

T/= 283.15 K, P,== 6.89476E+05 Pa, p = 4.983 I kg/m7, p = 1.0670E-05 Pa-s, k = i ,3622, p6 = 0.708 17 kglm'

T / = 255.37 K, P,== 6.89476E+06 Pa, pt,p = 1042.35 kg/m', p = 1.5430E-04 Pa-s k = - l . O , p b = 1.86131 kg/m3

5.158 15E-01 3.58599E-01 t.6 1287E-O i I .OOO00E+O( 2 5.12304E-01 I .5 1376E-01 i. 13274E-02 2.99840E-01 1 i l 1984E-01 I .365 12E-01 1.92767E-01 ).99938E-01 )

6.10758E-01 2.55467E+O( 1.37251E+O( 1 .OOOOOE+O( 2 6.08545E-01 4.50765E-01 2.42 l76E-O 1 9.98561501 2 6.08334501 4.06896E-01 5.74573501 9.99442E-01

6.06910E-01 l.O1543E+Ol 5.45545E+00 1.00OOOE+ûC 2 6.05653E-01 1.75569E+W 9.43254E-01 9.7697 1E-01 2 5.05502E-01 1.60644E+00 2.26843E+00 3.91074E-01

lj= 255.37 K, P,== 1.37895E+06 Pa, pt,,, = 32.783 kg/m3, p = 1.3520E-05 Pas, k = 1.3198,p6= 1.86131 kg/m3

1.04169E+00 1.47432E+00 5.59652E-01 7.92090E-01 9.921 64E-0 1 9.84007E-O 1 2 2 6.06426E-01 6.05793E-01 9.44095E-O1 1.34303E+00 1.33315E+00 1.89648E+00 9.96963E-01 9.93801E-01

ïj= 283.15 K, P,== 3.44738E+06 Pa,

k = 1.3622, pi, = 0.70817 kg/m3 = 26.627 kg/m3, p = 1.131OE-05 Pa-s,

6.071 1OE-01 6.76121E-01 9.54744E-0 1 9.98450E-01

lj= 338.71 K, Pf= 6.89476E+06 Pa,

k = 1.3622,p6=0.70817 kg/m3 = 44.168 kg/m3, .U = 1.3650E-05 Pa-s,

i. 11705E-01 1.761 18E-01 !.48695E-01 3.99969E-01 ! i.11251E-01 i.03764E-01 1.24376E-01 .OOOOOE+OO !

6.08147E-01 5.25156E-01 7.41568E-01 9.99721E-01 2 6.07855E-01 1.80125E+00 9.6773 1E-01 1.OOOOOEtOC 2

6.06283E-01 6.05663E-01 1.22009E+OO 1.73845E+00 1.72288E+00 2.45484E+Cû 9.98481E-01 9.96900E-01 2 2 6.06071E-01 6.05474E-01 4.19056E+00 5.98062E+00 2.25 140E+OO 3.213 13E+OO l.OOOOOE+OO 1.OOOOOE+00 2 2

5.05377E-01 2.08230E+00 2.94039B+OO >.95536%01 2 5.05199E-01 7.17348E+00 3.854OOE+OO i.OOOOOE+OO

lj= 333.15 K, P,== 1.37895E+07 Pa, pl,p = 520.04 kg/m3, p = 4.1710E-05 Pa-s, k=-l.0,p6= 1.86131 kg/m3


A P I M P M S * L 4 - 3 - 4 92 0732290 O506423 365 9

1.60636E+Oo 4.67318E+00 5.13068E-03 l.OOOOOE+00 -5 8.16001E-01 2.32744E+00 2.55529E-03 l.OOOOOE+OO -4 6.27946E-01 1.91626E+ûO 1.91816E-03 1.OOOOOE+00 3 6.14197E-01 1.82562E+00 1.82743E-03 I.OOOOOE+OO 2 6.14089E-01 8.59906E-02 4.61990E-02 9.97825E-01 .-,

SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS. PART 4-BACKGROUND 135

1.165 15E+00 1 .O 1822E+W 9.34395E-0 1 1.01690E+01~ 1.481 lOE+OI 1.90283E+Ol 1.1 1645E-02 1.62610E-02 2.08912E-02 1.000DOE+00 l.OOOOOE+OO l.OOOOOE+00 -4 -4 -4 6.68533E-01 6.50958E-01 6.42337E-01 5.72052Et00 9.28353E+OO 1.28248E+Ol 6.28056E-03 1.01924E-02 1.40804E-02 l.OOOOOE+OO l.OoooOE+OO 1.OOOOOE+OC 3 3 3 6.16496-1 6.13002E-01 6.11115E-01 5.64402E+OO 9.35335E+00 1.30544E+01 5.64961E-03 9.36262E-03 1.30673E-02 1.00000E+00 I.OOOOOE+Cû l.OOOOOE+OC 3 2 2 6.08468E-01 6.06599E-01 6.05564E-01 5.42582E+OO 9.01523E+00 1.25998E+01 5.43120E-03 9.02416E-03 1.26123E-02 l.oooOOE+OO 1.00OOOE+oO I.OOOOOE+C€ 2 2 2 6.08492E-01 6.06748E-01 6.05868E-01 2.51 165E-01 4.02588E-01 5.31731E-01 1.34940E-01 2.16293E-01 2.85676E-01 9.80421E-01 9.45614E-01 8.93403E-01 - - -3

Table 4-C-6Selected Round Robin Test Results Matrix-SI Units ( D, = 0.073670 m, % = 0.00001 11 6 m/m-K, d, = 0.0551 66 m, al = 0.00001 665 m/m-K)

2.22876E+OI 2.23097E-02 1 .oooOOE+00 2 6.04170E-O 1 2.15499E+O 1 2. I57 l3E-02 1.00000E+00 2 6.05092E-01 6.99777E-01 3.75959E-01 6.86734E-01 2 6.02945E-01 1.48952E+Gû 2.10334E+00 9.55390E-O 1 2 6.02873E-01 2.25221E+01 1.21001E+OI 1.00000E+00

How Conditions T/= 255.37 K, Pf= 1.01325E+05 Pa, pf,p = 932.26 kg/m3, p = 1.8650 Pa-s, k = -1.0, pb = 910.83 kg/m3

2.5976OE+Ol 2.60017E-02 1 .OOOOOE+00 2 6.03822E-01 2.5 127 1 E+O 1 2.5 1520E-02 l.O0000E+00 2 6.05 161E-01 6.82000E-01 3.66409E-01 5.7361 1E-01 2 6.02699E-01 1.70778E+00 2.41 154E+00 9.3928 1E-0 1 2 6.02602E-01 2.6264OE+Ol 1.41 105E+OI 1.00000E+00

Tf= 293.15 K, Pj= 1.01325E+05 Pa, pf,p = 907.60 kg/m3, p = 2.1220E-01 Pa-s, k=-1.0, pb=910.83 kg/m3

1.31506E-01 1.85698E-01 9.99690E-01 2 6.10492E-01 1.90055E+OO 1 .O2 108E+00 l.OOOOOE+OO 2 6.07506E-01 3.35349E-01 1.80168E-01 9.99840E-01 2 6.07228E-01 3.02441E-01 4.27074E-01 9.99938E-01

ïj= 353.15 K, Pf= 1.01325E+05 Pa, pf,p = 868.43 kg/m3, p = 1.7490E-02 Pas,

3 k = -1.0, Pb = 910.83 kg/m

3.90769E-01 6.46523E-01 8.97187E-01 5.5 1801M1 9.12949E-01 1.2669 1E+W 9.97212E-01 9.92255E-01 9.84820E-01 2 2 2 6.06183E-01 6.04751E-01 6.03954E-01 5.66146E+00 9.41345E+00 1.31615E+01 3.041 65E+OO 5.05743E+OO 7.07 107E+OC l.OOOOOE+OO I.OOE+OO l.OOOOOE+OC 2 2 2 6.04281E-01 6.03199E-01 6.02596E-01 9.99439E-01 1.65848E+00 2.31062E+OC 5.36955E-0 1 8.9 1030E-O 1 1.24 139E+OC 9.98561E-01 9.96004E-01 9.92167E-01 2 2 2 6.04096E-01 6.03040E-01 6.0245 1E-01 9.02205E-01 1.49956E+00 2.09420E+OC 1.27399E+00 2.1 1751E+00 2.95720E+OC 9.99442E-01 9.98451E-01 9.96964E-01

T/= 288.71 K, Pf= 1.01325E+05 Pa, pf,p = 999.01 kg/m3, p = 1.1990E-03 Pas , k=-I .o , &=999.01 kg/m3

3.89520E+00 2.09272E+00 9.76981E-01 2 6.0 1652E-0 1 3.56413E+00 5.03287E+00 9.91078E-01 2 6.01535E-01 4.61994E+00 6.52377E+00 9.95538E-01 2 6.01382E-01 1.59162E+OI 8.55 109E+00 l.O0000E+00 2

T/= 372.04 K, Pf= I.O1325E+05Pa, pf,p = 941.75 kglm3, p = 2.8250E-04 Pa-s, k = -1.0, pb = 999.01 kg/m3

4.50425E+00 2.41994E+00 9.68669E-01 2 6.0 1453E-O 1 4.14327E+00 5.85067E+00 9.87856E-01 2 6.0 l339E-01 5.37946E+OO 7.59628E+00 9.93926E-01 2 6.01 193E-01 1.8563 IE+Ol 9.973 13E+00 l.O0000E+00 2

T/= 255.37 K, Pj= 1.01325E+05 Pa, pf,,=2.1181 kg/m3,p= 1.3070E-05 Pa-s, k = 1.3198, pb= 1.86131 kg/m3

6.06980E-01 3.90206E-01 5.51007E-01 9.99969E-01 2 6.06592E-01 1.33784E+OO 7.18760E-01 1.00000E+OO

ïj= 283.15 K, Pf= 6.89476EtO.í Pa, pf,p = 4.9831 kg/m3, p = 1.0670E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

6.03926E-01 6.02895E-01 6.02318E-01 1.16445E+00 1.93647E+00 2.70646E+OC 1.64431E+OO 2.73448E+00 3.82176E+oC 9.99721E-01 9.99225E-01 9.98482E-01 2 2 2 6.03675E-01 6.02688E-01 6.02135E-01 3.99424E+00 6.64617E+00 9.29610E+oC 2.14593E+00 3.57070E+00 4.99439E+OC l.O0000E+OO l.OOOOOE+OO 1.00000E+OC

ïj= 255.37 K, Pf= 6.89476E+06 Pa, pf,p = 1042.35 kg/m3, p = 1.5430E-04 Pa-s k=-1.0, pb= 1.86131 kg/m3

ïj= 255.37 K, Pf= 1.37895E+06 Pa, pf,p = 32.783 kg/m3, p = 1.3520E-05 Pa-s, k = 1.3198, pb= 1.86131 kg/m3

T/= 285.15 K, Pf= 3.44738E+06 Pa, pf,p = 26.627 kg/m3, F = 1.1310E-05 Pa-s, k = 1.3622, pb=0.70817 kg/m3

T/= 338.71 K, Pf= 6.89476E+06 Pa, pf,p = 44.168 kg/m3, p = 1.3650E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

Tf= 333.15 K, Pj= 1.37895E+07 Pa, pf,p = 520.04 kg/m3, p = 4.17iOE-05 Pa-s, k=-1.0, pb= 1.86131 kg/m3

Cell dalue

cd 4111

Q v Y [CD cd 4111

Q v Y [CD cd 4nr Q v Y iCD

4111

Y ICD cd 4111

Q v Y [CD cd 4111

Q v Y [CD

-

_.

-

- cd

Q,

-

-

- cd 4nr Q v Y ICD cd 4111

Q v Y ICD cd 9111

Q v Y ICD

cd e 1

Q v Y I a 3 cd 4ni Q v Y ICD

%I

Y ICD

-

-

-

- cd

Q v

-

L I’ I’ I ‘ 6.10484E-01 I6.06181E-01 I 6.04760E-01 I 6.03976E-01

55950.8 1.53657E+W 4.52392E+01 4.96681E-02 1.00000E+OC -5

8.532 19E-01 2.48218E+Ol 2.725 18E-02 1.00OOOE+OC 4 6.35054E-01 1.81135E+OI 1.98868E-02 1 .OOOOOE+OC 3 6.09400E-01 1.85968E+OI 1.86152E-02 1.00000E+OC 2 6.04609E-01 1.797 13E+Ol 1.7989 1E-02 l.o0000E+oC 2 6.0523 1E-0 1 6.64582E-O 1 3.57051E-01 7.82454E-O 1 2 6.03264E-01 1.25964E+OC 1.77873E+oC 9.69021E-01 2 6.03214E-01 1.8779OE+Ol 1.00892E+01 1.00000E+OC 2 6.02040E-01 3.27074E+OC 1.75723E+oC 9.84015E-01 2 6.0 1904E-O 1 2.97952E+OC 4.20736E+OC 9.93804E-01 2 6.01782E-01 3.85681E+OC 5.44616E+OC 9.96901E-0 1 2 6.01620E-01 1.32688E+0 I 7.12873E+N l.OOOOOE+O(

I -

8.13806E-01 I 7.81200E-01

4



Table 4-C-6-Selected Round Robin Test Results Matrix-SI Units ( D, = 0.1 02270 m, g = 0.00001 116 m/m-K, d, = 0.076795 m, al = 0.00001 665 m/m-K)

Cell Value

Pa

13987.7 I 27415. I 55950.8 559.5 I 5035.6 80569. I Flow Conditions TI= 255.37 K, PJ= l.O1325E+O5 Pa, pf,/, = 932.26 kg/m3, p = 1.8650 Pa-s, k=-1.0, pl,=910.83 kg/m.’

109663.5

G/ 9llI

Qv Y ICD

Cd qlll

Q” Y ICD cd 41,r

Q” Y ICD

c, Q,

-

-

-

4111

Y ICD cd q l l l

Q” Y ICD

4111

Q” Y ICD Cd 4ill

Q” Y ICD Cd 9,. Q” Y ICD cd %i

Qv Y ICD c, 4111

Q” Y ICD Cd 9111

Q“ Y ICD Cd 4111

Qv Y ICD

-

- cd

~

-

~

-

-

-

3.0606 1 E+00 2.05802E+O( 1.75067E+OI 3.53 I60E+OI 1.92206E-02 3.87734E-02 1 .OOOOOE+OO 1.00000E+O(

1.45976E+W I .07087E+CK 8.25062E+00 1.81580E+01 9.05835E-03 1.99357E-02 t 1 .00OOOE+00 1.00000E+O(

I .73496E+OO 1.55891 E+OO 1.39865B+O( 4.96203E+OI 6.24191E+01 8.OOO35E+O1 5.4478 1E-02 6.85299E-02 8.78359E-0; I .00000E+00 1 .00000E+00 I .00000E+O( -5 -5 -5 9.3793 IE-01 8.60054E-01 7.8252 IE-01 2.65063E+Ol 3.40276E+OI 4.42287E+Ol 2.91012E-02 3.73589E-02 4.85587E-0; I .OoooOE+OO 1.00000E+00 1.00000E+O( -4 -4 -4

1.3258 1 E+O( 9.10044E+O 9.99 137E-0; I .OOOOOE+O( -5 7.43997E-01 5.04615E+O 5.540 I7E-0; I .OOOOOE+O(

1.26848E+@ 1 .O I 580E+O: 1.1 1525E-O 1.00000E+O( -5 7.1 1685E-01 5.63 149E+O 6.18282E-02 1 .OOOOOE+O(

r/=293.15 K, PJ= l.O1325E+O5 Pa, pf,p = 907.60 kglm’, p = 2.1220E-01 Pa-s, k = -1 .O, p,, = 910.83 kg/m3

?= 353.15 K, PJ= 1.01325E+05 Pa, pI,+ = 868.43 kg/m’, p = I ,749OE-02 Pa-s, k = -1 .O, p,, = 910.83 kg/m’

6.41001E-01 6.33877E-01 6.27798E-01 1.77606E+OI 2.45885E+03 3.47895E+OI 1.94993E-02 2.69957E-02 3.81954E-01 1.00000E+00 1 .00000E+00 I .00OOOE+O(

6.25158E-01 4.157 19E+O 4.564 18E-0; I .OOOOOE+O( 3 6.05048E-01 4.3047OE+O I 4.30896E-0; 1 .OOOOOE+O( 2 6.01075E-01 4. I6537E+OI 4.16950E-0; 1.00000E+O( 2 6.01919E-01 1.35097E+O( 7.25814E-01 6.85996E-01 2

6.23 134E-01 4.83435E+O 5.30763E-02 1.00000E+O( 3 6.04504E-01 5.01763E+0 5.02260E-0; 1 .OOOOOE+O( ‘I

3 13 13 6.0891OE-O1 I6.07251E-01 16.05738E-01 Tj= 288.7 I K, Pf= 1 .O1 325E+05 Pa,

of,+ = 999.01 kg/m3, p = I . 1990E-03 Pa-s, k=- l .O, p,,=999.01 kglm’

2.52022E+OI 3.59 134E+O1 2.52272E-02 3.59490E-02 1 .OOOOOE+OO 1 .OOOOOE+O(

6.023 18- 1 6.0 l467E-O I 2.43483E+01 3.47341E+03 2.43724E-02 3.47685E-02 i 1 .00000E+00 1.00000E+O(

1.80686E-02

1.741 82E+01 1.74355E-02

3 6.09944E-01 3.52234E+M 3.52583E-03 1 .OOOOOE+OC 2 6.09869E-01 1.659 16E-01 8.91394E-02 9.97819E-01 2

2 6.04898E-01 1.04797E+Ol 3.049OlE-02 I.O0000E+M 2 6.04939E-01 4.85098E-O1 2.60622E-O 1 9.80375E-01 2

ï j = 372.04 K, Pf= 1.01325E+05 Pa, of,p = 941.75 kglm3, p = 2.8z50E-04 Pa-s, k = -1.0, p!, = 999.01 kg/m

6.00764E-01 4.85709E+O 4.86190E-0: 1.00000E+O( 2 6.01983E-01 1.3 1574E+O( 7.06890E-01 5.72605E-01

I‘ I‘ 6.03392501 I 6.02609E-01 I 6.02043E-01 Tj= 255.37 K, Pj= 1.01325E+05 Pa,

o,,p = 2.1 18 1 kg/m3, p = I .3070E-05 Pas , G = 1.3198, p,,= 1.86131 kg/m3

7.77728E-01 1.02722E+W 1.28353E+O( 4.17839E-01 5.51879E-01 6.89582E-01 9.45485E-01 8.9315 1E-01 7.8 194lE-01 2 2 2 6.0 1616E-01 6.009 17E-0 1 6.00280E-O 1 1.24954E+00 1.73419E+00 2.43500E+O( 1.76446E+OO 2.44884E+00 3.43843E+O( 9.92237E-O 1 9.84784E-O 1 9.68948E-0 1

7j= 283.15 K, P/= 6.89476E+05 Pa, 3f,1> = 4.9831 kg/m3, p = 1.0670F-05 Pa-s, k = 1.3622, p,, = 0.70817 kg/m

6.06696E-01 2.53908E-01 3.58541E-01 9.99689E-01

6.02883EGO1 7.55064E-01 1.06622E+00 9.97205E-01

5.99995E-01 2.87942B+CK 4.06600B+O( 9,55285501 2 5.99935E-01 4.35434E+OI 2.3394OE+O I 1 .OOOOOE+O[ 2 5.98963E-01 7.53178E+M 4.04649E+oC 9.76927E-01 2 5.98838E-01 6.89 198E+OC 9.73209E+oC 9.9 1057E-01 2 5.98723E-01 8.93377E+ûC 1.261 53E+01 9.95527E-01

5.99775E-03 3.30133E+O( 4.66178E+O( 9.39 137E-01 2 5.99693E-01 5.07802E+03 2.72819E+OI 1 .OûûOûE+O( 2 5.98785E-01 8.70955E+0( 4.67926B+O( 9.68595E-01

2 12 12 6.01613E-01 I6.00901E-01 I6.00240E-01 7 j = 255.37 K, P’= 6.89476E+06 Pa,

?f,p = 1042.35 kg/m3, p = 1.5430E-04 Pa-s ¿=-l ,O, ph= 1.86131 kg/rn3

3.66956E+00 I .O93958+0l 1.97149C+W 5.87730EtOU 1 . O E + W 1.00000E+00 2 2 6.04065E-01 6.01 194E-O1 G.47836Ea I 1.93 18 1 E+OO 3.48054E-01 1.03788E+00 J.99840E-01 9.98558E01 2 2 5.03813C-O1 6.01024E-01 5.84289E-01 1.74392E+00 5.25068E-01 2.46257E+00 3.999388-01 9.99441E-O1 2 2 5.035838-01 6.008628-01 7.538688-01 2.25087E+O I.O6453E+W 3.178438+W 1.99969E-01 9.99720841 2 2 5.032408-O1 6.0064OE-0I 2.58484E+00 7.721 16E+00 I .38872E+00 4.14824E+OO I .00000E+O0 l.OOOE+(X) 2 2

3.63046E+01 1.95049E+03 1 .OOOOOE+OC 2 5.99190E-01 6.324 17E+OC 3.39770E+ûC 9.83977E-01 2

r/= 255.37 K, P’= 1.37895E+06 Pa, ?f,p = 32.783 kg/m3, p = 1.3520E-05 Pa-s, i = 1.3198, ph= 1.86131 kg/rn3

rf= 283.15 K, Pf= 3.44738E+06 Pa, >f,p = 26.627 kg/m3, p = 1.1310E-05 Pa-s, := 1.3622, ph = 0.70817 kg/m3

6 . 0 ~ 8 1 c ~ i 5.99553~~11 5.~063ri-01 2.89908E+(K) 4.04908E+Oo 5.76132E+OC 4.093768tOO 5.71767E+00 8.13550D+ûC 9.98447E-01 9.969578-01 9.93790E-01 2 2 2 5.9994 1 E-0 1 5.99425E-O 1 5,989458-0 1 3.743838+00 5.232948+00 7.457798+W 5.286628+00 7.389398+00 1.0531 18+01 3.99223B-01 9.98478E41 9.96894E-01

5.98660E-01 8.01206E+O( 1.13137E+OI 9.87827E-01 2 5.98548E-01 1.04028E+01 1.46897E+OI 9.93912E-01

rf= 338.71 K, P/= 6.89476E+06 Pa, ++ = 44.168 kg/m3, p = 1.3650E-05 Pa-s, : = 1.3622, pb = 0.70817 k g h ’

%= 333.15 K, P’= 1.37895E+07 Pa, + p = 520.04 kg/m3, p = 4.1710E-05 Pa-s, :=-1.0, p,,= 1.86131 kg/m3

5.99757E-01 5.99262E-01 5.98800E-01 1.28497E+01 1.79747E+01 2.56583E+Ol 5.90356E+00 9.65700E+00 1.37851E+01 1.OOOOOE+00 l.OOOOOE+W l.OooOOE+00 2 l 2 /i 5.98587E-01

3.07790E+OI 1.65362E+01 1.00000E+OO 2

5.98417E-01 3.58987E+OI 1.92868E+01 l.OOOOOE+OC 2 I


A P I M P M S * 1 4 * 3 * 4 92 0732290 O506423 I138

Cell Value

c d q,,, Q, Y ICD Cd q,,, Q, Y


559.5 5035.6 2.39586E+OO 1.64930E+60 5.3 6 16 1 E+O 1 1.10728E+02 5.88651E-02 1.21569E-01 l.OOOOOE+OO l.OOOOOE+OO -6 -5 1.20140E+OO 8.98193E-01 2.65662E+Ol 5.95850E+01 2.9167OE-O2 6.54183E-02 1.00000E+00 l.OOOOOE+C€

Table 4-C-&Selected Round Robin Test Results Matrix-SI Units ( Dm = 0.202729 m, a;! = 0.00001 11 6 m/m-K, d, = 0.1 52003 m, al = 0.00001 665 m/m-K)

55950.8

1.15506E+OO 2.58489E+02 2.83795E-01 1 .OOOOOE+OO 4 6.78543E-O 1 lSOO45E+02 1.64735E-01 1.00000E+00 3 6.15992E-01 1.33549E+02 1.46623E-01 l.OOOOOE+OO

Flow Conditions 80569.1 109663.5 1.09942E+OO 1.05522E+OO 2.95243E+02 3.30605E+02 3.24148E-01 3.6297 IE-01 1 .OOOOOE+OO l.OOOOOE+Oa -4 -4 6.69599E-O 1 6.62896E-O 1 1.7768 1E+02 2.052 19E+02 1.95076E-01 2.253 lOE-01 I.OOOOOE+OO l.OOOOOE+OC 3 3 6.14137E-01 6.12702E-01 1.59776E+02 1.85969E+02 1.75418E-01 2.04176E-01 1.00000E+OO 1.00000E+00

~~

Tf= 255.37 K, Pf= 1.01325E+05 Pa, pl,p = 932.26 kg/m3, p = 1.8650 Pa-s, k = -1.0, pb = 910.83 kg/m3

q,,, Q, Y ICD

q,,l Q, Y ICD Cd qia Q, Y

c d

Tf= 293.15 K, Pf= 1.01325E+05 Pa, pl,p = 907.60 kg/m3, p= 2.1220E-01 Pa-s, k=-1.0, pb=910.83 kg/m3

1.45273E+Ol 4.12733E+OI 1.59495E-02 4.53139E-02 1.00000E+OO l.OOOOOE+Oo 3 3

1.41904E+Ol 4.20722E+Ol 1.42045502 4.21 139E-02 l.OOOOOE+OO 1.00000E+00 3 2 6.03062E-01 5.99236E-01 1.3625OE+O 1 4.06 162E+O 1 1.36385E-02 4.06565E-02 l.OOOOOE+OO l.ooOoOE+OC

6.11773E-01 6.04594E-01

Tf= 353.15 K, Pf= l.O1325E+O5 Pa, pl,p = 868.43 kg/m3, p = 1.7490E-02 Pa-s, k=-1.0, pb=910.83kg/m3

5.999OOE-01 1.39 15 1 E+02 1.39289E-01 1 .OoooOE+OO 2 5.96595E-01 1.34790E+02 1.34924E-01 l.OOOOOE+OO

Tf= 288.71 K, Pf= 1.01325E+05Pa, pl,p = 999.01 kg/m3, p = 1.1990E-03 Pa-s, k = -1.0, pb = 999.01 kdm3

5.99373E-01 5.98957E-01 1.66835E+02 1.94505E+02 1.67000E-01 1.94698E-01 1 .OoooOE+OO l.OOOOOE+C€ 2 2 5.96291E-01 5.96051E-01 1.61666E+02 1.88534E+02 1.6 1826E-01 1.8872 1E-01 1.00000E+00 1 .ooOOOE+Oû

Tf= 372.04 K, Pf= 1.01325E+05 Pa, pCp = 941.75 kg/m3, p = 2.8250E-04 Pa-s, k=-1.0, pbr999.01 kg/m3

5.97508E-O 1 3.98542E+OO 2.141 19E+OO 8.93287E-01 2 5.96193E-01 6.73155E+OO 9.50555E+OO 9.84804E-01 2 5.96188E-01 9.87542E+Ol 5.30563E+Ol 1.OOOOOE+00

Tf= 255.37 K, Pf= 1.01325E+05 Pa, p , -2.1181 kg/m3,p= 1.3070E-05Pa-s,

f P - k = 1.3198, pb= 1.86131kg/m3

5.97070E-0 1 5.96975E-O 1 5.97023E-0 1 4.98189E+OO 5.24507E+OO 5.11007E+OC 2.67655E+OO 2.81795E+OO 2.74541E+W 7.82218E-01 6.86394E-01 5.73 148E-01 2 2 2 5.95698E-01 5.95477E-01 5.95306E-01 9.45420E+OO 1.1 181 1E+OI 1.28208E+Ol 1.33502E+Ol 1.57887E+O 1 1.8 1041E+O 1 9.68987E-01 9.55341E-01 9.39215E-01 2 2 2 5.95675E-01 5.95438E-01 5.95250E-01 1.40956E+02 1.69080E+02 1.97 198E+02 7.57295E+01 9.08392E+O1 1.05946E+U2 l.OOOOOE+OO 1.00000E+OO 1.00000E+C€

Tf= 283.15 K, P'= 6.89476E+05 Pa,

k = 1.3622, p b = 0.70817 kg/m3 = 4.983 1 kg/m3, p = I .0670E-05 Pas,

qm Q, Y ICD

q,,, Q, Y ICD

qI,, Q, Y ICD Cd qni Qv Y ICD

q,,, Q, Y ICD

c d

c d

c d

Tf= 255.37 K, Pl= 6.89476E+06 Pa, = 1042.35 kg/m3, p = 1.5430E-04 Pa+

k=-1.0, pb= 1.86131 kg/m3 1.42132E+OI 4.24324E+OI 7.63611E+00 2.27971E+Ol 1.00000E+OO 1.00000E+W 2 2

2.51 175E+OO 7.49785E+ûC 1.34945E+Oo 4.02826E+00 9.99840E-01 9.98560E-01 2 2

2.26555E+OO 6.76891E+ûC 3.19916E+OO 9.55831E+C€ 9.99938Eol 9.99442E-01 2 2 5.98236E-01 5.96135E-01 2.92325E+OO 8.73688E+0(1 4.12790EtOO 1.23373E+Ol 9.99969E-01 9.99721E-01 2 2

1.00245E+Ol 2.99726E+Ol 5.38570E+OO 1.61030E+01 1.00000E+00 l.OOOOOE+OC 2 2

5.98628E-01 5.96415E-01

5.98428E-01 5.96275E-01

5.97974E-01 5.95964E-01

Tf= 255.37 K, Pj= I.37895E+06 Pa, pl,p = 32.783 kg/m3, p = 1.3520E-05 Pa-s, k = 1.3198, pb= 1.86131 kg/m3

5.94858E-01 2.4564OE+Ol 1.3 1972E+01 9.83997E-01 2 5.94752E-01 2.23782E+01 3.16001E+Ol 9.93797E-01 2 5.94645E-01 2.8968OE+Ol 4.09055E+01 9.96898E-01 2 5.94534E-01 9.96687E+Ol 5.35476E+01 1.00000E+OO 2

Tf= 283.15 K, Pf= 3.44738E+06 Pa, pl,p = 26.627 kg/rn3, p = 1.1310E-05 Pa-s, k = 1.3622, &,= 0.70817 kg/m3

5.9468 1E-0 1 5.94543E-0 1 2.92572E+Ol 3.38348E+01 1.57 186E+01 1.8 1779E+01 9.76956E-01 9.68635E-01 2 2 5.94576E-01 5.94438E-01 2.67722E+01 3.1 1253E+01 3.78048E+01 4.395 18E+O1 9.91068E-01 9.87843E-01 2 2 5.94473E-01 5.94336E-01 3.47039E+01 4.04130E+01 4.90051E+01 5.70668E+01 9.95533E-01 9.93920E-01 2 2 5.94368E-O 1 5.94235E-O 1 1.19569E+02 1.39466E+02 6.42392E+Ol 7.4929OE+Ol 1.00000E+OO 1.00000E+OC 2 2

Tf= 338.71 K, Pf= 6.89476E+06 Pa, pl,p = 44.168 kg/m3, p = 1.3650E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

T/= 333.15 K, Pf= 1.37895E+07 Pa, pl,p = 520.04 kg/m3, p = 4.1710E-05 Pa-s, k=-1.0, pb= 1.86131 kgh3

ICD 1-5 1-4 Cd I6.70076E-01 16.34574E-01

ICD 12 12 CA I 6.03036E-01 I 5.99299E-01 gD 1 ~1851E-011:,,,2E+00 3.44838E-01 1.01016E+OO

9.97822E-01 9.804OOE-01

6.00631E-01 5.97712E-01 e,, 9.83447E-01 2.92874E+ûC Q, 1.38872E+OO 4.13565E+ûC ICD Iz.99690E-01 I z.97209E-01

CA 6.00648E-01 5.97724E-01

13987.7 1.40824E+0(1 1.57573E+02 1.72999E-O 1 1 .OOOOOE+o(1 -5

7.84949E-01 8.67873Etol 9.52837E-02 l.OOOOOE+OC -4 6.25047E-01 6.77559E+Ol 7.43891E-02 l.OOOOOE+C€ 3 6.02306E-01 6.98547E+Ol 6.99239E-02 l.OOOOOE+C€ 2 5.97963E-01 6.75497E+Ol 6.76 166E-02 1.00000E+OC 2 5.98111E-01 3.01633E+OC 1.62054E+OC 9.45555E-01 2 5.96734E-O 1 4.84899E+OC 6.84721E+oC 9.92247E-01 2 5.96739E-01 7.06039E+01 3.79324E+Ol 1.00000E+OC 2 5.95664E-O 1 1.24487E+01 6.688 12E+OC 9.95999E-01 2 5.95543E-01 1.12564E+Ol 1.58951E+01 9.98449E-01 2 5.95420E-01 1.45367E+Ol 2.05272E+Ol 9.99224E-01 2 5.95279E-01 4.98968E+OI 2.68074E+OI l.OOOOOE+OC 2

Pa

27415. 1.27622E+OC 1.99922Et.02 2.19494E-01 1 .OOOOOE+OC -5 7.13885E-01 I . 10502E+02 1.2 1320E-O 1 l.M"IOE+OC -3 6.20204E-0 1 9.4 1233E+0 1 1.03338E-0 1 1 .OOOOOE+OC

6.01052E-01 9.75929E+OI 9.76896E-02 1.OOOOOE+OC 2 5.97253E-01 9.44573E+01 9.45509E-02 l.OOOOOE+O( 2

5.95245E-01 1.73487E+Ol 9.32069E+O( 9.921 59E-0 1 2 5.95 133E-01 1.57247E+01 2.22047E+01 9.9696 1E-0 1 2 5.95019E-01 2.03226E+OI 2.86973E+OI 9.984805-01 2 5.94894E-01 6.98103E+Ol 3.75060E+Ol 1.00000E+O( 2



Table 4-C-6-Selected Round Robin Test Results Matrix-SI Units ( D, = 0.36351 3 m, q, = 0.00001 11 6 m/m-K, d, = 0.272653 m, al = 0.00001 665 m/m-K)

- Cell

Value Pa

Flow Conditions 80569. I 9.44490501 8.16344E+0: 8.96264E-01 1.00000E+O( -4

109663.5

9.07450E-01 9.1505 1 E+02 1.00463E+OO 1.00000E+00 -4 6.422 14E-O 1 6.398988+02 7.02544E-01 I .00000E+OO 3 6.06635501 5.92624E+02 6.50641 E-01 1.00000E+00 2 5.95947E-01 6.22878E+02 6.23495E-01 1 .OOOOOE+OO 2 5.93596501 6.04306E+02 6.04905E-01 1 . o m E + o o 2 5.94403E-01 1.6371 IE+Ol 8.79546E+ûû 5.73019E-01 2 5.9301 1 5 0 1 4.1 Iû42E+01 5.80429E+O 1 9.39196E-03 2 5.9297 1E-01 6.32258E+02 3,39684E+02 l.OOOOOE+OO 2 5.92398E-01 1.08505E+02 5.82947E+01 9.68626501 2 5.92308E-01 9.98 I87E+01 1.40953E+02 9.87839E-01 2 5.922 14E-01 1.29606E+02 1.830 16E+02 9.939 18E-0 I 2 5.92134E-01 4.47290E+02 2.40309E+02 1 .OOOOOE+OO 2

T/= 255.37 K, Pj= 1.01325E+05 Pa, p,,p = 932.26 kg/m3, p = 1.8650 Pa-s, k=-1 .0 , pb=910.83 kg/m3

GI 4111

Q v Y ICD

Cd 411,

Q v Y ICD

cd q111

Q v Y ICD Cd 4111

Q v Y I O

4,,,

Y ICD cd 4111

Q" Y ICD Cd 4111

Q v Y ICD

-

-

-

- cd

Qv

-

-

T/= 293.15 K, Pf= 1.01325E+05 Pa, pf,p = 907.60 kg/m3, p = 2.1220E-01 Pa-s k = -1.0. pb = 910.83 kg/m3

1.02805E+OO 7.69481501 6.84269501 6.67053501 6.52787501 7.31671E+01 1.64295E+02 2.43501E+02 3.32324E+02 4.64596E+O: 8.03302E-02 1.80379E-01 2.67339E-01 3.64858E-01 5.10079E-01 I.OOOOOE+OO l.OOOOOE+OO 1.OOO00E+OO I . O ~ E + O O 1 .OOOOOE+O( 4 -4 4 3 3 6.47068E-01 6.22607E-01 6.15779E-01 6.12237E-01 6.091 I 1 5 0 1 4.5 1513E+O1 1.30335E+02 2.14841E+02 2.99048E+02 4.2503OE+O: 4.95716E-02 1.43094E-01 2.35874E-01 3.28325501 4.66641E-01 l.OOOOOE+OO I.OOOOOE+OO 1.00000E+00 1.00000E+00 1.000OOE+O(

6.46757E-O I 5.52364E+O: 6.06441E-01 1 .OOOOOE+O( 3 6.07719E-01 5.08870E+O: 5.58688E-03 1.00000E+O(

Tf= 353.15 K, Pf= 1.01325E+05 Pa, p,,p = 868.43 kg/m3, p = 1.7490E-02 Pa-s. k = -1.0, pb = 910.83 kg/m 3

T/= 288.71 K, Pf= 1.01325E+05 Pa, p,,p = 999.01 kg/m3, p = 1.1990E-03 Pa-s. k = -1.0, pb = 999.01 kg/m 3

4.52373E+01

I.OOOOOE+OO

5.99188E-01 4.35711E+01 i; 1.00000E+OO

4.52821E-02

4.36143E-O2

6.00408E-01 5.98610E-01 5.97616E-01 5.96701E-01 1.34473E+02 2.23450E+02 3.1231 1E+02 4.45475E+O: 1.34607E-01 2.23672E-01 3.12621E-01 4.459 17E-01 I.OO000E+OO l.OOOOOE+OO 1.00000E+OO 1 .OOOOOE+O( 2 2 2 2 5.96154E-01 5.95135501 5.94565E-O1 5.94035E-O1 1.30053E+02 2.16383E+02 3.02646E+02 4.31966E+O; 1.301 82E-0 1 2.16598E-O 1 3.0294650 1 4.32395E-O I l . O ~ E + O O I.OOOOOE+OO 1.00000E+OO l,OooOOE+O(

5.96280E-01 5.34193E+O: 5.34723E-01 1 .OOOOOE+O( 2 5.93790E-01 5.18 146E+O: 5.18660E-Ol 1.00000E+O(

TJ= 372.04 K, Pf= 1.01325E+05 Pa, pf,p = 941.75 kg/m3, p = 2.8250504 Pa-s, k = -1.0, pb = 999.01 k g h 3

2 5.95277501 9.66201E+OC 5.19097E+OC 9.45538E-01 2 5.94164E-01 1.55394E+OI 2.1943OE+Ol 9.92244E-01 2

2 5.9479350 1 1.27685E+03 6.85993E+M 8.93255501 2 5.93728E-01 2. I576 IE+Ol 3.04674E+Ol 9.84799E-O 1 2

ïj= 255.37 K, Pf= 1.01325E+05 Pa, pbp = 2.1181 kg/m3, p = 1.3070E-05 Pa-s, k = 1.3198, pb= 1.86131 kg/m3

5.99192E-01 5.96227E-01 2.05265E+00 6.02052E+oC 1.10280E+OO 3.23456E+oC 9.97822E-01 9.80394E-01 2 2 5.97284E-01 5.94951E-O1 3.14762E+OO 9.38271E+OC 4.44472E+OO 1.32492E+Ol 9.99690E-01 9.97208E-01 2 2 5.97302E-01 5.94966E-01 1.54909E+01 1.35940E+02 2.44402E+01 7.30347E+Ol 1.00000E+00 I.OOOOOE+ûû

5.94441E-01 1.59624E+03 8.57592E+0( 7.82 15350 1 2 5.93329E-01 3.03074E+OI 4.27967E+OI 9.68978E-01 2

5.94364E-01 1.68053E+Ol 9.02876E+0( 6.86300E-01 2 5.93 149E-01 3.58457E+OI 5.06173E+OI 9.55328501 2 5.93123E-O1 5.42075E+02 2.91233E+Oi 1 .OOOOOE+OC 2 5.925 10501 9.38209E+O 1 5.04059E+OI 9.76949E-01 2 5.92420E-01 8.58546E+01 1.21235E+O2 9.9 1066E-01 2 5.92325E-01 I , 1 1292E+02 1.57155E+02 9.95532E-01 2 5.9224 1E-0 1 3.8346 1 E+02 2.060 I7E+02 1 .OOOOOE+00 2

~~

ïj= 283.15 K, Pf= 6.89476E+05 Pa, P,,~ = 4.9831 kg/m3, p = 1.0670E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

cd 4111

Qv Y ICD Cd 4111

Q v Y ICD

Cd 4111

Q v Y ICD

cd %li

QV Y ICD c, 4111

Q v Y [CD

-

-

-

-

5.94174E-01 2.26265E+02 1.2 1562E+02 1 .OOOOOE+OO

5.93729E-01 3.16533E+02 1.70059E+02 l.OOOOOE+OO

5.93315E-01 4.51875E+02 2.42772E+02 1 .OOOOOE+OC

ïj= 255.37 K, Pf= 6.89476E+06 Pa, p,,p = 1042.35 kg/m3, p = 1.5430E-04 Pa-r k=-1.0, pb= 1.86131 kg/m3

Tf= 255.37 K, Pf= 1.37895E+06 Pa, P , , ~ = 32.783 kg/m3, p = 1.3520F-05 Pa-s, k = 1.3198, pb= 1.86131 kg/m

5.92654E-01 7.87668E+Ol 4.23179E+01 9.83993E-01 ,l

5.956918-01 5.939128-01 5.93306E-01 5.92967E-01 5.04450E+3+00 2.403080+01 3.99078EtOl 5.562368+01 1.321968+00 1.291078+01 2.144078+01 2.988418+01 9.998408-01 9.985598-01 9.959988431 9.92 1568-0 I

.-I .-I .-I L L L L L

L955258-0 I 5.93794E-O 1 5.93203E-0 1 5.9287 I 84) 1 5.92562B-0 1 7.256398+00 2.169531:+01 3.608698+01 5.041818+01 7.175998+01 1.024678+01 3.063588+01 5.095XOE+OI 7.1 1949E+OI 1.013318+02 1,999381:-01 9.99442E-01 9.98449E4l 9.969608-0 I 9.93796E-0 I

ïj= 283.15 K, PJ= 3.44738E+06 Pa, p,,p = 26.627 kg/m3, p= 1.1310E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

T/= 338.71 K, Pf= 6.89476E+06 Pa, p,,p = 44.168 kg/m3, p = 1.3650E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m 3

5.95361E-01 5.93671501 ?.36339E+OO 2.80037E+OI 1.32219E+Ol 3.95438E+Ol L99969E-O 1 9.9972 IE-0 1 ? 12 ( 2 j.95151E-0lI5.935338-O1 I5.929808-01I5.926688-O1 15,923768-01 r f = 333.15 K, Pf= 1.37895E+07 Pa,

p,,+ = 520.04 kg/m3, p = 4.1710E-05 Pa-s, k=-1.0, pb= 1.86131 kg/m3

1.59975E+02 2.23847E+02 3.1 9623E+02 8.59473E+Ol 1.20263E+02 1.7 l720E+02 1.00000E+00 1 00000E+OO I.OOOOOE+M) 2 1 2 I ?


A P I M P M S * L 4 . 3 - 4 92 m 0732290 0506425 T O O W

1.55368E+OO 4.7 1346E+02 5.17490E-01 l.ooOOOE+OO -5

O

1.12772E+OO 9.84428E-01 9.01873E-01 8.21 113E-01 1.02637E+03 1.49326E+03 1.9 1524E+03 2.49 105E+03 1.12685E+OO 1.63944E+OO 2.10274E+OO 2.73493E+OO l.OOOOOE+OO l.OOOOOE+OO 1.00000E+OO l.ooOOOE+OO d d d d


7.8 1570E-O 1 2.84531E+03 3.123 86E+00 I.OOOOOE+OO -A

Table 4-C-&Selected Round Robin Test Results Matrix-SI Units ( Dm = 0.746150 m, a2 = 0.00001116 m/m-K, d, = 0.559594 m, al = 0.00001665 m/m-K)

7.48693E-0 1 3.17989E+03 3.49 1 20E+OO l.OOOOOE+OO d

How Conditions

2.55595E+02 2.80618E-01 l.OOOOOE+OO -4 6.28736E-01 1.84788E+02 2.02879E-01 l.ooOOOE+OO

Tf= 255.37 K, Pf= 1.01325E+05 Pa, pl,p = 932.26 kg/m3, p = 1.8650 Pa-s, k=-1.0, pb=910.83kg/m3

6.05290E+02 9.76685E+02 1.34536E+03 1.89554E+03 6.64547E-01 f.O7230E+OO 1.47707E+OO 2.081 llE+OO l.OOOOOE+OO 1.00000E+OO l.OOOOOE+OO 1.00000E+W 3 3 3 3 6.12914E-01 6.08275E-01 6.05815E-01 6.03609E-01 5.40419E+02 8.93878Et-O2 1.24637E+03 1.77404E+03 5.93325E-01 9.81389E-01 1.36839E+OO 1.94772E+Oû l.OOOOOE+OO l.OOOOOE+OO l.OOOOOE+OO l . ~ O E + O o

Tf=293.15 K, Pj= 1.01325E+05 Pa, pl,p = 907.60 kg/m3, p = 2.1220E-01 Pa-s, k = -1.0, pb = 910.83 kg/m3

2.26106E+03 2.48242E+OO 1.00000E+OO 3 6.02616E-01 2.12535E+03 2.33342E+OO l.OOOOOE+OO 2 5.94193E-0 1 2.24213E+03 2.24435E+OO l.OOOOOE+OO 2 5.92275501 2.17685E+03 2.17901E+OO 1.00000E+00

Tf= 353.15 K, Pf= 1.01325E+05 Pa, prp = 868.43 kg/m3, p = 1.7490E-02 Pa-s, k=-1.0, pb=910.83 kg/m3

2.62586E+03 2.88293E+OO 1.00000E+OO 3 6.01838E-01 2.47637E+03 2.7 1881E+OO 1 .OOOOOE+OO 2 5.93940E-01 2.6 147 1E+03 2.61730B+OO 1.00000E+OO 2 5.92126E-01 2.53902E+03 2.54153E+OO I.OOOOOE+OO

Tf= 288.71 K, Pf= 1.01325E+05 Pa, pl,p = 999.01 kg/m3, p = 1.1990E-03 Pa-s, k = -1.0, pb = 999.01 kg/m3

5.97295E-01 5.63461E+02 5.64019E-01 1.OOOOOE+OO 2 5.94080E-01 5.45872E+02 5.46413E-01 l.OOOM)E+OO

Tf=372.04 K, Pl= 1.01325E+05 Pa, pl,p = 941.75 kg/m3, p = 2.8250E-04 Pa-s, k=-i.û, pb=999.01 kg/m3

5.9595 1E-01 5.95204E-0f 5.945 12E-01 9.36986E+02 1.31014E+03 1.86945E+03 9.37915E-01 1.31143E+OO 1.87130E+W l.OOOOOE+OO l.OOOOOE+OO l.OoooOE+C€ 2 2 2 5.93304E-01 5.92869E-01 5.92463E-01 9.08596E+02 1.271 10E+03 1.81462E+03 9.09496E-01 1.27236E+OO 1.81641E+OG l.OOOOOE+OO l.OOOOOE+OO l.OOOOOE+W

T'= 255.37 K, Pf= l.O1325E+O5 Pa, pl,p = 2.1 181 kg/m3, p = 1.3070E-05 Pa-s, k = 1.3198, pb= 1.86131 kg/m3

5.93437E-01 4.05705E+Ol 2.17967E+Ol 9.45543E-01 2 5.92581E-01 6.52771E+Ol 9.21772E+Ol 9.92245E-01 2

Tf= 283.15 K, Pf= 6.89476E+05 Pa, = 4.9831 kg/m3, p = 1.0670E-05 Pa-s,

k 1.3622, pb = 0.708 17 kg/m3

5.93067E-01 5.92798E-01 5.36249E+Ol 6.70492E+01 2.88103E+01 3.60226E+Ol 8.93264E-01 7.82171E-01 2 2 5.92246E-01 5.91940E-01 9.06511E+Ol 1.27355E+02 1.28008E+02 1.79837E+02 9.84800E-01 9.68980E-01 2 2

Tf= 255.37 K, Pf= 6.89476E+06 Pa, P,,~ = 1042.35 kg/m3, p = 1.5430E-04 Pa-s k=-1.0, pb= 1.86131 kg/m3

5.92739E-01 7.05928E+01 3.79264E+O 1 6.86327E-O 1

Tf= 255.37 K, Pf= 1.37895E+06 Pa, pl,p = 32.783 kg/m3, p = 1.3520E-05 Pa-s, k = 1,3198, pb= 1.86131 kg/m3

5.92769E-01 6.87694E+01 3.69468E+O 1 5.73056E-O 1

Tf=283.15 K, Pj=3.44738E+O6 Pa, pl,p= 26.627 kg/m3, p = 1.1310E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

1.50639E+02 2.12715E+02 9.55332E-0 1 2 5.91787E-01 2.27806E+03 1.22390E+03 l.OOOOOE+M) 2 5.9 13 15E-0 1 3.94375E+02 2.11880E+02 9.7695 1E-01 2 5.91240E-01 3.60897E+02 5.09619E+02 9.91066E-01 2 5.91 155E-01 4.67835E+02 6.60625E+02 9.95532E-01 2 5.9 1092E-0 1 1.61 199E+03 8.66051E+02 1 .OOOOOE+OO

Tf= 338.71 K, Pf=6.89476E+O6 Pa, P,,~ = 44.168 kg/m3, p = 1.3650E-05 Pa-s, k = 1.3622, pb = 0.70817 kg/m3

1.72747E+02 2.43934E+02 9.39202E-O 1 2 5.91670E-01 2.65721E+03 1.42760E+03 l.OOOOOE+OO 2 5.9 1229E-O 1 4.561 17E+02 2.45052E+02 9.68628E-01 2 5.91 153E-01 4.19614E+02 5.92534E+02 9.87840E-01 2 5.9 1070E-01 5.44844E+02 7.69368E+02 9.93919E-01 2 5.9 1OO9E-O 1 1.88039E+03 1.01025E+03 1 .OOOOOE+OO

Tf= 333.15 K, Pf= 1.37895E+07 Pa, pl,p = 520.04 kg/m3, p = 4.17 1 0 M 5 Pa-s, k=-1.0, pb= 1.86131 kg/m3

5.94974E-0 1 1.90859E+02 1.02540E+02 l.OOOOOE+OO 2 5.93753E-01 3.37729E+Ol 1.81447E+Ol 9.99840E-01 2 5.93620E-01 3.04659E+Ol 4.30207E+Ol 9.99938E-01

- Cell lalue

-d

- r.

In1

Y [CD

7111

Y [CD cd ?"I

Q v Y [CD

cd li11

Q v Y [CD cd Bi Q v Y [CD cd ?SI

Q v Y LCD

7111

Y iCD cd 9m Q v Y [CD cd 4ni

Q v Y ICD cd 9,li

Q v Y ICD cd 4rii

Q v Y ICD

cd (In1 Q v Y ICD

2,

G

2,

-

-

-

-

-

- cd

Q"

-

-

-

-

-

-

5.932OOE-0 1 5.92594E-O 1 5.92253E-0 1 5.70876E+02 9.50485E+02 I .3299 1E+03 3.06707E+02 5.10654E+02 7.14504E+02 l.OOOOOE+OO l.OOOOOE+OO l.OOOOOE+OG 2 2 2 5.92393E-01 5.91928E-01 5.91667501 1.00958E+02 1.677OOE+02 2.33772E+02 5.42405E+01 9.00979E+01 1.25595E+02 9.98559E-01 9.95998E-01 9.92157E-01 2 2 2 5.92297E-01 5.91843E-01 5.91588E-01 9.1 1497E+01 1.51649E+02 2.11900E+02 1.28712E+02 2.14141E+02 2.99222E+02 9.99442E-01 9.98449E-01 9.96960E-01

Pa

5.93483E-01 3.93139E+Ol 5.55 148E+O 1 9.99969E-01 2 5.93325E-01 1.34839E+02 7.24431E+Ol 1.00000E+OO

559.5 I 5035.6 I 13987.7 I 27415. I 55950.8

5.92191E-01 5.91747E-01 1.17657E+02 1.95850E+02 1.66 142E+02 2.7655 8E+02 9.99721E-01 9.99224E-01 2 2 5.92087E-01 5.91661E-01 4.03677E+02 6.72309E+02 2.16878E+O2 3.61202E+02 I.OOOOOE+OO l.OOOE+OC

- 1 . I ' I ' I '

8.52642E-O1 I6.73057E-OII6.51622E-O1 I6.41140E-01 I6.3233OE-O1

6.01355E-01

1.89282E-01

1 X2837E-0 1 l.OOOOOE+OO

5.96395E-01

5.93 182E-01

9.97208E-01

5.9 1935E-01 1.89886E+03 l.û2017E+O3 1.OOOOOE+OC 2 5.9 1426E-0 1 3.3 1077E+02 1.77873E+02 9.83994E-01 2 5.91350E-01 3.01632E+IX 4.25932E+02 9.93796E-01

5.91497E-01 2.73870E+02 3.86729E+02 9.98480E-01 2 5.9 1420E-O 1 9.40851E+02 5.05478E+02 1.OOOOOE+OC

5.9 1263E-01 3.90468E+02 5.51376E+O: 9.96897E-01 2 5.91 196E-01 1.34356E+O: 7.21837E+O; l.OOOOOE+O(

80569.1 1 109663.5 I

I '

6.28554E-01 I 6.25684E-01


Order No. 852-30354

1-1700-11/92-1.5M (5A)


American Petroleum Institute 1220 L Street. Northwest


Date post:	30-Jan-2016
Category:	Documents
Upload:	nguyengiadinh1980
View:	474 times
Download:	68 times

API MPMS 14.3.4

Documents