NON-NEWTONIAN LOSSES THROUGH DIAPHRAGM VALVES

NON-NEWTONIAN LOSSES THROUGHDIAPHRAGM VALVES

By

DIEUDONNE MATANG'A KAZADIBSc (Chemical Engineering) University of Lubumbashi

Dissertation submitted in fulfilment of the degreeMAGISTER TECHNOLOGIAE

In the Department of Chemical Engineering(Flow Process Research Centre)

Cape Peninsula University ofTechnology

Supervisor: Dr.Veruscha PienaarCo-supervisor: Prof.Paul T Slatter

August 2005

Preamble

ABSTRACT

The prediction of head losses in a pipe system is very important because head losses

affect the performance of fluid machinery such as pumps. In a pipe system, two kinds of

losses are observed: major losses and minor losses. In Newtonian and non-Newtonian

flow, major losses are those that are due to friction in straight pipes and minor losses are

those that are due to pipe fittings such as contractions, expansions, bends and valves.

Minor losses must be accurately predicted in a pipe system because they are not

negligible and can sometimes outweigh major losses (Edwards et al., 1985). There is

presently little data for the prediction of non-Newtonian head losses in pipe fittings in the

literature and little consensus amongst researchers (Pienaar et al., 2004).

In the case of diaphragm valves, usually, only one loss coefficient value is given in

turbulent flow or in laminar flow with no reference to a specific size of the valve,

assuming geometrical similarity that would lead to dynamic similarity. However, no one

has done a systematic study of various sizes of diaphragm valves from the same

manufacturer to establish if this is true. This could be the main reason for discrepancies

found in the literature (Hooper, 1981; Perry & Chilton, 1973; Miller, 1978 and Pienaar et

al., 2004). This work addresses this issue.

A literature revIew on the flow of Newtonian and non-Newtonian fluids has been

presented. The work of Hooper (1981) on diaphragm valves and the works of Edwards et

al., (1985), BaneIjee et aI., (1994) and Turian et al., (1997) for non-Newtonian fluids in

globe and gate valves were found to be relevant to this work. An experimental facility

referred to as the Valve test rig was built and commissioned: Diaphragm valves of 40, 50,

65, 80, 100 millimetre nominal bore diameters from the same manufacturer were used.

The tests were carried out on these valves in the fully open position. Seven different

Newtonian and non-Newtonian materials were tested in each valve. The experimental

results are presented in the form of valve loss coefficient (ky ) against the Slatter Reynolds

number (Re)).

Non-Newtonian Losses Through Diaphragm Valves DMKazadi

Preamble 11

Loss coefficients obtained in this investigation confirmed the general qualitative trend

given in the literature that in laminar flow the loss coefficient increases significantly with

the decreases of Reynolds number and is a hyperbolic function of Reynolds number. In

turbulent flow, the loss coefficient is constant, for any type of fluid, Newtonian or non

Newtonian. It also confirms the general theory that in fittings in general and valves in

particular, the transition from laminar to turbulent occurs earlier than in straight pipes.

Tills work also shows that the Slatter Reynolds number is a useful tool and compared to

other Reynolds numbers (the Newtonian Reynolds number and the Metzner and Reed

generalised Reynolds number), can be used for design purposes. From our analysis, it

was established that geometric and dynamic similarity was not achieved in the diaphragm

valves tested.


Preamble

DECLARATION

111

I, Dieudonne Matang'a Kazadi hereby declare that this thesis represent my own unaided

work and has not been submitted for a degree at another university. Further more it

represents my own opinions and not necessarily those of the Cape Peninsula University

of Technology.

Dieudonne Matang'a Kazadi


Preamble

DEDICATION

IV

I dedicate tbis work to my parents: Papa Kasongo and Maman Milemba who

continuously insisted that I studied and encouraged me during my studies.

To my wife Therese (TMthe) and son Ronald Kazadi for their encouragement, moral

support and affection.

To my brothers, sisters and all my future children.

Psalm 23:

"The Lord is my shepherd; I shall not want. He maketh me to lie down in green

pastures; he leadeth me beside still waters. He restoreth my soul; he leadeth me in paths

ofrighteousness for his name's sake. Yea, though I walk through the valley ofthe shadow

ofdeath, I willfiar no evil: for thou art with thy rod; thy staff, and me they comfort me.

Thou preparest a table before me in the presence ofmine enemies; thou hast anointed my

head with oil; my cup runneth over. Surely, goodness and loving-kindness shall follow

me all the days ofmy life; and I will dwell in the house ofthe Lordfor the length ofthe

days".


Preamble

ACKNOWLEDGEMENTS

v

I thank Prof. P. Slatter for the opportunity he gave me to complete my studies within his

research unit.

I thank Dr. V. Pienaar for accepting to supervise this work, and for all her support during

the completion of my studies. I also thank all the staff, colleagues and students of the

Flow Process Research Centre for their assistance, encouragement and friendship during

the completion of this work.

Thank you also to the Cape Peninsula University of Technology through its R&D

Department and the NRF for their financial assistance without which I could not have

completed this work.

Thank you to Thandiwe Caroline NgamIana ofthe writing centre for editing this work.


Preamble

TABLE OF CONTENTS

VI

ABSTRACT I

DECLARATION III

DEDICATION IV

ACKNOWLEDGEMENTS V

TABLE OF CONTENTS VI

LIST OF TABLES X

LIST OF FIGURES X

NOMENCLATURE XIII

CHAPTER 1

INTRODUCTION 1.1

1.1 Introduction 1.1

1.2 Statement of research problem 1.1

1.3 Objectives of the Study 1.2

1.4 Research design and methodology 1.2

1.5 Delineation 1.2

1.6 Importance and Benefits , 1.3

CHAPTER 2

LITERATURE REVIEW 2.1

2.1 INIRODUCTION 2.1

2.2 Classification of fluids 2.12.2.1 Newtonian Fluids 2.12.2.2 Non-Newtonian Fluids 2.2


Preamble VII

2.2.3 Time Independent Non-Newtonian Fluids 2.32.2.4 Time Dependent Non-Newtonian Fluids 2.52.2.5 Rheology 2.7

2.3 FLOW IN STRAIGHT PIPES 2.102.3.1 Shear Stress Distribution in a Straight Pipe 2.102.3.2 Energy Loss in Straight Pipe 2.102.3.3 Newtonian Transition from Larninar to Turbulent and Reynolds Number 2.112.3.4 Newtonian Laminar Flow in Straight Pipes 2.112.3.5 Newtonian Turbulent Flow in Straight Pipes 2.122.3.6 Non-Newtonian Flow in Straight Pipes 2.152.3.7 Non -Newtonian Transition from Laminar to Turbulent Flow and Non-NewtonianReynolds Numbers 2.152.3.8 Non -Newtonian Laminar Flow in Straight Pipes 2.19

2.4 Rheological characterisation 2.21

2.5 Flow in Pipe Fittings and Valves 2.242.5.1 Classification of Fittings 2.242.5.2 Determination ofNewtonian and Non-Newtonian Losses Across Pipe Fittings andValves 2.24

2.6 FLOW IN VALVES 2.262.6.1 Definition of Valves 2.262.6.2 Classification of Valves 2.262.6.3 Diaphragm Valves 2.272.6.4 Newtonian and non-Newtonian flow in valves 2.31

2.7 DYNAMIC SIMILARITY 2.432.7.1 Geometric Similarity 2.432.7.2 Kinematic Similarity 2.432.7.3 Dynamic Similarity 2.442.7.4 The Application of Dynamic similarity for Non-Newtonian Fluid Flows in Valves........................................................................................................................................ 2.44

2.8 Conclusion 2.45

2.9 RESEARCH ASPECT IDENTIFIED ~ 2.46

CHAPTER 3

EXPERIMENTAL WORK ~ 3.1

3.1 INTRODUCTION 3.1

3.2 DESCRIPTION OF THE TEST LOOP 3.1


Preamble Vlll

3.3 INSTRUMENTATION 3.33.3.1 Pipes & Valves 3.33.3.2 Pressure Lines, Pressure Lines Board, Tappings and Pods 3.83.3.3 Pressure Transducers 3.1 03.3.4 The Hand Held Communicator 3.1 03.3.5 The Data Acquisition Unit or Data Logger 3.103.3.6 Computer and Software 3.113.3.7 Flow meters 3.113.3.8 Tank and Mixer 3.113.3.9 Pump 3.113.3.10 Manometers 3.113.3.11 Pressure Gauges 3.123.3.12 Temperature probes 3.12

3.4 EXPERIMENTAL PROCEDURE 3.123.4.1 Calibration 3.123.4.2 Experimental Test Method (Valve Pressure Drop Test and Straight Pipe Test orTube Viscometry) 3.18

3.5 EXPERIMENTAL ERRORS 3.233.5.1 Error Theory 3.233.5.2 Gross Errors 3.233.5.3 Systematic or Cumulative Errors 3.233.5.4 Random Errors 3.243.5.5 Precision and Accuracy 3.243.5.6 Evaluation of Errors 3.243.5.7 Error in Measurable Variables 3.253.5.8 Axial Distance 3.253.5.9 Weight 3.253.5.10 Flow Rate 3.263.5.11 Pressure 3.263.5.12 Error in derived variab1es c 3.26

3.6 MATERIALS TESTED 3.353.6.1 Introduction 3.353.6.2 Water 3.353.6.3 Carboxyl Methyl Cellulose Solution (CMC) ~ 3.373.6.4 Kaolin Slurry 3.39

3.7 CONCLUSION 3.43

CHAPTER 4

ANALVSIS OF RESULTS 4.1


Non-Newtonian Losses Tbrough Diaphragm Valves DMKazadi

Preamble IX

4.2 Rheological characterisation 4.14.2.1 Newtonian fluids 4.14.2.2 Non-Newtonian fluids 4.3

4.3 Flow in straight pipes 4.7

4.4 Loss coefficients 4.94.4.1 Procedure for calculating the valve loss coefficient 4.94.4.2 Graphical presentation of the valve loss coefficient kv versus Reynolds number 4.12

4.5 Effect of Reynolds number on the valve loss coefficient 4.19

4.6 Conclusion 4.22

CHAPTER 5

DISCUSSION AND EVALUATION OF RESULTS 5.1


5.2 The Literature review 5.1

5.3 .Experimental test loop 5.2

5.41nstrumentation and machine 5.2

5.5 The experimental method ...............................•.......................................................... 5.3

5.6 Materials tested 5.3

5.7 Rheological characterisation 5.4

5.8 Loss coefficients 5.4

5.9 Comparison with literature and originality of this work 5.5

5.10 Similarities analysis 5.8

5.11 Conclusion 5.11

CHAPTER 6

SUMMARY, CONTRIBUTIONS AND RECOMMENDATIONS 6.1


6.2 Summary 6.1


Preamble x

6.3 Contributions 6.2

6.4 Recommendations 6.3

REFERENCES 1

i\1'I'ICN])ICICS..........••..............•............................................................1

LIST OF TABLES

Table 2. 1 Rheological Models available in the literature. (Chhabra & Richardson, 1985).................................................................................................................................. 2.8

Table 2.2 Valves (pienaar et al., 2001) 2.41Table 2. 3 Loss coefficients for turbulent flow through diaphragm valves (Perry &

ChiltoD, 1973) 2.42

Table 3.1 Nominal and internal Dimension of Pipes and Valves 3.3Table 3. 2 Internal dimensions of diaphragm valves tested 3.6Table 3. 3 Calibration constants for different transducers 3.15Table 3. 4 Expected Highest errors and experimental errors in the measurements of the

Valve test- rig pipe diameters 3.27Table 3. 6 Highest Expected errors of the Valve loss coefficient.. 3.32Table 3.8 Errors of the Valve loss coefficient 3.34Table 3. 9 Physical properties of dry kaolin 3.40Table 3. 10 Chemical properties ofdry kaolin 3.40

Table 4. I Properties of glycerine 100% tested 4.2Table 4. 2 Properties of glycerine 75% tested 4.3Table 4. 3 Fluid properties ofCMC 5% tested 4.4Table 4. 4 Fluid properties ofCMC 8% tested 4.4Table 4.5 Fluids properties of Kaolin 10% tested 4.6Table 4.6 Fluids properties of Kaolin 13% tested 4.6Table 4. 7 Summary of Cv and kvvalues obtained in this work 4.19

Table 5. 1 Transition by intersection for the different valves.: 5.sTable 5. 2 Comparison ofloss coefficients of this work with literature 5.6

LIST OF FIGURES

Figure 2. 1 Newtonian fluid flow curve 2.2Figure 2. 2 Non-Newtonian fluids flow curves (paterson & Cooke, 1999) 2.6Figure 2.4 Definition of the loss coefficient (Miller, 1978) 2.26Figure 2. 5 The weir or dam type diaphragm valve 2.30


Preamble Xl

,II

/

Figure 2. 6 The straight-through type diaphragm valve 2.30Figure 2. 7 Typical representation ofk. vs. Re for a fitting (Pienaar et aI, 2001) 2.32Figure 2. 8 Diagram illustrating the calculation of valve loss coefficient 2.34Figure 2. 9 Loss coefficient vs. valve opening (Miller, 1978) 2.41Figure 2. 10 Diagram illustrating the calculation ofvalve loss coefficient.. 4.11

Figure 3.2 Diaphragm valve 3.4Figure 3.3 Connection of diaphragm valves with pipes 3.4Figure 3.4 Internal structure of the valve in the fully open position 3.5Figure 3. 5 Internal dimension of the 80 mm nominal bore diaphragm valve 3.6Figure 3.6 Schematic diagram ofthe Pressure Lines Board 3.9Figure 3.7 Connection of the PLB (the rectangular central part) to Pods and Pressure

Transducers 3.9Figure 3. 8 Calibration regression lines of the DP cell of 6kPa span range showing

calibration regression lines for 0-6kPa range and 0-lkPa range 3.13Figure 3. 9 Calibration regression line ofa Point pressure transducer of 130 kPa 3.14Figure 3. 10 Calibration regression line of Load Cell 3.16Figure 3. 11 Calibration regression line for the Krohne flow meter. 3.17Figure 3. 12 Over view of the Valve test- rig direction valves. Valves (1&2) are on-off

valves to direct the mainstream flow 3.20Figure 3. 13 DP Cells position in the American Standard Method 3.22Figure 3.14 Comparison of variation ofprincipal parameters of the Valve test rig 3.30Figure 3. 15 Comparison ofwater test results with Colebrook & White equation 3.36Figure 3. 16 Comparison of water test results with Colebrook & White equation in double

logarithmic scale 3.37Figure 3. 17 Typical valve pressure drop curve of water in a 40 mm Diaphragm valve

(V=1.79 mls and Re]=75753.99) 3.37Figure 3. 18 Straight pipe test ofCMC 5% in three pipe diameters 3.38Figure 3. 19 Typical valve pressure drop curve of CMC 5% in a 40 mm nominal bore

Diaphragm valve (V=3.04 mls and Re]=0.042) 3.39Figure 3. 20 Particle Size Distribution (PSD) Graph for kaolin powder 3.41Figure 3. 21 Straight pipe test for kaolin 10% in three pipes diameters 3.42Figure 3. 22 Typical valve pressure drop curve of kaolin 13% in a 65 mm Diaphragm

valve (V=0.029m1s and Re]=4.30) 3.43

Figure 4. I Flow curve ofGlycerine 100% at an average temperature of21 °C 4.2Figure 4. 2 Flow curve of CMC 5% ~ 4.4Figure 4. 3 Flow curve of kaolin 13 % 4.6Figure 4.4 Comparison of experimental values of the friction factor in laminar flow for

different fluids in straight pipe of diameter 42.12 mm ID pipe 4.8Figure 4. 10 Comparison of loss coefficient using Re] and RCMR for a Pseudoplastic fluid.

................................................................................................................................ 4.20Figure 4. 11 Comparison of loss coefficient using Re] and RCMR for a yield pseudoplastic

fluid 4.22


Preamble XIl

Figure 5. 1 Comparison of this work turbulent flow valve loss coefficients to valve losscoefficients found in the literature 5.7

Figure 5.2 Variation ofloss coefficient in laminar and turbulent flow 5.9Figure 5.3 Diaphragm valve loss coefficients for CMC 8% in laminar flow 5.10Figure 5. 4 Diaphragm valves loss coefficients for water in turbulent flow 5.1 0


Preamble xm

NOMENCLATURE

Symbol Description Unit

a acceleration rn/s2

A cross sectional area m2

Cv laminar flow valve loss coefficient

D internal pipe diameter m

E sum of mean error squared

f Fanning friction factor

g gravitational acceleration rn/s2

H head m

I intercept

K fluid consistency index Pa.sn

K' apparent fluid consistency index Pa.sn

k hydraulic roughness m

kfitl fitting loss coefficient

kv valve loss coefficient

L pipe length m

Le equivalent length m

M mass kg

m slope

N number ofdata points

n flow behaviour index

n' apparent flow behaviol!l" index

p pressure or static pressure Pa

Q volumetric flow rate m 3/s

R radius m

Re Reynolds number

ReCTi' Critical Reynolds number at the transition

Rewt Metzner & Reed Reynolds number

Re3 Slatter Reynolds number


Preamble xiv

r correlation coefficient

r radius from the centre line

t time s

u point velocity m/s

V average velocity m/s

z elevation from datum m

a kinetic energy correction factor

y shear rate S-l

!'J. difference

f.l dynamic viscosity Pa.s

f.l' apparent or secant viscosity Pa.s

p fluid or slurry density kgm-3

t shear stress Pa

'0 wall shear stress Pa

'y yield stress Pa

cr standard deviation

Subscripts

0 at the wall

ann annulus

calc calculated

US upstream

DS downstrewam

fitt fitting

v valve

obs observed


Preamble

max

m

p

maximum

model

prototype

xv


Chapter 1: Introduction

1.1 INTRODUCTION

CHAPTERlINTRODUCTION

1.1

The prediction of head losses in a pipe system is very important because head losses

affect the performance of fluid machinery such as pumps. In a pipe system, two kinds of

losses are observed: major losses and minor losses. In Newtonian and non-Newtonian

flow, major losses are those that are due to friction in straight pipes and minor losses are

those that are due to pipe fittings such as contractions, expansions, bends and valves.

Minor losses must be accurately predicted in a pipe system because they are not

negligible and can sometimes outweigh major losses (Edwards et aI., 1985). There is

presently little data for the prediction of non-Newtonian head losses in pipe fittings in the

literature and little consensus among researchers (Pienaar et al., 2004).

In the case of diaphragm valves, usually, only one loss coefficient value is given in

turbulent flow or in laminar flow with no reference to a specific size of the valve,

assuming geometrical similarity that would lead to dynamic similarity. However, no one

has done a systematic study of various sizes of diaphragm valves from the same

manufacturer to establish if this is true. This could be the main reason for discrepancies

found in the literature (Hooper, 1981; Perry & ChiIton, 1973; Miller, 1978 and Pienaar et

al., 2004). This work addresses this issue.

This investigation gives loss coefficients data for diaphragm valves and analyses dynamic

similarities of diaphragm valves, using the hydraulic grade line (HGL) approach, in the

different flow regimes. The diaphragm valve is used owing to its importance and wide

usage in the industry de.aling with slurries (Brown & Hey\vood, 1991). This work also

contributes to the commissioning, optimisation and verification of the reliability of the

new state-of-the-art valve test rig.

1.2 STATEMENT OF RESEARCH PROBLEM

There is no experimental loss coefficient data available for a range of diaphragm valves

of different sizes from the same manufacturer for both Newtonian and non-Newtonian

fluids in larninar, transitional and turbulent flow regimes.


Chapter 1: Introduction

1.3 OBJECTIVES OF THE STUDY

1.2

The objectives of this study were:

• To commission the Valve test rig.

• To determine the loss coefficients for diaphragm valves of 40, 50, 65, 80 and 100

millimetre nominal bore diameter, in laminar, transitional and turbulent flow for both

Newtonian and non-Newtonian fluids using the valve test rig.

• To evaluate dynamic similarity.

1.4 RESEARCH DESIGN AND METHODOLOGY

The experimental tests were carried out in the slurry laboratory of the Flow Process

Research Centre at the Cape Peninsula University ofTechnology in Cape Town using the

Valve test rig.

Diaphragm valves of 40, 50, 65, 80, 100 millimetre nominal bore diameter were used.

The tests were carried out on these valves in the fully open position.

Different materials at different concentrations were used: water and glycerine (100% and

75% volume concentrations) as Newtonian fluids and carboxyl methyl cellulose

(CMC)(5% and 8% weight concentrations) and kaolin slurries (10% and 13% volume

concentrations) as non-Newtonian materials.

These materials were rheologically characterised by tube viscometry. The hydraulic

grade line (HGL) approach was used to determine the valve loss coefficients. In this later

approach, each test section as it will be explained later, consisted of two removable pipes

of the same diameter in series joined by a diaphragm valve. On each pipe, upstream and

downstream of the valve were tapping points where the static pressure drop was

measured along the test section. The results for each test were presented in the form of

valve loss coefficient (kv) against the Slatter Reynolds number (Re)).

I.S DELINEATION

This work was limited to Newtonian and non-Newtonian fluids flowing through

diaphragm valves in laminar, transitional and turbulent flow regimes. Only national

trading company (NATCO) diaphragm valves were investigated in the fully open


Chapter 1: Introduction 1.3

position. These 5 diaphragm valves were tested in the fully open position only due to

time factor and also due to the workload as one of the objectives of this work was to

commission the test rig.

Fluids, which have time-dependent and settling behaviour, were not investigated.

1.6 IMPORTANCE AND BENEFITS

This work provides loss coefficients data in laminar, transitional and turbulent flow

regimes for non-Newtonian slurries flowing through 5 different sizes diaphragm valves

from the same manufacturer. This data can be used directly for practical plant design. It

also provides a dynamic similarity study and contributes to the commissioning,

optimisation and verification of the reliability of the new Valve test rig.


Chapter 2: Literature review

2.1 INTRODUCTION

CHAPTER 2LITERATURE REVIEW

2.1

In this chapter, fundamental concepts on fluid classification and fluid rheological

characterisation are presented. The relevant theory on fluid flow in straight pipes, pipe

fittings and valves is also presented. Both of these are presented in laminar and turbulent

flow regimes, with the emphasis on non-Newtonian fluids. The need for an in-depth

understanding of the flow phenomena of non-Newtonian fluids through valves is very

important in this work, especially through diaphragm valves. This explains the emphasis

on flow through diaphragm valves. The theory on dynamic similarity of geometrically

similar valves is also presented and its application for non-Newtonian flow in valves.

2.2 CLASSIFICATION OF FLUIDS

Generally fluids are classified according to the way they respond to externally applied

pressure or to the effects produced on them by the action of shear stress. In this

investigation all the fluids tested are assumed to be incompressible fluids and the effects

produced by the action ofa shear stress is of high interest (Chhabra & Richardson, 1999).

These fluids include single-phase liquids, solutions, and pseudo-homogenous mixtures

such as slurries that may be treated as a continuum if they are stable (Govier & Aziz,

1972)

In general, fluids belong to one of the three main categories: Newtonian fluids, non

Newtonian fluids and settling slurries (Brown & Heywood, 1991).

2.2.1 Newtonian Fluids

A Newtonian fluid is one in which an infinitesimal shear stress will initiate flow and for

which the shear stress is directly proportional to the shear rate.


Chapter 2: Literature review 2.2

The flow curve of a Newtonian fluid at a certain temperature and pressure is a straight

line passing through the origin. The slope of the flow curve is constant and is the

viscosity of the fluid (Chhabra & Richardson, 1999).

The Newtonian fluid flow curve equation is:

't = !!NY (2.1)

where IlN is the Newtonian viscosity.

Some common examples of Newtonian fluids are: water, mineral oil, glycerine and

glycerine-water mixture. Figure 2.1 illustrates the flow curve of a Newtonian fluid.

..E::!.'"'"........'"...'"....c

00

Shear rate [lIs]

Figure 2. 1 Newtonian fluid flow curve

2.2.2 Non-Newtonian Fluids

A fluid is said to be non-Newtonian when the relationship between the shear stress and

shear rate is non-linear or does not pass through the origin (Chhabra & Richardson,

1999). Non-Newtonian fluids are classified into three main categories:

• Time independent non-Newtonian fluids (pseudoplastic, dilatant, Bingham plastic and

yield pseudoplastic fluids)

• Time dependent non-Newtonian fluids (thixotropic and rheopectic fluids) and

• Viscoelastic fluids.



Time dependant non-Newtonian fluids and viscoelastic fluids are not in the scope of this

investigation.

2.2.3 Time Independent Non-Newtonian Fluids

Time independent non-Newtonian fluids are fluids for which the shear rate at any point is

determined only by the value of the shear stress at that point at that instant (Chhabra &

Richardson, 1999).

The constitutive equation of time independent fluids can be written as:

r", = f(T '" ) (2.2)

or its inverse form:

(2.3)

Time independent non-Newtonian fluids are classified into three main categories:

• Pseudoplastic or shear thinning fluids

• Dilatant or shear thickening fluids and

• Viscoplastic fluids (Bingham plastic and yield pseudoplastic)

2.2.3.1 Psendoplastic or Shear Thinning Fluids

Pseudoplastic or shear thinning fluids are time independent non-Newtonian fluids ID

which the apparent viscosity decreases with increasing shear rate (Chhabra &

RichardsoD, 1999). For these fluids, an infinitesimal shear stress will initiate flow, the

flow curve passes through the origin.

Generally these fluids are modelled using the power law model equation, which is a two

parameter equation:

't = Kt' (2.4)

where K is the fluid consistency index in Pas" and n is the flow behaviour index or

power law exponent and n < 1.



2.2.3.2 Dilatant or Shear Thickening Fluids

2.4

Dilatant or shear thickening fluids are time independent non-Newtonian fluids in which

the apparent viscosity increases with increasing shear rate. In this case, as for

pseudoplastic fluids, an infinitesimal shear stresswill initiate flow, the flow curve passes

through the origin.

Generally these fluids are also modelled using the power law model equation (2.4).

But in this case the flow behaviour index or power law exponent n is greater than one (n

> I).

2.2.3.3 Viscoplastic Fluids

Viscoplastic fluids are fluids characterised by a yield stress Cry), which must fIrst be

exceeded before the fluid deforms or flows (Chhabra & Richardson, 1999).

Such materials will deform elastically when the applied shear stress is lesser than the

yield stress. In this category they are classifIed Bingham plastic fluids and yield

pseudoplastic fluids.

• Bingham Plastic Fluids (BP)

Bingham plastic fluids are fluids that require a non-zero shear stress in order to initiate a

signifIcant flow. The flow curve of Bingham plastic fluids does not pass through the

origin and there is a linear relationship between shear stress in excess of the yield stress

and the resulting shear rate (Chhabra & Richardson, 1999).

The Bingham plastic model is described by a two parameter equation:

"t = "tyB + J.IBY

Where "tYB is the Bingham yield stress and J.IB is the Bingham plastic viscosity.

• Yield Pseudoplastic Fluids (YPP)

(2.5)

Yield pseudoplastic fluids are fluids that require a non-zero shear stress in order to

initiate flow. In yield pseudoplastic fluids the increase in shear stress with shear rate in

excess of the yield stress decreases with increasing shear rate (Chhabra & Richardson,

1999).



The flow curve does not pass through the origin and is non-linear.

Yield pseudoplastic fluids can be modelled using the Herschel-Bulkley equation, this

model is a three parameter equation:

(2.6)

where 1:YHB is the Herschel-Bulkley yield stress K is the fluid consistency index and n the

flow behaviour index.

2.2.4 Time Dependent Non-Newtonian Fluids

Time dependent non-Newtonian fluids are fluids that have an apparent viscosity that

varies with the shear rate and the time of application of the shear rate (Chhabra &

Richardson, 1999).

Time dependent non-Newtonian fluids are also classified into two categories:

Thixotropic and rheopectic.

2.2.4.1 Thixothropic Fluids

Thixothropic fluids are fluids when sheared at constant shear rate, their apparent viscosity

decreases with the time ofshearing (Chhabra & Richardson, 1999).

2.2.4.2 Rheopectic Fluids

A fluid is said to be rheopectic when its apparent viscosity increases with time of

shearing. Figure 2.2 illustrates the flow curves of different non-Newtonian fluids as

classified above.


Chapter 2: Literature review 26

NON-NEWTONIAN SLURRIES

TIME INDEPENDENT SLURRIESr

• ~... Ir ...BlNGHAM I YIELD

PLASTIC PSEUIlOPLASTIC I PSEUDOPLASTIC DlLATANT I YIELDD1LATANT

"'

• •ri

Rheogramsr~.

f

TIME DEPENDENT SLURRIES

THIXOTROPHIC

f

Rheograms

Figure 2. 2 Non-Newtonian fluids flow curves (paterson & Cooke, 1999)



2.2.4.3 Settling Slurries

2.7

Settling slurries are solutions or pseudo-homogeneous mixtures where particles in

suspension settle very quickly relatively to their residence time in the pipeline (Brown &

Heywood, 1991) or a mixture in which solid and liquid phases are separated and the

liquid properties are generally considered to be unaltered by the presence of solids.

Particles are supported by turbulent mixing and antiparticle collisions (Paterson & Cooke,

1999)

2.2.5 Rheology

2.2.5.1 Def"rnition

Rheology is defined as the viscous characteristics of a fluid or homogeneous solid-liquid

mixture (Chhabra & Slatter, 2002).

2.2.5.2 Rheological Models

Various rheological models may describe the viscous characteristic of fluids. In this

investigation the following models were used:

• The Newtonian model

• The Pseudoplastic model or Oswald-de-Waele model

• The Bingham plastic model and

• The Herschel-Bulkley or yield pseudoplastic model.

2.2.5.3 Rheological Characterisation

Rheological characterisation in the context of this work is the choice of a convenient

rheological model that fit better the experimental data. The choice of a suitable

rheological model is very important in the characterisation of non-Newtonian fluids and

there is divided opinions on which rheological model to use in the literature to model

laminar flow.



The choice of models is ill fact extremely important not only for rheological

characterisation in laminar flow but even more important in turbulent flow predictions

(Hanks & Ricks, 1975). The reason for this is that the data is usually extrapolated

(Thomas & Wilson, 1987) to much higher shear stresses for turbulent flow predictions

than can be measured in laminar flow, even in small diameters (Shook & Rocco, 1991).

Table 2.1 gives different rheological model available in the literature, showing the depth

of the field of Rheology.

Table 2. 1 Rheological Models available in the literature. (Chhabra &

Richardson, 1985)

Fluid model Constitutive equation Number of ParametersParameters

Newtonian,=~{-~)

1 !l

Bingham plastic ,=, +K(- dU) 2 ,yand K

Y drCasson

.Jr=.f»Pc(- ~~)2 'y and !le

e-functionP=Po exr[m(- ~~ ) ]

2 Iloandm

Oswald de Waele

'=K(-~~J2 Kandn

or power-law(pseudoplastic)Ellis Po 3 Ilo,a and '112p=

1+(xJa 1

Herschel-Bulkley ,=, +K(_dUJ 3 'y, n andKor

Yield pseudoplasticY dr

Carreau n-l - 4 !l~ .Ilo, A. and n

:~~o =[I+(A(-:)J]-'Cross :-;- ++(-:Jfj 4 !l~ , Ilo, A. and n

Cross and Carreau models are mainly used for polymer solutions, zero shear viscosity is

usually associated with very low flow, shear rate 10.3 S·l (Malkin, 1994).



(2.6)

For suspensions, yield pseudoplastic, Bingham plastic and power law models are more

appropriate (MaIkin, 1994). Also because the effects produced by the action of a shear

stress is of high interest in pipe flow (Chhabra & Richardson, 1999), these equations are

also used in this work because, in pipe flow the shear rate is directly calculated.

2.2.5.4 The Yield Pseudoplastic Model

The yield pseudoplastic model will be used in this work to characterise all fluids as it is

explained in section 2.3 .8. The yield pseudoplastic model (YPP) incorporates the features

of all models used in this work: The rheogram curvature of the pseudoplastic model and

the yield stress for the Bingham plastic.

The yield pseudoplastic model is very sensitive to small variations in the rheological

parameters and requires a sufficient amount of good laminar data to ensure

reproducibility of the model to different data sets (Johnson, 1982).

The constitutive equation ofthe yield pseudoplastic model is given by equation (2.6):

, = 'yBB +K(

This equation is a three parameters equation:

• The yield stress ('yHB)

• The fluid flow behaviour index (n)

• The fluid consistency index (K)

Rheometry or viscometry deals with the establishment of a relationship between shear

stress and shear rate. This is required to establish the rheological parameters such as 'yHB,

K, and n, which are used for the specific fluid.



23 FLOW IN STRAIGHT PIPES

2.3.1 Shear Stress Distribution in a Straight Pipe

The shear stress distribution in a pipe is given by the relationship:

'\pr,=-2L

2.10

(2.7)

where: '\p is the pressure gradient in the portion of a straight pipe of length L and the

radial distance r (Chhabra & Richardson, 1999).

At the pipe wall equation (2.7) becomes:

'\pD, =--• 4L

where D is the pipe diameter.

2.3.2 Energy Loss in Straight Pipe

(2.8)

(2.9)

When a fluid flows in a straight pipe the dissipation of energy manifests itself as head

loss and can be calculated using the Darcy-Weisbach formula (Massey, 1970):

,\H =4fL (V2

)

D 2g

:<u

Where f is the Fanning friction factor defined as (Massey, 1970):

f = 2,.pV2

The velocity V is obtained from the continuity equation and is given by:

V=QA

(2.10)

(2.11)

Equations (2.7), (2.8), (2.9), (2.10) and (2.11) do not depend on the nature of the fluid

(Newtonian or non-Newtonian) or on the nature of the flow (laminar or turbulent). They

depend on the homogeneity of the fluid and on the development of the flow (Massey,

1970).



2.3.3 Newtonian Transition from Laminar to Turbulent and ReynoldsNumber

2.11

There are two types of flow: laminar or streamline flow and the turbulent flow. Laminar

flow occurs at lower velocities, the fluid particles are moving in straight lines, but the

velocity with which the particles move along one line is not the same as along another

line (Massey, 1970).

In turbulent flow, the path of individual fluid particles are not straight anymore but are

sinuous, intertwining and crossing each other in a disorderly manner so that a mixing of

the fluid takes place (Massey, 1970).

Experimental work has shown that the transition from laminar to turbulent flow happens

at some fixed value of a dimensionless group called Reynolds number (Massey, 1970).

The Reynolds number is the ratio of the inertial to viscous forces and is given for

Newtonian fluids by:

pVDRe=--

II(2.12)

where p is the fluid density, V the fluid velocity, D the pipe diameter and II the fluid

viscosity.

The general accepted point of transition from laminar to turbulent flow is Re=2100. But

the transition can happen at a Reynolds number higher than 2100 or lower than 2100

depending on the vibrating nature of the surroundings (Massey, 1970).

2.3.4 Newtonian Laminar Flow in Straight Pipes

2.3.4.1 Velocity Distribution

The velocity distribution in a pipe in laminar flow (if there IS no slip or hold up effect at

the pipe wall) is (Massey, 1970):

(2.13)

u is maximum for FO and is:

Non-Newtonian Losses Through Diaphragm Valves

(2.14)

DMKazadi

Chapter 2: LrternurrereTIew

And the mean velocity is:

v:= umax

2

2.12

(2.15)

(2.16)

2.3.4.2 Hagen-Poiseuille Formula

For an incompressible Newtonian fluid in laminar flow, the Hagen-PoiseuilIe formula is

(Massey, 1970):

(2.17)

(2.18)

2.3.4.3 Friction Factor

In general the friction factor is determined using equation (2.1 0). The friction factor is

generally a function of both the Reynolds number and the pipe wall roughness. In

Newtonian laminar flow, the pipe wall roughness has no effect on the friction factor and

the friction factor is given by (Massey, 1970):

f=~Re

2.3.5 Newtonian Turbulent Flow in Straight Pipes

Turbulent flow is a flow characterised by large, random, swirling or eddy motions.

Particle path cross and velocity (both direction and magnitude) and pressure fluctuate on

a continuous and random basis.

Turbulent flow is very complex and a consistent mathematical analysis is not yet done

and predictions are obtained empirically from experiments (Massey, 1970).

The friction factor in urrbulent flow is a function of the Reynolds number and the pipe

wall roughness k. It can be obtained using the Colebrook and White equation (Massey,

1970):

_1_ = -410 [_k_+ 1,26 ].Jf g 3,7D Re.Jf


(2.19)

DMKazadi


It must be noted that the Moody diagram presents the friction factor f vs. Re and is a

useful tool when it comes to the friction factor determination.

Fig 2.3 gives the Moody diagram.

In a case of a smooth pipe and for Reynolds numbers between 3000 and 100000, the

Blasius equation is used to determine the friction factor (Massey, 1970).

f = 0.079 (2.20)(Re)'''


!"-+>

n.[&'!':'t'"'ij'

!"Cl:;.~

~

~

f,~~

:N"a:

~~

0.02

0.011

0.00)

«tm ~L.mIOarflow'F=~( I I 11 nmTI0.02 Laminar bilkal o:!'ansitiOll:t;; '. ;;:', :Complete turbulence, rough pipes .. • 'r- ..•,

flow '''Vlono "- >one \ ••s0.011 ' •

I/, \001' 1('....,.... .~., • ... , , •• " ., .'..

• 1\ l t r~ •.••o.oI4H·H --' ... - ,,- .,. - , .. - , _

0.012H-H]t\ : ' \'_"'"''h'''11 ,~t'o ~11 I .~~ r--..~ .

m'Htl \ :.iI~ r---::: -... 0.01

1J1 R~rit t~ If .. :----- t- " ... -' - - .,•••o.ooalit']~ , .0007"u~~-W1 I~" ,. ." .... ,,_ ., ., .· \ "~~j-.. "-o.oo.HHt-- .... ~ '''. .,•.,

o.oosHt·jtl-Hti ~ ~~. .. - -ill . klmm) .. ~t::-- .. , .. ... "-

0.004 . Riveted steel 1 - 10 .""~ ICoocrete 0.3. 3 1 '!'Wood slave 0.2 -1 _ '- I IC.sllron O. 25 ~

··'G.I,."iled steel 0.15 1- - ~ -- . ..... I 11Asphalled casllron 0.12 Smooth pipes r""'b-- ".

,.Commerclal steol • -_•., - ... l .•••,••, ..or wrought Iron 0.045 " j ,•.•••,••, IIIKI

Drown tubing 0.0015 IIIII l11 ,I .wo002ULLl _, ., .Jl.U

· 7.234.161' .2i04S679 2a."7' 234.'79234$679~ l~ l~ ~ ~ I~

R uclReynofds number e::: lJ

«tOO25

~

[

z0~z~0e.§t'"'0V>V>

"V>

~~0

4-~.

~

.g

Eg-o>

8~'".g<:.....~

<"V>

Fi2ure 2. 3 The Moody Dia2ram (Massey, 1970)


2.3.6 Non-Newtonian Flow in Straight Pipes

2.15

The fundamental relationships (2.7), (2.8), (2.9), (2.10) and (2.11) on the shear rate,

energy loss in pipes and velocity are also valid for non-Newtonian fluids as stated earlier

in sections 2.3.1 and 2.3.2.

2.3.7 Non -Newtonian Transition from Laminar to Turbulent Flow and NonNewtonian Reynolds Numbers

In this section, the different criteria for the determination of flow regime for non

Newtonian fluids are presented.

In non-Newtonian flow as in Newtonian flow there are also two kinds of flow: laminar

and turbulent. Many criteria have been established for the determination of the nature of

flow. Although this investigation uses the Slatter Reynolds number, other non-Newtonian

Reynolds numbers and criteria relevant to this work are also presented. The Slatter

Reynolds number is favoured because it can describe the behaviour of a wide range of

non-Newtonian fluids (Chhabra & Slatter, 2002).

2.3.7.1 Newtonian Approximation

In the Newtonian approximation method, in order to evaluate the transition from laminar

to turbulent flow, the Newtonian Reynolds number is used but because a non-Newtonian

fluid has a variable viscosity, the apparent or secant viscosity is used and in equation

(2.12) the term viscosity /l is replaced by /l'the apparent or secant viscosity and equation

(2.12) becomes:

Re =pVDNowt ,

/.l

with the apparent viscosity:


(2.21)

(2.22)

DMKazadi


where: [- : 1is the velocity gradient at the pipe wall.

2.3.7.2 Metzner & Reed Generalised Reyno1ds Number

It has been demonstrated that for laminar pipe flow of any given time independent fluid

that 8VID is some unique function of "to only (Metzner & Reed, 1955). This may be

expressed as:

"t = D.6. P = K,(8V)"'o 4L D

(2.23)

where in the most general case K' and n' are not constants, but vary with 8VID. Thus on

logarithmic plot of "to versus 8VID, Equation (2.23) is simply the equation of the tangent

to the curve at a given value of 8VID, n' being the slope of this tangent and K' its

intercept on the ordinate at 8VID equal to unity (Skelland, 1967).

Metzner & Reed (1955) developed a generalised Reynolds number from the

considerations above as:

ReMR

8pV2

(2.24)

This relation may be rewritten after transformation as:

(2.25)

(2.26)n

In practice, n' is the tangent of the double logarithmic plot of "to versus (8VID) at any

particular value of"to or 8VID. Log K' is the intercept on the y-axis.

d(Log"tJ

d(Log 8;)

It has been found experimentally that for many fluids K' and n' are constant over any

range of "to or 8VID for which the power law is valid. This is not the case in general (the

log-log plot is not always a straight line) and care must be taken to ensure that the range

of application is narrow. The quantity n' characterises the degree of non-Newtonian

behaviour for a given fluid, The greater the departure of n' from unity the more non-



(2.27)

Newtonian is the flnid. The quantity K' is a measure of the consistency of the fluid, the

larger the value ofK' the thicker or less mobile is the fluid (Metmer & Reed, 1955).

For power law fluids or pseudoplastic models:

K' = Ke:: 1rand n=n'

Thus (2.25) becomes:

(2.28)

For a Bingham plastic fluid (Skelland, 1967):

(2.29)

(2.30)

For yield pseudoplastic fluids, no relationship has been derived for yield pseudoplastic

fluids and this has been done as part of this work. It has been demonstrated in this work

that (see Appendix 5):

and



2.3.7.3 Slatter Reynolds Number

2.18

The Slatter Reynolds number takes directly in to account the yield stress of non

Newtonian fluids but other non-Newtonian Reynolds numbers do not take directly into

account the yield stress. An unsheared core is formed in larninar pipe flow of a fluid with

a yield stress. Slatter has proposed a Reynolds number which seeks to express the ratio of

inertial forces to viscous shear forces in the sheared portion of the flow (Shook et ai,

2002).

The Slatter Reynolds number is given by:

Re, = 8pV~

"ty

+K(8V"",,)"Dsbear

(2.33)

For fluid with a yield stress there is a plug flow at the centre of the pipe in larninar flow

and the radius of the plug is:

The sheared diameter is:

D",,'" =D - Dplug

The mean velocity of the annulus is:

v =Q"""""" A

ono

where Qono = Q - QP'Ug

and Qplug = up1ug .Ap[ug

(2.34)

(2.35)

(2.36)

(2.37)

(2.38)

(2.39)

Where Uplug is given by equation (2.41) in section 2.3.8.

The transitional value of the Slatter Reynolds number from laminar to turbulent flow in

straight pipes is Re] = 2100 (Shook et ai, 2002).



The Slatter Reynolds number can accommodate different rheological models: the

Newtonian model, the power law model, the Bingham plastic model and the yield

pseudoplastic model, as it will be demonstrated in this investigation.

2.3.7.4 Intersection and Deviation Methods

• Intersection Method

This is a practical method. It uses the intersection of the laminar and turbulent flow loci

to predict the critical point.

The degree of accuracy of this method depends on the turbulent flow model used and this

method is also incompatible with Newtonian fluids (Chhabra & Slatter, 2002)

• Deviation Method

This method uses the point from which data starts deviating from the laminar flow line to

define the transition region and that deviation happens before the intersection.

This method is relevant for this study because in most cases, the transition from laminar

to turbulent regime in pipe fittings and valves occurs earlier than in straight pipe flow

(Pienaar et aI., 2001) and can be detected using the deviation or intersection method.

2.3.8 Non -Newtonian Laminar Flow in Straight Pipes

The following rheological relationship can be accommodated in the yield pseudoplastic

model equation (2.6):

Yield dilatant (-ty > 0 and n > 1)

Bingham plastic ('y > 0 andn = 1)

Dilatant ('y = Oandn > 1)

Newtonian ('y =Oandn =1)

Pseudoplastic ('y = 0 andn < 1)

In laminar flow, the velocity distribution of a yield pseudoplastic fluid is for R > r> rplug:



R n [( fr+l ( fr+l]U =---- "[ -L' Q - 't-"[ n.'c n+l 0 Y Y

K "Lo

When 0 < r <rplug the fluid moves as a plug at a uniform plug velocity Uplug:

2.20

(2.40)

(2.41)

The volumetric discharge Q and the average velocity are obtained from the relation:

32Q 8V 4n ( ¥-:':"[(ro -'YY 2'Yk -,J '~]- =- =-- '0 -, J n + +-- (2.42)nD3 D .'c 3 Y 1+ 3n I + 2n 1+ n

KOLa

With '0 as defined by equation (2.8) and V=QIA equation (2. I I)

For a Newtonian fluid K=Jl and n=l, equation (2.42) becomes:

8V'0 =Jln (2.43)

Equation (2.43) shows that wall shear rate at pipe wall for a Newtonian fluid is 8V. For. D

non-Newtonian fluid 8V is called the pseudo shear rate or nominal shear rate. The plotD

of '0 versus 8V is called the pseudo-shear diagram. It is of great importance in nonD

Newtonian fluid flow in general and in this investigation in particular.

2.3.8.1 The Rabinowitsch-Mooney Relation

The true shear rate can be obtained from the pseudo shear rate of a non-Newtonian fluid,

by multiplying the pseudo shear rate by the Rabinowitsch -Mooney relation:

[_ dUJ = 8V[3n' :1]

dr 0 D 4n

n" is calculated as:

(2.44)

n (2.26)

Non-Newtonian Losses 'Through Diaphragm Valves DMKazadi


(2.45)

The coefficient n' is obtained as the slope of a double logarithmic plot of 'to versus 8VID.

In the case the rheological parameters of the fluid are known ('ty. K and n), n' can be

obtained directly using relations (2.27) for pseudoplastic fluids, (2.29) for Bingham

plastic fluids and (2.31) for yield pseudoplastic fluids.

2.3.8.2 Friction Factor for Non-Newtonian Fluids

In the case of inelastic non-Newtonian fluids, the fanning friction factor in larninar flow

is given by (Chhabra & Richardson, 1999):

f=~ReMR

with f given by equation (2.10).

Slatter (1999) also developed a friction factor for non-Newtonian fluids with a yield

stress:

f =~"'" V 2

P "'"

In this case the transition is considered to occur when fannequals 16/2100.

2.4 RHEOLOGICAL CHARACTERISATION

(2.46)

The rheologica1 characterisation of non-Newtonian fluids is not easy (Chhabra &

Richardson, 1999), and can be done using a rheometer or a tube viscometer. In the

context of this investigation, tube viscometry was used because the experimental test loop

could also be used as an in-line tube viscometer having a range of 5 different pipe

diameters.

Rotational viscometry

The instrument used to measure viscous properties ofnon-Newtonian fluids in this case is

known as a rheometer. The rheometer usually consists of a concentric bob and cup, one

ofwhich is rotated to produce shear in the test fluid that is in the gap between the bob and



the cup. The shear stress is determined by measuring the applied torque on one of the

elements.

The rheometer is a very sophisticated instrument and is capable of measuring the full

range of rheological phenomena. The rheometers can be found using one of the many

. geometries, among others: Concentric cylinders, cone and plate, parallel disks. And the

main measurements are angular velocity and applied torque. The software connected to

these instruments converts these signals into shear rate and shear stress (Chhabra &

Slatter,2002)

Tube viscometry

In a tube viscometer the test fluid flows at a controlled, measured rate through a tube of

known diameter and the pressure drop over a known length of the tube is measured.

Data from tube viscometer yields a series of coordinates of pseudo shear rate and wall

shear stresses (8VID, 'to) these data must be processed in order to give the required

rheology.

Assuming a yield pseudoplastic rheology (2.6):

32Q = 8V =~(r -'t f![('to-'trY + 2'tJo -'tJ+~] (2.42)nD3 D .!. 3 0 Y 1+3n 1+2n l+n

K"'to

The following technique was used (Slatter, 1994):

A pseudo shear diagram was plotted using the pseudo shear rate (8VID) as abscissa and

shear stress (D~p/4L) as ordinate. Data points in laminar flow only from all tubes are

used. The best curve is fitted to the data by eye. A realistic value of'ty is set according to

the data as the ordinate intercept. The value of'ty is then adjusted until the error function

is minimised. The error function E is the root square ofdifference between observed data

and calculated as:

E=N-l

and K value for minimum error Kmin is given by:


(2.47)

DMKazadi


2f(8V)/8KMIN = 1/ ID,

~( ~[(r. -"trJ 2"tyk, -"t,) "t~]nL., 'to - 'ty J n + +--'~l 1+3n 1+2n l+n

Errors in tube viscometry:

"

2.23

(2.48)

• Wall slip: this effect occurs when the layers of particles near the wall are more dilute

than the bulk flow (Heywood & Richardson, 1978). As a result the viscosity near the wall

will be reduced and apparent slip will occur. Chhabra & Richardson (1999) warn that

serious errors could occur when the wall slip is not accounted for. To account for the wall

slip, more than one diameter tube should be tested. Their laminar flow data should

coincide if there is no wall slip. If they do not coincide then the slip velocity must be

calculated for each tube and deducted from the measured mean velocity (Heywood &

Richardson, 1978).

• Entrance and exit losses: it is important that the entrance and exit losses in the tubes

that are used are minimised. This is possible by making sure that the flow is fully

developed before differential pressure readings are taken.



2.5 FLOW IN PIPE FITTINGS AND VALVES

2.24

In this section, the relevant theory on Newtonian and non-Newtonian losses in pipe

fittings and valves is given in both laminar and turbulent flow regimes.

2.5.1 Classification of Fittings

Fittings are generally classified in one of the categories below:

• Branching fittings, e.g.: tees, crosses, side outlet elbows, etc.

• Reducing or expending fittings: in which there is a change III the cross section

of the pipe e.g.: contraction, expansion, etc.

• Deflecting fittings in which there is a change in the direction of flow e.g.: bends,

elbows, return bends and

• Combined or hybrid fittings are a combination of the aforementioned e.g. valves.

Other fittings do not offer any resistance to flow such as couplings and unions. (Crane

Co., 1981)

2.5.2 Determination of Newtonian and Non-Newtonian Losses Across PipeFittings and Valves

2.5.2.1 Losses Across Fittings

The Bemoulli formula gives the macroscopic mechanical energy balance for a pipe

system and gives the total head loss in the system and is used in the determination of

different losses in the system (Massey, 1970).

The Bemoul1i formula for a system of two pipes in series connected bya fitting, can be

written as follows:

a v,2 P a V2 pZ +_'_1+_1 =Z +_2_2_+-1.+H +H +HI 2 I fin 2

2g pg pg pg(2.49)

where z is the elevation of the datum, a is the kinetic energy correction factor, p is the

static pressure and, H the head loss.

Subscripts 1 and 2 are for upstream and downstream pipes respectively.

H fiI, is the fitting head loss in metres and is predicted using the formula (Massey, 1970):

Non-Newtonian Losses Though Diaphragm Valves DMKazadi


- For a valve it is written:

y 2

Hv=ky -

2g

2.25

(2.50)

(2.51)

where kfit• or kv is the fitting or valve head loss coefficient and is defmed as the non

dimensionalised difference in overall pressure between the ends of two long straight

pipes when there is no fitting and when the real fitting is installed (Miller, 1978). This is

shown graphically on Figure 2.4 for a valve.

2g(2.52)k fitt = H fitt y2

or:

k - ~Pfitt (2.53)fitt - 1/2py2

The loss coefficient can be calculated in two ways, by including or excluding the length

of the fitting.

If the length of the fitting is excluded, kfitl is called kgros and is obtained by the equation

(Turian et ai, 1997):

1 [ P y2 4f ]k =-- -~p---(L +L )gm" Py2 2 Dud

2

(2.54)

If the length of the fitting is included, k fitl is called kne. and is obtained by the equation

(Turian et ai, 1997):

1 [ py2

4f - ]knot =--2 -~p-----(Lu+Lfitt +Ld )py 2 D

2

(2.55)

With the exception of abrupt contractions and expansions, all other fittings have a

physical length. The length of the test valve was included in all calculations in this work.



Static Pressure gradientwitho ut wlve. 1

2 '&, =k,pV /2:L

i'.i :II•II .i StatIc Pressure gradient

~~'h1tl(l,"Fe\llir:::~,~ ~;:i?,1Distance [m]

Figure 2. 4 Definition of the loss coefficient (Miller, 1978)

2.6 FLOW IN VALYES

2.6.1 Definition of Valves

In the industry generally valves are used to isolate, regulate or direct the flow (Lahlou,

2002). From an engineering perspective, a valve is a contraction followed by an

expansion (Mc Neil & Morris, 1995).

2.6.2 Classification of Valves

According to their resistance to fluid flow, valves are classified either as low resistance

valves or high resistance valves. Low resistance valves are those in which there is only a

change in the flow cross section and high resistance valves are those where there are both

changes in the flow cross section and direction (Crane Co., 1981).

In the industry dealing with non-Newtonian fluids or slurries, valves are used mostly for

isolation purposes and rarely for regulating or throttling. However in applications such as

polymer processing, valves are used as throttling devices (Mc Neil & Morris, 1995).



It is not possible to do any systematic classification, due to the great variety of valve

designs. However, there are five basic valve designs: gate, ball, plug, butterfly,

diaphragm and pinch (Heywood, 1999). There are designs intended for a particular

application or that combine certain features of other valves for improved performance.

These are known as hybrid valves.

According to their mode of operation, valves can be classified as: manual valves, check

valves, pressure relieve valves and control valves (Lahlou, 2002).

Diaphragm valves are the objects of this study and a thorough description is given in

section 2.6.3 due to their wide usage in the slurry industry and in the mineral processing

industry (Brown & Heywood, 1991)

The selection of the right valve in a piping system is crucial because poor selection can

lead to problems: excessive high initial and maintenance costs, downtime, leakage, poor

performance, dangerous vibration and excessive noise. Many variables are to be

considered when doing a slurry valve selection. Slurry valve selection is complex and is

not in the scope of this investigation. However the first rule is to avoid the need for

valves whenever possible. The need for a valve must be carefully scrutinised. It must also

be said that high resistance valves in general are unsuitable for slurry service (Brown &

Heywood, 1991).

2.6.3 Diaphragm Valves

The diaphragm valve has a valve body assembly with a single flexible diaphragm, which

isolates the actuating mechanism from the flowing fluid.

There are two basics designs: the weir or darn and straight through types.

The body can be manufactured from cast iron, bronze, gunmetal or stainless steel. It can

be lined with various elastomers, polymers or glass for highly corrosive and/or abrasive

applications.

Diaphragms are ill elastomeric material or polytetrafluoroethylene (PTFE) with an

elastomer backing. Because the diaphragm isolates the moving parts in the bonnet from

the flowing fluid, the bonnet assembly can be manufactured from cast iron or plastic

coated materials. Cast iron is used for most applications. This is because it renders the



valve suitable for handling aggressive fluids including those containing suspended solids

as well as clean fluid applications (AEA Technology, 1996).

Diaphragm valves can normally operate within a wide temperature range depending on

the valve material choice. The application of both types is limited to about 10 bars

maximum (lower in large valves) with temperatures and products limited by the

diaphragm and optional body linings (typically 100°C).

The weir or dam type diaphragm valve (Figure 2.5) has a body with a transverse weir

above which a flexible diaphragm is mounted. Tight closure of the diaphragm valve is

obtained when the diaphragm is screwed down by means of a hand wheel, pneumatic or

electric actuator until it touches the weir.

The movement of the diaphragm, even from the fully open to the fully closed position, is

relatively short; the result is a long diaphragm life and low maintenance. This type of

valve is suitable for throttling applications and is by defInition a high resistance valve

because there are changes in both the diameter of the cross section and the flow direction.

The straight-through type diaphragm valve (Figure 2.6) may have a parallel or tapered

bore through the body. A wedge-shaped diaphragm completes the closure. The method of

sealing requires a longer diaphragm movement, which tends to result in a shorter

diaphragm life.

The full bore opening offers minimum resistance to flow in the open position and this

valve is by defInition a low resistance valve because there is change only in the cross

section diameter. However, the material choice for the diaphragm is much more limited.

The advantages of the diaphragm valve reside in the fact that the operating mechanism,

called the compressor, is above the diaphragm, not in contact with the flowing fluid. Its

unlined solid-alloy bodies are relatively less expensive than those of some other types of

valves because of the smaller metal mass.

No packing is required. The interior is very smooth and can be easily cleaned.

As limitations, larger sizes of this valve become more difficult and expensive to produce.

The valve leaks upon the failure of the diaphragm due, for instance, to excessive cycling.



Diaphragm valves are particularly suitable for less arduous slurry service (Brown &

Heywood, 1991). With particularly abrasive slurries, the weir type may be subject to

erosive wear and the passage constriction is some times undesirable with large particle

slurries.

The straight-through type is better suited for use with high solids content, coarse

particles, high viscosity and Iow pressure, low temperature abrasive slurry systems. It can

be found in the brewing, chemical processing, dairy, food, minerals processing, paper and

pulp, power generation and water industries (AEA Technology, 1996).



WEIR

Figure 2. 5 The weir or dam type diaphragm valve

~--nI I. COMPf1ESSOR

2.30

tllAPHRAGM

Figure 2. 6 The straight-through type diaphragm valve



2.6.4 Newtonian and non-Newtonian flow in valves

2.6.4.1 Pressure Drop in Valves

2.31

The loss ofpressure due to a valve consists of three parts (Turian et aI, 1997):

1. The pressure drop within the valve itself due to the viscous stresses that cause internal

friction and separates flows.

2. The pressure drop in the upstream pipe in excess of that which would nonnally occur

if there were no valve in the line. This effect is small.

3. The pressure drop in the downstream pipe in excess of that which would nonnally

occur if there were no valve in the line. This effect may be comparatively large.

2.6.4.2 Valve Loss Coefficient

Friction losses for valves are obtained using equation (2.51) where

kv is the valve loss coefficient or resistance coefficient and is defined as the number of

velocity heads lost due to a valve.

The head loss is independent of the Reynolds number for turbulent flow through valves,

because inertia forces dominate. It is clear that the loss coefficient in turbulent flow is

independent of the Reynolds number. In laminar flow the valve loss coefficient is

Reynolds number dependent and in laminar flow is defmed as Cv ,the laminar flow valve

loss coefficient(Pienaar et aI., 2001):

Cv= kv.Re (2.56)

The loss coefficient is usually presented as a fimction of the-Reynolds number. The loss

coefficient is on the y-axis and the Reynolds number on the x-axis on logarithmic scale.

In laminar flow the loss coefficient is a hyperbolic function of the Reynolds number and

it increases significantly as the Reynolds number decreases. Figure 2.7 gives a typical

presentation ofkvvs Re.



1.CE-t05 r------------------------,

2.32

1.CE -t04

1.CE-t03-=...;g1.CE-t02.......Q

U~ 1.CE-t01~Q...

1.CE-tOO

1.CE-DJ

Transitioo by Deviatioo Method

Transitioo by Intersection Method

•••

Transitioo Region

1.CE-tOO 1.CE-tOl 1.CE-t02 1.CE-t03 1.CE-t04 1.CE-t05 1.CE-t06

Reynolds Number

1.CE-02 '----'----'----'----'----'----"----'----'

1.CE-02 1.CE-01

Figure 2. 7 Typical representation of kv vs. Re for a fitting (pienaar et ai, 2001)

Figure 2.7 shows the transition from laminar to turbulent flow. Some authors defme it as

the intersection of the laminar loss coefficient and turbulent loss coefficient loci and

others as a point where the experimental data start to deviate from the laminar flow line

(pienaar et aI, 2001).

Determination of the laminar valve loss coefficient.

The laminar loss coefficient in equation (2.56) is determined from experimental data in

the laminar flow region by the least square method.

It is obtained by minimising the logarithmic least square:



Methodology

2.33

(2.57)

Generally, there are two methods used in the determination of valves or fittings loss

coefficient: The hydraulic grade line (HGL) approach and the total pressure method.

BaneIjee et al., (1994) and Baudouin, (2003) adopted the hydraulic grade line approach

for the determination of loss coefficients, the first for loss coefficients in valves and the

latter for loss coefficients in sudden contractions. It consists of measuring and plotting

the static pressure gradients upstream and downstream of the valve in the region of fully

developed flow far from the valve plan to avoid disturbance of the· flow due to the

presence ofthe valve.

The valve pressure loss is obtained as an extrapolation to the valve plane of the pressure

gradients measured in the fully developed flow regions upstream and downstream of the

valve.

To measure static pressure at different points upstream and downstream of the valve,

BaneIjee et al. (1994) used V-tube manometers containing mercury beneath water

connected to pressure tappings. Baudouin (2003) used point pressure transducers and

differential pressure cells connected to pressure tapings.

Turian et al., (1997) and Pienaar (1998) used the total pressure method to determine the

loss coefficient through fittings and valves. Two pipes in series were joined by a fitting or

valve. The method consists of measuring the pressure gradient between two points in the

region of fully developed flow in straight pipes around the fitting or valve. Thus knowing

the losses in the straight pipe portions one can deduct the fitting or valve loss.

This investigation adopted the hydraulic grade line approach because the experimental

loop used was specially designed to accommodate this approach.

The technique for the determination of the valve pressure drop by the hydraulic grade line

approach is explained in Figure 2.8 below and will be explained in detail later in chapter

4 (4.4.1).



Dis tanc e [rn]

Figure 2. 8 Diagram illustrating the calculation ofvalve loss coefficient

On a graph, static pressure (P) vs. axial distance (X) points of coordinates (Pi, Xi) are

plotted from the experimental data. For the two pipes upstream and downstream of the

test valve, the curves of static pressure drops follow a linear law and are straight lines.

The coordinates of the point upstream of the test valve plane which is the y- axis in this

case, are used to calculate, by linear regression the slope m\ and intercept 11 of the line

upstream of the valve. The coordinates of the points downstream of the valve are used to

calculate also by linear regression, the slope m, and intercept h of the line downstream of

the valve.

In the case of valves, the pipes upstream and downstream of the test valve have the same

diameters, the two hydraulic grade lines upstream and downstream of the test valve are

parallel, m\ and rn, are equal and the pressure drop due to the test valve is given by:

L'.Pv = I, - 12 (2.58)

And using equation (2.51):



Equivalent length

k = Llpvv 1I2pV2

k = (11 - 12 )

v 1 V 2~p

2

2.35

(2.59)

(2.60)

Alternatively, the valve loss coefficient can be expressed in terms of the equivalent length

of straight pipe of the same diameter and having the same loss as the valve. The

equivalent length is expressed in numbers of pipe diameters, (LelD) and is obtained by

equating the Darcy-Weisbach formula, equation (2.9) to equation (2.51):

(~) = ~i (2.61)

The drawback ofthis method is the fact that the equivalent length for a given fitting is not

constant, but depends on Reynolds number and roughness, as well as size and geometry.

Therefore, the use of equivalent length method requires consideration of all these factors

(Hooper, 1981).

It has been shown using dimensional analysis that kv for incompressible Newtonian fluids

is a dimensionless function of Re and of dimensionless geometric ratios characteristic of

the valve (Turian et al., 1997):

kv = fu (Re, geometric ratios) (2.62)

This relation suggests that the resistance coefficient is the same for all sizes of a given

type of valve provided dynamic similarity is enforced for instance equality of Reynolds

number and geometric similarity are maintained (Turian et a!., 1997).

2.6.4.3 Flow Coefficient

In some branches of the valve industry, particularly for control valves, the capacity of the

valve is expressed in terms ofa flow coefficient.



(2.63)

However there is no agreement on the definition of a flow coefficient in terms of SI units.

In the USA and UK the flow coefficient in use is designated by C v•lve and in other

European countries by KvaJve and are defined as:

CvaJve is the rate of flow of water, in either US or UK gallons per minute, at 60°F, at a

pressure drop of one pound per square inch across the valve.

K vaJve is the rate of flow of water in cubic metres per hour at a pressure drop of one

kilogram force per square centimetre across the valve (Crane Co., 1981).

CvoIve =0.0694 Q lP(p) (in US gallons)V~

where:

Q is the flow rate in litres per min.

p is the density ofthe fluid in kg/m3

~p is pressure gradient in bar.

It must be said that C vaJve is generally a fixed value for a specific type and size of a valve

regardless of the operating conditions. In practice however this is true in the turbulent

flow regime only where kv is not a function ofReynolds number (JadaIlah, 1980).

2.6.4.4 Previous work on losses in valves

Substantial work has been done on the prediction of minor losses in pipe systems. In this

section a brief review of work relevant to this investigation is presented. The different

types of valves tested found in the literature are presented in Table 2.2 and for diaphragm

valves in turbulent flow in Table 2.3.

The work of Edwards et al. (1985), Banerjee et al. (1994), and Turian et al. (1978), are

all based on gate and globe valves not on diaphragm valves. They are relevant to this

work by their methodology and mode ofpresentation ofresults.

• Edwards et al., (1985), tested a range of Newtonian and non-Newtonian fluid flow

through gate, and globe valves of25 and 50 millimetres fully opened. They found that

it is possible to present the data as a relationship between the loss coefficient and a

generalised ReynoldS number. They observed that in the laminar flow region, the loss

coefficient is inversely proportional to the Reynolds number and can be obtained as:



k = Cvv Re

2.37

(2.64)

(2.65)

This is the same as equation (2.56). At higher Reynolds numbers a rapid transition is

observed to a region in which the loss coefficient becomes constant, at about

Re=130. In the case of gate valves, for various test fluids and for the two sizes used,

the data falls together, and the analysis of experimental data gave the correlation:

k = 273v Re

For globe valves the data for the two dimensions do not fall together. The transition

from laminar flow is very rapid and occurs at a Iow Reynolds number of about 10.

For the particular design of globe valves tested, in the fully open position, the

following correlations were obtained:

For 25 millimetres valve: Re < 12

k = 1460v Re

Re> 12 kv = 122

For a 50 millimetres valve: Re < 15

k = 384v Re

Re> 15 kv=25.4

(2.66)

(2.67)

(2.68)

(2.69)

• BaneJjee et al., (1994), presented experimental data on the pressure drop across 12.5

millimetres globe and gate valves in the horizontal plane for pseudoplastic fluids in

laminar flow. They used generalised correlations in terms of various physical and

dynamic variables for the prediction of the frictional pressure drop for each valve.

lbree effects were studied:

I. The effect of pressure drop across the valve by plotting static pressure against

length for a designated fluid.

2. The effect of the valve opening on pressure drop across the valve by plotting

pressure drop against volumetric flow rate at different opening position: The

pressure drop increases with an increase in volumetric flow rate for a constant

opening. As the opening became smaller, the curve became steeper.



3. The effect of the non-Newtonian characteristics on pressure across the valves by

plotting pressure drop across the valve against the volumetric flow rate for

different concentration of slurries. At a particular opening of the valve, the

pressure drop decreases as the flow behaviour index increases.

The dimensional analysis of the experimental data, suggested the following

relationship:

Ap-2 =f(Re,a)pV

(2.70)

(2.71)

The functional relationships developed using the above equation through

multivariable linear regression analysis were as follows:

Correlation for globe valve:

Ap = 8.266Re-o.061±O.013a-O.797±O.OJOpV2

After plotting this the values of AP2 predicted using the equation above and thepV

experimental values, the correlation coefficient and variance of estimate are

0.9496 and 1.326 xlO-2•

Correlation for gate valve:

AP2 = 1.905Re-O.197±0046a -I.987±O.091pV

(2.72)

After plotting this the values of AP2 predicted using the equation above and thepV

experimental values, the correlation coefficient and variance of estimate are

0.9344 and 1.106 xlO-2•

• Turian et aI., (1997), determined losses for the flow of concentrated slurries of laterite

and gypsum solutions through 25 and 50 millimetres globe and gate valves. The loss

coefficients were found to be inversely proportional to the generalised Reynolds

number for larninar flow and to approach constant asymptotic values for turbulent

flow, through gate and globe valves,



The following correlations were obtained:

For the 25 millimetres gate valve the transition from laminar to turbulent flow was

observed between Re=IOO and Re=IOOO and kv=3201Re and after the transition, in

turbulent flow, kv=O,797.

For the 50 millimetres gate valve the transition from laminar to turbulent flow was

observed between Re=1000 and Re=10000 and kv=3201Re for the laminar region and

after the transition, in turbulent flow, kv=0,168.

For the 25 millimetres globe valve, the transition from laminar to turbulent flow was

observed earlier for Re<IOO and the correlation obtained was kv=1O,039 for turbulent

flow.

For the 50 millimetres globe valve also the transition was observed earlier for Re<1 00

and the correlation obtained was kv=6,7I9.

• Hooper, (1981) using the two-K method defmed a dimensionless factor K, as the

excess head loss in a pipe fitting, expressed in velocity heads. K does not depend on the

roughness of the fitting (or attached pipe) or the size of the system, but is a function of the

ReynoIds number and the exact geometry of the fitting and is given by:

K =~+K~(l+~J (2.73)ReMR D

where: K1is K for the fitting at Rl:MR=I,K~ is K for a large fitting at Rl:MR= 00 and D the

pipe internal diameter. He found that: KI = 1000 and K~ = 2 for a dam or weir type

diaphragm valve. Doing the analogy with the definition in this study, it can be said that

Cv =1000 and kv=2.

• Pienaar et al., (2004) tested a 40 mm nominal bore diameter diaphragm valve over a

Reynolds number range of I to 50000 using various Newtonian and non-Newtonian fluids

and obtained Cv=IOOO and kv=2.5.

• Miller, (1978) classified the valve loss coefficients in three classes:



Class 1 or def"mitive loss coefficients: Loss coefficients in this class are based on

experimental data usually from two or more sources or from research programmes, which

- have been crosschecked against other work. The loss coefficients are considered

definitive.

In practice the loss coefficients in class 1 are usually not directly applicable, because of

the severe restraints imposed on inlet and outlet conditions and geometrical accuracy

Class 2 or adequate loss coefficient for design purposes: Experimentally derived loss

coefficients from isolated research programmes where no detailed crosschecking is

possible against other sources.

Estimated loss coefficients from two or more research programmes whose results do not

agree with what could be expected to be the experimental accuracy

Loss coefficients from class I converted to apply outside the strict limitations imposed in

class 1 coefficients and for which experimental information is available to predict the

effects ofdeparting from class I conditions.

Class 3 or suggested loss coefficient: Experimentally derived values from less reliable

sources

Loss coefficients from class I and 2 converted to apply outside their range of application

and about which there is little or no information to predict the effects of departing from

the conditions under which they were derived.

Loss coefficients in diaphragm valves are classified as class 3 and are given in turbulent

flow; these loss coefficients can be obtained from the figure below for both weir and

straight through diaphragm valves (Figure 2.9)

In fully open position in turbulent flow, the loss coefficient is approximately 0.8 for the

straight-through diaphragm valve.



lOO F"--CC--,---,---------,.,o=--------,

50r--;T+----!

10~

E 5~

·C

""~cu::;0 LO.....

tJ.5

0.1 L.k!~~~~klL____'L__J __~o 0.2 OA 0.6 O.ll LO

CI-(.)sed Valve opening ()pen

Figure 2. 9 Loss coefficient vs. valve opening (Miller, 1978)

Table 2. 2 Valves (pienaar et al., 2001)

TYPE SIZE [mm] REFERENCE Cv

25 Turian et aI., 1998

50 Turian et al., 1998 320

25 Edwards et aI., 1985 273

Gate 50 Edwards et aI., 1985 273

25 Turian et al., 1998

50 Turian et al., 1998

25 Edwards et al., 1985 1460

Globe 50 Edwards et aI., 1985 384

3-way plug - Steffe et aI., 1984

Check valves

Ball

Horizontal lift

Bronze disc swing Kiuredge & Rowley,

Composition disc swing 12.5 1957

Diaphragm - Hooper,1981 1000

.

2.41



Table 2. 3 Loss coefficients for turbulent flow through diaphragm valves (Perry

& Chilton, 1973)

Operating mode Loss coefficient, k,

Open 2.3

% open 2.6

~open 4.3

Y-open 21



2.7 DYNAMIC SIMILARITY

2.43

In this section, the theory related to the establishment of dynamic similarity and its

~ application to the flow ofnon-Newtonian fluids flow in valves is presented.

2.7.1 Geometric Similarity

Geometric similarity is similarity of shape (Massey, 1970) and is the fust requirement for

the establishment ofphysical similarity. If two systems are geometrically similar the ratio

of any length in one system to the corresponding length in the other system is everywhere

the same and this ratio is called the scale factor.

Geometric similarity exists between a model and a prototype if the ratios of all

corresponding dimensions in model and prototype are equal (Giles, 1977):

Lmodel

Lprototype

or L m =LL r

p

(2.74)

2.7.2 Kinematic Similarity

and Amodel _ L~odel

Aprototype L~rototype(2.75)

Kinematic sim.iIarity is similarity of motion (Massey, 1970). This implies first, geometric

similarity and then similarity of time intervals in the motion.

Kinematic similarity exists between a model and a prototype if the paths of homologous

moving particles are geometrically similar and if the ratios of the velocities of

homologous particles are equal (Giles, 1977):

Velocity ratio: (2.76)


(2.77)

DMKazadi


. . Q L3 rr l'Discharge ratio: ~~ m m ~ ,

Qp L3prrp L,

2.7.3 Dynamic Similarity

2.44

(2.78)

Dynamic similarity is similarity of forces (Massey, 1970). Dynamic similarity exists

between geometrically and kinematically similar systems if the ratios of all homogenous

forces in model and prototype are the same.

In the case of a fluid flowing in a closed conduit, as in this investigation, in a pipe, the

dominant forces are the viscous and inertial forces, other forces like the pressure force,

the surface tension force are negligible and do not affect the flow.

The only interesting ratio in this case is the ratio:

Inertial force

Viscous force~ pVI which for a Newtouian pipe flow is the Reynolds number Re and

I!

is in this case, equation (2.12):

Re=pVD

I!(2.12)

Thus two flows passing geometrically similar boundaries are dynamically similar if the

only forces affecting those flows are only viscous, pressure and inertia forces, if the

magnitude. ratio of inertia and viscous forces at corresponding points are the same. Since

this ratio is proportional to the Reynolds number, two systems are dynamically similar

when the Reynolds number of the two systems based on corresponding characteristic

lengths and velocity are the same for the two flows (Massey, 1978).

2.7.4 The Application of Dynamic similarity for Non-Newtonian Fluid Flowsin Valves

If only one kind of forces are dominant, apart from inertia and pressure forces, then

complete dynamic similarity is achieved simply by making the values of the appropriate

dimensionless parameter the same for model and prototype, in this case the Reynolds

number (Massey, 1978).



For the case of a Newtonian fluid, the Reynolds number is easily obtained and is used to

establish dynamic similarity, but for non-Newtonian fluids, the task is not simple because

: of other parameters like the yield stress and the rheogram curvature, which must be well

established.

For the flow of non-Newtonian fluids in valves, viscous forces are dominant and forces

due to weight and surface tension do not play a role. The dimensionless group known as

the Reynolds number is of prime importance and two systems are dynamically similar if

their Reynolds numbers are the same. Unlike the Newtonian model, where the rheology

is characterised by only one parameter the viscosity, the non-Newtonian model is

characterised by three parameters: the yield stress, the fluid consistency index and the

flow behaviour index. The Slatter Reynolds number accounts specifically for the yield

stress together with the other two parameters and can be used to establish dynamic

similarity (Slatter & Pienaar, 1999).

To conclude, two non-Newtonian flows in geometrically similar valves are similar if their

Slatter Reynolds numbers are the same.

As said earlier, the first requirement for physical similarity is geometric similarity, thus

this similarity establishment will be carried on the same type of valves from the same

manufacturer otherwise it will be meaningless (Slatter & Pienaar, 1999).

2.8 CONCLUSION

Far from being comprehensive, this chapter attempts to present the necessary theory on

Newtonian and non-Newtonian fluid flow in straight pipes, pipe fittings and valves, but

with an emphasis onnon-Newtonian materials flowing in valves especially in diaphragm

valves.

From the literature review, it was found that data on diaphragm valves are scarce. Perry

& Chilton (1973) give some values of the loss coefficient in diaphragm valves for

Newtonian fluids in turbulent flow. Miller (1978) gives a graph of kv vs opening of the

valve for the determination of an approximate loss coefficient in turbulent flow. Hooper

(1981) presents loss coefficient data for a dam or weir type diaphragm valve in the

laminar and turbulent flow regimes. Pienaar et al. (2004) present data for one size

diaphragm valve in both laminar and turbulent flow.



As said earlier, the work ofEdwards et af. (1985), BaneIjee et al. (1994), and Turian et

~ al. (1978), are all based on gate and globe valves, not on diaphragm valves. However,

they are relevant to this work by their methodology and mode ofpresentation ofresults.

2.9 RESEARCH ASPECT IDENTIFIED

After the completion of the literature review it has been obvious that there is a need for

much more data on loss coefficients through diaphragm valves for both Newtonian and

non-Newtonian fluids and there is also a need to evaluate existing data. Data on

diaphragm valves are scarce and are only approximations. Hooper (1981); Miller (1978)

and Perry & Chilton (1973) give the loss coefficient without specifYing the dimension of

the valve. Hooper (1981) gives the larninar loss coefficient Cv and the loss coefficient in

turbnlent flow. Perry & Chilton (1973) and Miller (1978) give only the loss coefficient in

turbulent flow for Newtonian fluids. Miller classifies loss coefficients in diaphragm

valves as class 3 data, i.e. data from less reliable sources. Data from other type of valves

has been converted to apply to diaphragm valves and about which there is little or no

information to predict the effects of departing from the conditions under which they were

derived (Miller, 1978).

It also became apparent that there is a need to define experimental procedures in the

determination of loss coefficients in valves because the value of the loss coefficient is

dependent on the experimental procedure used and definitions (Chhabra & Slatter, 2002).


Chapter 3: Experimental work

CHAPTER 3EXPERIMENTAL WORK

3.1 INTRODUCTION

3.1

This chapter describes the experimental test loop. It also provides an in-depth geometric

analysis of the type of diaphragm valve tested. The description and calibration of the

instrumentation used in the test work, the experimental procedure of the test work, the

description of all materials tested and the general theory on errors are also given. Raw

results from experimental tests are also presented.

The experimental test loop used is the new Valve test rig. After the construction of the

test loop and the calibration of the different instrumentations, commissioning was

successfully done by running water tests in all the pipes, followed by tests with non

Newtonian slurries.

3.2 DESCRIPTION OF THE TEST LOOP

The test loop used is the new state-of-the-art Valve test rig. The Valve test rig is 22m

long and 2,6m high. It consists of a storage and mixing tank of 1,75 m3 with a header or

weigh tank of 500 litres on top. The fluid is forced in the test loop by a positive

displacement pump. Before reaching the test sections, the fluid passes a surge damper,

then through a heat exchanger. The fluid passes through two magnetic flow meters in

parallel; one for the lines of 50 and 63 millimetre outside diameters and the other one for

the lines of 75, 90 and 11 0 millimetre outside diameters. The test section consists of 6

lines of 50, 63, 75, 90 and twollD millimetre outside diameters respectively. At every

entry of a test line there is a diaphragm control valve to direct the fluid. The fluid exits all

test lines through a manifold. For each test line there are two pipes of 10 metres long

joined in series by a diaphragm valve. Figure 3.1 gives a schematic diagram of the Valve

test rig.


~Z"~S.§

b'"'"Dl

tCl

f~Dl

Cl~

[

r' i

..' 42.12 mm ID pipe .. '.. 40 mm Diaphragm valve ...11"" ...-"" ~

..'52.8 mm ID pipe ... '.. 50 mm Diaphragm valve ..,.

: ~ 60 mm Diaphragm valve...-.. h~ rlR mm mninl' IlL,. ... ... JP"

.", ~ Rn lI.~ mm m 1'111'1'" • .. Rn mm n; ~f\h"'~/m1 U~ lUll •,.. po ... ,..-

.. '99.11 mm iD pipe ~ ' .. 100 mm Diaohramn valve ~,. ...-"" ..

~~ONE ..'97.17 mm ID pipe ~ --' 100 mm Diaphragm valve

~,'. mete 11"" ...-"" ,.. ...-

11!~~ 1< WeightIh'

~ ••~ SAFMAG • l' tank

I'·cmFlow meterMixingLTank

Heat exchanger PDPump

I:>' I--C) ('--'F'" I •..

.....•..,. '.• ',',

Figure 3. 1 Schematic diagram of the Valve test rig

Q~(iw

f~.[

!

wN


3.3 INSTRUMENTATION

3.3

This section describes the instruments connected to the test loop when running different

~ tests in order to collect experimental data.

3.3.1 Pipes and Valves

The pipes used for the test loop were all PVC pipes clear or non-clear with negligible

roughness.

The valves used for determining the loss coefficient are the NATCO straight-through

diaphragm valves of40, 50, 65, 80 and 100 millimetre nominal bore diameter and are low

resistance valves.

Table 3.1 gives the outside diameters (OD) or nominal diameter of the six test lines and

their internal diameters (ID) as were determined experimentally. The experimental

method for the determination of ID is explained later in this Chapter 3 (3.5.12.1).

Table 3.1 Nominal and internal dimension of pipes and valves.

Outside Diameter Internal Diameter Valve DimensionTest Line Number [mm] [mm] [mm]

I (Top) 50 42.12 40

2 (2nd Top) 63 52.8 50

3 (3rd Top) 75 63.08 65

4 (4th Top) 90 80.43 80

5 (2nd Bottom) 110 99.11 lOO6 (Bottom) 110 97.17 lOO

Figure 3.2 gives an external view of the diaphragm valve used and Fig.3.3 shows the way

these diaphragm valves were connected to pipes, Fig.3.4 shows the internal structure of

the diaphragm valves at the fully open position.



Figure 3. 2 Diaphragm valve

Figure 3. 3 Connection of diaphragm valves with pipes.

3.4



Figure 3. 4 Internal structure of the valve in the fully open position.

3.5

The diaphragm valves tested are also characterised by some internal dimensions

characteristics that are: Cross section dimensions (Width & Depth), Diaphragm

dimension (Height, width, Per rev) and bore dimension (A, B and C.). Figure 3.5 gives

such approximate dimensions for an 80 = nominal bore diameter diaphragm valve. The

diaphragm valve manufacturer supplied the information given in Table 3.2 and Figure

3.5. It is obvious that the dimensions are not always exactly the same for each nominal

bore size valve. They are within a certain tolerance as specified by the manufacturer.


Chapter 3: Experimental work 3.6

Width

Internal dimensiolls of the bore

1 Rev=5mm

112mmWidth

A 40mm

~ ~ :, ~E: ~~ -§ •

~......Cross sectIOnal areaof flow through valve

A 40mm,

Diaphragm dimnsioDS

Figure 3. 5 Internal dimension of the 80 mm nominal bore diaphragm valve.

Table 3.2 gives such dimensions (in mm) for all 5 sizes of diaphragm valve tested and

Table 3.3 gives such dimensions for all 5 sizes in a dimensionless form, dividing all

dimensions ofa given valve by the nominal bore size.

Table 3. 2 Internal dimensions of diaphragm valves tested

Bore size Cross section area Diaphragm Dimension Bore dimensionDepth Width Height Width Per Rev A B C

40 35.26 42.78 36.00 47.38 3.00 26.18 45.02 65.3450 46.65 64.26. 47.00 66.34 4.50 36.26 66.71 81.0065 62.42 90.82 63.00 92.14 5.00 40.00 88.00 125.0080 68.92 112.00 69.00 114.20 5.70 42.26 111.00 140.50100 74.72 124.46 75.00 129.92 6.50 - 62.14 128.00 150.40

Table 3.3 Dimensionless Internal dimensions of diaphragm valves tested

Bore size Cross section area Diaphragm Dimension Bore dimension

Depth Width Height Width Per Rev A B C1 0.88 1.07 0.90 1.18 0:08 0.65 1.13 1.631 0.93 1.29 0.94 1.33 0.09 0.73 1.33 1.621 0.96 1.40 0.97 1.42 0.08 0.62 1.35 1.921 0.86 1.40 0.86 1.43 0.07 0.53 1.39 1.761 0.75 1.24 0.75 1.30 0.07 0.62 1.28 1.50



From these data, a geometric similarity analysis was done based on the fact that

geometric similarity exist between a model and a prototype if the ratios of all

"': corresponding dimensions in model and prototype are equal:

L model

L prototype

L ratio (2.74)

Taking every size as a prototype and comparing with all other sizes and also by analysing

the dimensionless sizes of the diaphragm valves tested, it was found that no geometric

similarity could be observed between the 5 sizes of diaphragm valves used.

From Fig.3.4, it can be observed that the type of diaphragm valves used has a tapered or

narrowed bore through the body of the valve. The full bore opening is characterised by an

obstruction of the diaphragm through the opening and the size of the obstruction varies

from size to size and is respectively 4.74, 3.35, 2.58, 11.03,25.28 millimetres for the 40,

50,65,80 and 100 millimetres bore nominal diameter. And the scale factor of the height

of the obstruction on the nominal bore diameter is 0.12, 0.067, 0.04, 0.14, 0.25 for the 40,

50, 65, 80 and 100 millimetres bore nominal diameter. Once again, no geometric

similarity was found. All dimensions above mentioned are tabulated in Table 3.4.

Table 3.4 Obstruction size and scale ration for the diaphragm valves tested

Bore size Obstruction size Obstruction/Bore size

40 4.74 0.12

50 3.32 0.0765 2.58 0.04

80 11.03 0.14

100 25.28 0.25



3.3.2 Pressure lines, pressure lines board, tappings and pods

Nylon tubes of 3 mm internal diameter were used as pressure lines. They were connected

- to the test section by tappings via pods and the pressure lines board (PLB) to pressure

transducers.

Each test line had tappings at various positions from which the experimenter could

choose according to the type of the experimental test to be run.

The pressure line board (PLB) as designed by the author of this investigation, IS a

hydraulic circuit that allows to select points where the static pressure can be read off. It is

also used to set the technique to be used while running the experimental tests. As it will

be explained later in this chapter there were six techniques using the PLB and the nine

point pressure transducers and two differential pressure transducers to run experimental

tests on the Valve test rig: automatic mode (AM), manual single (MS), manual all (MA),

American standard method (ASM), straight pipe test (SPT), HGL DP Cell mode. The

PLB is a very useful tool and consists of a circuit of nylon tubes and ball valves on a

perspex board. The nylon tubes are classified in four pressure lines (PU, 2, 3 and 4) and

the ball valves in: deviation valves (D), isolation valves (I), exit valves (E), bypass valves

(B) and connecting valves (C). Deviation valves allow to isolate the PLB and to work in

automatic mode with all the pressure transducers at the same time. The isolation valves

allow to separate two or more given tappings from other tappings. The exit valves allow

to isolate a given tapping from the other tappings. The bypass valves allow to isolate a

pressure line and the Connecting valves allow to connect a given PL to a pressure

transducer. Figure 3.6 gives a schematic diagram of the pressure lines board and Figure

3.7 gives the connection of the PLB (the rectangular central part) to the test line and to

pressure transducers.



lJ J2

".Ic: 1'£4

]}

c-' t· 7

Bl B2

F'L -4PL-] t-k,in \./0 t~(

'::1..Ipply,-----JI-----(1''----.----

F'L-2PL-l

&3 P4

Bc,

F'L; F't-~5~Ut''''' Lir'~5

D: De,j·)+j·:.r. \-',:,1,,'0'::E: E·it '·i""I·.,.",,:=:I; Is,:,I-:,tj(d,'/.:,I .. ",-s

B' £/1=");:= ,/,)I,,.-::=:1_ ((ll,,(,o:,:+il-I';J'.:,I ;.,:s

Figure 3. 6 Schematic diagram of the pressure lines board

I 4 5 , 8 9

'---- -

jrl , ,/ I PLB 11 \ Moir-,

W'oter; ,\ :;UPI=·ly

/ ,I I

./ / I,

I/ I \

",;/,, \

t(l\\I

'I (7) ('l \ ('I

b E f J J JIJ

Figure 3. 7 Connection of the PLB (the rectangular central part) to pods and

pressure transducers.



3.3.3 Pressure Transducers

Two kinds ofpressure transducers were used:

- a) The Point Pressure Transducer (pPT): It is used to measure static pressure at a given

point in the test line.

b) The Differential Pressure Transducer (DP Cell): It is used to measure the difference

of static pressure between two points.

At the time of the completion of this investigation, the Valve test rig had nine PPT and

two DP Cells in operation. The nine PPT's have a range span of 130 kPa and are mostly

used to run the tests in: automatic mode, manual mode, manual mode all. The two DP

Cells, has the range span of 130 kPa and 6 kPa respectively. They are mostly used to run

test in the HGL DP cell mode, Straight pipe test and American standard Method. These

pressure transducers are connected to the PLB by means of nylon tubes as shown in

Figure 3.7 and to the data acquisition unit (DAD) by means of electrical cables.

Included in Appendix I is a picture of the pressure transducers used (point pressure

transducer and differential pressure transducer).

3.3.4 The Hand Held Communicator

The type of hand held communicator (HHC) used is the FXW 10 AYI- A3. It is a

portable instrument with many features and is used for the zeroing, calibration, change of

unit, range setting, span and damping time setting of both the differential pressure

transducer (DPT or DP Cell) and the point pressure transducer (pPT). The hand held

communicator is also a display unit of pressure transducers and the two instruments are

twins as one cannot be used successfully without the other.

Included in Appendix 1 is shown the picture of the hand held communicator.

3.3.5 The data acquisition unit or data logger

The data acquisition unit used is the model HP 34970A, which is equipped with many

channels and it converts electrical signals from pressure transducers, temperature sensors,

flow meters and load cell connected to it into digital signals that are logged to the

computer.



Included in Appendix 1 is the picture of the Data Acquisition Unit.

3.3.6 Computer and Software

3.11

A Celeron 300 was used for data capturing and processing. Test programs were written in

Visual Basic 6. The data capturing, analysis and processing was done in Microsoft Excel.

3.3.7 Flow meters

Two magnetic flow meters were used during test work and they were both mounted

vertically:

• A Krohne IFC OlOD of50 millimetre internal diameter

• A Safmag 100A2NESSR0032 of 110 millimetre internal diameter.

Include in Appendix 1is the pictures of the flow meters.

3.3.8 Tank and Mixer

The 1.75 m3 storage tank was fitted with a mixer of the type SEW EURODRIVE ARF 57

DT 90L4 with power of 3 kW. It also has on top a header or weight tank of 500 litre

capacity for the calibration of flow meters and flow rate determination in the flow region

where the flow meter reading becomes inaccurate.

Included in Appendix I is the picture of the mixing tank and the weight tank on top.

3.3.9 Pump

The pump used is an Orbit reversible positive displacement pump of the type B400l Cl

EN8 NIT with a power of 5,5 kW, with a helical rotor. This pump is fitted with a variable

speed drive, which allows shifting the speed of rotation of the pump rotor.

Included in Appendix 1 is the picture of the Pump used.

3.3.10 Manometers

Two U-tube manometers were used for calibration ofthe pressure transducers:

-A mercury- water manometer was used for the calibration ofhigher pressure ranges.

-A water air manometer was used to calibrate lower pressure ranges.



3.3.11 Pressure Gauges

Digital pressure gauges were used mostly to verifY the pressure readings of the hand held

- communicator and that of the computer programme output after the calibration

coefficients have been included.

3.3.12 Temperature probes

The temperature of the slurry was measured at two positions in the Valve test rig using

temperature probes. The first position was: at the end of the heat exchanger and the

second at the mainstream flow exit. Both temperature probes were linked to the data

acquisition unit that reads the temperature in degrees Celsius. As the data acquisition

reads the temperature directly, no signal calibration was required.

3.4 EXPERIMENTAL PROCEDURE

3.4.1 Calibration

The calibration of the instruments was done for two major reasons: firstly in order to get

reliable results and secondly in order to transform the electrical signal from the

instruments in a digital signal to be read to the computer workstation. The computer

program needs some calibration constants called signal calibration.

3.4.1.1 DP Cells

Two DP Cells were used during the test works. One of the range span of 130 kPa and

another of the range span of 6 kPa.

The calibration of the differential pressure transducers was done in the following manner:

-Prior to everything, the DP Cell is manually zeroed and than electronically zeroed with

the Hand Held Communicator when there is no external pressure applied to both sides of

the DP Cell.

-Than the DP Cell is connected to the manometer so that the high and low sides are

respectively connected to the high and low side ofthe V-tube manometer



-All the air bubbles are flushed from the lines using the main water supply connected to

pressure lines of the DP Cell.

-A differential pressure within the range limit is set up in the V-tube manometer.

-The differential pressure is read digitally using the Hand Held Communicator at the

same time the DP Cell DC voltage output is read from the Data logger.

-The differential pressure is than decreased uniformly in 5 parts and the previous step is

repeated until the equilibrium is attained.

The calibration line is obtained by performing a linear regression on the pressure

difference and the transducer DC voltage output. The coefficient of correlation R2 should

be at least 0.999. Figure 3.8 shows an example of the calibration regression lines of the

DP cell of 6 kPa span range for two ranges.

y =2S0.27x - 242.64

R'= 1

_e--oE)_0- --E>--

,= IS04.8x - 1496.8

R2 =O.9999

1 234Voltage (V)

5 6

<> 6 kPa range

-Linear (6 kPa range)

o 1 kPa range

- -Linear (1 kPa range)

Figure 3. 8 Calibration regression lines of the DP cell of 6kPa span range

showing calibration regression lines for 0-6kPa range and O-lkPa range

3.4.1.2 Point pressure transducer

The calibration of the Point Pressure Transducer was done in the same way as for the DP

Cell described above with the only difference being that the pressure line of the PPT was

connected to the high side of the V-tube manometer. The differential pressure was read

between the higher meniscus and the centre line of the PPT. Figure 3.9 gives an example



of the calibration line of a PPT of 130 kPa in the range of 0 to 40kPa. Table 3.3 gives the

calibration constants for different transducers.

"""",,--

4 4.S3.5

y = 9950x - 9980

R2= 1

z1.505

oJ-----~~-_--_-_-- --_··-·__·_o

moo

sooo

~30000

boO=25000."«f" 20000..=~~

~ 15000Q"

Ii:Q" '0000

Voltage[VI

o Volt vs kPa - Linear CVolt vs kPa)

Figure 3. 9 Calibration regression line of a Point pressure transducer of 130 kPa



Table 3. 3 Calibration constants for different transducers

PPT RANGE Ax B R2

1 0-40 10010.35x -10046 10-130 32476.02x -32544 1

2 0-40 9950.038x -9980 10-130 32382x -32498 1

3 0-40 9986.15x -9996.4 10-130 32783.99x -32303 1

4 0-40 9990.15x -9994.7 10-130 32419x -32478 1

5 0-40 9962.22x -10046 1

0-130 32413.23x -32484 1

6 0-40 9975.65x -9985.6 1

0-130 32435x -32475 1

7 0-40 9973.85x -9987.4 1

0-130 32542.59x -32542 1

8 0-40 9971.99x -10002 1

0-130 32422.77x -32516 1

9 0-40 9987.98x -9992.4 1

0-130 32457.46x -32422 1

3.4.1.3 Load Cell

3.15

The load cell that supports the header or weigh tank is depicted in Appendix 1. It is used

to weigh the fluid diverted from the mainstream flow. To calibrate it, the fluid is weighed

in a container using an electronic scale. The fluid is then poured in the weigh tank, and the

container is weighed again to take the difference in masses. Once the difference in mass

between the container with fluid and the empty container is taken, the voltage output is

recorded. For every increase in load, the increase in voltage is recorded.

The recorded values of the increase in load are plotted against the recorded values of the

corresponding voltage as shown in Figure 3.10. A linear regression of the plot will give



the relationship between the load and the corresponding voltage. This is then entered in

the program to be used to calculate the flow rate.

y = 40043x - 80.718

R2= 0.9994

500

450

400

350

300

:§~ 250~

";:;200

150

100

50

00 0.002 0.004 0.006 0.008

Voltage [mY10.01 0.012 0.014

o Mass vs Voltage - Linear regression line

Figure 3. 10 Calibration regression line of Load Cell

3.4.1.4 Flow meter

The materials tested vary in chemical composition and concentration, so each material is

tested over the flow rates used by diverting the flow into the weigh tank. The flow meters

that measure the flow rates are, according to the manufacturers, accurate for slurries. To

confirm this, each flow meter is calibrated with each slurry concentration that will be

tested.

The calibration procedure is as follows:



For each flow meter the flow rate range is divided into 12 different flow rates over the

whole range that the flow meter can measure. Each flow rate is then weighed with time in

- the weigh tank. The data logger continuously samples the change in weight with time, and

from these readings the average flow rate is calculated. The sampling period varies from

120 s for Iow flow rates to 12 s for the high flow rates. 1bis is repeated for all the flow

rates.

The flow rates versus voItages are then plotted and the straight-line regression gives the

relationship between flow rate and volts as well as the error fit. Figure 3.11 gives a typical

calibration regression line for a flow meter.

3.5~-------------------------~

3

2.5

0.5

y ~ 0.7454x - 0.7405R2 = I

6543

Voltage [mltl

2o+----_---_---_---~,,_------_1

o

Figure 3. 11 Calibration regression line for the Krohne flow meter



3.4.2 Experimental Test Method (Valve Pressure Drop Test and Straight PipeTest or Tube Viscometry)

The valve test rig is a versatile instrument and is a miniature pipeline. Two principal

types of tests may be conducted on the valve test rig: the viscometry test or straight pipe

test and the valve pressure drop test. These tests may be conducted simultaneously or

separately.

The rheology or straight pipe test consists of measuring the pressure drop in the straight

pipe sections at different flow rates whereas the valve pressure drop test consists of

measuring the pressure drop incurred by the test valve at different flow rates.

Generally, there are two approaches to measure the valve pressure drop: The hydraulic

grade line (HGL) approach and the total pressure drop approach. In the context of this

investigation, as said earlier, the hydraulic grade line approach was used. Because the

valve test rig was specially designed for that approach. This approach can be applied in

an automatic mode or a manual mode depending on flow conditions as follows:

In automatic mode, all the pressure readings are taken simultaneously using all the nine

transducers and every transducer reads a pressure on one tapping.

The HGL automatic mode is selected when the static pressure in the test section is high

enough so that different PPT's can measure accurately the pressure gradient along the test

section. This condition is likely to happen when testing small diameters (50, 63 and 75

millimetres OD) or bigger diameters at higher flow rates (90, 11°millimetres OD) or

testing very dense materials.

The HGL manual mode is the technique in which, one transducer is used to read the static

pressure drop at each tapping at a time and this technique is facilitated by the PLB. This

technique is selected when the pressure drops between different pressure tapings on the

test section are small and can be measured accurately by one Point Pressure Transducer

(PPT) at a time. This condition is likely to occur when testing bigger pipes (90 and 110

millimetres OD) or very light materials.

DP Cell mode: this mode is also manual and consists of measuring the HGL but using a

DP Cell this mode is also applicable on bigger pipes. Using the PLB, the high side of the

DP Cell is connected to the fIrst pod and the low side to the other pods, one by one. The

DP Cell mode is also used for the straight pipe test or rheology test.



The American standard method (ASM): this method uses two DP cells at the same time

to measure pressure gradients between 10 diameters and 20 diameters upstream and

downstream ofthe valve.

The HGL automatic and ASM may be conducted by one operator whereas the HGL

manual and the DP Cell mode require at least two operators.

The operating procedures of the modes cited above are explained in the sections below.

3.4.2.1 Main stream flow



2A

2R

2e2D

2E2F

,....I......r-F:I:::::j....,,·low meters

3.20

1R Test valves

I....------&EI----I.------------<:I====:IlA

Figure 3. 12 Over view ofthe Valve test- rig direction valves. Valves (1&2) are

on-off valves to direct the mainstream flow

3.4.2.2 HGL automatic mode

The automatic mode on the Valve test rig is achieved by setting the ball valves on the

Pressure Lines Board (Figure 3.6) as follows:

The exit valves: El, E2, E3, E4, ES, E6, E7, E8 and E9 are closed. The deviation valves:

Dl,D2, D3, D4, DS, D6, D7, D8 and D9 are opened. The pressures coming from all nine

tappings and pods are directed straight to the PPT.

In this mode the static pressures are read for all the tapping points simultaneously to

obtain the pressure gradient upstream and downstream the test valve.

3.4.2.3 HGL manual mode

The manual mode on the Valve test rig can be conducted by using only one PPT:

• On the PLB (Figure 3.6), the exit valves: Elis open to read the pressure on taping 1

• E2 to E9 are closed.



• The deviation valves: Dlto D9 are closed. The isolation valves (ll, 12 Band 14) are

also open

• The by-pass ball valves (BI, B2, B3, B4, BSand B6) are closed, also closed are all the

connecting ball valves C except Cl.

• CI is connected to a pressure transducer.

• Take the reading.

• Close valve El and open E2

• Read the pressure, close E2 and open E3

• Continue this procedure until valve E9 is open.

3.4.2.4 DP Cell mode

This procedure is used in three ways:

• The straight pipe test

• The hydraulic grade line and

• The American standard method

3.4.2.4.1 Straight pipe test

The straight pipe test can be done simultaneously downstream and upstream of the test

valve and the procedure is as follows.

1.. Choose the straight pipe sections in which the pressure drop will be measured,

upstream and downstream of the test valve and record the tapping distance

respectively.

2. On the pressure lines board (Figure 3.6) close the isolating valve II (or 12),13 and 14

(or IS)

3. Open the valves E according to the test sections chosen, deviation valves D and other

E must be closed

4. Close the bypass valve B2, B4, BS and B6

S. Use the pressure lines PL-I and PL-2 to measure the pressure drop upstream of the

test valve by opening the connecting valves Cl and C2



6. Ensure that the pressure line PL-I is connected to the high side of the DP Cell and

PL-2 to the low side of the DP-Cell

7. Use the pressure lines PL-3 and PL-4 to measure the pressure drop downstream of the

test valve by opening the connecting valves C3 and C4.

8. Ensure that the pressure line PL-3 is connected to the High side of the DP Cell and

PL-4 to the Low side of the DP Cell.

3.4.2.4.2 The hydraulic grade line

The HGL in this case is done using a DP Cell by isolating the first pod from the others

and by opening the pods (pressure tappings) one after another and recording the pressure

gradient. The procedure is the same as the straight pipe test described above up to step 8

then proceeds:

9. Open the isolating valve I3

10. Open the respectively E2, take the reading, close E2 and open E3 and continue up to

E9

11. Change the flow rate and repeat step la.

3.4.2.5 The American standard method

3.2 D

!OD 10D 10D laD

L1PI L1PI I I L1P2 L1P2

C 0 V b c

/ "I_Mv ·1-r "'\

\"'3.1 D)

Figure 3. 13 DP Cells position in the American Standard Method



In this procedure two DP Cells are used. The DP Cells are connected as shown in Figure

3.13. The tapping points for the first DP Cell are placed respectively at IOD upstream and

downstream of the test valve and the tapping points for the second DP Cell are placed

respectively 20D upstream and downstream from the test valve.

The procedure is the same as the straight pipe test described earlier.

3.5 EXPERIMENTAL ERRORS

Absolute accuracy in measuring or counting does not always happen, unless the data are

discrete numbers. It is important to be able to determine the margins of error which may

be found in a set of data and to know how they are affected by various arithmetic

processes such as addition, multiplication, root extraction, etc.

3.5.1 Error Theory

There are three types of error: Gross errors, systematic errors and random errors.

3.5.2 Gross Errors

Gross errors are due to blunders, equipment failure, and power failure. A gross error is

immediate cause for rejection of a measurement (Benzinger & Aksay, 1999)

3.5.3 Systematic or Cumulative Errors

Systematic errors result in a constant bias in an experimental measurement. Systematic

errors are those that are due to known conditions. These conditions might be:

• Natural (temperature, pressure, humidity, etc.)

• Instrumental (calibration, graduation, range, etc.)

• Personal (poor sight of the experimenter, inability of the experimenter to take correct

reading, etc.) size (Barry, 1991).

In this work, systematic errors are not taken into account. Precautions were taken to

prevent these errors from occurring: e.g. checking the calibration of instruments by

another instrument not related to the instrument in use or independent calibration and also

by checking the reproducibility of results.



3.5.4 Random Errors

3.24

Random errors are those that are due to chance variation. Most experiments proceed with

minor variations that change from event to event and follow no systematic trend. The

same quantity may be measured many times, giving close but not identical results. The

fluctuations in the measurement are assumed to be random and lead to a distribution of

values.

3.5.5 Precision and Accuracy

Precision and accuracy are terms that refer to the quality of data.

Accuracy distinguishes systematic errors, highly accurate measurements have minimal

systematic error (Benziger & Aksay, 1999).

Precision distinguishes random errors. Precision is a gauge of the variation of repeated

measurements. Precise measurements have minimal random error.

3.5.6 Evaluation of Errors

3.5.6.1 Single error: absolute and relative error

The absolute error is the difference between the true value of any number or quantity and

the value obtained or used for that number or quantity in a given circumstance. If the true

value of a number or quantity is X, the value obtained or used for that number or quantity

is A, and the absolute error is M then:

X=A±M (3.1)

This means that X is comprised between A-M and A+M. M is called the maximum

error or absolute error. If X is a quantity, M is expressed-in the same unit. M is here

the smallest division of the instrument, the smallest value detected by the instrument

(Barry, 1991). M is calculated from the standard deviation of a set of repeated

measurements as well. The absolute error for A at 99,9% confidence interval is given by

the equation:

M =3,29u (3.2)

If a 95% confidence level is considered, then the absolute error may be approximated by:



M=2u

The relative or percentage error of a number or quantity is calculated by:

i3A = !':>.AA

3.5.6.2 Combined errors

3.25

(3.3)

(3.4)

When a variable is a result of a computation of other variables with their subsequent

errors, the resulting error is the combination of the independent variable errors (mean

quadratic value of the independents errors). If a variable X is a function of n other

variables i.e., X=F (a, b, c...n), the expected highest error (Brinckworth, 1968) can be

calculated from:

(3.5)

Where X is the computed result

!':>.X is the computed result absolute error

n are the independent variables involved

!':>.n are the independent variables absolute errors.

3.5.7 Error in Measurable Variables

3.5.8 Axial Distance

The axial distances or tapping point distances are measured using a measuring tape

graduated in millimetres. The absolute error of the measurement is 0,001 m.

3.5.9 Weight

The weights of all the samples were measured using the balance in gramme. The absolute

error on measurements is 0,001 kg.



3.5.10 Flow Rate

3.26

The flow meters used are accurate to 0,001 lis, which can be assumed as absolute error.

3.5.11 Pressure

The pressure transducers used are accurate at 0,25%. Care should be taken in calibration

so that a correlation coefficient must be 0,999. Such calibration can rise to an average

error of 0,35% (Baudouin, 2003).

3.5.12 Error in derived variables

In this section the different equations used in the determination of all derived variables

are given. The application of the equation (3.5) to all the equations is also given.

3.5.12.1 Pipe internal diameter

The pipe internal diameter was determined weighing a mass of water (MHO) in to a,

D=

known length ofpipe (L). The pipe diameter is then calculated using the formula:

4MHO, (3.6)

The highest expected error in calculating the pipe diameter is obtained by applying the

equation (3.5) to equation (3.6) and that yields:

8D =±~ (8MH,o)2 +(8L)2D 2 MH ° L,

(3.7)

The highest expected error and experimental errors on the measurements of the five

diameters of the valve test rig is given in the Table 3.4:



Table 3. 4 Expected Highest errors and experimental errors in the

measurements ofthe Valve test- rig pipe diameters

3.27

Pipe Nominal Diameter OD Mass-average Length Highest Expected ExperimentalIposition [mm! [kp] [m';;1 Error [%1 Error 1%1

Top 50 0.0421 1000 2.38 0.632nd Top 63 0.0528 1000 1.90 0.323rd Top 75 0.0631 1000 1.59 0.454th Top 90 0.0804 1000 1.25 0.22

2'"Bottom 110 0.0991 1000 1.01 0.36

Bottom 110 0.0972 1000 1.03 0.37

3.5.12.2 Velocity

The velocity in a pipe is detennined from the continuity equation (2.11):

QV=

A

Qand A are respectively, the flow rate and the cross section area of the pipe.

The application of equation (3.6) to equation (3.11) yields the highest expected error on

the velocity given by:

3.5.12.3 Pseudo shear rate

The pseudo shear rate is detennined using the relation (2.43):

. 8Vr'=j)

(3.8)

The application of equation (3.5) to (2.43) gives the expected highest error of the pseudo

shear rate and it yields:


(3.9)

DMKazadi


3.5.12.4 Wall shear stress

3.28

The shear stress is determined from the relation (2.8):

i1PD1: =--

o 4L

The application of equation (3.5) to (2.8) gives the expected highest error of the shear

stress and that yields:

(3.10)

3.5.12.5 Viscosity

The rheological characterisation was done most of the time with a correlation coefficient

of at least 99%. Thus the error in viscosity or other rheological parameters did not exceed

1%.

3.5.12.6 Reynolds number

The Reynolds numbers errors in this work are evaluated on the Newtonian Reynolds

number Re equation (2.12):

Re= pYD

!!

Application of equation (3.6) to (2.12) yield:

(3.11)

3.5.12.7 The valve loss coefficient

The valve loss coefficient is obtained from the equation (2.51):y 2

Hy =k y -

2g



or the pressure loss due to a valve is related to the head loss by:

then:

k = L'.Py

v 1 V'-p2

3.29

(3.12)

In order to determine different quantities entering in the determination of experimental

errors, valve pressure drop tests for clear water were run in the Valve test rig, for all the

five pipe diameters. The technique consisted of keeping the output of the pump constant

and taking 100 runs reading. The data was analysed statistically by determining the

following quantities: mean value, average deviation, spread, median value. Equations

(3.2) and (3.3) were used to calculate the absolute error and Equation (3.4) to calculate

the relative error. For the variables: velocity, pseudo shear rate, shear stress, Reynolds

number, valve loss coefficient and valve pressure drop (My.).

From the data above mentioned can then be calculated the highest expected errors of each

of the above variables mentioned using equations (3.8) to (3.12) and the actual errors of

the valve test rig. The highest expected errors and actual errors of the valve test rig are

given in tables 3.5, 3.6, 3.7 and 3.8.

Figure 3.14 illustrates the variation ofnormalised principal tests parameters for the line of

42.12 mm diameter.

On the x-axis is the name of the test and on the y-axis every parameter divided by its

average value for the test described above. It can be seen that the wall shear stress and

the valve loss coefficient present bigger variations than other parameters and eventually

bigger errors.

In Tables 3.5, 3.6, 3.7, and 3.8, all the errors are calculated at 99% confidence level.

These errors give the degree of confidence of a variable, the smaller the error, the more

precise is the variable and the bigger the error, the less precise is the variable.



" ..* x' '", x

X .. , ' "X ~ ~:. : X.XX

1.5

1.4 x'xx ' ,

1.3"

," X # " X

1.2 ",,X x ~, X " x~X,·X .. ~, ". ,' .. X " " ...

1.1

0.9 X Xx:0.8 x

0.7

0.6w ~ ID - ~ _ ~ - ~ - ID W ~ W ID

_ _ N N M M V V ~ ~ ~ W ~ ~ ro 00 m m

Data

--Reynold numbers- + - flow rate- -e - wall shear rate

-0-- Loss coefficients--* --Wall shear stress

Figure 3.14 Comparison of variation of principal parameters ofthe Valve test

rig

Non-Newtonian Losses Through Diaphragm Valves OM Kazadi

~p,

fe.g;t;~(Il

ICl~..g

ff

ClE::

~~~.

Table 3.5 Highest expected error in measurable variables of the Valve test rig:

...... .... , ,.... .•..i OD ID Average Velocity (V) Pseudo shear rate, 8VID Wall Shear Stree('c" ) Reynolds number (Re)

, [mmJ Imm] [115 ] [s'}1 [PaJ -i 50 42 1.895 1.997 11.802 1.549

! 63 53 0.668 0.740 0.372 0.372

i 75 63 17.557 17.562 17.539 17.539

90 BO 1.788 2.026 21.910 1.747

i 110 97 1.298 1.350 16.679 1.129

f">$"go

~~~

",L,-


Table 3. 6 Highest Expected errors of the Valve loss coefficient

Valve Dimension Loss Coefficient (kv)

[mm]

40 12.38

50 11.16

65 40.80

80 22.20

100 16.88

3.32

In Table 3.6 the diaphragm valve of 65 mm nominal bore diameter has the highest

expected error on the valve loss coefficient (kv) compared to the other valves. The

standard deviation, the spread and the average deviation of the variables studied (average

velocity (V), pseudoshear rate (8VID), wall shear stress (To) and Reynolds number (Re)

are higher than in any other line).


~p

z~i:!.§\;'enena

Io~.

.I!J

i~en

o~

~~~.

Table 3. 7 Errors ofthe Valve test rig

.... ......... , . , .....

Wall Shear Stress('t:o)OD ID Reynolds number (Re) PseudoShear Rate (8VID) Average Velocity (V)[mm] [m] . [1/BJ [m/sJ [PaJ

50 42 0.532 0,532 0.532 4578663 53 0.169 0.169 0,169 725975 63 3,016 2.894 2.871 644390 80 1.469 1469 1.469 28,810

110 97 0.766 0.791 0.791 6.900

Q.I!J~w

ig'"S-e:.

!

wWv>


Table 3.8 Errors ofthe Valve loss coefficient

Loss Coefficient (kv)

Valve Dimension Error 1%1Imml -

40 8.841

50 9.594

60 18.316

80 20.389

100 13.252

3.5.12.8 Slurry Relative Density

3.34

The Relative Density Test was done on the tested fluid by collecting a sample of the fluid

under test.

The test was performed as followed:

a) Three clean, dry volumetric flasks were weighed respectively (Mr)

b) The fluid was poured in those flasks to approximately half the volume and weighed

respectively (M2)

c) Water was added up to the graduated mark of the flasks, and weighed respectively

(M]). The flasks had to be shaken gently to remove any air bulbs.

d) The flasks were emptied and rinsed with water and alcohol to dry. Afterwards they

were filled completely with water and weighed respectively (~).

Calculations

Mass of fluid: M2-Ml

Mass of water filling the flask ~-Ml

Mass ofwater filling the space left by the fluid: M]-M2

Mass of water having a volume equal to that of the fluid (~-Ml)-(MJ-M2)

therefore:


(3.13)

DMKazadi


The arithmetic mean of the values obtained from the three flasks was taken as the actual

RD.

The mass was measured with an electronic balance accurate to ±0,001 g, which is an

absolute error of ±1 O-<i kg.

3.6 MATERIALS TESTED

3.6.1 Introduction

The different materials tested were: water, glycerine, CMC and kaolin. The materials

tested were selected in a way to represent different characteristics needed in this

investigation. Water and glycerine being Newtonian fluids and CMC and kaolin non

Newtonian fluids, with CMC presenting pseudoplastic behaviour and kaolin yield

pseudoplastic behaviour.

Fluids were selected that exhibit Newtonian, pseudoplastic and yield pseudoplastic

behaviour to demonstrate that dynamic similarity can be obtained at the same Reynolds

number provided that the Reynolds number correctly accounts for the viscous properties

of the fluid.

3.6.2 Water

Water was used as a standard liquid, to commission the experimental test loop, to

establish its credibility, accuracy and precision, because of its well-known properties and

availability.

Tap water was used in both straight pipe tests and the valve.pressure drop test (hydraulic

grade line).

The water straight pipe results were correlated to the Colebrook & White equation (2.19).

Graphs for different pipe sizes are presented in Appendix 2. Figure 3.15 gives a typical

graph in linear coordinates and Figure 3.16 in logarithmic coordinates for the pipe of

42.12 mm ID (50 mm OD).



The valve pressure drop tests were also conducted and results were compared to the

results found in the literature. These results are presented in Appendix 6. Figure 3.17

gives a typical valve pressure drop test for water.

3.503.00

.'.'

2.501.50 2.00Velocity [mfs]

1.000.50

01--:e::::::::::..--_--_--_-_-__---10.00

20.-----------------------........-..."..-_-./

/

//

//

//

//

//

//

/

"/,.-

",.-

"

15

"E=.~

~

~

<:~

~ 10=~-;;-;~

5

Collebrook White <> Experimental Data +20% Error band - - ~ - - -- 20% Error band

Figure 3.15 Comparison of water test results with Colebrook & White equation

100

"..!:!.~~..~-~..".. 0.1-=~Oi~

0.01

0.0010.00 0.01 0.10

Velocity [m's]lOO 100.00

- Colebrook White <) Experimentlll~~



Figure 3.16 Comparison of water test results with Colebrook & White equation

in double logarithmic scale

•Distance [m]

.. "

_Figure 3. 17 Typical valve pressure drop curve of water in a 40 mm Diaphragm

valve (V=1.79 m1s and Re3=75753.99)

3.6.3 Carboxyl Methyl Cellulose Solution (CMC)

The CMC used in the test work is supplied in a powder form by Protea Chemicals and is

dissolved in tap water to make a solution. CMC is widely used in industries as paper glue,

protective colloid and resin emulsion (Pienaar, 1999). The powder was slowly dissolved

in water and mechanically mixed using an agitator and care was taken to avoid the

formation of large lumps. Mass concentration of 5 and 8% were tested.

Figure 3.18 gives a typical straight pipe test for CMC and Figure 3.19 gives typical valve

pressure drop curve for CMC.



lS,-------------- ---,

3.38

Oi'e:.'"'"'" 20.....

<J1..0=

'",:::"'"--;~

10

50 100 ISO 2011 Z50 3JJJJ lSO 4IIIJ

<><>

'"

<> SOmmOD

8vm [lis]-63mmOD x7SmmOD

Figure 3. 18 Straight pipe test of CMC 5% in three pipe diameters



20000

-6 o

Distance Im]• 10 "

Figure 3. 19 Typical valve pressure drop curve of CMC 5% in a 40 mm nominal

bore Diaphragm valve (V=3.04 mls and RIlJ=O.042)

3.6.4 Kaolin Slurry

The kaolin used in the preparation of kaolin suspensions is also supplied in powder form

by Serina Kaolin (Pty) Ltd, and is mined in the Fish Hoek area near Cape Town. It is

dissolved in tap water to obtain kaolin slurries. Volumetric concentrations of 10% and

13% were tested. Table 3.9 and 3.10 give the physical and chemical properties of dry

kaolin and Figure 3.20 gives the particle size distribution (PSD) graph for kaolin powder.

Figure 3.21 gives typical straight pipe tests curve for kaolin and Figure 3.22 gives typical

valve pressure drop curve for kaolin.



Table 3. 9 Physical properties of dry kaolin

3.40

Physical Properties Typical

1 Abrasiveness (Einlehner tester) 35 glm2

2 Particle Size Distribution:

below 20 micron 100%

12 micron 94%

10 micron 90%

6 micron 80%

4 micron 70%

3 micron 60%

2 micron 48%

3 Reflectance Minimum (Elrepho) 83%

4 pH Value 5

5 Residue (Screen 45 um) MaxO,20%

6 Specific gravity of kaolin mineral 2,60

7 Moisture:

Powder 0-1%

Pellets 8 -12%

8 Oil absorption of powder 45 - 50%

9 Bulk density ofpowder in bags 0,7g1cc

Table 3. 10 Chemical properties of dry kaolin.

Chemical Analysis Typical %

Si02 46,00%

Ah03 38,00%

FeZ03 0,85%

TiOz 0,58%

CaO 0,10%

MgO 0,18%

KzO 1,00%

NaJO 0,20%

L.O.I. 13,10%



100 -,--------------?O--------,

~ 90Sc:~ 80...'"c:.'" 70.::-'"'3 608c:U 50

40 -1-------------.,-------------11 10

Particle size lm m]

1--<>- Particle Size Distribution 1

100

Figure 3. 20 Particle Size Distribution (PSD) Graph for kaolin powder



"r-----------------------~

"-Ii 15 1

~ i'"

3.42

'00 "" ""SVID (lis)

300 "" .. ""

o 50 mm OD -63mmOD :I( 75 ID

Figure 3. 21 Straight pipe test for kaolin 10% in three pipes diameters.



'"~ 50000

'"...=.,.,'"...p.,

'":;:: 30000eo-00

20000

10000

o 2

Distance [m]• 6 • 10

3.43

"

Figure 3. 22 Typical valve pressure drop curve of kaolin 13% in a 6S mm

Diaphragm valve (V=O.029m1s and RC]=4.30)

3.7 CONCLUSION

In this chapter the experimental test loop, the valve test rig, has been described.

The diaphragm valve used has also been analysed and it has been established that there

are no geometric similarities among the 5 sizes of the diaphragm valve tested.

Experimental procedures (calibration and experimental tests procedures) have been

explained.

Experimental errors have been quantified.

The materials tested have been described and raw experimental tests results of these

materials have been presented and will be analysed in the next chapter.

Water test results in straight pipes have been correlated to the Colebrook & White

equation and are within 20% error limits.

In conclusion, the valve test rig has been shown to be a reliable tool for valve pressure

drop tests and for tube viscometry.


Chapter 4:Analysis of results

. CHAPTER 4ANALYSIS OF RESULTS

4.1 INTRODUCTION

4.1

In this chapter, the analysis of experimental results is explained and presented: This

includes the rheological characterisation of materials tested and the presentation of loss

coefficients in laminar, transitional and turbulent flow regimes. The study of the effect of

the choice of the Reynolds number on the loss coefficient is also done.


Two types of materials were tested: Newtonian fluids and non-Newtonian fluids. In this

section, the determination ofrheological parameters of these materials is presented.

In this investigation, rheological characterisation was done using tube viscometry. The

effect of entrance and exit losses during tube viscometry was avoided by doing the

straight pipe test in the region of fully developed flow (50 diameters after the entrance

and 50 diameters after the test valve). The wall slip was evaluated by doing straight pipe

test in pipes of three different diameters and the no-slip condition was confirmed.

4.2.1 Newtonian fluids

Newtonian materials tested were: water, 100% and 75% volume concentrations of

glycerine.

The Newtonian model fitting was done to determine the viscosity of the two

concentrations of glycerine.

The flow curve of a NeWtonian fluid is a straight line and -the slope of the straight line

gives the viscosity of the fluid: Considering the laminar flow data ('to, 8VID) of the fluid

through a straight pipe, using excel, a straight line trend passing through the origin is

fitted and the slope of the straight line gives the Newtonian viscosity of the fluid IlN.

An example of such a fit ( Figure 4.1) gives the flow curve of glycerine 100%. Table 4.1

and Table 4.2 gives the properties of glycerine 100% and 75% tested.


Chapter 4:Analysis of results 4.2

120 l

100

'"=. 80'"'".....-00

60...'"..-=00- 40'"~

20

00 20 40 60 80

y = 0.8434x

R2= 0.9997

100 120 140

Pseudo-shear Rate, 8Vm [lis]

I 0 Experimental data -Linear (Experimental data) I

Figure 4.1 Flow curve of Glycerine 100% at an average temperature of21 °C

Table 4. 1 Properties of glycerine 100% tested

Date fl [Pa.s] R2 Density [kg/m3] Temperature [0C]

2311 112004 0.842 1 1270 21

2411 112004 0.843 0.9997 1270 - 20

25111/2004 0.844 0.9977 1270 20


Chapter 4:Analysis ofresults

Table 4. 2 Properties of glycerine 75% tested

Date f![Pa.sl R2 Density [kg/m3] Temperature [OC]

01/12/2004 0.0196 0.7639 1197.2 2130/11/2004 0.0184 0.9041 1197.2 22

4.2.2 Non-Newtonian fluids

4.3

Non-Newtonian materials tested were: 10% and 13% volumetric concentrations of

kaolin, 5% and 8% mass concentration of CMC.

All concentration of CMC were characterised as pseudoplastic fluids and those of kaolin

as yield pseudoplastic fluids. The Rabinowitsch-Mooney method was not used for

rheological characterisation for non-Newtonian fluids in this work. In this work, an in

depth investigation on the calculation of n' and K' was done. It was observed that when

using the classical method of calculating n' by fitting a polynomial equation to the double

logarithmic plot of 1:0 vs. 8Vm, if the multiple regression correlation coefficient (R2) of

the fit is between 1 and 0.98 the percentage error was acceptable. Below 0.98, the error

increased, resulting in higher errors for the calculation of the true shear rate using the

Rabinowitch-Mooney relation. An equation was derived for calculating K' and n' for

yield pseudoplastic fluids. The derivation is given in Appendix 5.

4.2.2.1 Fitting the pseudoplastic model

All concentrations of CMC were characterised as pseudoplastic fluids: The laminar data

from a straight pipe test were plotted on linear scale and using excel, a power law trend

curve was fitted to the data to give the constant n' (apparent flow behaviour index) and

K' (apparent fluid consistency index) because for non-Newtonian fluids:

(2.23)

To obtain n, for a Pseudoplastic fluid: n = n' and


(2.27)

DMKazadi

Chapter 4:Analysis ofresults 4.4

Figure 4.2 gives an example of a fit of the pseudoplastic model for a CMC 5% solution

based on three pipes tested on the same day confirming that no slip existed at the pipe

wall. Table 4.3 and Table 4.4 gives the properties of CMC 5% and CMC 8% tested. It is

clear that the fluid behaviour changed daily and the rheology was tested each day and

used for calculations. Using the rheology of the previous day could lead to errors on the

f-Re graph of up to 6 % in the calculation of the friction factor (f). The reason for

changes in the rheology did not form part of this investigation. An effort was however

made to accurately account for the changes.

~ 35co

C:!. 30'" 25'""..... 2000...

15co" .--= 1000.- 5..~ 0

o 100 200 300 400 500

Pseudo shear rate 8Vm [lis]

! 0 42.10 mm ID • 52.8 mm ID X 63.08 mm ID -Power law model I

Figure 4. 2 Flow curve of CMC 5%

Table 4. 3 Fluid properties of CMC 5% tested

10291028.2

3/11/2004 1024 0.442 0.67 0.9937

Table 4. 4 Fluid properties of CMC 8% tested


Chapter 4:AnaIysis ofresults

DensityDate (kg/m3

] K n R2

5/11/2004 1040 5.252 0.799 0.9976

9/11/2004 1037.5 5.252 0.790 0.9667

11/1112004 1040 6.434 0.503 0.9948

12/11/2004 1040 5.908 0.799 0.9984

4.2.2.2 Fitting the Yield Pseudop1astic model

4.5

All kaolin suspension concentrations were characterised as yield pseudoplastic fluids.

The method ofcharacterisation was explained in chapter 2 (2.4).

Figure 4.3 gives an example of a flow curve of a kaolin suspension of 10%. Table 4.5

and Table 4.6 gives the properties of kaolin 10% and kaolin 13% tested. E in Tables 4.5

and Table 4.6 is the root mean square error of the fit function and is given by equation

2.47.



70

60 v ~

~ 50

~Q

~

~ Q Q

'" X'"" 40...-m...~

" 30-=m-';~

20 I10 ~

I0

0 100 200 300 400 500

Nominal Shear Rate 8V/D lis

• Experimental Data - Yield Pseudoplastic model Fittingl> 42.12 mm ID x 52.8 mm ID

Figur~ 4. 3 Flow curve of kaolin 13 %

Table 4. 5 Fluids properties of Kaolin 10% tested

DensityK [Pa.s'"[kg/m3

] <. [Pal n E

1172.4 10.7 2.2 0.32 11.30

1163.4 9.4 2.2 0.32.

8.46

Table 4. 6 Fluids properties of Kaolin 13% tested

DensityK [Pa.s'"[kg/m3

] <. [PaJ n E

1214 35 0.8 0.5 2.48

1214 30 1.37 0.5 9.25

4.6



4.3 FLOW IN STRAIGHT PIPES

4.7

In the laminar flow regime, in straight pipes, the well-known f - Re relation relates the

friction factor f and the Reynolds number:

For Newtonian fluids:

For non-Newtonian fluids:

and

f=~Re

f=~Re MR

f = 2 To = D L'1ppV2 2 pV2L

(2.18)

(2.45)

(2.10)

In this investigation, experimental results for straight pipe sections for both Newtonian

and non-Newtonian fluids were obtained from the same experiments from which the data

for the valve loss coefficient was obtained.

Because the Slatter Reynolds number takes into account the yield stress and can

accommodate any rheological model, this Reynolds number was used in the relation f-Re

(2.18) and (2.45)

A plot of the Fanning friction factor (t) against the Slatter Reynolds number (Re)) for

both the Newtonian and non-Newtonian fluids tested is shown in Figure 4.4. In Figure

4.4 it can be observed that the experimental results of this work, fall within ±200/0 of the

calculated theoretical line.



1000 -,-------------------,

.-

10000 100000100 1000Re3

10

10

0.1

100

0.01"~

0.001 +,---.--------.-----.-----.-------.---"-·.::.---"10.1 1

'- 1

16IRe3o Glycerine 75%o Kaolin 10%

-20%

xBlasius equationCMC5%Kaolin 13%

• Glycerine 100%x CMC8%

- - - 20%

Figure 4. 4 Comparison of experimental values of the friction factor in laminar

flow for different fluids in straight pipe of diameter 42.12 mm ID pipe.

(2.20)

Such an agreement indicates the validity and degree of accuracy of the experimental

technique and equipment used in this investigation and was used as the fIrst criteria in the

validation of experimental results.

In the turbulent flow regime, in straight pipes, the well-known BIasius equation relates

the friction factor f and the Reynolds number:

f = 0.079(Re)025



In this case also the Slatter Reynolds number was used. This also gives a first good

degree of validity of experimental results in turbulent flow. For water in turbulent flow in

straight pipes, as said in chapter 3, the experimental data were compared with the

Colebrook &White equation:

1 _ -41 [k 1,26 ]Jf - og 3,7D + ReJf (2.19)

It must be noted that for Newtonian fluids the Slatter Reynolds number reverts to the

Newtonian Reynolds number and that was observed during calculations made on the

experimental results on Newtonian fluids.

4.4 LOSS COEFFICIENTS

4.4.1 Procedure for calculating the valve loss coefficient

The following steps were followed in the calculation of the valve loss coefficient as

illustrated on Figure 2.8 (After the establishment of the appropriate f-Re relationship as

defined above):

• Measurement of static pressures at different points upstream and down stream ofthe

test valve (In total 9 points were used, 4 points upstream and 5 points downstream of

the test valve)

• Calculation of the shear stress in the two pipes upstream and downstream of the test

valve in regions of fully developed flow (50 diameters of the entrance length of the pipe

upstream the test valve and 50 diameters of the exit length of the pipe downstream the

test valve), 6 points were used to calculate the shear stress, 3 points upstream and 3.

points downstream respectively of the test valve, all in regions of fully developed flow

as defined above. The 3 points close to the test valve, I point upstream and 2 points

downstream were discarded because they are in the region of influence of the fitting

(valve). The shear stress in the two pipes upstream and downstream is calculated using

the following equation:

~pD"[ =--

o 4L


(2.8)

DMKazadi


• The friction factor was calculated using the relation:

f = 2'0py2

In laminar flow, the above friction factor was compared to:

f=~Re

and in turbulent flow to the Blasius equation:

f= 0.079(Re)025

4.10

(2.10)

(2.18)

(2.20)

• The valve pressure loss is obtained as an extrapolation to the test valve plane of the

pressure gradients measured in the fully developed flow regions upstream and

downstream of the test valve. The slope and intercept upstream and downstream of the

test valve (in the regions of fully developed flow) are calculated (in this case using

Excel). Six points were used to calculate the slopes and intercepts, 3 points upstream

and 3 points downstream respectively of the test valve, all in the region of fully

developed flow as explained above. It must be established that the slopes upstream

(SUS or ml) and downstream (SDS or mz) are parallel, thus the difference of the

intercepts upstream (illS or 11) and downstream (IDS or Iz) yields the pressure drop due

to the valve (6.pv):

~pv = I, - 12 (2.58)

The slopes ml and mz can be visually parallel but there is always a percentage error

difference involved (%Error = m, - m2 *100 ) and it was observed that for a percentageID,

error of up to 20 %, the slopes IDt and IDZ were still parallel and that was retained as a

cut-off value. For errors greater than 20% negative pressure drop were observed in

extreme cases. The percentage error in this case varies from materials to materials for

fluids like CMC and glycerine the percentage error was always less than 10%. For water

and kaolin this was not always the case and one had to be careful when observing the

data because many points deviated from 20% and had to be discarded.

Non-Newtonian Losses Through Diaphragm Yalves DMKazadi


• Calculation of the valve loss coefficient from the relation:

k = i1pvv 1 V2-p

2

which yields:

k = (I, -12)v I V 2-p

2

4.11

(2.59)

(2.60)

Distance [m]

Figure 2. 10 Diagram illustrating the calculation of valve loss coefficient



4.4.2 Graphical presentation of the valve loss coefficient k vversus Reynoldsnumber

It is customary in fluid mechanics to represent experimental data of loss coefficient on a

graph kv versus Reynolds number (Edwards et al., 1985; Turian et aI., 1997; Pienaar,

1998).

In this investigation, the Slatter Reynolds number (Re3) is used to make such

representation. It was very difficult to identitY the transition by deviation for the

diaphragm valves. The intersection method was therefore used to obtain the point of

transition.

4.4.2.1 Diaphragm Valve of 40 millimetres nominal bore diameter

For the 40 millimetres diaphragm valve the loss coefficient in larninar flow Cv = 1200. In

turbulent flow the loss coefficient is constant and an average of kv= 7.96 (0.226 standard

deviation) was calculated. The range of Reynolds numbers is between I and 100000.

The transition by intersection of the 1arninar and turbulent loci is calculated at Re:; =

150.75. The loss coefficient data are presented in Figure 4.5.

4.4.2.2 Diaphragm valve of SO millimetres nominal bore diameter


turbulent flow the loss coefficient is constant and an average of kv=2.53 (0.209 standard

deviation) was calculated. The range of Reynolds numbers is between I and 100000.

The transition by intersection of the larninar and turbulent loci is calculated at Re3 =

373.9. The loss coefficient data are presented in Figure 4.6.

Non-Newtonian Losses Through Diaphragm Valves OM Kazadi

Z na ::r'::l

~Z 10000 ....<1l<1l ....

~ .l>-a [S.§ kv =1200/Res '<:t""' '"~.a '"'" 1000 a'"<1l .....,'" Ci1

~ '"aaa g-a

c§. _\ 8 '"

9.1 ~ 100

{I I J:",:z..x..R A

-<

~I 10 1 - -y

~ .....~-aa

a

a

I1

0.1 1 10 100 Re3 1000 10000 100000 1000000

C' 0 Kaolin 10% • Water A Kaolin 13%~ • CMC5% • CMC8% • Glycerine 100%~ c Glycerine 75% - - kv average turb --kvCalc

l I~Fie:ure 4. 5 Loss coefficient I,v vs Reynolds number for 40 millimetres bore diameter diaphrae:m valve

z0I:l

Z 10000"g0e.

()

§ 1000=946fRe3

I:l"

t""'

.§

0

...

en

~

en

"X

"'"

en

~100 2

i

'"'§.

en

~

Vi'

t:J10

0

~.

......

.§

rl

B"

enE.

CS

0

[;j

1-<

0.:g .....

~

. _.:~ .....

8~~

"en 0.1

8ot:g

0

10000010000100010010O01 ' ,

• I I I I I i

1

Re3

~

[• Watero Glycerine 75%

A Kaolin 13%"o Kaolin 10%

x CMC 5%--kvCalc

l CMC 8% • Glycerine 100%'"- - kv average turb

:l>o-"'"Figure 4.6 Loss coefficient kv vs. Reynolds number for SO millimetres bore diameter diaphragm valve


4.4.2.3 Diaphragm valve of 6S millimetres nominal bore diameter

4.15

For the 65 millimetres diaphragm valve the loss coefficient in laminar flow Cv = 555. In

turbulent flow the loss coefficient is constant and an average ofkv=1.21(0.121 standard

deviation) was calculated. The range of Reynolds numbers is between 1 and 100000.

The intersection of the laminar and turbulent loci is calculated at Re3 = 633. The loss

coefficient data are presented in Figure 4.7.

4.4.2.4 Diaphragm valve of 80 millimetres nominal bore diameter

For the 80 millimetres diaphragm valve the loss coefficient in larninar flow Cv = 515.14. I


deviation) was calculated. The range ofReynolds numbers is between 0.1 and 100000.

The intersection of the laminar and turbulent loci is calculated at Re3 = 202.76. The loss


4.4.2.5 Diaphragm valve of 100 millimetres nominal bore diameter



deviation) was calculated. The range of Reynolds numbers is between 0.05 and 100000.

The intersection of the laminar and turbulent loci is calculated at Re3= 53. The loss



10000 I iI~s.§

S'enen~

It:l~.

{~~en

1000

100

~ 10

0.1

xkv=7661Re3

x

lI! xx

":B~ - .u\.. -•

f~

~';:;i~.

eng,

i

0.01 I I I i I i I

10 100 1000 10000 100000 1000000

Figure 4. 7 Loss coefficient I,v vs. Reynolds number for 65 millimetres bore diameter diaphragm valve

t:l3::

[

o Kaolin 10%x CMC 5%o Glycerine75%

• Waterx CMC 8%

--kvCalc

A Kaolin13%• Glycerine 100%

- - kv average turb

;I'>~

0\

Q~

~

"'"[~~.

'"g,

i-,'0.-.i5lg IJQb----

•00A A

••

k.,=515IRe3

•

10 100 1000Re3

10000 100000 1000000

• Kaolin 10%

• Glycerine 100%

+ Water

IJ Glycerine 75%

A Kaolin 13%

--kvCalc

• CMC 5%

- - kv average turb

• CMC 8%

Figure 4. 8 Loss coefficient ky vs. Reynolds number for 80 millimetres bore diameter diaphragm valvet:I~

[ ;l'>--...l

10000 i I

zgZ~8.§t'"'o~I1ltIl

Io~.

I<:~~

]

1000

100

10

0,1

x=691ReJ

~

~ x,:,- i.. ~~~~~ ~~~,~x ~~~ ~ 'tl 'l'X

" )(.x, "~ ~ ~ ~ li· x .K- _... x•.) )(.X~.' <;-• ' ... "-'0= ,/IX X 0• I '. ~.~ ..... x

o •x ~ 0

~ ••~ x.

~..!~-

Q>§(i

i~.

tIlo......ii

~

~

1000000100000100001000100100.10.01 I I i i X i I I i I

0,01

Re3

Figure 4. 9 Loss coefficient kv vs Reynolds number for 100 millimetres bore diameters diaphragm valve

~

[• WaterIJ Glycerine 75%

• CMC5%o Kaolin 10%

~ CMC 8%kvCalc

• Glycerine 100%- - kv avera,ge turb

:I"00


Table 4. 7 Summary of Cv and kvvalues obtained in this work

Valve dimension[mm] Cv kv

40 1200 7.96

50 946 2.5365 555 1.2180 515 2.54100 69 1.30

4.19

4.5 EFFECT OF REYNOLDS NUMBER ON THE VALVE LOSS COEFFICIENT

In this analysis, other Reynolds numbers are used to predict the laminar loss coefficient

and to predict the larninar-turbulent transition in valves for individual fluids of given

characteristics. The Reynolds numbers used are the Newtonian Reynolds number and the

Metzner and Reed generalised Reynolds number. The results are than compared to the

results obtained using the Slatter Reynolds number.

The Newtonian Reynolds number is generally used when the fluid has Newtonian

behaviour and the Metzner and Reed generalised Reynolds number is used for fluids

exhibiting non-Newtonian behaviour especially pseudoplastic fluids.

In comparison with the Slatter Reynolds number (Re}), the Newtonian Reynolds number

gives the same result as Re} and the prediction of the larninar loss coefficient and the

transition region, using the two Reynolds numbers is the same and that was experienced

with"water, 75 and 100% Glycerine. In this case the Slatter Reynolds number reverts to

the Newtonian Reynolds number.

In the case of the Metzner and Reed generalised Reynolds number, this Reynolds number

was used for pseudoplastic fluids and yield pseudoplastic fluids using relations (2.27) and

(2.31) and 2.32) in section 2.3.7.2. For pseudoplastic fluids, the Metzner and Reed

generalised Reyno1ds number predicts a lower loss coefficient than the Slatter Reynolds

number and even the transition using the Metzner and Reed generalised Reynolds number

is earlier than the transition predicted using the Slatter Reynolds number. This is

illustrated on the FigA.1 0 for the loss coefficient of a 5% CMC solution in a diaphragm

valve of 50 millimetres nominal bore diameter.



From Figure 4.10 the difference between the prediction of the laminar valve loss

coefficient (Cv) and the transition from laminar to turbulent flow values, is 10.89%

greater when the Slatter Reynolds number is used than when the Metzner and Reed

generalised Reynolds number is used for this pseudoplastic material.

10000 ,-------------------------------,

1000

~ 100

10

kv=512/ReMR

kvCalc Re3

10000 100000100 1000

Re3

kvvs ReMR'kv avera e turb

•-10

kvvs Re3kvCalc ReMR- -

1-1----_---_---_----~---_-----1

0.1

Figure 4. 10 Comparison ofIoss coefficient using Re] and Re~1R for a

pseudoplastic fluid.

In the case of yield pseudoplastic fluids, the Slatter Reynolds number gives also a higher

loss coefficient than the Metzner and Reed generalised Reynolds number. The prediction

of the transition is earlier with the Metzner and Reed Reynolds number, which is

illustrated on Figure 4.11.



Figure 4.11.shows the difference in the prediction of the laminar loss coefficient. In this

case it is about 6 % greater using Slatter Reynolds number than when using the Metzner

and Reed generalised Reynolds number.

The essence of this analysis is not to determine which Reynolds number better predicts

the larninar loss coefficient or the transition, and is beyond the scope of this investigation

and could be a subject of future investigations. This analysis showed that the Slatter

Reynolds number can be used for design purposes for Newtonian, pseudoplastic and

yield pseudoplastic fluids.



10,--------------- --,

k,,=5781Re,

~

•

k. = S4S.41IReMR

100001000100

0.1 +---------.--------~-------_____j

10

Re3

)I( kvvs Re3

- - - kv Calc ReMR

• kvvsReMR

--kv Calc turb

--kv Calc Re3

Figure 4. 11 Comparison ofloss coefficient using Re] and ReMR for a yield

pseudoplastic fluid.

4.6 CONCLUSION

The rheological characterisation ofall materials tested has been presented.

Flow in straight pipes has been analysed and compared to theoretical models for friction

factors.

Loss coefficient values in laminar flow, transition and turbulent regimes have been

calculated in diaphragm valves of 40, 50, 65, 80 and 100 millimetres nominal bore

diameters.



The effect of the choice of the Reynolds number has been established and it has been

shown that the Slatter Reynolds number is a very useful tool and can be used for design

purpose when dealing with non-Newtonian material.


Chapter 5: Discussion of results

CHAPTERSDISCUSSION AND EVALUATION OF RESULTS

5.1 INTRODUCTION

In order to evaluate, the objectives of this investigation, the subject ofdiscussion are:

• The literature review

• The experimental test loop

• The experimental method

• Materials tested

• Rheological characterisation

• Loss coefficients

• Comparison with literature and originality of this work

5.2 THE LITERATURE REVIEW

5.1

An in-depth literature review has been done in this investigation from both a theoretical and

practical engineering point of view to establish the need for the investigation. Thus giving

to the reader a comprehensive overview of valves in general and diaphragm valves in

particular.

It has been established after review of the open literature that data on non-Newtonian loss

coefficients through diaphragm valves are scarce. Most of the data on non-Newtonian loss

coefficients through valves are on gate and globe valves and were only relevant to this

investigation by their methodology.

Some work on fluid flow through diaphragm valves was found in the literature, on

qualitative and quantitative analysis of Newtonian loss coefficients in diaphragm valves

(Hooper, 1981). The work of Hooper, (1981) using the two-K method defmed a

dimensionless factor K, as the excess head loss in a pipe fitting, expressed in velocity

heads.

The drawback of Hooper's work is the fact that there is no valve dimension specification,

assuming geometric similarity. This work investigated the assumption of geometric

similarity by testing several sizes ofvalves from the same manufacturer.



5.3 EXPERIMENTAL TEST LOOP

5.2

The experimental test loop used is the new state-of-the-art valve test rig. The valve test rig

was designed and built at the Cape Peninsula University of Technology. The valve test rig

has 5 diaphragm valves ranging from 40 to 100 mm nominal bore diameter. It is fitted with

multiple transducers. It can accommodate other types of valves as well as contraction and

expansions with minor modifications. From a practical point of view, viscometry tests as

well as tests for the determination of loss coefficients for many types and dimension of

valves can be performed on the valve test rig.

The Valve test rig is a plant in miniature and experimental values obtained for loss

coefficients on this test loop are reliable because it simulates what happens in industry

when a fluid is being pumped from one point to another. For that reason values obtained for

valve loss coefficients from this test loop can be used for design purposes for 100% open

NATCa diaphragm valves.

The Valve test rig as it is presently built can perform beyond its present capabilities, but is

limited by instrumentation capabilities.

5.4 PUMP AND INSTRUMENTATION

The main components of the valve test rig when running tests are the pump, the flow meters

and the pressure transducers.

The pump used is a progressive cavity positive displacement (PD) pump and the main

drawback was that the flow rate was pulsating and it could not deliver very high flow rates

due to power limitations.

The difficulties experienced on the Valve test rig were most of the time due to the limitation

of the instrumentation mentioned above: materials with low viscosities could not be tested

within a very large range of Reynolds number in bigger pipes, due to very low pressure

drops between tapping points even in small pipe diameters and could be tested only at very

high flow rates, because of the limitation of the PPT and DP Cells ranges.


Chapter 5: Discussion ofresults 5.3

Materials with very high viscosity could not be tested in smaller pipe diameters due to the

limitation of the pump power. In bigger pipe diameters where pressure drops between

tapping points were very small, the PPT and DP Cells limitation was a problem but also the

pump power not allowing to reach very high flow rates.

5.5 THE EXPERIMENTAL METHOD

The experimental method used is the hydraulic grade line approach. This method is

expensive compared to the total pressure method because of the number of pressure

transducers (in this case nine) is needed, compared to 1 differential pressure transducer in

the case of the total pressure method. The approach was used because the Valve test rig was

especially built to accommodate this method. The positive fact about this method is the fact

that the frictional losses are actually measured in the straight pipes and need not to be

estimated. In the calculation of the valve loss coefficient; it does use only the definition of

loss coefficient given by Miller (1978)(Figure 2.4).

The difficulties observed at this point were the fact that with low viscosity materials like

water, the two slopes of pressure gradients upstream and downstream the test valve in

regions of fully developed flow were not always parallel.

In some cases with very viscous materials, especially in bigger pipes, the slope of the two

pressure gradient upstream and downstream of the test valve were not always parallel and

in some cases, the intercept of the pressure gradient downstream was bigger than that of the

pressure drop gradient line upstream of the test valve. The difference in the upstream and

downstream slopes may be due to the slight differences obtained in the actual internal

diameter of the pipes during the manufacturing process.

5.6 MATERIALS TESTED

The materials tested were selected to represent different characteristics needed in this

investigation. Water and glycerine were selected as Newtonian fluids and CMC and kaolin



as non-Newtonian fluids. CMC presents pseudoplastic behaviour and kaolin yield

pseudoplastic behaviour.

Water was used to obtain very high flow rates thus very high Slatter Reynolds numbers,

Glycerine 100% was used to obtain valve loss coefficients in laminar flow for Newtonian

fluid and Glycerine 75% to obtain data for loss coefficients in the transition region and the

early turbulent flow for Newtonian fluids.

CMC and kaolin were used because of their well-known non-Newtonian rheological

behaviour, being pseudoplastic and yield pseudoplastic materials respectively. High

concentrations ensured that sufficient data could be obtained in laminar flow.


Rheological characterisation was done by tube viscometry test. Glycerine 75% and 100%

were characterised as Newtonian fluids, CMC 5% and 8% were characterised as

pseudoplastic fluids and kaolin 10 and 13% were characterised as yield pseudoplastic

fluids.

Rheological characterisation is not easy and is beyond the scope of this work and is used in

this investigation as a stepping-stone. Rheological characterisation is said to be a stepping

stone because, it is used in this case to determine rheological parameters which are used to

verifY some correlations in straight pipes (2.20) and (2.45) and not used for an in-depth

study ofrheological behaviour based on the physical or chemical basis of the slurries.

5.8 LOSS COEFFICIENTS

Loss coefficients obtained in this investigation confIrmed the general qualitative trend

given in the literature that in larninar flow the loss coefficient increases significantly with

decreasing Reynolds number and in turbulent flow, the loss coeffIcient is constant. This is

true for any type of fluid, both Newtonian or non-Newtonian.

The transition from larninar to turbulent flow by deviation, for all the valves sizes starts at

Reynolds number between 10 and 100 and confIrms the general theory that in fittings in

general and valves in particular the transition occurs earlier than in straight pipes.


Chapter 5: Discussion of results 5.5

For all the diaphragm valves diameter, the transition region where there is transition by

intersection, goes from 10 to 1000 Slatter Reynolds number and in that region the flow is

very unstable and the value of the valve loss coefficient is fluctuating.

The transition by intersection for the different valves sizes is given in Table 5.1 below.

Table 5. 1 Transition by intersection for the different valves.

Valve nominal Transition

bore diameter Reynolds

[mm] number

40 150.75

50 373.9

65 633

80 202.75

100 53

5.9 COMPARISON WITH LITERATURE AND ORIGINALITY OF THIS WORK

Values found in the literature on diaphragm valves in fully open position are as follows:

Hooper(l981): Cv=1000 and kv=2

Miller (1978): kv=0.8

Perry & Chilton (1973): kv=2.3

From the literature, it can be seen that little data on non-Newtonian and Newtonian losses

are found in the literature and these data are scattered.

The work of Hooper, Miller and Perry & Chilton do not specify the dimensions of the

diaphragm valves tested. This work investigated and addressed this issue. Table 5.2

compares values of diaphragm valve loss coefficients from the literature to this work.

A comparison of values of the valve loss coefficients of this work to that from the literature

in the turbulent region is given in Figure 5.1.



Table 5. 2 Comparison of loss coefficients of this work with literature.

5.6

Perry &This work Hooper Miller Chilton

Valve dimension[mm] Cv kv Cv kv Cv kv Cv kv

40 1200 7.96

50 946 2.53

65 555 1.21 1000 2 - 0.8 - 2.3

80 515 2.54

100 69 1.3

It can be seen that the value of the valve loss coefficient given by Rooper in laminar flow is

more or less equal to that found in this work for the valve dimension of 50 mm in laminar

flow. And Perry & Chilton's value for turbulent flow coincides with the value found in this

work for the valves of 50 and 80 mm nominal bore diameters in turbulent flow.

The value of the valve loss coefficient given by Miller in turbulent flow does not coincide

with any loss coefficient value in this work and is under predicting the loss coefficient. This

confirms the need that studies should be carried out with a range of diaphragm valves of

different sizes and that the details of the valve should be supplied together with the loss

coefficient details.



10 •

8 • ••••••• • •• hI••• ••

•1<,,~2.3 (Perry's)

~ 6

-----------

4

BD D B

1<,,9l.8 (Miller)

••••••••••••

100000 120000 140000 16000080000

Re3

600004000020000

o+---~--~--~--~--~--~--~--~

o

• 40 mm valvex 80 mm valve

D 50 mm valve:K 100 mm valve

" 65 mm valve

Figure 5. 1 Comparison of this work turbulent flow valve loss coefficients to

valve loss coefficients found in the literature

Non-Newtonian Losses Through Diaphragm Valves DMKa2adi


5.10 SIMILARITIES ANALYSIS

5.8

Although geometric similarity was not achieved for the type of valves tested, a dynamic

similarity analysis was done on experimental data obtained for the 5 valves sizes, to

establish if any analytical relationship could be established between the size of the valve

and the loss coefficients in laminar and turbulent flow regimes.

According to 2.7.4 two systems geometrically similar are dynamically similar if their

Reynolds numbers are the same. Also Turian et al., (1997) suggested that because it has

been found using dimensional analysis that kv for incompressible Newtonian fluids is a

dimensionIess function of Reynolds number (Re) and of dirnensionIess geometric ratios

characteristics of the valve:

kv=fn(Re, geometric ratios) (2.62)

Thus the valve loss coefficient kv is the same for all sizes of a given type of valve

provided dynamic similarity is enforced for instance equality of Reynolds number and

geometric similarity are maintained. Around these two assumptions above mentioned will

gravitate the similarity analysis.

As shown on Figure 5.2, for the laminar loss coefficient (Cv), there is a big variation of

the larninar valve loss coefficient as a function of the valve dimension. This variation is

almost linear, the laminar valve loss coefficient is a function of the valve size, and the

laminar valve loss coefficient increases with the decrease of size and vice versa. Figure

5.3 gives diaphragm valve loss coefficients for CMC 8% in laminar flow. But for

turbulent flow there is no big variation of valve loss coefficient with size, and the values

of valve loss coefficients are random but close beside the 40 mm valve and follow the

trend given on Figure 5.2. Figure 5.4 gives the values of different valve loss coefficient

obtained in turbulent flow

Both in turbulent and larninar flows, dynamic similarity is not achieved because of lack

of geometric similarities.

In conclusion, it has been established that dynamic similarity is not achieved with the

diaphragm valves studied as opposed to other type of valves in the literature. In general,

valves of different sizes and from different manufacturers, although apparently similar,

are not always geometrically similar. For instance, in small sizes, one valve body may be



offered with a variety of end connection sizes and in some cases a valve of one nominal

size may be available with several seat sizes. Also in this specific case of diaphragm

valves studied, dynamic similarity is not achieved as in other types of valves. This could

be due to the fact that the internal lining of the valve is in rubber and is inserted manually

compared to globe valves for example where the internal part of the valve is machined

from metal to exact repeatable dimensions.

Valve Diameter [mm]40 60 800

1400

1200

1000

800...U

600

400

200

00

20

20 40

q'.

'-'-0-"

60

.-0- ..

80

100

100

1209.00

8.00

7.00

6.00

5.00

~4.00

3.00

2.00

1.00

0.00120

Valve Diameter [mm]

1--Cv variation - , 0 - - !cv turb variation I

Figure S. 2 Variation of loss coefficient in laminar and turbulent flow

Non-Newtonian Losses Through Diaphragm Valves DMKa2adi


o. ,

• 40 mm valvex 80 mm valve-50mmCv

- - 'lOOmmCv

o 50 mm valvex 100 mm valve

65 mm Cv

t:. 65 mm valve--40mm Cv

'80 mm Cv

Figure 5. 3 Diaphragm valve loss coefficients for CMC 8% in laminar flow

• ••: ::: •• • ••tttt It:

12

10 •8

.. 6""4

2

00 20000 40000 60000 80000

Re3

100000 120000 140000 160000

[ • 40 mm valve 0 50 mm valve t:. 65 mm valve x 80 mm valve x 100 mm valve I

Figure 5. 4 Diaphragm valves loss coefficients for water in turbulent flow


Chapter 5: Discussion ofresults

5.11 CONCLUSION

5.11

It has been shown that there is lack of data on diaphragm valves in the literature and the

available data in the literature are scattered.

The experimental test loop has also been discussed and proved to be reliable and accurate.

The experimental method has been discussed and evaluated.

The instrumentation has been described and evaluated.

Materials tested have been discussed and their use justified.

The diaphragm valve loss coefficients and the rheological characterisation has been

discussed and evaluated.

A similarity analysis has been done and it has been established that dynamic similarity is

not achieved with the diaphragm valves studied and possible reasons for this were given.


Chapter 6 Contributions and reconunendations

CHAPTER 6SUMMARY, CONTRIBUTIONS AND RECOMMENDATIONS

6.1 INTRODUCTION

6.1

The literature review, the experimental method, as well as the analysis of results and

discussion and evaluation ofresults have been presented.

In this chapter the contributions of this work will be summarised and some

recommendations proposed.

6.2 SUMMARY

This investigation was concerned with the evaluation of valve loss coefficients in

diaphragm valves when non-Newtonian materials flow through the valve in laminar,

transitional and turbulent flow. Qualitative and quantitative data on non-Newtonian

losses in diaphragm valves is scarce.

An experimental test loop referred to as the Valve test rig was designed, built,

commissioned and optimised. The Valve test rig was fitted with five diaphragm valves of

40, 50, 65, 80, and 100 millimetre nominal bore diameters. Various Newtonian (water

and glycerine) and non-Newtonian fluids (CMC and kaolin slurries of various

concentrations) were rheologically characterised and the valve loss coefficients were

determined using the HGL approach.

The results were presented as plots of valve loss coefficient versus Reynolds number.

Loss coefficients for laminar, transitional and turbulent flow were determined for all five

valves.


Chapter 6 Contributions and recommendations

63 CONTRIBUTIONS

6.2

The present investigation has confirmed the general theory on valve loss coefficients in

laminar, transitional and turbulent flow and in particular:

• It has confIrmed that the loss coefficient in laminar flow increases signifIcantly with

decreasing Reynolds number and is a hyperbolic function of the Reynolds number:

k = Cvv Re (2.56)

• This investigation has also confIrmed that in turbulent flow, the valve loss coeffIcient

is essentially constant and is independent of the Reynolds number.

Further more this investigation has:

• Confirmed that the transition from turbulent flow to laminar flow occurs earlier in

valves than in straight pipes.

• Highlighted the usefulness of the Slatter Reynolds number for both Newtonian and

non-Newtonian fluids for the fIrst time.

• Produced quantitative data on loss coeffIcients through diaphragm valves (Table 4.7)

for use by slurries pipeline design engineers.

• Highlighted the need that studies should be carried out with a range of diaphragm

valves to establish if geometric similarity is achieved and subsequently to establish

dynamic similarity.

• Highlighted the need to investigate the internal details of the valve with the

corresponding loss coeffIcient details and not to conclude at fIrst sight that geometric

and dynamic similarities are achieved.


Chapter 6 Contributions and recommendations

Table 4.7 Summary of Cv and kvvalues obtained

Valve dimension[mm] Cv kv

40 1200 7.9650 946 2.5365 555 1.2180 515 2.54100 69 1.30

6.4 RECOMMENDATIONS

The following recommendations are suggested:

6.3

• Further experimental test work must be done on the determination of valve loss

coefficients in general and diaphragm valve loss coefficients in particular.

• The determination of valve loss coefficients should be done for different valve

openings (fully open, % open, Y, open and Y. open) for different types of materials.

But for a refmement in the research, fluids of the same characteristics (Newtonian,

pseudoplastic, yield pseudoplastic and Bingham plastic) should be tested and

evaluated separately.

• Further study on geometrically similar valves in general and diaphragm valves in

particular from other manufacturers should be done.

• The two experimental methods: the Hydraulic grade line approach and the Total

pressure method should be done on the Valve test· rig, evaluated and then discussed.

• Further market research on the available fluid flow instrumentation should be done so

that instruments with very large capabilities can be identified.

Non·Newtonian Losses Through Diaphragm Valves DMKazadi

References

REFERENCES

1

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Non-Newtonian Losses Through Diaphragm Valves DM Kazaifi

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Appendix

CONTENTS

APPENDIX I: photographs of the experimental test loop and instrumentation

APPENDIX 2: comparison ofwater test results with Colebrook & White equation

APPENDIX 3: rheograms of fluids tested

APPENDIX 4: comparison of experimental values of the friction factor to the theoreticalvalues for different fluids in straight pipe (f - Re graphs)

APPENDIX 5: Calculation of the apparent fluid consistency index (K') and the apparentfluid behaviour index (n') for a yield pseudoplastic fluid

APPENDIX 6: diaphragm valve loss coefficients data

LIST OF PHOTOGRAPHS

I

Photograph 1. Overview of the Valve test rig 6Photograph 2. Diaphragm valves connected to pipes 6Photograph 3. Diaphragm valves, pipes, PPT and DP Cell 7Photograph 4. PPT 8Photograph 5. DP Cells: 8Photograph 6. PLB 9Photograph 7. Hand Held Communicator. 9Photograph 8. Data Acquisition Unit 10Photograph 9. PC and Data Acquisition Uuit... 10Photograph 10. Krohne magnetic flow meter 11Photograph 11. Safmag magnetic flow meter. 11Photograph 12. Mixing tank 12Photograph 13. Weight tank wit Load cell 12Photograph 14. Orbit PD pump 13

LIST OF FIGURES

Figure I Comparison with Co1ebrook and White for water test, pipe of

52.08 mm .14

Figure 2 Comparison with Colebrook and White for water test, pipe of

63.08 mm ·· 15

Non-Newtouian Losses Through Diaphragm Valves DMKazadi

Appendix


80.43 mm .16

2


97.17mm .17

Figure 5 Rheogram Glycerine 100% 20Figure 6 Rheogram Glycerine 100% 21Figure 7 Rheogram Glycerine 100% 22Figure 8 Rheogram Glycerine 75% 23Figure 9 Rheogram Glycerine 75% 24Figure 10 Rheogram CMC 5% 25Figure 11 Rheogram CMC 5% 26Figure 12 Rheogram CMC 5% 27Figure 13 Rheogram CMC 8% 28Figure 14 Rheogram CMC 8% 29Figure 15 Rheogram CMC 8% 30Figure 16 Rheogram kaolin 10% 31Figure 17 Rheogram kaolin 10% 32Figure 18 Rheogram kaolin 13% 33Figure 19 Rheogram kaolin 13% 34Figure 20 Comparison of experimental values of the friction factor with the theoretical

line for different fluids in straight pipe of Diameter 52.8 mm ID pipe 36Figure 21 Comparison ofexperimental values of the friction factor with the theoretical

line for different fluids in straight pipe of Diameter 63.08 mm ID pipe 37Figure 22 Comparison of experimental values of the friction factor with the theoretical

line for different fluids in straight pipe of Diameter 80.43 mm ID pipe 37Figure 23 Comparison ofexperimental values of the friction factor with the theoretical

line for different fluids in straight pipe of Diameter 97.17 mm ID pipe 38

LIST OF TABLES

Table 1 HGL Test for water. 43Table 2 HGL Test for water 43Table 3 HGL Test for water 44Table 4 HGL Test for water. 45Table 5 HGL Test for water.. 46Table 6 HGL Test for water. 46Table 7 HGL Test for water. 47Table 8 HGL Test for water. 47Table 9 HGL Test for water. 48Table 10 HGL Test for water.. 48


Appendix 3

Table 11 HGL Test for Glycerine 100% 49Table 12 HGL Test for Glycerine 100% 50Table 13 HGL Test for Glycerine 100% 51Table 14 HGL Test for Glycerine 100% 52Table 15 HGL Test for Glycerine 100% 53Table 16 HGL Test for Glycerine 75% 54Table 17 HGL Test for Glycerine 75% 55Table 18 HGL Test for Glycerine 75% 55Table 19 HGL Test for Glycerine 75% 56Table 20 HGL Test for Glycerine 75% 56Table 21 HGL Test for CMC 5% 57Table 22 HGL Test for CMC 5% 58Table 23 HGL Test for CMC 5% 58Table 24 HGL Test for CMC 5% 59Table 25 HGL Test for CMC 5% 60Table 26 HGL Test for CMC 5% 61Table 27 HGL Test for CMC 5% 62Table 28 HGL Test for CMC 5% 63Table 29 HGL Test for CMC 5% 64Table 30 HGL Test for CMC 8% 65Table 3I HGL Test for CMC 8% 65Table 32 HGL Test for CMC 8% 66Table 33 HGL Test for CMC 8% 67Table 34 HGL Test for CMC 8% 68Table 35 HGL Test for CMC 8% 69Table 36 HGL Test for kaolin 10% 70Table 37 HGL Test for kaolin 10% 70Table 38 HGL Test for kaolin 10% 70Table 39 HGL Test for kaolin 10% 71Table 40 HGL Test for kaolin 10% 71Table 41 HGL Test for kaolin 10% 72Table 42 HGL Test for kaolin 10% 72Table 43 HGL Test for kaolin I0% 72Table 44 HGL Test for kaolin 10% 73Table 45 HGL Test for kaolin I 0% 73Table 46 HGL Test for kaolin 10% , 74Table 47 HGL Test for kaolin 10% 74Table 48 HGL Test for kaolin 10% 75Table 49 HGL Test for kaolin 13% 75Table 50 HGL Test for kaolin 13% 76Table 51 HGL Test for kaolin 13% 77Table 52 HGL Test for kaolin 13% 77Table 53 HGL Test for kaolin 13% 78Table 54 HGL Test for kaolin 13% 78Table 55 HGL Test for kaolin 13% 79Table 56 HGL Test for kaolin 13% 79


Appendix 4

Table 57 HGL Test for kaolin 13% 80

Non-Newtonian Losses 1brough Diaphragm Valves DMKazadi

Appendix

APPENDIX 1PHOTOGRAPHSOFTHEEXPE~NTAL

TEST LOOP AND INSTRUMENTATION

5


Appendix

Photograph 1. Overview ofthe Valve test rig

Photograph 2. Diaphragm valves connected to pipes

6


Appendix

Photograph 3. Diaphragm valves, pipes, Point Pressure Transducers andDifferential Pressure Cell

7


Appendix

Photograph 4. Point Pressure Transducer

Photograph 5. Differential Pressure Cells

8


Appendix

Photograph 6. Pressure Lines Board

Photograph 7. Hand Held Communicator

9


Appendix

Photograph 8. Data Acquisition Unit

Photograph 9. PC and Data Acquisition Unit

10


Appendix

Photograph 10. Krohne magnetic flow meter

Photograph 11. Safmag magnetic flow meter

11


Appendix 12

Photograph 12. Mixing tank

Photograph 13. Weigh tank with Load cell

Non-Newtonian Losses lbrough Diaphragm Valves DMKazadi

Appendix

Photograph 14. Orbit PD pump

13


Appendix

APPENDIX 2COMPARISON OF WATER TEST RESULTSWITH COLEBROOK & WHITE EQUATION

14


z ;g0.,,z ""

.,~

P-

O

~.

8.§t'""'0

'"'"""'I I / ./ /~0

'"'§.Cl

ls~ ..gff"' IfJQ

S-<

~e:..<:"'"

~

Cl~~

~

01 i ~'i i i i i i i Iom o~ OM om om 100 1~ 1M 1m 1m 200

VeIDcity Im/.]

I CollebrookJVhite <> Experimental Data - - +20% Error band - . - .-20% Error band I

Figure 1 Comparison with Colebrook and White for water test, pipe of 52.08 mm

Vl

~[-';.<

,,

",

""",

"

"

"

15 I ;;;< I

-&:';10III

~..~i::I 5

~

[~t:l~.

{~<:f1lVl

z

ii:!.~r-<o[1;f1lVl

3.002.502.001.50

Velocity [m/sl1.00

~~~-~-~

0.50

01 F:'~0.00 =; i i i i I

t:l3::~

~

- CDUebrook_White <) Experimental Data - - +20% Error band -20% Error band

-0\

Figure 2 Comparison with Colebrook and White for water test, pipe of 63.08 mm

--.j

2.001.801.601.401200.80 1.00

Velocity [m/s]

0.600.40

-CoUebrook_White <>- .• Experimental Data - -+20% Error band -20% Error band

020

I ~.- Io , ; ; i i , I i i I

0.00

z~0

I:l '0

ZI I

"I:l" 10 I ( 0-

~ / I ~.

;><0~.§I-0UlUl

"Ul

gJ0

'"~ 7tJ ~~ . 5.§i:f -11

5'" ~CS f.i<: ..e:. "< ~

"Ul

tJ3::

iFigure 3 Comparison with Colebrook and White for water test, pipe of 80.43 mm

I -Collebrook_White <> Experimental Data - - +20% Error band ·20% Error band I

~::>Z"~01 58.§r<0V>V>

"V>

gJ0

e§-t:! i;'~..g f::!.[!

...."

OS tl-< ~e:- "< '1i"V> =;

ts:

~"=l

2-x·

~

00

1.20

", ."

"

100

"" '......

0.800.60

Velocity Imfsl

./,/./

,/

,/,/

./,/

./

/./

././

.//~t:d'/./

//

//

.---'---

0.40

._.~ ~

7_7'-'

0.20o0.00t:!

2:::

[Figure 4 Comparison with Colebrook and White for water test, pipe of 97.17 mm

Appendix

APPENDIX 3RHEOGRAMS OF FLUIDS TESTED

19


Appendix 20

GLYCERINE 100%

SLURRY PROPERTIESDate 22/11/2004Slurry Relative Density 1270 kg/m3

Volume Concentration 100%Viscosity 0.842 Pa.s

Temperature 2S.SoC

90,--------------------------------_-,

120lOO8080

Pseudosbear rate (1IsJ

4020

01L:'-----_-- ---- - --'o

70

80

20

10

~ 30

I <> Experimental data -Nemonian Fit I

Figure 5 Rheogram Glycerine 100%


Appendix 21

GLYCERINE 100%

SLURRY PROPERTIES

Date 19/11/2004

Slurry Relative Density 1252.61 kg/m]

Volume Concentration 100%

Viscosity 0.175 Pa.sTemperature 27°C

"'r--------------------------------,

250200ISO'00sool.""=-----------------------------------I

o

30

10

3S

•'"'";; 2'1

~~ 20••-;;- I'"~

Pseudoshear rate (Vs)

I 0 Experimental data -Newtonian fit I



Appendix 22

GLYCERINE 100%

SLURRY PROPERTIES

Date 25/11/2004

Slurry Relative Density 1256 kg/m3

Volume Concentration 100%

Viscosity 0.693 Pa.s

Temperature 22°C

60,-----------------------------------,

8070605040

Pseudoshear rate Ills]

302010

01-"'=- ---_---_---_---_- ------1

o

10

50

-= 20~

! 0 Experimental data -Newtonian fit I



Appendix

GLYCERINE 75%

SLURRY PROPERTIES

Date 1/12/2004

Slurry Relative Density 1197.2 kg/m3


Temperature 21°C

23

,.,,-----------------------------------,

··~ ,~«~-= 1.5•d:<

,.,

'"

,l"""=-- ---1

,Pseudoshear rate Ills}

<> Experimental Data --Newtonian fit



Appendix 24

GLYCERINE 75%

SLURRY PROPERTIES

Date 30/11/2004



Temperature 21°C

1.2y------------- --,

60

J--Newtonian fit

30

Pseudoshear rate [lis]

20

o Experimental Data

0-"""'------ -4

o

Q.2



Appendix

CMC5%

SLURRY PROPERTIES

Date 22/10/2004


Mass Concentration 5%

Fluid Consistency Index 0.304 Pa.sn

Flow Behaviour Index 0.723

25

30

1

1

25 ~

_ 20~

=.~ I~

u

15 j~

0;~

~u.;;

lOj"~

I5 j

III

00 50 100 150 200 250 300 350 400

y= O.2199xO.7873

R' ~ 0.9993

450 500

Nominal Shear Rate. 8V/D Cl/s}

• Exprimental Data" 42.12 mm DS

o 42.12 mm US- Power Law Fit

Figure 10 Rheogram CMC 5%


Appendix 26

CMC5%

SLURRY PROPERTIES

Date 26110/2004





25.--------------------------------_

20

Y"" 0.3226xo_1415

R' ~ 0.9937

5

25020015010050o-l--------------------------~-------1

o

• Experimental Data o 42.12 mm lJ. 52.8 mm - Power Law fit 2



Appendix 27

CMC5%

SLURRY PROPERTIESDate 2/11/2004





7r------------------------------,

403S302S201S10S

y = O.1574x1.036

R.? = 0.914

S

6

2

o+-li---_---~---_---_---_---~---~---__l

oPseudo shear rate {lis]

1 <> ExperimentalData 0 42.12mm 6. 52.8 mm -Power Law fit I



Appendix

CMC8%

SLURRY PROPERTIES

Date 12/ll/2004



Fluid Consistency Index 5.908 Pa.s"


28

7ll

60

-so"=.~• <0l::

'"~=• 30-;;;;~ 20

10

00 10 20

• Experimental data

30 so8vm Ills)

x 42.12 mm

60

/;. 52.8 mm

7ll

y = 3.5524xO.6141

R'=O.9976 *

60

- Power Law Fit

100


Non-Newtoman Losses Though Diaphragm Valves DMKazadi

Appendix

CMC8%

SLURRY PROPERTIES

Date 08/1112004





29

100

.,

so

..- 70

=.~ 60~

<L;50~

="-;; 40

":< 30

20

IQ

°° 50 100

8vm [lIsJISO

y ~ 4.9524x0 5407

R' ~ 0.9984

200 250

o Experimental Data x 42.12mm ... 52.8 --Power Law Fit



Appendix

CMC8%

SLURRY PROPERTIES

Date 10/11/2004





30

80r-------------------------------,

70

60

-;; 30:s:

20

10

20 40 60

8VID (lIsl

80

y = 5.847xll.5J21

R' = 0.9948

100 120

• Experimental Data x 42.12 mm :I: 52.8 mm - Power Law Fit



Appendix 31

KAOLIN 10%

SLURRY PROPERTIES

Date 20108/2004

Slurry Relative Density 1163.4kglm3


Yield stress 10 Pa



30 ,-------------------------------~

25

20

10

5

600500400300

Pseudoshear rate [8VID]

200100

o-l-----_---_----_----_----_-------.jo

o Experimental data -YPPFit )I( 42.12mm x 52.8mm

Figure 16 Rheogram kaolin 10%


Appendix 32

KAOLIN 10%

SLURRY PROPERTIESDate 11/08/2004

Slurry Relative Density I I72.4kg/m3


Yield stress 10.7 Pa



30 r/-----------------------------,

I25 i

t.. Experimental data -YPPFit

I__~ -----,----------1

140 160

x 52.8mm I

120100

o 42.12 mm

80gvro Ills]

604020

-=·20=.


Non-Nev-tonian Losses Through Diaphragm Valves DMKazadi

Appendix 33

KAOLIN 13%

SLURRY PROPERTIESDate 30109/2004



Yield stress 35 Pa



70 r-----------------------------,

60

50

20

10

-------i

450 50040035030025020015010050O+-----~-------~--~----~-

oNominal Shear Rate, 8VID [lis]

L.i::::Experimental Data - Y PP model Fitting t:. 42.12 mm x 52.8~I



Appendix 34

KAOLIN 13%

SLURRY PROPERTIESDate 07110/2004



Yield stress 35 Pa

Fluid Consistency Index 0.55Pa.sn


60

l!l

50 '" ""..

l!lIII

l!lM~. 'l!" l!l

?if

~40 III

~

'" r...-~..." 30'"..c~

;;:?;

20

IO

50045040035030025020015010050

O+---~--~---r---~-~--~-~--~-----,-------j

oPseudoshear rate [8YID]

• Experimental data -YPPFit [;. 42.12 mm X 52.8mm



Appendix 35

APPENDIX 4COMPARISON OF EXPERIMENTAL VALUES

OF THE FRICTION FACTOR TO THETHEORETICAL VALUES FOR DIFFERENT

FLUIDS IN STRAIGHT PIPE (f - Re GRAPHS)


Appendix

1000 I,

I100

~

10 11 I,

0.1

0.01 1I

0.001 J0.1

-fCalc.1am

:t:: CMCS%

10

- -fCalc.turb

o CMC8%

Re3

100

• Glycerine 100%

X Kaolin IQ%

1000

o Glycerine 75%

6. Kaolin 13%

36

10000

Figure 20 Comparison of experimental values of the friction factor with thetheoretical line for different fluids in straight pipe of Diameter 52.8 mm ID pipe

Non-Ne1Ntonian Losses Through Diaphragm Valves DMKazadi

Appendix 37

1000,------------ ---,

10000 100000100010010

100

10

0.1

0.01

~ 1

--0.001 +- ~----~----~----~----~----_____11

0.1

fCaIc lam.

X CMC5%

feaIe. Turb.

6. CMC 8%

• Glycerine 100%

• Kaolin 10%

o Glycerine 75%

X Kaolin 13%


!ODD ,.-------------------------------,

'"

"

"

0.01 --Il_UOIl-------_---- ----_- --__-'

--fCalc.lamo CMC 5%

f Calc.turb.x CMC 8%

• Glycerine 100%" Kaolin 10%



Appendix 38

1000,---------- -,

100

10

0.1

0.01

Ir-___ I- .... -..~

100000100001000100100.1

0.001 +----_---_---_----_---_---_-----10.01

1-===ff~C:;;al,tc~.ilam;;:;;_.----:---=----:-=-ff:cC~a~lc~.tur;;-;;:b~.-----;.-(Galy;';'cerine 100%

o Glycerine 75% x CMC 5% + CMC 8%



Appendix 39

APPENDIX 5Calculation of the apparent fluid consistency

index (K') and the apparent flow behaviour index(n') for a yield pseudoplastic fluid


Appendix 40

It has been demonstrated that for the laminar flow of any given time independent fluid,

8Vro is some function of 'foonly. This may be expressed as (Metzner & Reed, 1955):

(2.23)

To derive the relationship between K' and n' and the parameters characterising the

Herschel- Bulkley model ('fy,K and n). It must be proceeded as follows:

For a yield Pseudoplastic fluid:

(2.42)

(2.42) In logarithinic form:

(8V) 1 1+n ( ) [('fo-'fy1 2'fyk-'f,) 'f~]Log - = Log4n - - LogK - 3Log'fo + --Log 'fo - 'f, + Log + . +--D n n 1+3n 1+2n l+n

(1)

Differentiating (l) with respect to d (Log'fo ):

(2)

By definition:

, d(Log'fo)n =

d(Log8V/D)


(2.26)

DMKazadi

Appendix 41

, 1n=----:--------------::-~,_______;_;_-_o;_--___,___-------

l+n , 2'0(l+n)(,0 +2mo +m )-3+ 0 + y

n '0 -'y (1 + n)(l + 2n)(,0 - ,y + 2'/'0 - 'y)(I + n)(l + 3n) + ,~(l + 2n)(I + 3n)

Knowing that (2.23):

8VID is obtained from (2.42) thus:

K' = '''--0 ---,-

!~(, _, F[k -,rY+2,Jo -,J+l])O'~ JOY 1+3n 1+2n l+n

Ko,o

(3)

(4)


Appendix 42

APPENDIX 6DIAPHRAGM VALVE LOSS COEFFICIENTS

DATA


Appendix

Table 1 HGL Test for water

43

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Appendix


44

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" ,. ,. ,. ,. rll]1iU!7ID5 2ill4.12.4 25S16J5l:l ,495SJl76 2l959-5C6 2llQ.l.m Dl15.ill lae24.llS1 11'147.41:1 'J6427lOJJ16 26.SStitl\ ill54.76B .""" mmS7 210991111 JJm975 18715J46 I""m ''''

- !69&1.1l1 2ill7549 l.lmJW 2'92lJll 2l91D« 210362Jl "'"'' 18ill59~ 1?'X91Z3 'J!2!6~l\H% 26117.3iJi ""'''' 24STl426 21T.l4..m Z914S11 Imllll 11l761Jf.1 j1)56.iJ4 ll!l

I 2652l.m 26lalf.45 ill4IJ.%7 24556.548 21165119 ;I9T;.!&l 19'J~!34 Im1744 I19SH:Ja n"26~1JIl m2.611 2...~119 24Bun 21741.6!! l'mi€il l~lJl6 18751.113 l1'1Z2,~.l ''''2nJU~ ""'''' .mm lJ&Jl'" ml1ml mll.i97 rmJJl16 186.5irm 119~.D&4 llElillI1.482 :z.l.9'ilJ.l11 24mE I l>i1Jl1l 21178.895 :JllJl'" 1974Lm: llEli.681 11.l~.IID ""illlHJl 2-i89f.1l3 24m.m ~776B 21239-TI9 IlSl1.195 Iw,m 18715JlS 179:l1.951 "",""'" 24065.131 :m1415S """" "",mo 2J232Jl1 19S14jJ7 It'ig217S Iml.14U """,pm 241I41ZJ lW.l95 """'" I.'ll45.7J6 E!l1Jrrl 19DHJ.l 1&!l2U59 I1lDl9.\9 118l

-m4HIl 27595910 !T.l12.2ll'7 2699L!185 255m426 ID6l.471 251SY.ne 2467611J 2'156..564 """"'''' 21611.113 2'm5:m 2U.CSIi_~ 2.~,m lll'Jl.1JJ nl.DU 2464S.m ~)(s.m I'"ZT'-"'5134 211[SJ44 ""'JI2l ""'.. 2.m~J4ll ~jl.l.23 2511Q-alB 2471l.m }Io\21615 ""

Non-Newtonian Losses Through Diaphragm Valves DM Kazadi

Appendix 45

Table 4 HGL Test for waterIw·;,;,~ I I101ft ...... "?<wit ~, ~, F.... ~, ~. ~, Pod ~, .1.__"-_,. ,. .. , ,. ,. ,. ,. ,. ,.

=~, .=~ 25!9UJ4 21111.lQ ::l<9O.l .. I ~m "'1~~ l'llJ ,-= .~= om~m m'lO.;l< , ";$<373 2.l;oo.m 2491:5.3!.l ~= 2<169 2Il1 2~_1'l)J .=~ om2nJ.O.,oo ~.m 2S1~5\l\l :ll~!OI.l" 2.\WQ~1 24D1.U:5 241rll:.6 ,~= 2<5iJIl.!llI.:l om=lm 2Slla..n6: ~'i).1l9\l mum ~,u "9""16"..6 2""J~ ;!<IilII.l:!3 ~~ om:w&1:512 2S5oIil.l'lll ::54111 OS' , m.'Q ~S)(I 2<mn:l ~<S08~ ~47QH'T.l

-~ 0=.... ~$l' 2S6St.7M =3<Il ~w 2.lHl.410 .m= 11l1llll.l!19 ,_m 2lSll<l94 ,~

ll7I:!~lO ~m = ~ 2.l,zun ~_'OO .4lR)B(ll .mm 24B;.7.14 ,m..... ~= _.m lhI:H.414 2fiD!.on 1!=.lO~ =l..l.l..'i =.171 :!t7(ll! 6iU :;l4.g1.'1~1 ,~

:!E1lti914~- """~_1lJl ~= 2.l'~5.m IDj]36Sl 1.'Cl2ll1fl 14$'.2lil l<QI!I9!l4 ,~

~7" 2ll6tl.tJ.\1 _<)<9 -- ma._ l.'25ll.l<O nC1l9all 24tiR-"!<2 ;;uN(b!J ,~

....•.•.•.. ~- -- n_= ll~.u<6:! =«:1:11 -= .~= ~= :M:l4l.&'TI "<

:::llIl;J.6U -- 17lli.4:31 27::J4.11~ llil~~7 =-- 1l11llS2il 2ol6£r!._ :l<m.01\ J~~

~-:rnI4!1.lIl11 11$(\011 n!~.l4] 2S<1.463 .mm nl3lom 2~.!7!I l<:.:l1511 ,~

~- -~ n:mm :n~1l_<63 ~~, 2557a.3lI7 2.l13li.4!1!l 24/iIHiL 24::6I.!~ ,~

~1'J.(l16 -- :28466.15l1 ~,- ~= :l$I.]1;Ii ~~ 2'~.7<e 1<1...= H1iIl..... 1l1S.771 _m ~11.7'2 I -= ~rn :m'1li.Jli1 251S1m :l<:>'iI7'I'l ~BI!J H:tI

:l'll:l'l.!n =.171 341'J..l18 , -«' 26JZl Jrl 25lInEll 12llIl7. ,_m ~rn H:l6:l'll1O~ 2lllMl3Ce 341'9.&4&

-~;'6J71 .•:tI 21aoJ.!lIl 2:i:!17"'1 l'l6l]J.T.ll ~= H:'lI

:llli><8211 2II'l!l1OO -= l7~.611 1!..."<1'.719 2«l6.1Sl ~m =m , 22217".. ,~

:l'l1l7ll29 28710.252 Im7.= 2715>:l~ ~.6:'9 lm11J1 ~~-~

22IllHOl l.JJ1

....._m 2WS...ll 2lI1J1liW =~ m!3.'!n 1<SJ.SJ!91 ~= ~~.a~ , 2lUl.2./iS6 ,~

~~ :llllll• .l27 2lI!l.:i.l':ll V1EO.1l95 2S2IH:tI .. ITI.:lIU 2:15<9'::4 ml1m , 2lll11.{;IfI ,m-= ~~ =~ V''1481! Zl:1.£l..21\ l«Ull!l 2:16iIU1. WI1-977 2l1~~.II21 ,m~.l21 2li1'T.!.EI9l 15On.071I ,_ru :n'fflJlI l:l'/6O.7\l1 IWJ~-*! 111'1:2'<3 17llI:Ll19 ,~

~= 2liHl.aJ:l 15012%11 :!<lSa:m 117J9S1J J:mIl.l52 ,~m 111&1.7" ,=m l,607

......... _.m ::ll!iln-1'l 25«<.'33 1<60782~ 11746..21!6 :;!:l'>.lIH6.l 1\I9}(J.tlSI JI1'J-03l ,~ ,~,

:I6Ii'TI.•JlI :lii1<1i.1M llS+4..ln-~

:lI7U-lY ~,= Im'55J ,~= 17SJllllID ,~

2£1'7~ ~"= =. 14711.'l/Si 117ll.$U :un<i.15fl ,_m ,=- 179<& SO:l 32111!T.l16.9!U ::ll!i7J11l] ;'{il6lIm 2';)'IlI.ru 11!llll~<O 2IDjl.i!lS ,~m lMlll.'n 178&257. ,=!'1'nD.7.ll1 .~= J&<."l!l.&ll n!61~1 2!!le.l.666 [email protected] _m ,~= 17ll1l.''IlI l.12'!T.lJ'Jll ~= :l&1:;U5>:l n!M..Dl :l1~}!I.7OSI 2!00J.:J:tl == 1ll72l:.M 1111.IHlI\! '"'m.un :l619ll.l!~ :!&UIIJ.119 n16!l.1ll2 :lllIU.~S 21011.71'9 ,-~ 1ll73ll17' lJll19._ lJll

..•. =~, 21i:V.UW =~ 24181.'Tll 11699,1~ _m l\l\lIl.tl16 1111J.m 1~1.I2.l m26'.l16ll112 2M12.I2S =~ 2''1<11.'51 2PC26Jl :Da%170 11'95<.15< 1_~ I1l161.<0I1 ,~

l6!I.l'i."9 :26411.= 2l1l29:;:; 2'~1~.= 2H;,.....400 ))9:0.<;]9 ,-~ 1_:m 1:moo.m lm=-'116 ~= 2l!l1~..I\Il 2'I~1:Im6 11~l~-!lOli 2ll1)<98lI JmiSll! ISS2C.1ll7 119<1.013 ,~

. =..116 ~fi' 2l764.'611 249J<.lI7l 219ll.J.l'1 21_.711 1llHI7.vn 111771-3<6 ,~= ,~

-,= ~'" =~ 26Z1.!Ill ll~15.1" ,,~ -- 18llOl3:i9 179<9.m ,~

..... -- ::ll!i1l1.ll2ll =~ 24m.•J6 ,,~= 1)'IIH71 ,~= Il1'7/ill.m 11'91&..\00 ,~,

allum. 1IillllllC-5-~ ~~- ~1~-119 2(1';'...1:._ 1!l!l'j).Dl 1ll71l.7" 11'95l.4J! ,=-= 1DOIl:l..~1I 2ll'i/i-119 24no.so1 ~17'i.6211 1)'1<;7.76ll 11'902.J16 1111lLBJ 11'9Z2.QCl ,=

., ................. ~.741l 14l1lll1._ .m= -~~1l17.81 =~ I~OI6 ,~= I1'9Si.~ JlllI

IDIHll2 :Honl.li1 .m~ -~, 1117l.!I9~ =m 1!l1<l.m ,~- 11'9~= ,-•....... - 2l:l16,11ll ~_1lJ 1<ID..l77 13Ml.l611 :l1Z31m Jllll7\lS 19711.71'9 !871~..I18 11'9J13~1 ,-

,-~ ~lJl llSR12 -~, =n JJZl2.111 19:1l• .D1 ,~, 1!lllJ.14C ~m

... 1"39.11'9 :Hll•.m llSiJ"I.19S = 1CllCS71f lJ2<1lCT.l 19TIH:J!I 11l6Jll~ 1!llll3S9 ,~

11&C6.1S1 21S93~IO m!UlI'7 l6'I"lEl8S 2:!\Il<.'Ui ~'" 2:!1S9T.!l1 2C671!1lJ .~~ ,~

~~ 21611-lD == -~ == :m5lJ.!3J 2:!1.lJ.n!i 246ol1-221 14J'1~:m ,~

273U1J4 211C!il.3U ~ru 26Sl!5,&S& ID19.34C ~IU1l DUOI11 2.T.5m 144111iU ,mTHil.'M1i 12J9I.':ll 21"lllm , 2061l.'12 1113Hi8< 164J831' llJJH):! 1:l9SlJ.!7:l 1;!81OIl21 J.7':l

~= -= 2161732. , 21141.J96 i14n.7M 16400.9<9 15<191!IJ ,-~ llmJll >.nom'll.lll6 == w.~ 2jl~'2511 172'/2.152 lillO.Il. 1525<.701 lJilllJ,j5< 11911 &lIlJ ].310

=~ ~= ='.111 2107'1l.T.'li l1Jll.l.!)I\l 164Jl156.l lsm.m 1:fJ9l!.'11~ ll7nm >.no=~ ww= U:ro.ll<1 :aD!l1.6J~ ,~= ,-- 1'~:l26 ,~~ 11!l1'.4:lli ,~,

-= ll_.11I3 l1m.m :lll:JJlI.!I91 1"'~1 1612<.112 15l2lS61Q 1:Z;C.6IU ,~~ ,=~.= 11!l921i1ll 11l'l19.!t5 , 2ll42!1.6:!1 16!l!lll.1.l6 16UI:l~ ISl'~~1 1:1'711912 119!19:m ,~

, ..n3'16.•n 21il/il.111 11261i.'" 2Ql~.nl 169llll.61~ 161llli.7!lO l=~l l:JT.lllill21 12!l1l.J1' ,~

nl62Hl 11NlBj -- l!/'l1(l.W 168UI6Ii 1.wl1.G l.m.:m t:17'J.1!l ,== 'B.. _ .....•. _..... ,,~= 21~19!i111 2OJIlIboI3 2Q1971Z2.l 16112S.:l16 1.lll1i1.109 1:lG01.«7 l391HG. l2!I6J1ill ,=

,,~ 2166S.JCIl _m ~m ,~= 1541.CO< 14_.:J[IJ l:lSum ,== J.1101

... :::::: 112!l1:1I5 >=>= :!IIoIJ..2.lll 19S5JO 16SJll.l1!1 mSJ.lilS 1<ll6..l.l71 lJ65~.7:lJ 1:l:!:l1n9 Jl:l6112,1I1i'n == 2D3j~.II'I!I 19131,186 ,-- l.lillll4S1 ,-- ,=~ ~~, 3l3J

llJ1llSl'21~15__

Jll:lli.191 lms.m 1~I::l11.lllIli 1~.121 t<T/Jnl. moo 261 12lllll.l!ll l-l:J!l..."oo~ :Jl7'Ll3Il 2Il164.13 lmUiU~ l6Jllll.1l:l9 1571H" ,=- tl866.163 131lS212 ,-

. 1I017.1ii6 =lil.1JJ 200/;II.'904 191'"--'JS6 1!L'2!I.42Sl 1:l6n2l1 I_.m 1:lllOl:.m< ,~~ ,~

-,= 2lI1Q4.al :9JliJ549 1~J.S11 lW4i.~' 1:l<11~7 I~D.1cn I~.lll l3lj6.711' ,~

-,= 2!l13.BS 1_2:l6 , 18SU9a 1~)7I.421 ,~= 15211.1l:l:J 1'1I01lJ8 lJollS.m ,~

lfiUl.14li ~~ ~,~ 2'::l1.ll26 2162!l,il98 m<= ,-~ 1=.6:0 ,=~ J.ll!1lfillli.1'1\1 L'7W.l6IJ ~- 2'll<.~7 21~1'i.21'1l lliI~6.tll' ,~~ 1!l"~.JlI1 lliG47..l1iS J.161

-= -= 2l7S6U1 2<9l5.1n 21989.Dl 21111.11'9 1ll11I1.l27 11l8llj781 lIiIl52.492 ,~

:lI'1J1.7\B 1O':lJ2ml 2l7.!6.166 2'!llI.m ~.m 2109ll.;66 1ll111.l00 IIl116/i.l'1 ,-= ,~

~_T "'-~>1¥0 '_, 31

'i>1¥o;>o>il>= 0"",

~ =~Tnoo 'il_

I ,mI<[I'....J !l1lJ1


Appendix


46

",.,..

V.u....T1'lI"

Vil>o~"""l'

V.... ;IOrib:=

l'ipocn-nr{"""l~Tne:

o-i!rt~j

11M1J4

•

illWw

'"0.001

lOO)

0.001

\.l.iol.o;,;...". 'j" _H7 .ill! ,·!.'i:JI OjlO ""

, ". ,... ,...

'<hp;.." I ,",,", "'" ~3 "". "'" "". I "'" i>oi.S "'"

,,_1'__,. " ,. I ,. , ,. " ,. ,. .-,

.... "'''''' ESll4S1 2\4llJ.lli I Ili1Hil 17lli.604 164JB.>14 ISD"']] l:PJC.m 1<:&7ll.:m 11~S

227rl!i.::62 ""',. "~17.924 ZIl4l'J% 1142:1764 16400549 154t94~ 1:1i81 534 1:Il'lJ )1) Hlll233!1l.lilll ""'''' :ms'1!l I 21l~.:llO 1719:U.u 16]'l(1-"', 1~'7lr1 1:!88J954 1293J.!>illl """"""

,,..,,,, W'14.m 111l7'1,7:!6 IT.'6'SClIll 16(';'8%5 l~_m 13'98975 11143 n6 "">ill", Z!JOl.Irl IlJJS,!I47 <m'J1676 1~$3 """., 14;un; tmgm 1283436 1"[!:iol«.m 2l89f!.!lii 2J2Sl.2aS , :lIJ:7ll.INI lffi&.38! !6!14,11l:l l:illHIG 1:IDl1ill2 [E,irlB ,,.!242!l!r'J 21m_~ 11l1ll'il'5 Il4::UJ1 165'5'8.7$ l.til2j/jB ,51tH>'l l3711.n2 13@9:!Il ''''211%.412 1186J,m 1116li.447 <lJl14nl 1~61S 16106J9fJ iE99-11 JJ1'1HlTl 12!mJ14 ''''21102141 21m~5 """.. I ,mu.", l/i8ol1.!6/i 1S'!l_~ '''''''' Im31lJ ,,"'.., ".,,[mm 2161Ull! ""., I :lIH11T'.J 16ll1jj;lj 1!l!6ll?09 1~1.«1 mll'!IJ( !J8l!].5}[ unli!m.!!26 21665.w'i """" """on l!56C05,285 IJ!U2CO<1 145'«7lr1 """" l:Il'JJm u,"1!:J!I11.1S ""'''' mU150 l,illnJ 1657Bill7 115~ 11i.1 I~_m 1.365i7'il IJJS187!l l.lJ6212516'<1 """." lnl!HI9lI ,>,n1\86 "...'" l1BILl51 1484ti.iS I:mn~ IDJgj4S lln2I:m514 210J..'i9S/i 11130.191 I!roS219 16Hlll.1lIl6 125EE.ll 1417H7~ 1!1!Xl2eI IZ1<iI.I!7l H!llIOQ,6.Jl ),;741,4al ])16441] lrrA,&:'9 "."" 157!1044 """". n."" "mm ""210I77&!i m181ll :a:mB.4!M 1'11421:&6 16:J2e.4:l!1 1'irnZ7 148l!9.7Il! I:BJHJl4 '''''"'' ,'"..,.. 1JI041all ~J4g lil8!38U l&JolgjM 15<11.741 14'XJ'J1II; 11194.]1. m'ss7lll "'"1l49:i.BH7 2Jl:J1.5~ l~n!i "'1"" Im1ll411 "'"'" 15211.o.l:! 14!lOma n'15.672 ''''':=718m :2ii:lIO,m :IWlJ.74' 241m.4J:l .15JliJ:lll Dll29~ 19!1BS5:l1 1IJ141.114 '''''ill U21....m 1!i3419414i 1S6414llom1 24ii4.l&791 21647,1l4:Jll :om"", ,"'"", 1~9.7JG41 I~S9'lll!5 ,'"2€1413111B ""'''''' 25654.116n l4a11.44721 21E2l.~ mlllB'lS Im6.167'lJ IB11U:l2l!1 1?T.l6~141 ,m

.~ >ill"'" 26ll:lLIilP6 25341.J:l4691 24S1H0'i47 llrrll11lt1 :!l741J!nJ7 ,om"", lam,7CO!l l191:J.3*<lI 1.14112e€l.IDll ~5.i3417 IDIH5llJ 245!i9.lTI1l1 2JS6m1 2J1(i]6i!7S 1m82S171 1S75C77734 11%1.15586 1141

16444.Dmii 26nl.4315 ""'''''' 2462IJ574:l :l!.l2llJil%l """,,, 15""_ Ia7IOSI~ 119!3JJ359 mo16:84.168tl 0SSl.66406 2'iJ64.!TI42 244155016il1 :ll~J.001lI1 """'" 197467m5 1866I.E1l! """"99 ''''l!jlJ7.61Tii ID1SJ]l'i12 :mll~ 24396,67183 .lrs.91219 lJ61lHlJI:lS 191.'i8mn 1891.18ll 119!Hlm "'"""""'" 2fl4S$14 mnmiSiI ,~- .m:n6l11 1164146484 197~nr,n; I!l6ilS5293 11'J62.J2611 ''''lli6431im ,"',,"'" rEI'}!l!IS :mill.211E4 Ml.u.7l7:l4 Iwrrm I!n!iU0742 1&S".>li7:lS!l 119'iBIS61 '.m

.::ru61.TiIi'tS 2!!IH7T11 m55,SS6541 ",""rn 2D3Um44 19a5ol-J'S7 I!nU78111 ImUlIlliI 11ll2!,24-414 ""lli6!l.lli46> 2I!Zl31i'f1 228&HlllS, lli2HI1{i11 2fJ'.:6iIll484 J9a511C9375 IrnlI9li4:lB 1"'-4~:om lW.8DJB H!19

IillU!7IJ.! ""'''"' !lSUJ8ill!l1 "'"""" -- 1!lrn19I'l2 1!lli72S-492 11!541QolIlllI llll10911m 'jOl2J9l8D42!n 2l'MJ..'i625 21441,:li664 2lZlH61D lm~1 Z21~13I!2ll 15140.18515 24651.3J9ll41 24m,l:£r9 ,'"mta.'7ll7 :lmll.7S391 174<;).9@14:l :m~J.m1 ""'''''' illSIl!S.S47 15167ll94!3 ~hJ541 24jIQIS615 ''''


Ik.ii,i;;;~,...- ~~

--_.~ .. " ..-I

f··-'·' .__..-",.'.'.'. , ..... , ....

UIIJ·6511 ·111 .]JJ! ·IJJI o~o m U~ 1/66

I'",,,,, 01'011 1'012 1'011 1'011 !\Xl 1'016 Podl 1'011 1'019 lftlll:fur!tltp, F. p, p, F. p, p, p, p, ~I

f·El&.1I3\ 1Il1\J;<l 1~j;.1Ill l':roSLI~ l1mrn If/llljIIJ laIll\1l\ 1~1]1ll1 I\~m. l3ll

= :ll\lJ.Cll ~~111l I I~JjI ImUll 16Iilli84 1$61i44 mUI 14&Il"l U16mJ41 m«1 19111Jf18 1~01J 1!.'aJ1llI I~HlI IlOO'" 1&111 ImJ9<IJ m

..... 261Sl.148 2I5i419 JllllJl14 1<2l1l16 21&llISII mlJ2il WJJlI4 Imm 18J27144 ]J~

llllJ~ 2llJ)JIIJ ~J<8 24114161 2151n~ Dl16.fiI6 19%1j!6 11IJ~J!1 ISI413<l 1161-_._._.,..-

211ll.m ISlSl4\l2 11411mJJ1 J!4i4E1l Jl71!.861 249[5.1)5 21\'IIJnI 'i!l1ll1121 1~.181

. .. l!m.1IIJ 2i51lm lm\l" 2ml.61l mm 2IIl9!!156 ~II1JOO 1l1l&I.111 Imm ]344


Appendix


47

"""..VolnT1JIOV>hoo~_]

V.....~Fipo Di.o=t.. [.....jiIU!ooWT1I't:D...rity(k"."""J:JI[Pu!

~Dw...l~[.IIIIII.J;

MaluilI.TYJlI!:

DJ.Oll.,,'"000'

"

llDlOIDl

lhi.i.~ .."" -4911SS I ·'05 <m I "" ,.. "" 1$16 ...v....~ 0

Pooil '"'' ,," .... ..., "" ,,," "" "" "...... n,..m.,. ,. ,. ,. ,. ,. ,. ,. ,. ~l(11(35ll 400'.!7.iJ9ll 3a6SB94S ~s.Q40 :JZm.572 l147H11l ~:66 """" """" "'"U7!JOE 4OlY1.571l ID5Il91O 3E915316 m4~.:m m21492 Hlii!JJ( 29785J~ 22Q'3I.71ll 1119

'''''Hn J't~.:llie JSG1B18i! l!TI9i76 llil'i'7an llmn "'"'' 19'i36.66f """m ''''4!IJ8jMI 1>S:z.U;6 m"", ""''" ""'-'" l17OJ.(lli lm6.9Q4 m4a,m 1l5I61;85 7m6:5S6H!iS 3llCe6.121 3S1HS7 1."4«:15 )!EH5 """ '" lli01.l6ol Bmm 2lil!5sm U12:JI1S511142 :Jal!lll.m J6Tli.ill" 1S'.JM6ll 1l2Llg lJJ511 i161 DmJ4lJ 2'n2>Io1lJ 28667,1364 ,mWiJ.344 :l567J:rJli 1561HIS 342404ll6 1:64am .,""" "'""" ""'.m m7'JJ51 '"]J14l.m """'" m9ll.,* 34246.9l1 X62S.26ll lJJ63D12 195690:311 28iS7m W.S5242 ..~.,.n" :i54Gl,B:i!I 34:J07.3&3 33m,1!!l ""'''' :.:sm_~ ""'''' ""'''' ,m"" l.!llSJ/itn,7lI1 :lS47>,m ."'''' lllJZlJU mum 19$1'.l76 Zli3l6m 28041gm 219iB94g S9131547Uil2 lmsm mUD ll999.l!l 2'iD2nl _'" 287H9J6 ,..,,'" T:5!lBW jSlJ:l567UE6 W:l2.12!l """00 >:mill ~lHul "'"'''' 2IO'im moo'" 77~n& ,,"lmJ.'" ""''''' _m llZ76.ilJ ...,.,.

~2lS 2!I~.'iI16 mew ""'... 5(95

""'1>1 J4.:<61.a36 ml12Zl J2ill.l8:2 19J'11.2« .".~ ...", vm258 1754I.JS7 ''''..... laS07.7lI1 m!MIO ~7_!\I!; .,,"" :<mm :J:!lB.l14 275.H15 ....50< 18:l17861 ml

Jl'6UJi mn,,, 1S99Ha4 )4T.1l!Z4 .",'" lDI4.S4S ""'21' 2llll:Il,471 1e:I:ll,Ill 6o\,/ilJm:J~1 :l:2MI.12I 11294.648- lJ5TI.1Dl 2R516ft14 282jlJ81 ""'"' 27J4Lffi """'" .mm7lJ';S ""'''' J1J4ll,9'71 lJ62!!59 2ll491~1 ."",. =om """" 27OOU17 .m

"""" mn.~l 19-7.5108 2'.1247.1175 VE"'''' rn,,,,,, 27152.455 ",,= ~"'nJ ""lJ'}'il.299_.~

29141.l2'J 2927:.129 m5L127 274~.299 2714lHilIl >all"" ~:J)lq "'"ronm 29114.m 2lL'lI'lO 284%.010 267421J7 26ii6..m 167169!ii 26Sl418't 2/i19853l ""28400.461 ""'"' 181l8.187 274nlll "".'" E~.'m ,"'"" ~1l47 2S5'J4549 ''''


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I un.."" ''Il1 0381 19J8 HZ7 lo.m

IY<Mplore 0Poll "" Poll Pol' Poll 'od' Poll Pol' Pol' Annc;t /brnlt,. P. P. ,. P. P. P. P, P. ~l

]][6700 ml6.m mJJ1El ?li'9L922 ~1«3 ",,"" 2!i16168J 26159.498 L~J13 ,..lJll.l.TI4 ""m m62.m ...... 17811J8S 27413387 ""'.8J2 26!1L473 _on "I]

""'''' m1L492 2&591511 ,",Ul 17421410 "'""" "mm 261Rj,646 1SR3!im lJ)})

.... """l! 2lIJl.l1J5 ?E13H2( 28J16.ID 27DJ6i1J mi6./i61l 2647Yg]! 2612S.811 "".'" lla'iJ];6J]%'J ".."" 2II118.m 1781a496 ""'''I 266i1J.445 m.4)9 ""'Jlj mllm 'OIlEiU4Ul ".,,,,, 28:1SS.m 27m314 _Jll 2Em.574 "2'29" ""'jJJ 25m,SS1 ,.-

---,. "'''',. 11= WlOjlj8 2710&141 26.119,152 1El"D2J lmL418 25741fiSg Zllil451 H19...mS/m 17511926 mlilD "",'" ".."" l62l611l ""'7]] 2S148.l68 ""'''' 14"


Appendix


48

~I>i.mI!!K{mml

IiaImil T1lI!:

~IJ

J1[PU]

IiU3

W""lOOloml

lhi.ll~torl:e -ii.4\] .."" I -:l61 I ·15()'} om ''''' 1173 84" ,,~ IVllft plm, 0

Poll Poll Pol' Pol' Poll ,~, Fori? Pol' p."j9 AOWC!:Do""l

" " " " " p,

" " " Ui<l

"""" '",141' Z:57~.584 u.m.HIS 2T~.ID2 ",m" 26427119 llilL!589 256&1.918 "IlilJl:loU4/J 291l64,QJ) :Bill.ill I m14.&SlJ :z7'I..2635J lO<llll3 "'I"" llm.l11 256101!'>8 ''''IJ865.m '"""" lIJEmB 2S'l.l\jJ\ 11578947 2ellS57 2661l,16a :6OU14 2j711:l8.S9 ''''D62248 1156119S JJl7l.'" :&isa,7.l4 n59S.3ll7 2Sil.611 25591119 2lf.S6,+49 256B6.m D5Il31414.115 3111154-3 :D54.m lJ4lJ6.W m!H~ 27lJ41.%5 267l7,a::R 2H!9J4J mnm 5.nOJW79lB 11lS6.6l6 :m4IlHS )]43!ifHl Z182l,S$ mlm ,..",'" 2!:m11i1 2569111ll ,mmJjB11 :l1774C184 314aSilll 31051615 211121.4)] 1T'ill633 "'no.] ~J1.lli 2E4.goo 1DJI12217932 11812924 Jl622S(! 11023.150 2lI1S6.5J3 27!!L471 26%$JliI 16246.063 2S831:J91 lICl6

....32475.2Jj JIJe.m llHI5.406 313lll2l 2B296.7IJ 17414928 2&76.645 16Zl1611 '5Il"00J 11111

.. -'" 12155121 jJ18HSl 312151.58 281Uli62 27424(JJ2 27157l4O 26311.449 25H21J14 1374l%23J81 ""'.813 BJ'l.J.m 28819.127 Vl1Ul1 l6JOO"" ""',,, 2Si6H6! lli.il.248 ,,,,""'''' 2!!94761!l 2BS'<J.66i 284R1.495 "'I13!O 26...1.Ui.D61 ""'''' """" 25548.6Sll lJll4

"""" mJ.!.7ll Zl12S!JS4 lSE12.l11 "'''''' 2!i151~2 26367354 ml6Jr3 11""" "'"Table 10 HGL Test for water

Pipe DiamH [mm):IUlmalT)'jl£

----,.. -····Iiri.i ..,;;;" ·IillO -3M2 ·1.l41 I ~." 01llJ 2jJJ ~_4~'- ~m(J 9jll

v...... 0.-

Poll Poll Pol' Poll Poll Pol' Pol1 ,~, Pol' !~w.lilt

- ---!P, !P, !P, !P, IP, lP, lP, lP, !P,

" " " " " " " " " Ui<J- 01llJ 166~1 "l''' mm 906J4S 1000L'i6 U,il.m 11S8.4]2 1146.34.1 ",.,100 I·· 01llJ m.m 17LE 281.916 1Rill mm llll"" H84.K]2 1516151 HIS0,..

- .

01llJ 166.2\1 "55" 322.431 !ilJ6.748 10B2.1S6 IIjJ,n6 1138.432 1746341 ",.,r7.!1 01llJ m:m l7lJlS 2117.916 75tm mm Hm"" 118U32 I.m.251 H:J5

w"" Ollll Ill.m 1n248 31ilOO4 "'>JI I""" 1I319lJ Imm 1703315 611"IllIl

I ._-

01llJ 154m IW2i1 3151ll an'" ilmJn llrnl61 mum 1666516 ""--------- .-01llJ 1460J11a.rn!

.....191Zil "'''' ~38..6Ql 1192.44's 154l.elt 179i4fS 22!liJ54 ""01llJ 1IIJJllI ill'" 416.42.1 1154W1 1419JS8 ISlil.!iJ5 l'ffilm Z3l11J5 ''''.

.......... _- 01llJ 1611lll "''''' 1J6Jl3 1011911 1I61.DJ 1"'1lIJ 1..1lIJ 1824.a76 Hl't, 01llJ 16llWl ",m ,,,.,, 1007171 1166319 li75JJ1 lllm 18IU)) ''''01llJ miSt 161850 278.515 171.871 """ 1043116 1I84.9m 1531l.266 5.752

O.OOJ lll-'IJ las.m 2Il41n ""'" "'ZJl 1ll1l'" t'l2ll.11l Im042 5.81801llJ mm l38.l28 241.195 69J.7G6 a:J(JjJ] 9S6.a:!1 UQ7.127 1384.m ",.,01llJ IIJ4.a21 11949lJ mm 667.718 18IlJ91 B80,I% m"" IUIZ1 IZJl01llJ IIlH41 us.m ""ZJl "'313 1Jilll 7~j15 ."" ll!154B ,,~

O.llll~'" 112.'" 1"'" S41mi 109.006 fiM,1Il1 nr734 11J45.ll1 "54

01llJ 111JJ Rl2l1 111542 424.9% 16Il541 llllill Ml" ""JJ ,,'"01llJ '"'' "00 151%4 '2J8l 518.324 ""'" .,,55Il 7814:J( '1ll201llJ ".544 16.91 m.m 1JJJt6 1llli4 4~.862 mm "'''' Jilt

. 01llJ ~'54 2'" 79J~ nU7l ZlI'" "'''' D,411 "<J~ 2.111

.. 01llJ ~'" 47496 711477 12"J5 "'.2l1 ~'9J1 m'" 452.4)1) 2.1&1

Non-Nevvtonian Losses Through Diaphragm Valves DMKazadi

Appendix

Table 11 HGL Test for Glycerine 100%

49

-T~~ .."" H' -,'" <.m I 1076 I 2.5llS ---

'"" am~ 'm~~]io:Ie a

F~I F~l F'" F,," ""j F~' "'" "". "'" A?tI>CfbwroleT_ns<: ", ", ". ". ". ". ". ". ".l2IllmJ4 P. F. F. F. F. F. F. F. F. [L\]

"ili!T~: ""- OOOl "'"'' 9S85.11lJ 156lll,m 21742.D4J DIm 38LS9.6!lS 4E1J7l 492:!lj4J "'''i'bo~-,,=,l: ~....

orm 49S}.121 ~19.S83 1~_Zll 23642.2J1 """XJ] 3mB,am mW.on 49112.621 om'l'iInpositi:m: 0,.. aOOl ~UJl2j i!J341.Cffi I""'" 2llllI:m nm914 41JE9.J15 47f'«J86 illlO.£il amP;.;o! Diam.!tl [m::tt]" 41.12 aOOl )(91529 103«1Pl1 1'im7.Ilfi 2SB2JJm EI11J'j6 41Il4Zl1 47421051 mstl.l11 0-'"!IW!rialTypt': G1~100% arm ms,247 IlCOl.604 , llID6.l54 27401.451 32261.m 4]117 .ITi ""'.02l "m"" 03JJ~'J:

I121Il

IOJOl 19B2JDl lHI!7.419 11JJS9.l91 :mI'}.l:l.5 =I~ 4!186.1166 SJi:411,71D ID9l)j4J OJOO

ll!Pu] "'" orm 56"''' 1l%6.m 1'>469.695 2%4H6.'i 15414223 mn.441 S4:m203 61246.707 037>

·OJOl mO.153 1l&53.1lfi 1~21084 ~,412 J54C6.9i6 "mm4 54Zl110.'il 611151.48J 0'"orm rn.", 12571.463 Z1449.S19 31291898 37350426 497':tS,7I1 mU4SO 64262.012 C34JOJOl il:9iJ93 1246'1105 2J.4lt,B14 JII'lIJ39 m7un 4Sj1)963 S6777'" 6J9G5.957 aJ4llorm 119Ufi! 11lI1-'" l16Jl.m 3Jl!6527 3%IH76 5264111J94 6iJJ7Ul1 575'IB.)Q6 ",]0JllJ 7594 m 1",,1&1 2157601" 3llJl,17tl 3'.l498~J 3Z569J95 tm14.818 5m6.984 ".,orm 16505.65 13759.910 n44H9!! 34SJ4171 4l~9.l48 S4all.m 62ll65.ii1 1II1J!!ll6 ""000l 1I18~t 1ms12~ Z24J1,OIJ 3~]t5.rn Ul.S2J1.J 5455SH91 62t)4!H5 m:J81.H'15 "'''0.1IlJ Jel7.NJ 1~IZH1J 2:551.148 :l5631.859 ~241U'Jl 'i6ll1.4lIl 604S!T.lll5 T.di~')'Jn aJ85OJOl 8450'.119 nm.110 2l1OO.1lD 3S44152ll m55.84li 56221.84-4 541>11451 T.14C1D47 0"1OJOl !!219.1~5 11i1l1J46 227~9JlJ msH.115 'Il1II.l7Il m6Il.~10 63l!6J.l48 1!l!r6.H!I OJ7ll

......... OJOl .,,,'" 151604.011 1419'6m1 ,...,.. 4ilJ18J44 611~4.l84 7IJr,,,})• 1m11116 a,mOJOl 'J41.lJIO 1""00 24851.2lJ J8624,48IJ ,"',,'" 6124S.96.l 1II2l6,8)'J' lIDl'J',lD G4l5OJOl 1llIlJ94 15tZ2.5&J 15191.3« -'" 4656H-96 61m158 "'~m "'''''' O,~211

·QJOl 10'3<]" I""'" 11147.998 43318.723 574a06B4 76[85j~ 87238-861 """.7Il9 Ojl~

aDJ] ''']j'' 11~L492 :J4.IJ7.l!JI ll3S6.746 &56%.914 861'>6.414 9'}J1O.945 1(!l195j~ ""aJOl ""w ""'''-' 1J2llj,816 """'" 15441719 ~1lJ'J4 113165445 lZffii127 omorm IIDt.6)) ZJ9J1.4Sll ~Hllna 611J1.313 7%81$5 ""I'" 113596041 Im2,1)]] HSIorm I""'" 25EJD 'l3IliJDl '''''''' a:2l~.641 10S0ii6J15 lZlm.m I:J63tiSEB a.103a.1IlJ -I099.m 'mm "211'" !lm213 14118,504 1!llBJ,6a6 218tiJJ41 228!l.!OO O.l26

·OJOl _1Il911jJ ""-'" "'"'' 1184121S 14:l't).7'J6 1r.m467 Z3J111l3 2lJ61Ul')' O.l2Borm -all,,, SU6.985 ...'" lD618 1651236] mD,!!91 llZl6'" :;{w'i1tl.525 O.l~

OJOl .0.189 54:Jl'iJ95 ""'lID lJ549.6ll ",,,,,,, zmg,4.s9 2S24'J.984'"~'"

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OJOl "'U" 72J1.1j] 11827JJ7 l71mn 21:m.m 2ll1~3J57 32J]IJJI """.,, om01IlJ ...m IlJ7jJlll 13254-,64S 19962.7G!1 24lJ27.5iJ2 31'm,7Q 36178150 3I!liU!m omOJOl ""'" mum 13294,M9 lJDOIl 2400,416 3112Hl'1 """"" !ilJ)'J'lZl a.l21

.... OJOl mU7S 87891J71 14371,~ 2l7j2.1t9 16{""31 34m.449 :lm4852 ml9.lllll 0'"OJOl "".. ElL-46J !4:l9!1267 2l1JS.m <6llHJ82 )«7H4~ 39J35.19-1 42424,46S 0,241

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aJOl 7mh4ll 12184369 ['J'j5O.:JD mlJ3J ,..,,2J JBl93JlSl 'WJ2ll &H9j.m amarm 1S4lJ.765 12161216 11J911Jrtli :JJ6".e918 :!i5411fi2 ~"'''' 55lll.li9O ..,,"" a3l1

------'-aOOl 14[91943 1419'4.711 Jl6li!m 6-47l6.21 16f15.611 100420.7:34 11439J.406 1256118914 O.6-S9

.. 01IlJ 1:zm.644 ""'.021 nl55.211S 60168.758 i12IHlI 93~J19Jl! liAl68L4lI4 117mEi6 0.618OJOl iVI6..37I 110Jl.~9 ,,= "'."" 6ill1l.m· !l.m"S2111 ""'-'" 107854281 am

. 01IlJ 10731'" lBtal912 '""'" 48328.413S7313 ""

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.: ...orm !1J1l.606 149D45')' 144Z10Il 18179.&24 45541484 ."''''1 """~

75iJIB166 a 4117OJOl 6I:l669'8 10081.%5 IT18Sm6 rr.m.488 :m2IJ:n 4:!2Z4.582 49311411 "',,-'" amorm 14585.ll1 Zm9!l61 4IDll.:nJ 66E'£04,!I91 786%914 1IIl217.lli 111181586 1293«,484 "'''OJIll mBI516 ""'''' 4Ill!JJIl7 66714,Q4 ""'''' lirnUSI 117~~ 1294!n.148 01i74

OJOl 15401.742 '"'" '" 43151.357 004.344 ill41!lJj 1ll68U41 111VUll 140762134 a.'"


Appendix


50

lhial.di.~ I ..'" "ca I "" .'" [mE I 2(';;5 '''' 8.Q'n ,m,....... ,Poll Foi2 Poll Pol. PoI' PoI' Poll Pol. Pol' A_<ctr"",MT_

:rrc I DP, DP, DP, UP, UP, D?, DP, UP, D>,11ll9rn:... P. P. P, P, P. P. P. P. P. 11"1Vil;~T!1'l!: - 0.'"' Z1lJI912 4elHlJ 7~1i6S rma.88a 134940TI """" ;rQt..!61 2JlSLIrn ,..'i'~~III!II]: ~ OJ)]) 2689-1:M %ISJln 15:$,m llDa.1Jl 134j~,SI'i[ 1mB" ~_431 23174570 "illV~~ 0,.. 0'"' lIl37,., ."Cl ..,... 1:m6.6l1 14491524 19155.m. ZlISJ.7115 24W7.Ul 0.642Fipe Dia-tu (=1 m2 OJ)]) "".. 49]1.461 8121.4% IlJ61TI1 1«96234 1916.S:m ZmSlll4 2~484 0",WileriaITypl!" ~!1Il% OJ)]) Jl36.67lJ ~~,. .,413J2 1:J1J9.9lll 16JI1(l11 2Il~.l4S 24«5Jl!O m17411 0.112Dmity(kdm' ]: Ill.51 OJ)]) JI~670 ''''''' 119ll,4RIi lW,2&] l.m9J59 2IlS48fiI 144551BS4 21~~ om~IP~J om .

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Appendix


51

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0" 112JI.z36 "",m 19i77,lIm "'0"" JS3SJ.0l6 "'''''' n456.:l91 """.. 0.'"0"" IlEm 1S2'79.4ll 1991702l 297JS545 358/i51J6/i 45881U16 D411.111 ...."" ...a"" n",.", 17002lm Z201997S J3138!r.lO J9%1.2'ill ml4.m S!l4IJI80 610J.641 om0.. un;", 16!l17.l!/3 22OJt96J 3JllUNO :BT74.a2J m.S8.148 $!l151'S 612«375 om0.. 13«9.519 lm1400 23465--'in 3511019 42(206lJ ~JIJ 6319U7S 71676.523 "'''0.,", 'mT3J2 1796J1lD Dl2!l,6:.I1 JSlEI.547 42:JjO/i6ol 54642,471 0l1411lS 71109.J20 0""0.,", 1411Xi2!i6 1877L7Il:l 242972611 J6/iol:t.719 «2a741 ""'"" """'" 14457.3.:12 0""0" lmi.m liSS1152" 24171918 J6JJll.516 43801438 S6-028il16 67;]S1i44 7414063$ "'''0.. 144511.411 19704~S "'''''' J84s:l.115 462193$ ... no ,m"" 1Bll:l1.414 """0.,", 1467'!.1n 1!1657.639 1S34-U'il JII154141 46161.6'l1 5%211.715 ,.""" 1i936.IDI 'IDT

"'"' ",,,... lmJ.156 15IJJJ.ll5:I JSDHJO ~56llSZO .58740.'1% 671211.1J9 ,,"'= 11JJJ

... 0"" "'''''' 19144.1!95 2494J.~ mm" 45~.1J8 'ia6.S5.695 67614tn ".,,,'" UlIO

0"" 14SSti.tl% :!'JSS7.0I4 "',,'" ",",no ""'",, om.ill 72861)219 ""'''' '''''0"" l.ila8.lll :Di19.781 25J1I4.445 ""''''' ~,1l3 61I:JJ516 "mm 82214.J1j11 ''''0"" 1S934.!m 2liS1.l91 2tl959:l( 0134,426 5192(\48 ""'''' 7/Il6S4n 8mI.J5l1 un0"" 1SS1.'*G/i :2\144M3 _m 43S2~9 516i2.4iJ1 ""'''' 76S1i7(84

"'~'"1.141

0" 16254455 2]547.551 mlO!lS'l 44S1l590 n6'!n:il 6ll9'7lI516 '7S469.l41 SIl:lill.641 l.1!lll

0"" ""'''' :n41Lm 2!llT.l,S45 44451.12S' 53481.(194 6ll945.111 79:12lltn .,.",. I.Hl6

0"" ISI4li.1i4O 12IBS3'i9 El8./i.la7 44164.61J9 mll2.123 68611.602 7!107IU48 !l'>4!l1.m 1.110

0'"' '''''''' :l!m.!Illl 2l!!l39.16i1 «214816 mS0410 ""'''' 7!jSoI!i,155 !l932HJ8 1.I78

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~"""95628320 ""0.. 1749;$ 14[iU4J JI29711J 4&:«;3.344 'iSJ6~.4&J WiiJI!Il 8mJ'»l 97448,922 "". ... 17734.414 :24155.2S2 J1412.561 48l.79914 5n611l9 14m.m i.5414134 ""'... 'E'

0.. ISJ2!L316 249'>5.541 J:Z:l84,m S01971lJ9 6iJ2247SO n"""", sg14LHJ HJIQ'i1336 lJ19

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~mno 0"''''' 1IJ1SBJj70 """'"' 220l.!1I6 :lBJ4~3 """"" 6W532ll ;446i~ 955Zl.H5 10992ll8jJ 124478.406 """'"' 22n6.166 xmw :l!1S%W 6<!l79.113 741J1JIlII ~'iJ9ol6iS 10971l151I1. 124I79JJl6 ""A", """'" n;m4i'! wmm2 6~9S1S.&l n~)761J2,,,..,,,, 1l~46; 11!l611m Uj8'>

0", 22S7H41 T.lJ1HJs: 4[04.230 6($..<7313 7715/i 31J "'"' '" 114)!(l.rn lHl'9656 16!N

"", 2J24J1!41 J21~2,4S/i 4!;I')S..6iS 653$4iil na:'lJUl i98m813 llol.T!~.211 I~N ,'"0,", nl!!ll~16 """" 4!5:1l5S:! 64\143.:00 716#m mS6,7~ 1!41UJi!2J ''''''~ ,'"0", JI.5VJlI5 """" 383«.156' ""'''' 117l!iS$f 91S8t664 IOJSSIlJ7U 1191'Hn ''''


Appendix


52

··lbw.im-~--- -"'. ."" ·a85 -lI9n I l.J!6 I ",. 6_~Z1 8432 10.lSli........ •,~, "'" "'" "". "'" "'" "'" "'" "'" ..I._I'boo_

T_ uc '" ". '" ". ". ". ". ". <p.241l1r.ID4 ,. ,. ,. ,. ,. ,. ,. ,. P. ["J' .... T mm '"""" 29100,000 1143661J ~.S1 ~~_867 e.n'l,ll'1ll !17I92.1!l IwasaSOO 'DOY~~-.j " '101 :ill!l,177 744l)!DJ 9494.161 "'00.... tSl6il2SJ :lC:lHill7 "",m 16Nl.1n "'''v.r:.. pmitZm: - !:i[JJJ JI29.E:IO :ms.m ""'" rn,,,, !1017.1illl ll'iJ7.4fl lJ:30..517 [49ID6411 ~_429

l'ipo Diamo'"" ("",,]. ""' .cm 2Wi,!64 J!~1OS «>646IJ $-49110 7'341.016 !lol!1QB 1000Hl1 121'19499 OJSJIhl.,;,dTypot ~ri=100% .cm 24J'H[]1 :lC'lI_lIl~ 4'19'.11.11 m".~ m7.l~ '<34411i-l 10639,S'19 1:!!52,4n 0)45De=y('.qi='] "" .cm 24~j96 I Jl)7I.!~ 43Bi2.59 ~71J 7291.Gll !r.>l!i7i!ll lGS".!.SI'O 1JJS1,821 "'''!I{P....] .an .cm ",,,,, 37S9l>'J 5411~9 "'"" 89:lJ.211 m16364 Im3.m 14ai7W 0,427

ocm ""'" mui'7S """" nu.m 119IBll ll-a'i,rIl l3!49mJ 1411.1.!i25 U2!l.cm ",m, 4S191J7!l &Snail! il9105"Jl lll'iUl.loIa 1J99l.HO 16[i41Ull 1l118lHJIl 0..513,cm >mm ""'''' 6541,«0 ""'" l(J'lOl~ lEll,El 1558DJl Ilil6lJ(J1lJ a'"mm ...'" 412a:21S 1111.583 9'191.9-11 1l1U1,1l43 ISl21-Sli6 m'12.47S 19o\11l,32!5 o.mO.cm :l!1J.I.Sllll 4<lil249 7I!7l.m ;QS!l\Il 116SH14 LSl159.31l1 17216616 19411.113 .'"0101 4415916 :ms.m 784H68 11l42''usa 1:tm:s4 1~5iIll.7« 1!lOOl':!96 1144;1.449 0.-

."" 4J76JB ~..'ill """. l1li51U7~ 1:lSJg,2l56 ISM37l11 llfi'l6.1Si1 214162'>9 ,~,

ocm S,,,'" 6267,666 9'J74.1C1i 124:l:li$4 1lll6:Jl7 19746,8Il1 !261~..'i:U ",."" 0.712

.101 ='"' 6.J7iiOJ om 010 12li11l64 1~152.143 1~6aH84 ;2411.643 154S4,71J 0,718

0101 <m,", "iW),~57 ID749:;m 14571,195 1779:l;m """'" <!6ITIJ8.t ~IMl .""0101 6"<E4976 ""''''' 1041929-( i4minl 176....49% :lm4!lo11 261O'Sl9 1!tYlS',!l91 om

. 0101 ""'" ml.l" IHl9l241 l62'n.El5 2OO12.79Il 25977916 """'" ""'''' 0'"0101 ""''''' ...... m5ot7S4 '""''''' 19l1!!5:!!lI ""'''' 29'm.m mU74:! 1l,!I41

....,........... 0101 ""'" 8i.l1.3Jl 12714,366 11"..$',411 "mm ".-m 3l599.170 ID41.695 ""0101 ""'" ilIi49556 126106 17illSl7 2121H14 Z7Jl4.5U mS1.836 ""'-"" om, 0101 1'173.7:lJ %:JJm 14195611 l~ll1--'i86 D86illlJ ""'.ill m5ot..'i74 ",,,m 1.003

_. 0101 815Hn 9550250 142IJ,Z2J 11'2411l1 rJl6'''' )]682217 :l5114J36 "..OS, ,"", ....; . .._.. __ .. .cm ""'" li6lS.%} 17Ui2,166 "',,"" 286D2,771 36m9l51 4m7,l2l 4m73.734 UI9

...... .cm ;>ID'" 11782281 169-~I.as::2 D!7l,415 28647,6"16 36&36.422 4:llIU..- 47593.422 ''''0101 '"""DO IJI:l!J.!2.." '''''''' 1S'rn3SO JI961329 4ll!nH" 40U47.lM n:llill29J 14\10

L~:~0101 Ullllll.143 12877D14 Ill'lOOllill ""''''' J1761Hl 41517199 ...W. ""''"' ""OlD! UlIIJilD IJ981.6:lll 2ID7~m 17mm 3415ll.l7/i .""'''' 5ll45l1J5S2 57ll5.'i.3Jl U.,""" 11l47E Im~,4<j(J "'" '"' 17431.lm D6S8,J24 .:mIDI2 :mJ5.7J:l ~67.5'13 ''''0101 11771519 1.514,51. Zl259~ 28872..:l8 JS148,m 4lilli7.641 D7llUIIO ""'.. ,...0101 lll!il.m 14S1l,I19 21J571i26 ,.,,,"" 3j9]8HI .ID7,m ""'cm S9814.J5! ,...0101 11443911 1~311 2l'i34,nB ",~m :J97ll:l,1ll1 ,"',,'" S8147D.1l ",,,- Ul5

ocm lID4SlW !:5'¥4.14 DlS61171 31'm.92. 1]542469- -"" ,..,'" ""'ill 1.815

ocm 14232327 1m62,74ll 2.!n!.s63 J4m,O'1 .D7lI.l48 "",.m 5Z]J5I242 """m "n0101 14281.575 1708&].13 i.."lIl......'ilS 34455.a59 .2225,ill 54344375 62I7J.tilS 'm76.5'17 "'"0101 loi\li5:3.241 175l11j]<j(J """" J517lJ,191 .:13«,517 m33B5 tmOl!i.71~ 1ZJ:43522 ''''aim 14J76,3!17 111f14a:l!l ~,947 m.5lljl)] HIlJ7.J28 ""'", 64TI5.246 m4lll47 '.tm.101 I05l.m 11641.G82 m"... 3~1.6BJ .J292.172 S5612.:241i Olli6'" 71i2E!~ ""0101 I4m.ilIS 11641.75ll 15llS1371 ""'''' Hi'll12ll 'il!il1l.m 642601DV n,,,,,,, '""Oilll 149t9.8ll1 1tn91910 "'""" """"" .lil5'.1Il'iI ~4J2!ID !i!'iin.78! n6TI,I88 ,on0101 '''''''' lBm.65!i 26721.674 J6!HI.J;:4 4£llU51 .5lI14H14 6&5193"- m45.617 2.!lS1

0101 14ill.1I1l 17'm34B ""'''' :J61~5.Jl& ..on ... "'"SO "",.no 7.111.742 ,onam! ,,,,"m 185'!lfHI m",.. TT:54nG 46m.543 5%18..'iSSl &m6.789 11[05414 2.103

0101 149911723 IS5um 7'..638.211 """" ""'''' So419,m ""''''' "...", ll(J!I


Appendix


53

lA:.i.ol~ ..un ."" - ..i4cij""''' ,m "" "., 8,3111 ,~.....- ,

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,,,,'#&.~=l ~ 0<'" 17OU.Q62 2a7UUl =m "'"'" 774l.m 9Lll.7fit lrrH314 11S4801B 1063...... po1ib:= - ,~

"'''~ ;,ml.1D9- 2615'.4"79 4(llH01 ~_9"4 ""'" 1S'IC.im 1l"r.n.:J58 O.1r57P,,..D ,•• """j 8O.4J ,"" ,~= 2135742 21:nS/i5 4G:!3!ll1 ~711486 6738803 1S'J271J! 8T2l.nl ,mll~T~ G1~11ll% . m 1:'aSJ41 :JllS,06'I

~- '"'''' B491.2E!J JOO8IJ295 Iltl92JD OIDj-94l< J IJ6De..,ity["~l "" ,~ ,~- 31:l6,1'85 -"" cmuu 8521.li41 JOO6.l,m 11S9D81 1~_761 U'JI~iPul ,'" ...

,~ ;x:11m IJlI4_10~ 4IDI48 ~= 9]437';6 II()fSJ9lI 1:C:;!461 L4:>c276S ,=- ,"" nr.JC<l9 3J8lJ,m 43488'J$ ~~ ~,~ 1l044.9o\2 lDcO.66) 14W'l4O ,~,

,~ =.160 )147569 w.l7J7J "',,'" 11:078.257 \nM14] 14-t769J9 [$TI1958 "","" Z51.Q77 J7J6.1:!l Ill2IJJlI9 7:J6951S ''''''''' mn", 144ll249! lS'lJ7,61J lE,~

""'" 4[!:iZlO """" .,,,"" US58I2J 1:J641.4!/l'l 1611IMl 17719512 """"" :w7.lS1 4142291 5JSJ419 9Z2!ln! lusa.DJ 1:l6fIHOl '''''''' 116113..m ,,~

,~ Z7~~1 «J!~ mg,!i41 ""- !W!uiln 1<6:14.756 lruJ346 '~m,,.,

m mow «Z1112 mm ."". tnJS3118 1<8Jl14111 lnll:l9S IIl9S6.4OB ,=""" =>- 47l1L775 517S,7lJ7 ~m,7!a 1142HJJ 13104151 18oS8l1.5o\S .m21~ ,""""" 2!1l01411 4n4,5"l4 5155954 ~S1ll)M lJollO.:HI 151114 55'9 106!-5.896

_..1.7158

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"~ 3681415 5!lll],J61 15i2.lJl 1204USl 15l:l1.!l51 19115,2tIiJ D197556 3477.823 ,,~

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"~ ml,571 61*6.5:.:l:l ~,= 12MHTI 11S601n :lIl6'19S5:l 2'l34USli :<6687J8l! m'""" ""'" 6J_SiIXl 793JOll 1252S'SJ9 17_9SJoo :<ll6OI!.71i 2042_7666 -= m,".~ "" '" 64<lll,814 om on lD42.253 lISlOI,5 21SO.m 21521,63'1 :maUll ,,..

.. "~ 3llM,7ll M1U43 1Illl.614 1329L74O 1~,47l 21~.5Ill ~4U"JlI1 171l6U46 """~ '""''' 6784591 87S1.511 14074,690 19-4S2.1i2J 22B!l15'[)ol ~.~ 29525.466 "".. ''''' 4m,ll:! 1i16U12 VJl,W7 """'" ,,"'''' ...·9U2lJ ~"'~ """" "'"""" 4147.514 ""m ,,"m IS15L6lIl """'" 14&36852 2!l9SU54 :lIIi8li,~ ".,.. """ ",um

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,,~

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"~ fiJ21.2SS 9<41Hi)!l 12120.515 2lmm ""'''' 33416,m BI51GE 42/i91.«S H$12

Dem &170813 ""'" n:H3.% 2191l2,594 :N3S7nt J.l181.62!l <IOOfi1.297 4J6!l1l.:D9 ,=m -'" 951:.1.236 125-1-2,104 21154349 2'tln68B """""" :l9!tIl.2IS 43504,211 3543

Non-Newtoman Losses Through Diaphragm Valves DM Kazadi

Appendix


54

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J<1llJ87 JlQ1Hl!1 =-3BJ :l::::Mjl2-~

2l67',1<J ~,~ ~,m ::6<6IliJ9 "".. L_ .. _ "rn= ~,.. JJ!ilJ.JLS. m~ ~.i1l l'!ilSs::::l ;r.<,lUI 21ro,Ul ~'" aD}:Ill1500

-~J:!<J~ ,,~ :l\l'J:ll.m 1Il71Li'll] ~ 27Di,m 261"'''''3 ""!Jl!DIii =7l:l J11UW ]I:l'?[l?i52 :l94tHIl6 -ill :m67J56 27mm ~n... ='

]JIl97.lal Jlmrm: ~m _m ~B 2lC!I!PlI 111!iJ1.;m ~= :l6ill1,. ,~

ll6al!.tm JlmG15 ~'" :JlllllHl3!I ~'" -~11!m~ == ~n" =_m _m ~ B<1<:17l =.1!63 2lI(I<l-'lll 11QUlIJ ..= ~""

1.II<SE'ell.IOI l'l36<lil1S J(Ill:-6/il ~" 2Il<l2,1l3 :!lmS-'H;1 Z7'.\<J.311 =m _n, ,=_m ::O;<I';jO ~, -= ETl.J2!l 1T.'<Sltt Z7H;;I.l'll 1112L1:!l ~11.!l7] ,="..~ :ll'lQl!JIjJ """" -~ -~

117:.5,$56 mlC~ 171:JJ.4J! ~".. ,~

"",m J!WJ.02l ,..~ 1&:01 Ill!! 17m.m ro7'7!)111 ~ ...,. ;;Mi!l-Jl:ll Ull,."m 28.l:::lQI6 23<41.:;>;111 ~., 17l7'l-lliO ~.." _m , "..- ~.. ,m1i4~1ll 2iUIJ.lOO ~ 2171USl 21J<Ull ="" ~~ lS8'TH5a ~., L61lJ23><6rn "'~11r.J5 ~~ m.~ ~m ::n;Jm ~SC142 _m 1Ol1-ll11 U~


Appendix


55

. ...... _'-Tid~---

"~ "'" .,,,, ,'" ,,. "., ". "" ,m I,~ ..... ,

'- 2!"C l'ail .." .." ?.- .., ... .., ... ..,~-~-m''''' .. •• •• .. •• ., •• •• ., r.,1

V..... Tno c~ ""''" :§nJaQ .-roUJoII ='" :rull.•!! ~ .,.,,'" """. -" ,~

' ....~_l • l/ljI1l!!! Zl54lJ,'IXI :m1lI.ll~ ""'m ZHZli.J!.l ;1044-1-l9 JliiWHDl , 2!J:7.48I! -" .~v.o.-]IO>iliIm: .,. :m"1ll!lli 114'11J!DJ m:i4J!l'J lJJZ7Q41 '"""" m"", )\;jHIIl ~jll :l6ilOIDl D~2~~(_J '" . 311W.J1J3 l141l,JJJ JilOJ.Bt :I:I:51(tJ 2lI:iljOJ] !7S!l~1. :lSl)1DJ ~COJ :li!!lIHttl ""iLl.m!Tnoo: ~m-; ll::::!im =~ r~l17 )l7IWJ646 =1.381 mJ9]59 7JlOCOCll ~~ ;ol4ll[JJl ,mo.-,.,;.v...' 1m2 """'" """ :':<8,)3 Jl77HJol 2l!Slil!l m".:!,:'?9 17l3HlIl ~2'l5 , ""'''

..,'u oml ,- :l41:ll.!4i tt1!i1.l.lXlJ :l'.!:;;O.:.no J"....L"l') 1114 :l!!'1'>4J71 :llIl:;~ T.4llIiXll ::gm::m ~~(JJ] ,.,

J4C'7J,OoTi :ml~.IXlJ nmm :n!:"m ;:l!79lilll :3J3JlIl r.::9:!.OCl) ""'" :;64~rm .m. ~Hl'll!S

~" :l<:il0llS :nV!iJoll Zilm4"~ m;ll.1lI 116lJU811 ~" WOOOOJ ,~

lXJZ,Z$ :K'NJD1 :l<I1J::'.9llI :t!Zi4!T.! 2SIDI:Q4 ""'''' z;~m ~" ,.." l.al~

!15\1.56'l ""'''' 364<13J2 , Jj,I,H~a BW:!145 2Im4 nJ """" :m'll'1Dl WJIlOOJ U69:Il5!il!!1l :l&'n\l.lM !mS'.!i13 T.1DJ1'J 2997(1111 2l1~.n4 ~m 2$!1m ""'''' ,'"'l91:II,m ""'''' = .. J'1t!l1.361 DTlUIS <>m.. mmm :;s:lII.Jil1 Z!i37004 ,~

4J'm1l'i ~11.l76 Y.t63~ J7lE!JTl. "'"'" 2IXl1!1 T-U':;lJ ""'J' "",on ,'".~H3lI U:J4:!IJ.I 415ni<il , 4iilll..\7J mlUll lllQirn 28i!2J91 m!l914 :;s<m2!1 ,~,

mW.m ~.m 01>5281 4J5111J1 114Jl146S ~lil1f/1i ::?l54Hi"J ""'~ """" ,m474ll57O .~~

-~4:3fi7JI1'I D'"'' maUll ~~ 27+MJll """'" ,m"',,,,, '':972.816 14S'll'i.ll3 4:l:7H16 ll!Ml:IlJ 11l>1ll1 """.. 214~M ""'-'" "..

4il!3l.7el I&IE&S _m -.... ""m m,,,,, ""'.ill V""" ~'" ,m4971l!.m ~2.l17 _ill U>:il.l1lS :m4l.m ~:l16 3-S6.IlIJ vmm ~l.9'iol ""ml~.!!IIl IlSl'iE2 lW!2.l!1:l 476llN )l91H14 m4(l,m lll~C911 ~~ ""..", ,m"'~ 1IS36.J:li :'llJ4Q596 .r.t!lnt 3m2012 !'!!l4.:'m lllfifim "'"~

:lS79),41l1 ,..mll15a "",m "''''< .mm l!'iBJD3 "am ""'" 1lI11H61 mm., w,""'''' I:ll4J41'2 illl;lll2 5lJ!iill.;'4~ 36::'ll31& 341:l4il'Jl1 E7Cio1i ,..~ :l5'I2J.656 ""64S4i'6'1 ""'''' 6C!ll,m """" ~s~ :l/iJSH6i 11!Slf.Jl1 M4f!:t1S m:!l1tl "","".m 6116J.ill1 ,£ll';U:'l] j60j6'];ll J8ll1.!7:! :i!;15.m lIllf.61 ...~ """,. ""71023.21l &&illllH 6So6/i,MI 1£l::4.m

-~ !7874.TI/ ill19.2Sl ...'" :mS"J;./'i ""11o\81l.!Ilj 6e602.m::l ""'''' 6.mOO1 4059lS18 J78..'IJ,UI =rn 2!l6l15'll 254:;4316 ,..,~l2!l.m TID4766 694JHao ""'"' 4J'II'll4:l4 w=n _ill ""'~, "..'" ""1lIi;lJTI8 ""'-'" 694.\7114 fil.l14.Q41 41116i!!91 "m~ ""'''' ::!Ilm.!ll _no ,~,..,,," ,=~ 1l9'J1.7Z7 CIon 141 42fiS1 """" -~

:i5'1l2.l112 "mm """"'m 14188112 111'04.9014 ClIi71&l'.l 421"!.J.54] :!9)4'1.J19 D211.(JI 1lO'l4180 2Sl1lr.l '"'!:m17Zl ""'''' 1S17\1.61l2 ~." 43illam ~ NJ37lil. m34lD ~ =!1I11l.:m Tml.l~ ".mm fi7f)(lm :M9:1H1'.l ll%lJD _m 11461ljq 12ll\ll1.9"..'i ,m!I(5l1.m 7l\mSD 'mJ:E!'B 5T...'-4O:S l4lI1~:JIIl! "".m Zl..~J'}] 11:!iHW lNIIE] ,~

'""~I12W,W 17'iJ70 7ll11a41

-~ !Ll6l.ll1 nm~ 11'kil14 ,_w ,m

""'''' "'"ill a9nLl-;Q ..~" .""'" 4'llil.!9:1 ~"'" nlUI116 ",."" "m

Table 18 HGL Test for Glycerine 75%!hiMbtas I .."" "~" ."" -1.261 "'" m 5,449 1.454 9.4llf'f.ioo-plOllI "T_

m: Poll .." PoI' PoI' PoI' PoI' PoI' .., PoI' i""C"ibom.

lJIJOl> .. ,. " ,. ,. " ,. ,. ,. ~I

VilftTne: ~. jlJ'/i)@1 562M1l ""'... "'I'" 4<:8$.9'14 1'J(~-4111 34:l9rm liEn! 11846.451 i1'Jv.ml!iDeliJa[...j; "

. ~..

jl52l.ill l!JIIJll """" 49')51631 4E:4mJ ~:lil11 J1.m.191 3mWii 11867.4"". ,.'"VoMpiiim: 0,. 56ll1~.i ZllH1B mJIMl f/Qgllll 4124100 """" mu. "'''''' ,..,," Uti

Pit'oDia!M[lll!IIt 6108 .... "",m Sl191.Ii!: juaN7 47liU76 mn9Jl """11 = :mmn ,.,,'" ""lLl..wType: G,tm1% """" "'lI'" (IJm,~ m1i~ Jj~JJI ""'''' llJlI.. ])(li.lll ,.ill." '"Demiiy['..p:lt 1l01J '''''''' ""m ml1ill 4,iI8UI,i $ftlUIB !S24m )ll71!i!1 114:J.m 27lDJ5I' iD"",[pu] "Ill .....~ ."". ~jl1 en"" 42161323 :mn119 ilI9.l2t JlllDll 25915MI 17lIIllll ".

""OS" ""' '" 4iG46.Hl 4w:we ""'''' ~lW ""' .. ""''' """'I lOl...m 42811.1U <m1l-'" ...'" :im!422 """' 31iJ1'1.Bf mJl.'" V,"', .."omJ1l1 1:Jm.m m~104{l :B&l-illl J611ll':BS ""'ll> Jl5:J11Zi ""~, ~lll.~ ''''.... ~1l51B ""lJJ6 }7SJi.ill ~)H12 J:6(HQti lll.'lJli ""''' '''0£11 l1!J7Jl6 m<ill", mm ni54.m '."Jll n!il:!J1'I l2l7i1Jl El,'" Bl1l1ll """. '"1Ellm ""J17 ""'.. :m1t6li :J174~ID llill1!/. ""'''' :l8IilO87 V""" ,..

~---

_mJil~.l(15 :!S48.1j1 J:oo::fli Jt6~8£.ll JllJ1.ffi ,mu" 2S!lli1i19 V".." lm

1ml!76 "'"'" :ITiIUI) i :l2f%rUIi 312S!.6i( l14'U57 """" lm.9'i1 1!C!45) ""lffiBrl J«7L~i !354iIl'l1 :m-tl!!17 J116ol.469 ImS.77S -_..

2SlS4j12 17414~ ,....

llm.m :r~.4i3 """" ~2lU ""'... 2ID121'1 v;(lIRB 215311..- m... 1126


Appendix


56

[.1nl .... I ~_m I '" .,,, -L!' ,'" 1)111 W a.461 ,S>I'i'at~ 0,_ lIt "" "" PoI' PoI' "" "" Poll PoI' Pod, A""C!iblta,,,- P. P. P. P. P. P. P. P. P. [l!j

'1ih'l!T",,; ..... ...l~ma mr...B24 1%j.S! "'JJIIJ 3nn.m ::m.1ll 11:z;5143 m7.rn B126-16li ''''V~~lIllIll " 41618.367 *1154,a2l nJlI !m8.m 21139018 H61.... 3«13J16 ,,,,". nEjo(9 """11

icR~ 0,. ""'" ""'" D.347 n41l.ill :r::J63.71.\ I 31~..m Ja.U1 2546i1.102 ""Jj" un!IilRIliiaIer[l!!lIlt 1I),4J ~LII7.E l'iil4.324 E.J1~ l'l6'16161 BlHIII iltll166 :m~.IO 2Se!1~ ll!%4Jl. '''"IW!!iolT."I'" G,mJ.1.l". EJ4J1J m:as :W!~ ,,"15lJ J:1JHJ1 ]!2ii.lJ't ~j4.1J2 ""'" """" '"'~I ilm

.....',Dj:!) "".1!l !mtS)} :bm.l!J 125/i.6!Z )!D1m, "'"'' :l74Gi.ill ""'" ""~[pul Oill ll64EZl Ell]\I21 31!TIl.1l1 :K..I7Hl" mtm mma4 WA!ZI! """'" :lS'l95J43 ".13l1:.n 34'17i1ll W]jJ5!j I nU2i7 ]126t156 ])1~Jn 21~.IS Z643 200.!1S 4",J5mS61 w.l:lJ91 J.llllial Il71i1.1J4:i ],:liellj ))1;:),121 2l:!l,m: lliJ"" ""'1lJJ 4j~

J2l.16e1 :m16.l!i8 1174iJJ5 315a7Ola "',,,] N'.Bl3t:l ""'.'" ,"'''''' 2BIJll.JI3 "0

1Zi7UIT :Jm4J'lZ J!l'J5tIl , 3mlill "'''11 RlIB'i'l :R4i.lJ1 I """" 2!1~1~ ]mmm ""'" 11111'" I mJl.OO1 2ma9J5 ...J21 U.6ij I :!l~~j 2'i'jl!lI14 11lO",Jj" Emu lIDl.. I lI!l6jl6 mlL77ll ""'.Ill '«"4j j!ll)l '94 2lIJ!3E lS1'

Table 20 HGL Test for Glycerine 75%l!ri>ldirt..... .m .JJJ42 -1342 -1.040 I 011]] ''''' lJllI 5.010 9jlly.m, ~l.l!I! 0

Poll Poll Poll Poll PoI' p~, Poll PoI, PoI, AYWClfWDIl!T_22't "', "'. "', "'. "'. "'. "'. "', "'.lil_ ,. ,. ,. ,. ,. ,. Po ,. P. [lh]

Yh!T:ne' ,.,.,... 0.. 176.m 432.41l m", ,498214 2S91.191 JIll.n4 ]'Oll'O 485J76lJ 1J<O'iolndimmDn(lIlIlIj' Ill! 0.. mm .fC9.l74 m.66i 2438.115 2rn!ll1 1:56.486 :lt12.sa:i "1'" 1J<O

~~ "'" ....... 0.. = ""'" fG6.m ""'" lmJl4 :rn.,"" N,. 44211.l36 ""Ilip.Dimelor[1!llIIj 9711...

0.. ""~ 4m.ll3 @]J7ll 22lIL34-2 ""'"' M.916 3JlO.14ll #~'" U$

l(otHi>lT~ ~75% 0.. """ 374,152 "'''' DL8'lJ 1504JSl! ""'" }J8S.oH 4151,1~ '.121D!mi!nldm'J 11'" 0" :m,m 369.720 651.164 'Z\2fiEn 7)1148'2 2698,:m jHD~ 4l1IU8'1 ,../l[pu] 0"" 0.. m.m """ 51Hl69 UlBS.i"J'j 2224,476 239l.m l12JJll< J1]]illl un

. 0.. ItH8S ~9~j 597,069 1917.O'l.l l2l2&i5 2409.m 2'lS1.lli m9D29 'E0" 1401,rn alLlHl 0''''' ""'" !856'.@ll 1967.841 2Zil316 11J9.5U1 ""0.. 124.517 ""I 485.647 1~.l22 IMUll lm.l91 m1Jl1 """" ,rnOJXll %.%J 2nfi3 407.lJjJ 1J14.5m ImJ2B 1101134 I."" ""'" 5JI6

..0.. ~.m 2J')J<' 404.l2l 1111Jl21 mLlIl6 I"'''' 1891.J61 2631.722 S1280.. ~'" :!J,S,6S.l j18135 1051036 1248.m I"'''' 14i1Jill ,,,,,.,

""...

OJXll %YlJ [w.w; jI9,898 I"''''' Imm I"''' Im.m 21[12,416 4,619

OJIll ~"" IJ/iJ42 241611 811.4m mm IO"l8"~5 109100 16!i5l.821 4J>ll


Appendix

Table 21 HGL Test for CMC 5%

57

=VUftt'l'P"v.... _1V>lft\l<><ib:=

l'ipoDi-!,,(=]

W~T~'

om

l..l.ri.l~ I '''' .... .,,,,, .{l!21 Ul76 I UillS .... .,,, ,m,~- 0

"'" Pa.:i2 "'" "". "'" "". "" "" M1._1"__

,. ,. ,. ,. ,. ,. ,. ,. ,. ",""',u 2661S.ll74 ~~1 2611S-l>6 ::;sl5410 Z6511D 2.l2:i6.76a ~'i69161 2<l72'J711 0.07626i1S4.llM 4651')984 263121as <6170121 2S8S2t:l8 Z651:lSf. llill7.65lI 24%48~

~"'"",on

I """'" ~_ss ~-C!!lII a]861~ 16OO:l-D7 2S78$ I'll! :B3llln 2:m4S41 44749.TIS ,,~

zn::0494 ~_4}4 26SI9SS .,W"'" I mY7,066 mwilll l.~,1m lSU1HI,S 2fUlE ,,~

ZT-'Ii\35% ""'"" 26641473 26-«6,915 2tlCll4tl 2'ill6CI.i!5 "",= 2SJ4SB61 2f75aan 0.095

I mm.. """" 26l£l6.SlU ""'''' 26H1'11'H 2SL"J1!Sl 2J34im 2S¥4?1'n 247S110 ""ms114] 2'n6J.+1I I 26B3B4ilf 4IS611,lZi 262l1018l! ""'". 15411.1]7 25219m )f77lJ,an a.11D27~il3!II m>'>'" 2!il144~ 26t!:UI7! ""'~, 2S940611 :mr2.%1 ~4<4-41 1476U14 Ol!JlI2ll€It5[)5j 2an!I.412 27liIl4O/i tiDUn. 257Il.H3!l 264U&l7 m,,," ""'''' 24826!:lIJ OH92!!!HOSW 2lID].i8ll 2157S!lsg Z7J61.2,17 26:191.365 26"5'm 156912!!1 lli4llnJ 2mUll 0,149n.7,154 :S~.2ll] 28'7lJ.S5IJ 2eE.>36J I 27ill~ Il'iJ5i1!.1 :l6061,1Il!t 2sm.111 24i86.Il6S Ol14

""'''' """" :mum 2B27S15O nm7ll1_...

2605:54-47 L<459.JS2 _r~ o:mJIlI<9.834 '""'" 2'74:>01111 2Il'.l!l'l.S9 :zs!j6g./jll 27!OO.lil5 ,..,... ill"''' 24923.J40 ""l!!JN.2l!5 ~,.,," :G45:lo/IS 2S'll45137 29G73.6Q7 V'ilJ4:iili1 26:343299 ".,,,'" :o.92S.&5Il .'"-~, 3131Q23:l mlU43 ""u, ""'~ Zl'JIH:34 06-S6S7.s4 """" :24%C.CO'J 0.310

.. ...- JJJlUIJ 3I:n!$8lI == -'" """" """.. l£l61.1Il9 2S740.iB!l 249~.S!3 0.31lDnUM Wi4li.l411 31!ilJI-lBJ """" mlU4S '""'~ 26>9l,44S ""'''' 2'lJ13Q94 om"m"" m19.:i61 315$1m :m0l103 29"7C68 28643.lCN 2E'l@J,1J9 :zsg:!7.(Il4 2'lJ12.6~ ...:n7lH21 "",.ill 315:l9246 3J'>15441 ""'''' 286tlS83 :l6S'8J19J :zsg5llS16 1Sl10,1If1 ...",,,""' 15452.m JJ75J,%S ~ll1 """" 2!n425iilJ vrn.641 ""'.. "",n, ""... J65f9,6:17 ~"9H76 "',,,,, 12!i'55121 =,,,,, NTl.llill ".,,,,,, """'" aI.!I9,T./l ,,~

J8..'29.rn moo", 1.."29HI0 3«nll1 317171~ "..,'" ""'''' 26Dllm 1lIJ9.1la5 0.653J8SllJ.4Jo1 sm<", 3S3'17i8L 3«12%1 116i1l50 3QSI04")g 2llIlIS~ "",m. lllJ!i 1)9 0654".,,,,, 39154.m ""'.m JSllOS781 "",ro< 312711.213 ••'H" 267$,729 lllaJ.BlI'il 071>$~,.,'" JIiilITl.219 )69J:]1D1 35!lTI'l41 ~". 1111HJIiil -~, ,..",on 2S11l4,1l>l:J 0165.zm.7:'il 4ltIllS.aT4 :EUT0/14 """"" 3n:J6.J!l5 11SIII'.971 ""'."-' 1&11'1'. 1:l"15J,a32 0,8&3421'nIM 40112..598 ,.,.'" _'" :J:l21I441 31iffll71 ""'''' ..... 2S178910 "'"44111.l91 424n.iil4 19157.012 JIl.QJ'))l ""''''' 31410,824 """m 2107'HlS ll2!J!l924 0,%144146,B';9 424G2,1lC'l ~." :Ji49Q1l66 3l;81C1l "'"'" .""" """'" illm~ "'"4~1,695 ~314lJ,CK7 40421,4!n :El:l9,2.SB JoI3155I& nsBU13 ""'''' 27166469 :m:l:l..45:l ,..4~l.H8 432Cl5.1l1IJ 40438,&n J90iIJ,:i6J 3435H53 J21l'j&.404 2S'!36Olt 211&5,084 152)1.211 "'"41Ol1,J95 4511'1145 411!nJ40 401M418 lSllrl 511 """" ."",. 2734S.li57 25271.rn 111349J)S~1 472'i9.l:t1 «04ll41J 42492.043 3587&000 n;.&l,246 2Wl5ll'16 213H}J ""'''' ,m4-6&l.4.1IV .."""" 434&'i1Z5 41~'i4.39~ 3S6S0.406 J379UM ""'''' Z7S19185 Zfi)1.717 CCW5ll7't51i1J ~m.215 45"-69'191 430\;6.055 3M%!56a :J444lI816 lJ243.1SO m14170 "',,'" UtO,"'.... ~865) .•ll 452S12>a n72S!l7'i 364:>i!m "'..'" 3J2J1514 '""'" 25346,414 131154\14HI08 511-66.105 4%32.•114 .,m" :l7S-<9416 nS98.914 "",un :lllOi'\6Jl14 25426105 U"549&B.IPSI ""''''' WIO'1l!I 46't19LI'iI 31!il4lJ:1 156::l31lJ """'''' ""'''' 2543,1j1l7 15X1

""'-'" ""<SS, 50129-344 4K111m :l846il,4:U 3/i'B42.SIJ 3U!n.lJ8.t 2ll2'iCI02 :i54ti6.\41 "",56677/114 .5/oJD:UU 5OJ6J-.W ""'''' = 3liHUllll JIJ65E El"" -.m ,.._om

_.m Slm.9!l4 nJ91.JilJ J9146.719 J66llU26 114ll6.695 ",.".., 254~,262 1.71t_...5611(J.63 51m':;SI ""',. "'"~, 30168 84lI 3t531.5.:l1 2il41ljj7J

"'~""171t

"""-'" =U," S3634.4:J] S16f(l$j ml1i1J~ mos,m Jlm.4iIO .,.m", =~, ""'~953 ....'" ""''''' 51f>4Q.i55 J9t1427/ :l721551l2 311l7l7ll5l 2858S.441 lli7ll.65l1 ,,"oml.m 6':1181.45'6 55645«:1 ""'"'" <am'" J78.HSiI:l :a/MD! 'iil776G81 """m ""629->6!J!4 60147IIU ID6:lJU "'''-om 4C632676 :mJ51'i4 J216.S.1IS1 :lll7~L1" ","U2> ""....'" 61953.266 "",m~"""

41(l1;'4951 ..,,,'" 31451416 28916818 ""'.... 2Dl6IiSITI.648 "'"'"" S7n4ji8 mlSi!JJ 41l7ll.J:l2 ","rn ""cc'" ""'-'M' 25&26314 1.015(,Q)un 5361li3TI 58821.lilJ "'" '" 4194(1609 ...",~ m25.117 2S'llI1!l91:l ""''''' ''''

.-&ii699--'iJl 5J51D11 58lWm2 5651723:1 41il16.211 J8722815 3251''-49([ 2!1l09!07 11574,076 ''''6:l16U9S 1i58Gt.15B !iJ761D2IJ 58411.:l.3iI 4Il76101 l.l189,2S1 n8974:ll1 <5119879 25lIiIlI.404 2.214~.Q-47 6572ll'3lJ 60716,742 :m66.l1J 4232-4164 39164,«1 :m14.!51 15I156JlQ1 "'~= nu71146.1i95

_...!i2141.199 liQD1.461 42961844 ""m mm ... El"n m ..", ne.

7llUJ1J6 .".,,'" mm"" mns", .~"" J%nJJ3 ::mll\:llTI """'" """'" 2318

- ""'.... ~"""" ..,'''~ 6!1S02S48 4:D91!l1J 40101.5;19 3145.!.611 """'" m."" unmn." S4n.141 6ID"il1!14 6i66"871 4342t.539

-~ ""'''' 1!!470,1l3) _'" an_ .. 7Pl2,991 71741.D 661:!'.l.2S0 6JllJiI.156 44112.348 4Oli1S.J3IS m49.1i6 2%57KZ'J ~796.742 ,-,U

7D11.JD 7lIii!i.453 6liWI)·n ""'''' 4412fi.s~2 4OIi61371 DTI1.445_...

NlJll!Il '-'"""''''' """= ""''''' 6mB,Ill ...""., 41G47.&57 """.'" i5'1S8.J16 1:l"ll£l!!.?ji "m

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Appendix


58

V.JlwT;;<pt: !}~

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[Q'.ijll~38 99821914 9!66l119 ~38156 ma:!.!24 Wl6.l4il 3a3«J~ :l:n194Jl!l ~"':JJ7 JJ7l

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Appendix


59

~~IUll'n-4

1'01"",11'"'V.lft~"""J:

Vw-. pasitim:

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lluoriolTr,><.o-iQf~'J

T,:K..

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W"U

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= 1.'4C6.4lC 2..>"J~J% 2mo~ 25i6li;16 2:m:U::5 '.!iIJ95]l 248J(14ll 24li71_107 OOE

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26110.t39 2SSS6,m mli99ll Z647i1Jll ""'''' 2.'illi7'1l "..ill ."',. ~711,002 CO"]6U5_?'1l =305 2l1e16ol 25613.191 254IHS4 L<m,m 15JiI]Ol 2491J.J9! 1'l76H11 alID

. ""''''' """'" ~:m ""'''' "",an """"" :mn.434 2lI!1UJ11 1C79ll_1D! a",2ai'Il14Q 2.l!l97.l711 2~n5!t I 2.."1iBI6 255845] 2.WllI,7£l 2.'i!4SW 2("904 2479l!84i ""2!i49.481! 2l!164_1Cl'1 '2ro4USll 2SSICI2_36S ""'~, ~l.na 2..DJ6,21l ~14[lli 24814 m Oll81~2.2SIJ 2/;119U2 26iJ15_aM llil6Ci21 25tt...'\H,'i2 "'''''' 252)4 :;Q:l 25lJ.ns:!e 2'*812408 O.c81:!€UlI,l8J 2Mll,115 ""''''' 2l!IOOQ<49 2'E1!m Z56:lH'i6 2.'i:l98C1! """" 248J'J.241 0103W6H19 ""'''' :<:$2678..."4 26lJ8J..:5H 2Si:<sS49 256j7l\f9 2529:l.2J4 2..'U637W 2018J1.4llf. !UDfZ/111-Z9 26712-426 2:l521.47S ""'DO :<5::194:39 lmJoa 2'ib6.BI5 m~Jm 2"861887 om2710515lJ 26672.541 2:ls.:-I2'ilJ 2846.424 26U2'i~"'~ 2Y/5(J,Jll(l 254OO.15lJ l5l3J{!6e 24867.2Ql orll

... "m", 2708:4.408 268"".di..'i1l4 2!e121!n 2&4H:24 2WI1n!l 2m:ua. """... 2-4$91.il'lll 01662'7'i66.m "",,"m 1fia5J.:'HO ..."" 26240..'iJ7 m79m mm'" l!2U.4$4 ~.l5B 0.16628a7L5~ ~144.441 mum VS?J662 26'Illl~1 2!i.."!1221 """." 1.'<444.1147 ~~.rn ""2IlUL951 :ll!15!l.121 7lUa.4:l!l 2756L4S~ 2£l8Q117 """UIl """" 2544HJl 2<'~87221 am~1.035 2S!j]B.illi 2t'lJJ 37J mJ.l..9Jll V3JJJ99 2:9.D-S.fS """"" mm. 2:ilJJ6.'nS .3<02S«-8.rm .""" 2ll3:22.l)1 2192a.338 """" ""''''' :l6U6326ol m""" :m17(W .,,,msU/il .m", 2!ml!.m 2!tiM484 "m", m23rJ1 ...... """" :llIl66,471 D,441

""'''' 293&5.ol4 ""'''' lS4~m Jn62.29j !1m174 <&318366 """" """"" 0442

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... mnl~5 3167'.S41 JlI:ll438 mM'" """'" ....m 77'J5/i.77l 261....l1i4 :moo 41. 0766Jn7.all 31667.52:1 Jlll'71i.m

_...2!l239414 2Il413.1)74 """'" 2S11~1IJ3 :m94m 11.766

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J!l3'J?lIS ""'''' :lll4IHI65 ]4Q72.918 )m;D:.g lJ661as 2846644) ""'"" ~36.16lJ 147S:J!llliS0';4 J66Sl(J94 n",,,, 3«ll151ll 32318313 -'" 2S&lH16 von, '" """'" unJ':HQJ.J87 366713!lS 3J7!l7.s23 "",rn 3231Sl.2'i2 ""''''' ""''''' Z/llS2.412 25478.172 un

""'"" "",m 3IillH!iJ m3J51J Jm:2.~liJ JI1H7S64 1iJIZ7..576 Zl181.161 lli17S61 ""m:291Sl5 Jm"m 362!2.811 )SQ1SlIl2l JZ7[I1217 312l1~.t2!l "",on 21l71B63 llil1342 """""'" 3'iTJ'j4l8 367l1IDI 354.1$10 ""a" 3n2001O '2B976 B54 m",~ lli55.3J1 1.75!l

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Appendix


60

lffi"""'i".m.T,...Valw~=>I

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Appendix 61

Table 26 HGL Test for CMC 5%1An.l .....I -6.4n ~8ll9 -1610 -l.:m om 11117 I s.m 84tH "56V<il""I1D 0

Poll 'od' Pol) 'od' 'od' 'od' 'od1 'od' 'od' Aftli(I! na.. mfM', M', M', "'. M'. M'. "', M'. "'.,. ,. ,. ,. ,. ,. ,. ,. ,. [lh]

000ll 2HI,1i76 383.8211 741.644 ll34375 1594.971] l!tlJ.1:J3lI 2295.451 2S'21,2Il3 0'5'0.00ll 200.152 374G21 11111487 llOU61 1543,748 llm.m 21a9UJ 2Jl!1.llllll DB44

0.00ll Illl!JIJ 351214 6&527' Hl66,989 147lllll 1764.034 21~1873 220.1..915 0.752

4J 0.00ll 19"m ""383 614.793 1040.676 1""J2ll 18Oj.49421182 '"

228H43 0.769,%

..0.00ll 1745'03 312362 621.418 918924 1303E 1564.121 1S60.oo6 E213:Z18 o6BlJ

2 .. 0.00ll 11225B 3l1.387 614..596 921271 rm.27IJ lmJ96 lSSIJ.051 :!lSU!i5 06115

OlllO m.l7! 27YJ43 "'''' 82:Ull ll9UlS 143Lm 1694.IiU 1841.401 0.&:4.- . -, 0.00ll 17!UlrD :m,976 581941 866.811 1211.120 1441.390 1595J54 UI90,029 OS"

0.00ll 1.51.[143 "'30' 511.618 mEl 10«21 1116.399 1511.421 1660.033 0'"'aIm 152.211 271,994 512.334 762.513 10ti5S79 lm.719 1513934 1655210 0500

O.IXIJ 131187S 223.847 434.857 rn'" 911,OS6 1100.849- Im.6!!4 1432.643 0.421

01XlJ lTI.6S4 m.07e 42j.234 ~.429 904.415 1llS7996 1258,648 1437.4)(1 0.430

O.Im 111.631 185.73S ""91l6 s,-"., mMa 'EO j1J9 !1l7J24'] 11&l642 o.:mMlO 112.685 189276 3~2lil ", ... 1.5&.672 9::ll.86J 1058a'53 1163,624 0326

000l 88.a94 162.800 316.433 459.1139 633914 mJ'>l 921.628 m.ll23 '284OlDl 9lllaS 161.453 ""541 453.055 "'307 161.846 96i142O 975.801 om

..O.IXIJ 51316 81095 172D5lJ 245.(131 '" "" 4l6.4TI 488.840 543224 0129

..O.lDl 60.1!41 82.149 I""" 23231S 346.115 4l6,723 491.318 532,53] 0.124

0.00ll 31.595 42$9 98.721 lOlL'" 192.633 215.111ll """, 29)5lJll 0.065

'.Im

L09

om

1ll2ll

Ol.

'falw pos:itims:

Pipe Ili.umtu [mm]:

111 I"'"


Appendix 62


---lb.ddi;t~ -6.413 -4.acB -- -361 -1209 '1111 3001 ,.77 8.461 ..,.

V~"" pl.l. ,P.. I Pod2 Po" P.. o Po" Pool. Pool7 Pod. Pool' "....:ace n:...,.at.P. P. P. P. P. P. P. P. P. 0"

",02m 21282.6lJ 271D6.9{9 26750.6411 264IH8G 25916,m 25659563 25321.a6J 2511D"~ O,B42

274S1.211 27'~,818 VIICI-07S 267t7_~ 26404744 255lsonl 25674.428 m23.211 25128014- O~2

214-!1.Hl51 27'..62.439 27148.291 26781,9$ 2£195815 2~70666 25661943 25324,852 25136,JIJ 08422167.'lJ."i2 274G4iIS9 21241447 26881.:574- ~916 25m.X!6 2j7Ql.'l23 m""" 2.S140.6!t5 0,91427624,910 21412.949 m46.898 268E6.1J64 264g(J,a14 26015.258 2jIQUS4 25359510 25129969 090527991.055 21699590 27528.658 Z7142.4S6 26673.a::l9 26172.465 25804.436 :zj44J.535 2519Cl2ll9 1,069

27'.2ll1ll 27691.611 27522..3« 27121.B79 ",,,,,. 26168266- 25l31H12 25414.662 25186.753. 1,069

28J59-3lD 27B71U21 27693.074- 21265.6~ 2ti167.6L5 262437Jl:l 25861,2Jl 25419.084 25207.I1J Ins2S140.m 17884.142 2166957!1 272H.'i76 26746.1395 26229.117 2581."iIl6 25461428 illlJ.m 1.lJ62!l~,lO5 28152J!.59 27927738 2'1471080 26921.1198 26331.160 2598:HJ1J 2Sm'J9J 252.S9.5to 123228420JUJ 2S126,ng 27923.9W 2747lJ.699 269~J95 2616B,)\)(J 23m.6% 25536181\ 2523'';762 Im2io!i31.01B 2a34i!.15ii4 28144,29') )7628.2:25 27lJ7l(J(7 26461824 16lJ1B076 255nm ll29Sag. 1.3652B1i58.666 28347.4-96 2SQ9a.492 27/i4H39 27U79J16 2!S464,L78 261J:l9S26 255l15ll'T1 23271.102 1.366

..28404.459 2809:3.701 278SeJ26 27.U.336 26;40.$1 2!Sm.oo4 25963207 255:36.686 25256.660 126728758.166 :28466.879 2B2C4.86:3 27722J7J 27129.11:3 2650:3.531 ""'0'" 2560B.621 25297_8J.4. 1.4162ll7!§6,B57 2ll44Q75CJ 28199..699 Tn20197 27124.264 26489.3<0 26015.715 2S6ll1H77 25:303,422 1..1529022,420 2B67lJi59 28459574 21939.82. moo"", 26621.5% 26181,90) 25667.621 n:J:JJ.ill '-""29032.791 286T79S0 28455304 W2:3.l11 2729C.l)9 26625.734 26176.781 25676071) 25:318945 1306292l11.47! 28S29/iID ""'''' 201603.>0 27359.824 2M933S5 26221.90B 25701Jro =83< , 6Jll

2!n05.76lJ 28851.576 2B575.%1 28OCl9.51. 27357.152 ""'>2lJ 26:14B.6&i 2571B99:2 25377945 1.632

--- 29420295 2901(1.04-9 28149.461 28230102 21482.918 267BBJS9 26314.:350 25759379 ~BIB 172229-4Cl2,14.5 """~7lJ 28781_6'39 """." 114858~ 2/iml99 26J04'" 25758,711 254Hi.764 1,724

29699301 29357.686 29111.100 211515.393 zno<3<J "039320 26432.54~ 25851.520 2S«J396 1.87J2'174(1419 29332.162 29Cfl393J2 28480.139 216a2.1!i6 26958.434 26430.057 2j838811 25453949 1.....29818.580 ""'.0Jl 29053.!l76 28518.219 27678.8« 2S50.BO:l 26421500 ""'''' 25415.586 1.910

.......... 29112.813 2935131.5 29069.154 28ni,340 177llJ29' """'''' 26434.160. 25835809 25416.195 1.9O:l3llJ13.\88 29589--'l41 29296.6!IlJ 28662.836 278ll!l311S 21Il46941 26504.883 """'" 25512.803

1'"29999,424 29563.553 2!t241.211 28634.609 278ll!l'96 2711119388 26500.%5 25B151541 25506.8S1 1.9773O~_cm :11101.660 2onu" 29121.771 2!l1l3.44O 2'T232.18:Q 26661.490 25912.551 2555L166 22lJ13Jj1(.4-:3lJ 30100.8'-48 298C11.l(!j" 291361J68 2S!l9G61 21'2211(18' 266303) 25997686 z.B4j,668 2.203

Jlll106.m :30346242 """"'0 29316.oas 28236,8.42 meo,m 26733.412 260:16.131 25642.nl ,3JlO

30812.129 3OJ32.!l!n 29955.1lll2 29315.103 28m.615 27310.600 26723ll!!2 26041.94,S 25635.8'54 2.37"

:31426-021 3J89H39 3ll418_1~ JY154,668 2B'i5Q.CJ80 27538.961 26919008 26128m4 257065B4 2.649-

31TIlinJ JJS74.m 30475ll41 297Bl--'la2 2115S1643 21554141 26901291 26115.031 25726,1l9 2,645

31S88J86 31407.8'1-2 J0969.691 X1191.498 28814229 2n6S463 27091861 2625:1.209 25164551 '92831930-SB4 31376,039 31058,061 3lJ254.342 288-45j12 Tn57.819 27lJ7J'" ,,,"'... 25794.X17 292'32175.166 31599301 :H214-.879 """'3" 29015514- 21850.131 21120.527 25215.,209 2582J,OSQ ,OS>32181158 31549.lt!8 31236.559 30411.:396 """"" 218Tl.584 21202.441 263S-3T7 ~5..018 108S

3"'..566.947 J1955.)98 31:561.588 :307255'61 ~4291 2B045.441 272'a5.'504 ""'Ill) 25914.836 327':m9'"", J2013l!fi1 :315131.1)6 >mo= 291:52.426 2801D617 27268912 26401.ll63 25889,100 '.27JJ271(.D23 3226!H6J 31748.313 30926451 29276.71:1 280%.142 ""'S2/; 2<466"'" 25!721.3H 3'"3:1818.469 32254.561 :31W.1;J :30881.017 :29295-049 2B1132!l1 27352.41D """m 2:591:3.350 HOI

J3<"'" 32llO1.152 mM'" 31315902 2%63-406 28339,121 215.30,108 26531.600 25991.6U 3.715

-33454.941 327"""" 3ZJ211182 31JeO.l14 29614.11H 28351.(196 27491.148 2657lJ.9"n 26D41.2-4l) 3,713

=193 DXJ6SJ9 ""'066 31695.m 29797= ""'"55 2163l.185 2ti658.8l! 26045885 3.863

:D645.Ql2 D:l19.aaJ 3254:3.142 31615.848 298(2.111 28434299 216<!(1.09lI 266Sll= ""','" :3.852

34-148.648 3341tLJ15 )2968'.453 :32076.816 301CJ7,61O 2a611_7lJ3 """037 26759.840 26116.114 4.061

34138.4"i 3346J.66!l ~/l16 J2(Jj1J09 JUl26326 ""'."" 2177ll:m 26774.713 26l34,25O 4.071

""".7lJJ :34123195 33642_8:Jfi 32625.0:51 ~94.646. 2B9OiI955 279711J7. 2695U:lI 26271648 0302

34ffl.219 34150.676 33622.211 ""'30' :ll4C9.a88 2lmt.982 """,m 2ti9-41,416 ""''''' 032'

~109.242 34976,a28 """"" 33314.020 3:J9lJ15.990 2926(l,415 28251.461 2'7125.(82 26431.379 0.'"

.. 1515&,191 34912.i5.'i2 343l!O391 33314297 """",l 29250.60,:j 28253240 21105,623 2642:15104 ..'"3615lUOl 356Z1473 34991398 JJ8JlJ'" 3l2BI.B93 29439,396 2B:rJB.I.56 m50.1B5 265<lJ"", 0'"

--36351-3W 35ill.OOJ 3499:3,1501 ""''''' :312!!6.5'!iB 2941i3.Je:3 28483,851 272J6J93 26516.002 0'"J?142..:Dl .36327.449 357J2JE7 34511.434 31102258 29762.6$4 28721.055 21446.596 26648/iS8 ,=JmJm 36350305 357.'6332 34546.012 31~56,Z03 19159.Tn 286%170 27431.520 ""''''' 5.382

31919,:)B7 37022.1513 36371,934- 351B8D35 """971 29>16.,. 28942,25lJ 275886.'jIJ 2fi790JI6 ,'".

31841.602 31048.543 3/i4007Bt 35106.395 =.928 DJOOll6E 28889.4% 21573.113 26760.919 ''''3840t.!t53 31ill.42l'i 368882J4 35552105 =369 31254.12.5 ""'."" 2711OJJ7(J ,...,,., ,...383&5195 31575.848 369tO.lll3 ill86 :m 32327213 :ll168.2:sa 29076"709 ='" 215893.518 ,'"""'~ 38112.414 37411L457 3/ill41.B01 Tm22J411 3042l.618 29241m 21857332 2/i97161J 6159

J818lJ.711 :38103,648 Jml,4Ofi """'''' 32637.957 :Jj410.l56 29251.918 21815.3ll5 26W1,381 5164

1021

'''''0.558

D.6lD

80.43

CMC;S'A

V..l.... Typt:,

VU"" ~mr:nr:ml


Appendix


63

1,:

lOO

97.17

CMCYIo

HI11

0.000

Ull0.184

1....,..,= , ... , . .

·'s.Ol) ·354 -2.542 -1.040 0.1lJll 2"" 44!t9 lom 9.511

!Valwplme 0

Pod! Pod' "'" "". Pod' Pod' Pod1 "". "'"A~~Fbvult

12, lP, lP, IP. 12, lP, lP, lP, 12,P, P. P. ,. ,. " P, ,. P. [lh]

0000 llJ1535 165TIl 775.9lJ6 41!t.!m "'''' 681.901 165,099 108438li 0""0000 102.m 161.267 m.~62 420.511 551,267 616,24\ 755895 1084,208 0""O(J{)(J 118339 191.556 :!JIT531 485361 51GJJ'lI W"" 851818 ml all 1066

OJIOO 128.141 213.65IJ 3S2.76D ~6.m 6%.!l19 886.457 %J21S 1396,475 1,210

OroI 123.971 2H1.842 341.402 546.B46 ""lIB 864.265 951.949 Im4~ Llll1l

0.000 121j&S :m.m '''262 520.102 ,,,m '3<340 92U33 1312!n8 U5Q

0000 142.08li 229JBl 375.404 584.725 149.985 954,123 HDll19 1497783 Ll%

0.000 143.414 228.641 367.114 1722S11 74S.lJI 944.152 104L763 148S917 1,295

-0.000 142.251 234.860 391.406 616,330 791.442 992.111 \n9tinI4 1>B7266 1,401

0000 I&1J11 255321 4\OJ}4. 66llJ2ll 1136.136 I047.74S IIMBSS 1661756 l.tll9

0000 165.853 252.828 4011.578 656.5ll5 lI4(JJ71 1037124 1147.681 1561142 L...


Appendix 64

Table 29 HGL Test for CMC s%IADddirt=> -5ID!l -]3# -2.542 -1040 0"" '·2-"" ].5IlI lCllQ '511Iv;u~J1J.- 0

Pod I 'od2 Pod] ''''' Pod, Pod, ''''7 Pod. Pod, A~~Fiawr~e

", ", ", ". '" ". '" toP, toP.,. ,. ,. ,. ,. ,. ,. ,. ,. [lIo]

O.lIllll 98.489 170.!ilJJ 276091 430921 iSl.ooO 621UCl9 7:57.319 11094:11 0906

000l 134929 11O.l'i64 2!l1.391 429507 ~S.s.619 624457 755485 IlJ83l1B 0,907

000l 12Hi88 19L29lI 3D7.ll!2 ...504 6211.571 715396 873.426 121120«1 ICt2!Ollllll 12:1044 192.391 310.432 ...'" I2llm 695.491 850."" 1227846 I.lI22

-------0.00l 128549 199672 324.765 5lJ7m "'708 ".527 925.528 1284225 1,082

... 0.00l In.708 I"DIl9 :m,83B ID7J79 6511,642 72L722 S97.l86 12?41U3 1.081Ollllll lJ1.llD 229.148 365.454 jjSSU1 7.31.012 Bllll'" 99BJ'i 141B9(lj 1125

--Ollllll IE.iS? ","" 153.996 .554.164 112.984 807179 1000.890 1«3822 112'Ollllll \4Ui4'i 2IIJ12 Jll(J.485 W.l09 751.451 8&JJ'i1 10<6'" l.a4951 IJll7

000l 158.048 231 ,:m 369.(104 "'''' 742-546 843.147 lIID,54) 1487 m IZ190.000 le5l1lS 2'142U 479.532 TI6.82B 962195 \095jjJ 134llB07 1931244 1.1660.000 19'i1i77 lJ4.494 482C71 761148 992211 1098.5lil I]2S.49'1 193U79 1,764

0000 lJ4.l90 "''''' m.467 &79.126 lHIBBJ ma.SOl 1511.005 2168075 2.012Ollllll >J2.'" 329.470 535.158 H75,11B WI4.ass 1235.718 1j(J1.782 2172.9&i 2.Dll

0.000 236.143 381.646 610.817 ID2S317 1274916 1433JSlJ 17475119 2524356 2.376

0.00l 231227 3IlB2111 61J9.8134 HJ24.949 lZ79.1J2D 1422933 176.1311 2516100 2'"0000 Z71.1l7 432.639 701.1J1 12l7.l00 1503365 1689248 2049D81 2951,815 2.912

0000 "'= 438M3 102.e41 ma7l3 149(]:ID 16S5J6ll 2063.641 2917908 2913

0000 29LlI19 417.07'B 154387 13639-SS [69U13 1891.108 2))8.652 3244 860 1310

0000 278,414 473.629 763903 I:JtiJllSll 1681.995 1873.ru 2Z7S9J! 322L72lI 3314

0.000 329.484 527.897 838.001 lSi"d,9lD 1976916 m59:2 26:l15lll ml.J50 m7

0.000 m331 531.171 846.406 160U68 1953343 2198,468 2l!i5lJ681 3127,1!!4 , B27

0.000 362.115 5134.896 94.5.0482 I"'''' 2Ul.m 2513.863 :m7B91 421lQ24 423'0.000 367.631 576.817 944,90S 1811012 mUD ID"'" :D45917 4m,m .237

000l 387.675 614.211 ",:m 1944,D 2«.5.865 7111.B32 3215.8-41 45111!S1 '3560.000 ]70789 615,lm ""950 1938.448 2443285 2112990 JZ75374 4564631:1 'J6)

OJllll 4Q'EJlj 03llJ12 U132.8I]2 m:lJ6ll 1l14.l09 2866.51B 3449.408 4790 168 .8llll0.'" J71.08S 0311375 1"'912 2lD4.54 ""m 2B6U15 ""'" 4790Ja4 '.800

0.000 :m,512 ""81 1010.949 21l1l21 2722207 :JJ16665 3/ilJDti3 5014363 5071---

... 0]00 421].647 6.S11961 11173200 2145352 272CLOlB l)2J.176 36l7.m 5018,168 'DGl000l 416.691 667.612 10SlO.m 2204.'" 2Bll47BB 31lJ1.121 3714316 5I:l9.l46 5215

000l 421.543 O1O.O1ll 1090.405 219s.rn 28lll.765 3104.359 J106.624 5145.146 521ll

- OJllll 425.l73 65'3.426 1123.104 ",,92. 2938.461 ""359 39lllJ6J nar1l61 5.466

0.00l ,].1"" 6ll7.021 lL2S.428 zmlJ» 2924.122 3253.068 3889631 5364341 5.m

0.00l 417.15B6 706.941 1149.422 :mUJ5 "'139<5 TIB5J9!l ""m 5562834 5'"Ollllll 410.1Zl 7IJB.l91 114S3l1 7394129 ll6O,848 =Il'4 40«.719 .:i56ll,375 ''''0.'" 514.lD1 815.75lJ 1329.611 ="" 3847JS!1 4229.673 503lI.436 633637S 7002

OJIII "<:Illl 7nm 121l.ese 2642.435 D7l.llOO ElS.494 4-«9.711 6llli5113 ,=Ollllll 479.16ll 7BJJ4] 1299527 28S1954 364.:1342 4IJ4Q.117 4795.899 6:D6359 6,m

0.'" 176.499 469.154 745,474 1291.431 1613284 le15.415 22OI!S9i7 3187416 2949

0.00l 356.762 S7Hts ....>12 I"'Slll "',-'" 2S55,ll64 lJ62,461 4321.311 4.1ll1

OJIII 1114999 166.m 275.096 ~26.224 549.102 623.952- 161.494 1122540 O.ill

000l 981.40 160.174 264.JS6 413.111 534.466 6l4.197 741.671 l079ms 0'"0.00l 76.4115 1].1'" :m79O 347.aeo 441.287 5lJ.lS1 621,9B6 916.421 0""0.000 86.BI3 Imoo 211SOll ",m «0215 5llU135 618.268 8979], 0705

.. 0.'" 69658 105.126 1111.l5ll 779882 1611921 412.1O'J "'''''' rrl97' 0393

0.'" 76710 lQ9ru 184..., 2113918 "''''' 4ts.5a3 5lJ7J>l 144.H60 0-'"-

0.00l 58784 89297 m.1ll rn.416 31lJ89 "''''' 428.140 on366 OJll4.........

]Q7JQ4 341.416 4n541 "'599 1l.S210.000 64.~1 90216 !57.1ll.:i mm0.000 56001 13.229 128.033 194.119 174.612 294129 ].1'= 52U61 0.442

Ollllll 64306 69./i30 118.231 181953 240.836 m.!76 m.l02 4821116 0374._-0.'" 542« 65.39-5 115.636 110.626 nl,m 2SjJ6O 31l.1I16 45U17 0397

OJIII "786 :35.176 13.084 "llBIi IlJJ06 1511434 IB2Jllll 258.490 0.281

0.000 ~.I89 40658 "'.602 93.7l6 125.674 154.281 115.145 "'ID o.m

1025

100

l.l3lJ

0.000

0.784

!11.17

CKCS.4

Valn~

1,:

29f10J20Q4


Appendix


65

5/1l1JJ04V....""'T~V;o1~~"""l

v......~Pi:><DU-;H["""j;!Il..lt.n.l Typo~'J

'.K

12IIll2OO4V;o1~T!P'!

V~~~"""l:

V,oM,~

PiprD.:.:c..m r""",J:!lUteWTl'P'"~;im'.

"K"

42.12

CMC'"1"""

"""""''''

42.12CllCl'I'.-'

''''''''''"'l',m

IA:riol.cIisi,;,,;,.. "'" I ~"" r ·1.9&:1 -lI.!J! un< I J.Ql5 '"" um I "" I'VoJ.ve pkoe ,

Poll '01' Pool' ""'. ,.., ,..,l'oI' l'oI' Pool' ~_r_nt.

"', "'. "', "'. "'. "'. "'. "'. "'.P. " F. ,. ,. ,. P, P. I ,. ~'l

''''' S9:!4S'J3 nlm~1l :<9ll74957 "'135~ 867 W.50215 !II5:i67JS11 1/l)I.(l8?8 "",r_ c_m0"" S'4S2.671 nl~a4&S 29725375 41l98':42 49J'ia445 !'i!:57H38 76i'i5112 86:JJ81J23 0535

''''' gSillS.J6 234~5 JS5 :lOOJI364 41~';[Jm 498l!51371 rnl~]75 119'29445 !m7ll1S6 0552

''''' ~<;Qt3J nm,416 3IJ224.lJ!:l 4['>5.2.6.'i2 .,..,." S7m.1J] 1111 IS 359 87B,S,9jS 05504a.OOJ 10({4855 m21.2!l1 ill57.GlO 451):)j9& n74/dS5 nS9lU42 M4l!5,2S8 94mm 0633

''''' lCtX11763 """'" J:2499.2Jii 44m301 j42SiJ26:! """'" ll«5<I742 • )\136135.11 0635

''''' 10456j12 :z:i!m,I29 3J(61.71O 4i'i711.895 ~%I 14)41273_m

9'JQlt.ll86 Oh"0"" llJ.m1ll8 wo,'"" :nJS1,m telZl7Zl '''''''' 701.43'7,1'58 ll:i8026'i6 "'"'" ,'"''''' IIJ9.4!U92 ""''''' 3cl91J.TI4 ""',., TIS7UQl ''''''''lo 9!!'lOlill "......... '.m''''' lllTl9 941 26TlI,4S6 3'311U25 47'WJ.38i SSl611313 nmm 8!/S536D W1TJI8« ,m,oou 115l!I,m :ZSS:C;S,340 W-6ll.5'lO nnH52 ru-?Il,e63 84'M6.JIJ ~95:;-547 10!1?lS2.."O 0.840,.oou 121.51.1375 2R7lJ6211 Jr.dllS9fi 5Dlll.'l69 amm 84362.119 97411.078 10%19003 0.84l

..... ''''' lZrl1B4 mSIJI))! :>8234.266 'i400HlO 64%1129 om"" lill:m.54-1 lIJS298BJ 0971

"'lo 12493,JI5 "'"..., ~ml,445 54:a:1H1J6 _'" ""''''' 1Cffl914Jl! IlUIrn. '.m''''' 123lJ.487 JlIrB361 J928!1,S9.5 S.57~.219 6"J08:J1"12 'l(l(Ilil!.i156 11l)l.546(l !l69:lU2S 1024

''''' 12lm.i22 EW"" 392i4.HllI S~2U411 ..,."" !l'n56J!20 li])63J.J1S 116754-2.50 1.""

'''''' 1291J.72fl JI97J.793 41G85.1iS2 58823.016: 7lJJllC!94 5l4ID.1TI 10000000m "''''' "" 1.114

'''''' In!1B.14l] 324.51123 41662.Jai SB'117,81J 10161.711 51444-7,109 10ll8J2.J36: lLma()6J 1.164

"'lo J245.5.34lJ """"" 4OJ5El.4JO EiIm.7J5 ""'''' 91.a2,J02 JJ2156m lXl5640n 1.24.7

'''''' 12406927 ""'m 41.5S110U 610.5.5..5740 72881.7SJ 97S6!.l2.50 112251..5.'55 126514414 1251

'''''' 132BS,417 34187.316 44056.461 .,..."" """" 104:J9J..'i7& Il:l:i9IJ.1JJ iJ49"2J,969 1301

''''' 132l!3,ZlO J<!ws:;m «lO.H98 6.54'12.117 m56,984 1C4295.3'1!t ll'i'99957ll lJSl6Jl.56 Lm

''''' 13477,7Sll 14933910 49)91S70 67015.914 ='" II!11%S1U 123451ffi lJll3!18656 1.4S2

"'lo 13369 m )466:1414 U0l9,'lS1 66996,158 m76.2J4 107141-Zlil 1~S70 13&26lJ,1lO 1449

Table 31 HGL Test for CMC 8%LA.ri';i'~';' ..'" ~""

.... <Ell urn 2.6115 '"" B.Il'I5 '"''v.mpJ_ ,l'oIl "., ".3 """ """ '01' '01' '01' ,,," J,.-.~1bor","

"" "'. "'. ". "'. "'. "'. "'. "'.,. ,. ,. P. P. ,. ,. P. P, ~'l

'l"" 9052,2S5 249B02n JI6001IlJ ",..'" 516n.~ ""'''' ""''''' wmm O.66J

'"" 821Jl.on 24K>J242 3>D"m .","'" 5HJ.57~ ~341..'i9-4 8ll367.7)4 90599S13 ''''''''' SI.'il!912 21159227 2ll7519.iJ "'.,,,'" 461S9,m 6TI85~ T'....545.6l!B ""."'" '''''0."" "".661 2l4.'iD.564 2B323252 ""'><1 ~5079.5) C415.m ""'m """" "'''

..... ''''' 8<W8lJ """"" """'" 16m.7iS2 41SIUEOO S$4J.1lJ7 6llQ'mD.5S 767.52164 0516

0."" iI017.6811 19S49,HI9 m",,, 36414.881 4J54565'-1 saaJ561J2 1i8066,m 76a80.lS6 Ojl6

''''' 7m3l9 11l4(J!1:11 2J5l5119 "',,"" J'JTI1.16i 52056.484 61729363 srn"" 0.439

''''' Tm.51C 11ll1J96S Zl924.77IJ 32240.732 J9SOL984 "'" '" 62ll4sHS "",.n 0.441

L. ''''' ""'" 17555.lJ28 21005.sn 2947S.~94 3.5418406 ""''"' 56tl32586 """"' ,,,..,JID 6S54,IB6 J7..'iJ6.1JO 2J62lIJ47 3:1163.764 3574L62\1 4&1J2.£I51 "',.'" 62162914 '''''''''' ""'" IS"'m 19I1ll.D74 265S1!l.789 J1!36,llQ 4:mJ.121 5:-666,176 51179.742 0319

'"" SS4J.367 14810,656 195630911 27lJ59549 J24SL6ZJ 4:391;Sl4 jJ7211166 57U'JIS78 OJI9

'JID =«' 123ll12.54 16476,469 m«.I60 271J4~.56! J6llOB6"l1 42405.l76 """'''' ""''''' ",n.s&5 129171141 l64nm 22.541371 2'106OillQ )6694254 42464.*92 48l2J,61J "'~.....

0"" «al.25lJ lrmtl357 14019.441 '''''''''' 2l19S.4Gi Jl314.J1!] 36231 ()]') 409217J4 0.182

0."" 4532.615 lllm.637 1403692.S l!nJ1051 n122.tn 31JS59J2 3624SilJ5 _r" 0183

''''' 326S.'" 7155311 "''''''' J1S5lJoall lliID.I>4J mncm """gm 2!11JU« (UC11

"XII 3291.164 n""," ,,~m 13585,0.54 l6J41.7% 121m.2~ 2S616.447 28804963 O.H)4

''''' 23141149 5142.09J 647&.434 ftSJIl.67J '''''''''' l(361 j16 lC6lJ2,m 11>694,791 '"""DJ """" 5lDJ7:l "",m ll84H311 IIJ64.6.1I6 1437Lno 166J2m 18118.678 0,051


Appendix


66

ani""'"

D~'J

K,.

1[07.5

0.000

'252'799

lAnd dirl~ -6574--- .J~- -2.281 -1031 I "" 3m2 '''' '''' 9669....- 0Pod I Pod' Pod' Pod' Pod' Pod' Pod, Pod, Pod' A....~n..~OP, OP, OP, OP, OP, OP. OP, OP. OP,P. P. P. P. P. ? ? ? P. "",

0000 """291 77726.764 3763?..TI9 nlB6255 63513.742 82219,861 95354914 HI8:l65445 "".... 0000 5476.409 7609,6ll3 1Q5JS610 13822.9lT1 11113934 22IlL5.395 2:lrn490 29225084 0.2$

.. 0000 6062 ~83 ""519 11584163 15254948 IH847,945 :I«5H24 2829958'2 12114061 uno0110 6081.419 83811iSS 1164l.SUi 15248,iS2 187Sll.592 242jD.145 28224643 """'" 0""Qooo 7750.865 10465,762 [4m314 19201.941 TJ577,D96 3ll.5ll4586 35466451 <03Jll9lll3 0453QOllO m>."'l 10460.180 14889.371 1!n18.1:JB2 23636.656 30310.809 3S492,6)3 40172.762 0452

0.000 8258329 1I19!;.489 15779,969 20493,415 25215.984 32561183 m21.J98 4'2786.752 0""o0110 8156,892 11142.940 15830,169 2(\415070 25!4HOJ 324ll..'iI)TI ""',,, 42868 !!63 0""QOllO 8846.51L 11699,691 16641416 21511,723 26418,408 )4)87840 39748,188 4SiJ74.381 0,552Qooo 8852911 117'22.693 15634.602 215R26O 2647Qll9O 34297262 39834159 451l4ll853 0.5510000 9519.515 12316.499 173335JI 227%-557 278l!4.262 36417.711 418li1.n4 47592.754 OD'"0000 980U94 1236.2.Q)J 17408.719 221~.7J6 278'9lID66 )6326~ 41909.543 41:i09,414 0,6030.0ll0 IlJ72).ll41 13665971 1911)400 252111)98 ""'llU1 4OlI52.734 46429.176 5269.'HI66 0721Otro lOJI4-,DJO I_m 19073271 2519<lDS'8 JD924.71l 407IOJll'l ""'023 5l58:Hn 0'"

·0.000 11645.781 146451113 2!l«8.436 21118.039 33196-836 4396131114 4!t842172 WiJ2m 0.811

.... 0000 L0719.4<l1 14636.629 2l:l467.a26 21126.143 33162.566 437L8,625 4ge45~3 565591)') 0.1l19

..... 0.000 !223j.1611 1~10.14) 21828.615 29101.721 ill64.921 """", 5X14L146 6ll414,56) 0.9110.000 12403229- 15617.612 21al.:J.561 28904.411 35413.633 46646.863 5JIR961 60394,1lS5 0.9170.000 1184L147 16oS6<I."i18 2296llJJS4 3169U1O :m>J2B' 4V19..992 56661.150 64:i08514 '0360.000 1E31824 1665H811 22981.881 31661,lllJ 37854,941 .."'", 56861.S08 64ill4Bll 'll3ll0.000 Izm.140 17J19.15J 2:3861529 328OllJ48 =.>11 ~U1l6 59162.355 66910.156 1.1160.000 12362..598 172;lO,9OO Z3ll2fl.494 32763.152 3936"" 1115ll1.1Z7 59141910 61189406 1.1\70000 128973JlJ 18141156 24884.223 34:m.703 41368nJ rrm,)95 619511453 70363.4:38 1219

·0000 129ll131l1 1816J.336 24943.081 34402.758 41294.582 mtiS.tl23 62OOll.c55 ~5.227 IZlI0.000 1295LllJ5 1iIT.03Jll 245ti2,m 3400.319 41011'5.086 SJ282.219 616113211 1OO4ll'" '2!nMlO 12ll72.146 18105.861 2466),869 3413L6J7 4-1089.469 ""'''' 61663..898 70116,2131 L298omo 13432.3114 'ea72.563 m'"" 3568).516 42956.762 557l'J.54' 6444-4-.793 ""'.." '''''

... 0.000 13375255 Ismm 25119.1114 3:i46ll.150 41758.633 15542.441 64203A45 1Jll64"" 1.J980.000 L4184-034 19613il69 ""'1l9ll 31\74,840 «nS543 58012.195 67182.945 16261.391 l.5140.000 14049575 1961Jl.930 26a5<!i.135 31110398 ...",., """'"" 67041.103 76159,8'75 U140.000 148271i14 20413.8108 27950.14-3 3ll6D9.215 46616.3411 604-061115 6992(1.164 79311266 1,622

0.000 14824.1U 2lJ46G.1Gl '27976959 J8493.2n "'19211 6l15JO,449 70018.664 1961&%9 1,62tl

0000 1554.8244 21009551 28750111]1 """" 48llS8,631 62351.5116 72106.5Q8 81!7lJ.2OJ '7000.000 15732.7'34 21016,469 2llB7S.445 39686,010 48122.711 62295.197 72081906 81903.119 ,""0.000 LSBn.845 21746.443 29943914 4l301.I88 496Sll.852 64705m 74540.~5 84B5-4SOO 1810

0.000 LSll12.3S5 21811-015 """..., 4lG68158 49651,293 64520971 14141.516 841134.148 18060000 16321.6~6 22494.025 3074119'34- 423Sll31.;1 511881i4-8 66642.141 16B3Uaa 87464.859 ,'"0000 16676215 "'26"" l:t6331i19 41441.316 51233586 66412.063 17ll3U41 87457.063 '8960.000 1697LlD4 ZlllJ4D1' """..., 44413.461 .536JJ..ll5 ....,.... Bll428S5 91282703 '''''

·0000 18207.1114 234lJjJlll6 =zn «347293 5360.;1.012 69639.484 8O~.313 91473383 '''''

:0000 L74:n.191 24016.1163 32lI1OB79 45344,410 54914609 7l2llll--219 82357f1lJ9 93511.633 2.1211

0.000 17fin.m 2J916.SlI1 ""'348 45147340 54683.316 7105:l336 112181.297 9J23UZZ 2.125

: 0.000 l862(U81 24921992 """il' 41090,379 S1163922 14134-'145 115754672 97369.195 ,'"0100 !822S..lI40 24957213 J4O>I"" 471411320 ""'.9ll' 74021-625 8S64-9N mJ.l". ,,.,0.000 13814.5SS 24110:3.105 33844.617 ""'926 56'728.043 ""'-'" 85230961 96m"'1 '2720.000 19J'tJ..22S """-'" 34961[)4J m43,1JO ""'4ll2 16009--242 1m11.1I7 99803.4n '.'ll4

- 0.000 194J4jJ9 25579,604 34864035 -411118648 Sll51141i2S 759911.156 87904.461 .,." ... '''''... 0.000 19561B16 26225.15l1 35718,453 494-06."D8 59921.434 m""" 8991)2-461 1021720572 2.514

0.000 2lJo!i14.822 ",,,"" 35699.195 49269.9D 59299.449 1192lSl9 8991B.3JO 1022Jll,445 2.513

0.000 2!lXl1.\SO 2666CU27 36286.777 'jJ4l2160 61233.434- 195n.I38 !H1eJ.375 HM111.a'9! 2.612

0.000 tgen1i7S 26691.109 36363934 "'""" 61229.J2ll 79:J1l-594 91709031 104155m 2610

0.000 2lJ261.543 TT<l1:m =,.291 51626.652 62781.7liS 81249.111 94259.555 106814.1811 2.1'31

0.000 2D141.16l! 27J51JJ'J J11~JS9 51512.4&5 625?J32ll 81Zlll.789 945185i06 106533.813 2.131

0.000 203111.457 21620.709- J1659.5ll2 mn.9lQ 6339IUS6 """'" 95069.492 107855.930 ,'"0000 21mB48 215111.635 31m,881 n18UD\ 615OJ.115 ""'." 951711,)J6 1ClB1S1l,445 2-'195

.-0.000 21llliJ02 ,.".- 311555695 ""'.17ll 64946..l1SS 84211j86 ""''''' 110716898 2.919

0.000 20414979 Z8Z45.001 38491309 rn6H" 6J214.J05 84299.695 973U281 I1Dii18.695 2.5'21

0000 21rnIJ1S ~3834 :J94:lD.l21 54675.Sll4 '''''D1O ll6229.131J5 99528.352 1133llll53! 304-9

0.000 22ll4633ll ~2564 "",'" S46J4.949 66%6Jn 86200.539 99624 m 11314-2.07ll 3.Q47

0000 llJ97"l2ll 29.52tim6 4G2~8969 5S919JJ2 6;134.,695 88)[l2.422 1lJ2llSlS.B13 1160:B~42 3,173

0.0ll0 21093,182 29539.479 4O>J4906 "'"". 68141.197 88394641 102209.148 !l6143.125 3167

.-0.000 21226.4% 29936219 4Cll66,146 56823.680 69:313.664 ""'m 1{l)745.727 111lll'Jl1.4-TI 'lllllQtro 21440.\46 :m3112« 4('J9llj426 567U.H15 69162.406 89662.361 HI3ll90953 117842563 3.192


Appendix


67

Pip,. Di.lmeter{mmJ;

K:,.

-CllC8%

1037.5

OJlOO

'252

IAxial msti!=O -6,914- ':l!l65 -2lm5 I .ern om ,9Jll 6421 !l,4J2 104:13",..h", ~ 0

!'od 1 'od' !'od' """ 'od' 'od' !'od7 !'od' 'od' "'''''<'CI' n:,...u!~OP, OP, OP, OP, OP, OP, OP, OP, OP.,. ,. ,. ,. ,. ,. Po ,. ,.

~"000) 1rn967 !75~_1l4 14~243:n 189771177 2J4611l2J 3(1436.504 34720316 39494179 0800000) 1334447 9U7ll8O 1441t1821 18915234 23154.777

>no2 '"3%36158 39512758 0800

0000 7999,6B3 "".", 1.'1385393 20141.250 msa-373 J2J3.s:600 nUj.54l 42167617 052'

Ia.OO) 7554,899 100)l1.79r 14ti14.iJlJ6 2!m5<IT 24:941949 3211ll.llln 31J7419i 4112S~ 1J9280.00) i114.097 1(J}65.561 1625a.2Oa """'" 21751.104 ):;245.315 <ltl54'" 46114.117 1,0530.00) 8480.470 lLBlJ.149 168a2217 23SS8.75l1 2ll1lTI.142 36716ru 422..£1332 479lJ7.503 11171

OJlOO 87J6llCB 1l3Ol'l.77iS l!iTIl!i356 n568.Ol0 28.542.291 :m42.a38 42151..871 48046.617 t.l83000) 9llfi5l.l~ liJ)%,1l6 16304J5(] 22I!15,413 28383.910 367251112 '22:lll52l1 41m,sq U830.00) H1302!l59 128OD.lllD H!5lJlJlllJO 258«422 J1IT.HJ4 JSlSIlO.B5J "",,,,., 5!69U& ""0000 %49424 12WI.22S IS9'J(J!i09 25llO.S656 :;a4'H.rn :mn"" 45256.434 51/i76246 "3'0.00) !1'J23.541 13~333lJ 18922.2U3 24654.130 31296.611 4003'U52 46261.109 ""''''' l4330.1DJ tOJ71DUI 11643.15\ 17445.184 24966.225 J0924.043 4045(HJ9(J 46471453 52343121 L43\

... OlD! 1048226" 14050.834 2IJ95iJ.098 2llJ31Q29 m34.449 42969.8lJ! 'omm "'" '" LS81

Ol1Oll 108S2395 14562.ISJ =029 28ISHI41 =m 4)219.363 49578.090 56206 m L'"Ol1Oll 1ll633.6511 13199.799 2Il641.2!1 27131,215 34715Dt2 «294,945 "'''''''' S75661J2(] 1.681OJlOO H17Q9Bll7 14ll44,871 21023,691 :mo5.l52 34126J1l5 44WI.OI2 512«250 5784ll.7Cl7 I'"

·0000 11J612.7'36 137lr.3,JI5 19656645 28510420 35aJ6349 (501)4480 52289805 -S9528141 1770

OJlOO 10000.m D67lJ951 21216.215 28588816 ]~6]5:S14 456S.059 5]D4,266 596199112 Im0.1DJ um.m 14404211 21gJ5.100 28764.152 JM64449 46ll91.4lJ2 5(2«254 61J24t4li Lrn

... 0000 1l071,4jJ 1_= 22fJOO.52!J 1OOZ3.205 J65-MJ2O ,nS65.44j .HE.6a2 612Oj!J77 1.8750.1DJ 10704J04 1D66.499 m3S1112 29361,3<15 3600SltJ 46S71.IJ1 5J'7UOSIi 6lJ72D,176 ,11T10.00) 12lI!I9379 l51n.m 21999.330 31175029i 11469.418 "m"'l 54998.559 63198m 2.172

-0.00) Dl21910 15.'i09,ll29 22780293 306181&4- :36~.672 4SfiJI.801 56122.863 iS36163411 ,'"0.00) 1I61Ll211 166J:U46 21985963 29962012 38J68.l]7 4S707,2n S618JDJll 63726.781 1.'"0.00) 11947.200 15696.167 22514449 3134U91 J8083,I]7 49452,813 57102.5!t4 ""'''' 2.3.50

0000 12206,868 1661231l 21145,607 30649428 ]8218,683 .m99Jll SJ!l:l6572 64BaS.59lJ 23"0.00 12320313 16411.2'i6 2SlJ5JI52 JJ5iJ6.109 4(J('17.426 52216.676 6OJ43.555 68117-61] ,.mOJlOO 12226,973 15848.758 24459395

""'" 3«([]50304) 52243840 60201.75iJ ""'335 2.54ll

OlD! 129911i9O 17284.6!l 24m.OO8 34709.1l1 '25>O.B20 54642.115 6»t7.4llll 11004.898 2.16(

OJlOO "".." 1696[l!5!14 24746.088 J44nml 4Z7451il2 ~137,414 63442.879 7!J814JQS 2,166

01DJ !4306.660 (7510.0.(1 L~66,g](J 35948406 OJ41lI:D 56491nJ 65047.154 7l401.758 2936

Ol1Oll 14117.474 1",.,00 2~581164 '57>'305 44391398 56864270 64534.074 7322:],859 2930

Ol1Oll 14241.D9ll [7512.411 2T36OJJ86 [email protected] 4546S.m 589t1.844 61699453 76938,906 3129

Ol1Oll m:n.299 11l51S959 2691l3J9 m,,"" 466n,965 59521.680 61898.148 m6Jm 3.1Z1

0000 1""'= 19G6S.131 27J:l5225 3163J.191 45536.055 591Jl1.082 61842781 170)4l4 3.11S0.00) 14253241 IIlll93.799 21951.029 39255379 48424.2[5 62660.918 71= 81268789 3.356

-0000 14148.417 19JT.!.I64 27990.107 J84S8656 4aJll8.4]8 62475.871 1l1iOJ.B28 81149.m 3.350

0.1DJ wm:rn 19917.006 29lI9225' 40267861 49269.953 """.llll2 74124.703 82914.5:9-4 3541

·01DJ l5724.432 2OIgJ,754 27218,848 """"" 49100.426 ""'''' 7J77O.m 1lJ226.61] 3533

000) [7096.11ll lO5llOm 31lJ6(J.D21 414Z7.411! 51~52..328 65594.'161 7SS126a8 85595.141 '.123...0.00) I"",:rn 20086.525 31409.664 414554llO 50183,074 65696.742 75561.906 86774492 ,rn

......

000) 16(26.090 2111fj.4OlI J2Q9HJ4 42254.2S1 5)[]19,691 693'T.llall 18495.422 8'155U344 ""0000) 16597.4n 20479.061 3053:2-10 4JJ51l.l0S2 5J270.180 '_.000 7lI~.445 89411.'789 3985

0.000 l'1092.1Il33 21422.J]] 32319"" 44124,t64 5'663.105 1U146.OJI 80095.633 91?IJ'HI4 4164....._---54800.4)8 69480,711 1!O623.414 91054.8« 4.161

-Ol1Oll 17lI23ID7 '20331.117 31769.021 43995656000) 1?605.TIl! 1185.5.779 :rJll473<a 45999.613 55766.2RS 72148.531 8'1637844 !1448Uatl 4,381

·000) J142H2J :nJ4J.J91 33166..203 458ltJ.340 56J5J.DJ6 mJT010 82llOO.953 90J9.'7!l9 4<00

..o1DI 18189.59Q 23368:m 34217.8-40 46185895 582111.840 7Nf2,4n 85m.352 """.'Ill< 4.648

0000 117112IJS 23214260 3-4046.738 """m 57400S211 7J280.lllO 8~.21J 91ITI.484 4.641

0"" 119S7.9Oa "",= )6(]49 ':144 47673.027 59384.500 "","" 1l&O11.414 99651.1!l9 .'"-0000 18273.143 23986270 ID71320 47969539 ~98.217 7=om 87"'.5ll2 99463,443 4.895

000) HISC6.lJ5 24279254 36JQ6.7~ 491.57416 61472.008 7l1067.2.'i8 "'26l1Ol1 101419.53:1 5.043

0000 t8585344 24591.635 3S691215 48054117 011926770 17OO2.1C19 """'" 101743.181 5.Q42

000) 1""369 25414.451 J6m_184 4!t4509J8 6238.5.492 8J218.119 91ffi..664 102811.06) .5.261

OlD! 10407264 2476.'i38:3 J7!lOI27J .""m 62315.609 79264-"3 91902.9n 1lJ2731.9J9 ,=-"-_._,_ ..]7ll74311 63546219 81188.125 93474J95 11B6OJ.219 5.48501DJ 19244.113 24DO.2J6 51096565

000) 1951lJ.662 2561J.750 ,.,.,,.'" 1113li297 616t1.363 SOI33.117 934193211 ItBI.:W.414 ''''----

Non-Ne\Vtonian Losses Through Diaphragm Valves DMKazadi

Appendix


68

Hlflll2ClJ.

V.l... T)'pO

'0>1",,'

v...p~o;..""

lL.t""'-'ol T.

Do...itrlk~

"K

00.4]

cwsy.,.~

,~

IA.riol<!i.t 4413 .~ .7HIO .,= .= ''''' ,= I 8461 I ..~v... •Potl "", "'" "". "", "". ,." ,~. "", j, ...._F'.- ....,. ,. ,. h ,. ,. ,. ,. ,. .

.~ 1047.862 162&.47:5 "" '" Ja6O,2:l1 5;<E6.l5l!! 64266i1l 758HJ5 IlJs.=iO.50 0169

.~ lQ6lj2Cll 1611~:J9 Z'l42..st 4Q:!4 2~a ~a53155 &Sa2.H2 7ifnn4 .""~ 0164

-- .~ 1178998 1886,%\1 TIn.51l 4711.0.50 6642854 ""= 9J~na 10243.511 .m.~ 12~J72 lB76.n~ :n2ll 519 ~95Cll15 6;;2:! ~&1 'l'In6)l15 9"JS0331 lllnHlll 0:;0".~ lJ74.El22 2:!6<!m 4005717 ST..9.081 8lJ7ll.48Z 95&2.445- 113lll1,m 12419892 .on.~ 1420 ill 1:<62,146 0Il151WJ 512639& ~,~ 9~5)5 11J71.902 123:'4:JJS .'".~ LDB.7BSI 2lin.Jli7 46OIJ.Z17 ~9rlB6 ~= llU65..926 ID.....ICII lUll\l4S1 0.4:;0

.~ 17!DCf.n 25a_~4 458liml Mn= nn-S52 lH«l.lll6 l:!24&342 14&0).061 O.4:D

.~ 1721.615 2Il11.511J _,M nn~ 103JJ.747 1:;'245.769 l4566.lIJ 12/!!4.4l4 .'"

.~ 11401D7 2!D7!i49 3061.000 nM~ 10718.455 1219-4,4:1/ L45lJ.JlSl 1~3Sl5. UD

.~ 2101.959 ~~~ /il24.1i311 11514-S2l1 1nJ'/746 1","-,,1U7 In.:ll,IJl 11l92C.1S4 0.616

.~ 2IJ:lSS33 ]~94l1] ~~985 8607.212 ,-~ 1«84.Q1;l 17194.736 18881932 0676.= 2116.4l2 ]44'1I:!81 611!!l.1IJ1 ll'ffi..S.8l8 127~.471 111(l8~11__1,710

l'i7J!~ 0.711

••••••••

.~ ~,~ :M:l!l%3 ~13'l.747 8118275 J2IW1.9QSI 14'i7lJ.6:S 179Oll,936 ,-,., .m.~ 2ll1!!6t ~J,278 6T'..6,El'.l8 ~:598'i71 1J111379 ,om", t__.7~

2091'.279 0818

... .= 2274609 373160 MD.Hll ~$6011J 1JJ71JI:lti 16014.229- 1_7ztJ"""~ ".,

.~ IOt34&l ".."" Zl"n.6lS "".. %:54W -Sot9li47S ."'.. 713lJ.111 01211... 1016'189 137'.$77 231~,0l1 )3:~481 ""'''' -Sot97.'Dl 6110014 712116811 0116

.~ 716,11:2 9%,J'X 1119.912 21S6T.;t; 29'./05,410 ).5:3L42Sl 416'1.116 45JI9J8 .""

.~ "'.zn 953815 1518254 21&:l5114 29'l6~J )~1l.1IJl ~IM6'l'2 4:'5"086 01147

''''' 27J1.6lJ "'0", ~J4461'J6 m1/109 1.nzJ1JIJ lJ811.-44S' J~:'5ot.£i6 ZJ7&j,~S2 .m.~ 22J7.12B :l67H,/;1 6158;:'594 £l.l3L239 lJ361.691 ,== 11!95<.S14 207'I2.1ll:2 'm.~ 2623.481 4261340 7619./iIJ'iI 1l~3:D 156O/i,7lI1 lans221 ,.",,~ 2421H66 '''''...... .~ =4~1 4:UHOl 7623.= ,-- ,~ 18471-6l16 :z:D24.791 241:J9.1M ,....~ 2iI17.204 47D.<n4 8j76.500 ,=- 1149l1D27 =n~ --'" 27lnZllJ ,=.~ ~~= 47247211 8j8],421 12:Wj.4D 1736:'5.441

_.~

24t11J6.498 27106(Ul LW.~ 2972.706 ..972.938 8948,4(13 129li5.lU6 18424..3IB 219.50..389 ""mo' 2llm.OIB ,~

.~ JIJ1~.lOO ~~~11 8S'91J91 129li7.&W IBJ73J/1/ ,-~ --'" ~,~ L~

,~ ]18'.35'1 =,,, 9~l.J1I 13921.41:'5 1965i1.48Ii =~ %'1'86t.1I1 ""'~,,,.-,

.~ :Il9lIJ71 """" 9-S9L5Zl nn6CI~9 196101J112 -- 2767UJI 3l49Q.B75 1,j71

.~ 3419.327 """" 101~.749 148:JJ.1I6oI 21085,J(l5 ;W~94:m 2977H5I J269H06 ".,

.~ 34l7crJl :i6nl8J ,=~ 14?l!<l,6:i1l 211lJ62:Jl -." 29n'.M8 327.8.564 "..

.~ JS7J 749 5946S44 ,~= 1~14990 219l1HI8O 26036.7!I1 ]IOll~J:!1 34lJ12.391 ,",

.~ J67:3696 sns.:'54J 1lJ671.4-Oli 15:l7e.8IJ 2IB50D2lI 26113.916 ~''''' nm= ,""-,~ ""m ~"" U2Y1,19S 1!0J8.9J7 nI6i.~la 214H.2fi8 mn"" _m 2.160

.~ J7S92ll 6202629 1IZJ7,166 16n7.::l11 -= 17]78.21~ 327lJ4,I:i1l 318~a.'/;JJ 2.I$l

.~ Ja6.591 6J6l.252 1lS1!3.251 16816.64 2:J!In.OO4-~

:rrm.703 36lIJ!l.246 ''''.~ "".., ."'no 1l~1O.J6] ""'~ 2J7ll8.4:M ""'~ ""'~ """'" "". .= 394J.HI:2 l\4!n917 lIm.sn ImJ.1411 244~1,:J15 29076.064 ']4.781.014 3BO~U16 2,4:JJ

.~ 4Cl12Uf.l 546l1S46 l185l.2'i1 11427.619 24m.l99 29217 ..U7 34ti~i4111 JII102.496 2,421,~ ~~, 661~219 IE1J.~ 177\J67!J -,~ 2976JlJ12 =m _8625 BE._~

J9a5.~ ""'" 121.50.1IOl!i 11663.158 2.'iIl14.9Jll -= ~1~.96S ,,-m~ 2Jl1

.~ 4:56JJ04 '""~1261186"1 ,....~ "m~ JI2J~,';61 3718L79J

~""'2158.= 423S9111 S9Cl1l44 '''"''''' IllJ!I9.0S' :.l615o!i23l§ 31245.740 ""'.~ 4lJI02JI6 ,,,,

.~ 4:>42.327 71~J6ll 132llI.4Sl 19J4J.:no mu= J::!YJ61i91 _m 42S1l1.1B4 ,~,

.~ 4JRD:!1 1I1f1ll5 13193914 I!i4Xl.902 :!147H.S2 :'12591.202 ....,-'" U~J.::lS2 ,~,

... .~ 42liJ.712 7412.m 135018501 19909.:'527 2lIHD.291 b514.IM :l994l.8lIJ •..-m= J.I'IlI.= 4279.'n2 7417.152 ,,,,,= 199<0.4111 2lI036.1J7-~

~1.47J -,~ 3.l95,= 44ll2.613 7~H4ti 131l7.802 2IJ1!l4.3.55 ...,,= "..,= 4OS611477 44:D1.496 ,'".= 4444.676 7523841 13143.J79 2OJ1a.2S.'i-~

JJ9!13.J.i9 4OoI7!!.176 ....JJ7.44t "".~ 4~17,164 7639715 14317.JJ(J 20819.637 2913JZS 34lI9~.= 41611.941 456e1.62'i 3455

.~ 462l1.ru 7819689 14172,11i7 -= _", 34958.7.... 41686.1101 45W1li2 ,~

.= 4li:l9.D3 """" 14551.6&'1- 2l4$1.627 X/34S.B14 -~, 4:za.:;55711 470111.1f.lll 3.541

.~ 46lf.l.432 711711311 1445'16>'0 215ll9.977 JO:73IlJIO 36129234 42irr1777 4701695'1 "".~ ...."" 1Dli7~1 149Q2l1:JJ ran'""- 31:511.50:1-~ ....,"" o4lt774949 ,...

._~ 49l11.142 ="', 13l439!iil =~ 31460BI!I --'" 44110.793 -"" ,..o.~ S1.JJ618 S4U2-a~~ 1S403.714 2JIlXI.1I18 ~~ 38416949 4S7S91n ,,,,,,n 4,!I3

.om ll14151 ~'" ,=- -~ 324:'5Q.ill 38469.105 4.sl144.J16 =914 .~

O~ ""''''' ~'" ,-= 241::0..746 D74~949 ...,,'" 47!!J1.069 YlJ11.9lllI 4,414

.~ ,=no BlI2UjJ 1.594<5.1.50 -= "",-"" 40149.>tl2 4Tl12.Sl4 52424.s..i1 4.416

..•. .~ 613'1.9:5'2 9C85QSl 164llS.861 2SlIn.629 35119.041 4HI46.734 ._.ill "".- ...,.~ 51916&1 911J9919 164~~ ill 25lI.iLB.i4 -= 41611710 494~1.469 .i4296Q4J 4.7Sl

.~ 5423.7:!!I 9IJ49.SEI2. IlIllI0.961 2501B.463 ,,"'- 4D4tllloS 5027S227 5Sl'il074 .""

.~ S311.2l17 9::9J.467 t6llSl.961 2llJY.6JJ 3~.707 42194.Q47 5l:l"le9.7111 551Q,/;,.S51 un

.~ 54'i7994 9<112.302 17455.428 Z6Jll1.Jll 36.!591lO1 4]7lf.l.l101 S22lJ..»I SJ'IlI2.70"7 SiN

,~ 5596.741 mU49 ITn7J391 2.6216.043 -= 43ll8l!.441 51985,.S27 S71Tl.I64 '''',~ S"i0:2.:'57l! 9634.096 17841992 275:.'!9,421! J79:lOm5 4~17l.m S.JoI~751 .i!l6431M 5451

.. .~ nE1.869 9786.5lJ1 179:19.Hl\I 27Z"105n -"-" 4.0994B91 =570 58697.146 5451)

.~ ~£IlIno 9~3..illl1 ,~- 27lIll.:'590 J6716398 .=~ .i44711(lll/i-~

~6li1

.~ .i6i6.416 9674.415 ,-- 27969.441 J6711J3J1 45919,60~ .i4470.7IJ J!I6:l6.676 5,603


Appendix


69

II!llt2lJ04

V<l1,..,Tl'P"

Vill...,dim!~l!.(=l

VilI."" pantiQ",

IODo91.17

CM: 8:%

IC1<O

"-"0

-TA:o:i.>l~~ -5lllU -,,,, -2.542 -IJl<O 0700 2502 'jI)l S.Dl!l 9SHV..l""bJ.o.., 0

Poll P0I2 Pod, Pod. PoIS Pod. Pod, P'" Pod, A"u~ FloIo meP. P. P. P. P. P. P. P. P. M]

65!48UJJ 564SJ.c" 64Jll8.DJ 61284,051 56BG6.621 !3fJ1552D JIllJ4984 46640152 36419.172 578869420.781 ~664 64194289 61138926 56549,098 52ll?1.461 5Dl!60.023 46684.281 36J~4_047 S8ll7291126340 """000 28659357 213415,795 2'81J84691 277)158~ 27525.549 272Xl.42ti 2649()412 O.O'H29Q29117 2878J.1JI1J 28669.715 284211B03 2'S092rn 27802.188 27630.512 27289.1l26 """803 oll463Q63l1.J44 3IlJ3<Jooo 30121967 """jl)Q 29294.193 2lI864,99lI 28611.238 281U1S6 mm", 0Q89305S7.191 J:J::9262J 3Ql1:'i.668 2Y7lI.4.184- 29JII.ll5 2887ll.'" 28666.656 28155461 27014326 0.104

mlO.OO4 31765.719 J1S5Q.861 :ml'S.219 30488301 299.'i5~ 29651.254 29004351 27509.414 0.174

JJaJHJI ='" 3J{]146f]9 "'92398 Jlm.D7fJ 31049.648 3IJ67Hn 299t15.742 2l'JOOl.D2J 0256DJl57,J16 m6536J 33010382 32460.498 31619.917 JlOOI.S8'7 31J63(J.61a 23'll15,Socn

""'" 062 0=

.. J5t'ilun 35006.480 34S513« 338a9.617 32965381 321S9~1 31121.262 :D8Q2.1I55 2lI5S7.m ON

--35605.119 34ll84.B4S 34.1)6.501 33845-074 =953 32119.443 31571984 :J)16J.l89 ""'902 036<36562.525 3mB.ln 15371.305 '46J6234 J3625.m 311~j6J 32263.195 Jl2S0.951 ".,.1137 0.428

36650.426 J5ij:49m n441.488 "'''JJ39 3367232lJ nm.8211 :l229lJ.85J 11268.rn 2llnLm 0.422JSQ49,645 37196.m ,..,.,'" =.734 14116,906 33716.906 TII56,918 12019273 29257,791 0.l71

- - 38011.105 Jrn'!m 3669),438 15STU88 14149914 33765.lQj 332:<1.871 """'''' 293)L721 O.ill

J'nB883 3l!41J395 ""'.59, 36841359 35605.7513 34496.715 ""'... 32626.514 Bm.m 0E2139137.~ 381J4.020 37128.516 ]1:.1111219 ]5566.434 ]451]5.516 33812770 32634.002 """-'" 0.61840118.457 39120.631 38j99~5 37597.0'S6 36268.883 ]509:!.4:JJ ]4451.473 ]1165.917 29947,611 06934lll979'38 :N.:ll]242 38676Jf63 37684.1159 36m.551 35116.020 3"4j(j1.2OJ 331659:16 21'9<"'" 069341497951 40430.!Jjj 39124.289 31168].5]1 37227'" ]5974.820 ]5281..152 ]]ll'li7l5 3036J..'lTI 0.784415141]] 40.30262 3914]965 387115.746 31'l51234 ]598].06] ]52n4n ]3lIJ1.63J Jll162 &11 0"'"41934.176 403,'j].9E16 40145.152 J9117.m J'7631D55 ]6119,930 ]56\)]828 ]4110.895 3:1523.906 0.8474201]574 4Om,6t3 402C6.51O 39144.312 37648.5]1 36]1:3.914 ]5589.461 :wmSJ5 :xJ41a0J9 0.850424TI.066 41347949 40686.391 J5:108,969 :r19'3S.461 J662UjI)' 3.5910.480 34339.39S _2_ 090242417010 41218363 """'''' 39~.29J """= 3669].625 35919645 344IS88"1 """ 51' 0""45!'J3L996 4~81.152 42S41.Jl14 4Um.01fJ 19821.859 38269,[)2J 374n,4l)2 ~9.457 314J1..97) lJ624~10.J95 4JES1.m 42il5U132 41575852 39S17.691 """379 "'67262 356S5.801 31422,740 US?

46196518 44780.816 4JSB3J611 42607,824 40117,94l J9IOB.m ""'':XJ5 36316.]59 31792729 1316

46206.422 44lIlfi.ll:i9 4391J.461 42S79.168 4{]JlJ43t3 J9046.fill8 3llli2309 36162,008 31B05.J1I 131.547497.051 46ll17.2lS2 4.'HOS,DJ 43632.547 41680.297 39932551 389'22.195 36968.465 J21139.2S5 1.445

4749116G9 46lJ34jj9 4,'j112621 43638.121 41651.523 399Oll.-41-4 38953.93-4 369SJ.814 32191.248 1,448

4SS41.8J2 47342DJ 46334535 -44782953 42663.402 4Oll16m J97llD-'" J76136.l09 32605336 Uti

48S05.621 4721UlSl 46:lS6.m 44162.66B 420518.151 4OlllS.508 J971l7961 37668461 ""5m3 1.611

469'74.879 4541JJ.m 44324.887 '2S7al"" 40136213 JlI299jl)Q 37185JS18 35071.%5 295$l5.B73 1860

41ll64,648 45485,691 44321.602 42663.465 40425,695 38318.168 J12ll• .52ll 3.5048.395 B5n.m I'"

47'"-''' 46340313 45218328 43474285 41084.7JlJ J89<552JD 37856.031 15467,791 ""'= '"5647915.918 46J12.111 451J6.nJ -4Jo1.J7311 4lO179D 389222/13 ""'00' 35445914 197ZJ.Q45 2Jl51

48513.445 ~1,621 45721,&19 43851..516 41389.227 39J8J7IIl 3111B9953 ]5BI-4,4n 29919.963 2223

4902ll.313 47402.875 46265234 "",.- 41961.129 39750313 38542-043 361J75.612 :D15HiJ7 2339

5D1IJ5'" 48967.145 471118,984 45959.406 43208949 4Oll59.&.'i2 J9>9<!jlJ8 36972.074 :D114.234 '.57252131.914 50456:.340 49043,895 4"1052.426 44351.545 41937.'1U7 405lJli05 377!14,656 31l70.octl 2...,

-52679.711 5lJl[j6.1l1 49.s92.840 47S38367 44102.961 42214.051 """.707 38019484 31275.439 2965

5TIll.m 51501.398 S0127.027 47938.164 44948.219 42627965 4ll65.789 J8220.154 ]157]211 '1182llij2J51 51356-.198 49878668 48tJ62.500 45fJ1n,j(JJ ~2Sj2.742 4J2lJ.EJ.3 311367.480 31354-439 '.118254mml 51906.123 5iJ685,957 <ll57ll.Q51 4S1'93.89S 43174.199 41m375 J!lmjl)Q 31679D84 3.249

...54J74.246 51929.633 =836 48571949 4S129.164 43183145 41704324 3ll61-4.520 31846.422 3.249

54958.402 ll176.82IJ ,'jlS27.246 49281.234 457m" 43S85.324 42240.1:166 J922I.2lO 31rn.l56 HIO

34933_066 ""'!m 51J17.891 4Y364.o16 461as.541 43466.191 42148.017 'J92'a63S1 3t9ll334l1 '4lI2llm.895 TIllI2D59 51.s92_-418 .""= 46\15371 43763496 .,"'= 'J92'a1,008 =.258 3.412

...

552119 184 52943.586 5l689..55i 49Sll5D82 46195.189 43399168 42059.410 J9Jlnill 32110680 ,....""'''''1 5349t1816 51!1J1.617 49699.012 462!i9695 43950.D35 42486291 39257.844 32094357 '521

55SO::I:-181 STI5!.(llj 5UmB09 491524.996 466"3« 43836£15 42489.227 39254.414 J2133.39J ,.m55'J41.8:16 5JS97iTI ='" 5llJ51.242 46934.699 44269.414 42610,117 39714.094 32349457 ,...55901.246 5J854867 52246917 5O{ 10375 46Bllll ..-n 44W73lJ1 4Ul64.434 39721.719 32220.689 "37567S1.IBO 545080[6 53.:194.543 .'iiJ722.7U -41illS74 447li'S'.6!l1 -41)50.438 4(lQJ7191 32441.710 3785

,'j7544U4 11W.m 5J59432lJ SI26S.578 "",,"25< 45175.055 4J112.44,'j 40415.6lJ J27Sl!.JZ! 3.874

574S&.m 11164170 53654004 :HJ9o/i453 4802ll.637 45'190llfi./i 4J'711.488 40480,598 J2720DlO J.9l:J5

58210.148 55780_090 54228.766 11835.102 48446,539 45697605 44Q8O.195 40184.531 ""'.887 '.lJ3J

58199.142 5579lljl)Q ~24136J 51844.BJ6 4S«D!m 456lll1.461 «006.40 40866.055 J2977.9J4 'J!29


Appendix 70

Table 36 HGL Test for kaolin 10%

,,-i T1PO:, ~-J1.0-.,.,0'6=PipoD-.-...-[~T

n.-r;.p-'j

02.:1"",",,-lmI

un.lOilll

"0"

Iw~ r .,. ... r ."" r .G '''' ,." .~ ems - .m.~... ,

l'oI.! "" "" .., .., ... .., ... ... ,l._~_.," " " "

.," "

., 'llo1

- -~111$910 ""'"'" ~llJlm 4!1541i21 m;z..n mom :J:~m 2'1a::5.Jl!1 '9

54ll611all SlIm:n:J1 486Il.l.118""'~ 'P67m :mn_~19 n41.'57 <~~ l14Cr.. ,".

,JI.l>9«l.:l !l79::W f9J>?Y5J .J6774~ 411IHJ(1 ~.'3< ~"" l:Ull :'1 =!:ll a.!!'J

"""'" =U5< ""0 _'n> '2!ni16 lI'T)'un _'0 :J:II01.71l ~7411 O.IlQ571,. 1<'1 ,wn mZl~ 4l6llii1f"i 438$.158 -,., ...,'" Jl26HOO mtJ,o ""I··· 575O:lO'a :i$<.iIl.>il' ~l'dlm 47<;l,J11< ,""m J81~1~ J<'il:l,TIl JI:lll!ll57 VQl.jIlJ """"'-", "'"= wmm 01.19'1601

_on""'= ,..n~ JInr..:I1 .."m Q.lll

=~ ""'~ """"_on

«En,!J6

_mllm.i.J:! .:l131USl "",m ,m

t =w mlhll ~l7i ~,~ ..~57tI ""'-"" =Jll .:1111\434 VlCilTIl o~'O<I4l'lm ~_.~ ,mu. '91'i'Hi"1! .~~

_.,lOilll.J::1 JlllfJ.l1 281\9cm 0=

~"' ,..",~ lJi76..:!lJ _m '!7XSI1 ~~, :na<ll.611l llT?Ull == om61al1lm !&Il'l:.'n4 """" ~oo ""',.. ~ro )l,liUll') l19.\1 lCM :llWJIl.:lll ,=61'1070;;<1 $I!1.51io1 lll'JioUJ JI5.!;H3i" 471J!J.4;1f 1iOi'1.llJ ~~ ToDi7J1l! iJlIIIJP om51J8'l..'Il:! _m ""'''' 51~.:lII' <.!l'8E7!\I ~», ll:>tu« ~~ llIJ'IS.J42 ,m"""am 604l1JIl7 ~IJ S!l44.117'J '1·26.~ ""'~

..,,~ J1!JHlJ lllq9~ ,ru6<41!.48l! !i:o\ll64 jSJ',I!2 ~~ ,1011.:05 ~.J!il ~.!ll :mOJ'llf 2lml:;<J ,~

M21l.1.l8 Il6JU9'i 5ll1l!SS1 i}lJ?.9l~ "66J.TIII ""' .. >mm :l:l:llHlIll 2!T..!.1ll om"'"~ 116.>1.7% 5B:.":'<>RI """" 'i7!UIlO .Jl!5l)o.UJ )(So.m :Ul~j 011 == om

:66Tr'...J.~ ';i9lJ~ S9:!!l077 ~:!7SY.:! ~.13l :!I~""!'J1

""'~ =l-ll1 2flJ11J:>I ,~

""'~ ""'~SlIl:i1:;:l6 =,~ '7'J6l~ .moH' ~~ 121'l~ 31Sli' '.M

6lrm:lllO "21ll:!l1 ""'$ >:i6'<I<IJ~ ~IC-lU ~= """" l'.lIQ6jD """" ,~

lilIl2&603 1.0IU;1 """" 51.<93171 ~101!'i -"" J6n1b17 ~,m ,..,,.. '""_m""'~ mJlJ:l:! 07~.~ 03111311 :s:l11l.14l: J<S9lj_~1 l1611ll1S ...~ ,m

"""m _ro 51136;0: "..~ ""'"' JW!Jll n,m ]109~.Il'lS JlMSo,:J)6 ,mS710:;m 5OHlH71 Sl261125 ~7~6'1! "'"m ~7\l11 M_m ~1J7!W ""'00 ,mnE':zI/ -- Sll~.m ml1OZ; ".,~ ~"~ lOl:/ii;7ll ]I:l£l;i9 'llW;6.706 1.01

Table 37 HGL Test for kaolin 10%IhuI. """- I .... "'" .m1 - '''' ,." ... U'" om.~;- •

. "" .., .., Fo<' "" "" "" '"' "'0 ~....;z",- ....p, p, F, p, p, •• p. F, F, rJl]

6'm!056 "'''" ...,. ~.lIlI 4Sl!'S o\jJ17lJ.111 """" JL'ioIH15 VOl.119 l.l2S

""''''' !1'!Wl11 '-""on 11~32( ""''''' .m"" "'".. llIDl1!i Tl6(5,m 1121651Rm saBl4.964 ,..m S38/iil.m %,21JJ!1 (llII.\451 l)l15.m mlUll V6~Ij!i ""'_on 2tii.B1 S656L~ SJti'.II.1SJ ~,tl.6Ell .."" ]!i!lll,359 116lH,lJ """" ,m"""" 58Il'1llll ""'-'" ,..'" om.., "'''''' )1191824 116'111B4 Nl7t71 U"JU1Sil453 617um "'''''' mu, ........ """'" ..= ]lm11lZ Zi'ilW049 ,.'"""'''' ""'.., ",.,,, S1146S'i'a 46991.766 mm ...'" lln.l.7}l ""'''' 15'1

.."m ""'-'" ""'''' S74f1.~ '''''''' ""'-m ""... Jl£!!l.'1!:! llm" ,m

""'" ""''" WiS.lSl 6l1l!l.1l1 41So1U!l (14:l.711 ....m 11[IHll 114W4:d! "'""""" "'" '" 6JIl6Sj4! ,,10855'llJ 4mm ,,""" ...", ~11l34Di4 "'""" ""..1'[!iU:JIl "'",,, 6illll56 ""'~, 4m:!n!i ",,"" !lI!il11' J18'0614 m!lUlIl'I ""m:ulJ 1ri&l.141 68lJLD 614li051 418'1a.661l 4156Jfl6 PIl9441 31!lm1iia V5l,m ,..1l1\2im med2l 76ii2nl ''''''m mitIS 41667.746 1/1611.115 Ji$lOt9 ""',. ".mlllZl 791:ll;J8/i 16619.1Z1 'l'JTI6"1 .,"'. 4tmJ4f 'mm """ """" 1I~...'" 8tll'-9:J1l ""'-'" _ill ...'" ti'Jll.166 l>IUj86 ll2S152J >7l1m J'"...., m'iU41 "'"'''' 16...<;'}I'15 """,. 4im.4.\] JIlla6.l91 JlJll14l ~1.I13 H'

'wLciialllr.

117'l.4

"'"U

""'"V.... T1l'"'f';"'~-J·

liiftJlOli:im:Pipoow-t..-rlI.<m.lTJI'"~'J:,K

Table 38 HGL Test for kaolin 10%"'-'lwid";;'; r .,._._-

-=- .,. "'"" """

- - ,." _. ,,. ,,'" ""...... •.-.., "" .., "', .., "'. '"' "'. "" A_I"_""", p, ., p. p, p, p, 0, ,.

jll)!H~ ""',," """" n!l4JIll 457i~K9 ilCIl'lOlll ""'.. llSolun ,.,,," 1,12S

"",. ffilloIlll lm!.m 11!1-46!1'2( '''''''' """'" lmJ.,1lJ9 Jlml~ "'''''' ,.wrnoun Bi(:9ll~ l6'lll.ill D'''" ..111];'11 «044.457 )li!j[lJ '''''''' 116:11.561 ,m66IPllm ....., 56:iiL'!5'6 SEIJSIl l/iltHJJ ""'-'" lIU8J59 ]15(~.>'!lij ,."m ,m.. ""'.. mo1.004 ""'-'" ""'''' .",'" 0ll:2<l1.il27 l!i11'Jn 110SJ ~IM m.gm 'E'~!Sh53 6Il6Slii7 "'"on !1JlUl1 ........ 4UB1.m '",-'" m:l9-.Ja. """" """""'" ""'.., """" ""'''' -.. «l'17Hjt -

_m"n". ""'''' 15'1

.."m ""'''' ..,,,'" SJ«7~ ...,,'" C!lQ2.141 ...'" "..... llm'" ,m""m ""'~, 6J!nl180 6ll1ll1l1 17S021S5 •iHllll "",m ]iQOl nm.-• ".,'«>'" 5iill51101 1£lIiI!'f,!41 6,OOJ7tt 47.l95.iS9 """" .""., ])!Jfll/<o "",,,. ""-----~ ..1iJiUll "'""' i5IIIlfij'J6 ""'"' 47711336 41/il7fl1 1l1'iElJi6 lla.o6'1t %1~ii87 ""-_......7OJJJI] 1!J6/iIl.741 6aIJl!11I tJlilLilSl """. U!o6J.9'16 :J>11.9.4o\1 Jl36>1Q iml.!1ll ,..

...rnam """" t60n52ll '''''''" wn.C6ll (16!i7,706 1l11A1l5 """" 21J2Il,iOO ".""'OO i9111;jl6 ""'''' 1'J7lil!l ""',. ti5'nltl .",m JimJ7lj "''''' 1102...'" !lllli.9ll """'" 76C!16JS2 40113' ",.,. !l14olJ8l! llm.'J:l 3S1!1m ,..,I1RIl71 U27t.«1 ~.'"

, 76.l79.191 .oancal9 4lmt!J Jl8llIi.l91 ~1:J:IU41 "ut, ,~

42.l1....,li'lt~

iO~

11

-•...,,.,,,folftilJl<'

f ~=lv ~J'ipo~(-=!:

Ilueli.olTno;_...,K


Appendix


71

~

v 'rnof'

'1 ~-J,~

p;,.~t ..r-t_T......~,K

"""'"'<hooT,.,..'<hoo~-J

'<hoo,..Ab<t.<

42.12

~10%

lI68J

lVlll

"

•-a"Jl:o,lilt.Hl%

11£1.1

IQ.1!I1

"

1J..ri&"'" .~ ,~ .= I ·,m I ,., ,~ ,~ I ,m, 'i'iT1'v....~ ,

I'ooil ~, ~, ~. ." ~, ~, F... I ~, 1._1bo_• ,. ,. ,. ,. ,. ,. ,. h ,... 6nlJ.'!8i ~lJ,)l ~j.:'?ll

-~ .rn2'l....J P<IIJT.W ~m LIIiItIJJ1 :8fJl~ ~

~~ &oIll':'::.:IU !ll<:!3.\7 571SlG<:l '9'l4H17""'~

]C'ISOli J"~.Hl:.! ...- OD~~ lJ15.i,rn: 6ar.\I.>l1 S7Ul9S7 '>600.1",1] <:l<3oIJll:l JlliIU13 I J!l~8.J~' BJIll:m om~'.!ilII ~m lW!7Q Y7<O< 7fl '>01"J= '~'l' -~ ln119lt.l 111BI..\:l.l omlI~lU:la 67!'.•6.7/;6 ~:0;4.l.ll lilIl'li.4ll' ~'E ~Is]xn ~~ ~m 1'1011.nl ,~

l1Sll:it! 0=2 6lli6.<I!l 1ii38n2P- llJr.H17 "'13.5J:J JlJ'II.:JJ1 ni&\l )(5 ~17W ",71'IHSl ~oo UlU.l:J!I ~~ =./i.ll

-~ -~ ~= _m ,m7'SO<~ ~m ~IS!56 "m~ ml:P.6 ~= -," )JIlHTJ

""'~,~

_m t='<.!i!IJ ~J.o:sr ~m llEJ:rl 0<7C\In! :Slll7lm ==> ,,,,'Cm ,~

76<:l;qc 11'l'i'l.$4 fnlO,.;o ~ll:'a'il' !1~3U -cm JWlI.711 ~m """",~

lIr1lll0li ;!ll'iO~ 7:W!I1 Oil:1l'<\3J ~!mm ~ llB21.1'l ~,~ ~UJ'l ,~

J:<.<l341 l~~~ 11~:::l .1I"H~.IW lJ<07S38 "~m 3&7T!.!:l1 nll1.bl1 _n, =!I02"11lll 1~.'177 1[,,;;.m _0 11!J<1J< ......;1-46"1 _3 l3Ill:l47'l ;i!B1UJl ,~

_m 1lII4l.l-10ll 76U\1.1:" ~~ W.ilJl'l -,~ _m _m_a

~

14-m.m :lIlIlH" ':i'1lHll """" 117lC258 ":IIlI.2311 -~ ""'E _11.'57 """7~a."1 ~l" 'li17!-1'1 ?nll.W1 llwun 4i7!ll.11S-~

~m lIt71t9C L"'m:5.lT.l IllKl.lll _m -,~ ~= ...,= _rn 3C!~.Cl ZIl%t117 ,~

~'" -,- 1'IJ19.TIl 1Il1!0m ~.~ o$lll1.nn J'TJ::ll.::ll :l<1n.lC ~l" ,m"SJ.717 IJIllDili """m m.l:J:ilJIl ~l.m '",.<.0 -~

l'll~r:l 211'1"--'\.ll11l ,m-~ 1l'lll59<1 km,al' 11C41.J1J !."mnll "ln~ liIIMHi'IJ ~ltl .",," ,~

~~ Il'llu:o;J-~

Il~l!Itl2 -l'J'!":n!l ""~2,o)l _m_m

:lt71~3J< ,-~.• ='LO ~lllll.C,16 , nolll.7:l ~.179 ~Ia:z m,m

_..-~

,~

.. ~-mDt;.llll ~Sol:lo.m ~~ 502!lJ.m ~.m -- _m ~m ,~

l=-37S m4S1."" >641V!!l 92O!IlIm .~- <-WJU1'-~

~19<~ 2!I111!.!;l ,~,_m laU15Jl;! ..mSl 9rm.1<2 :l<lJH11 ~,m J9~.1l1 :m91.o:lll -- ,~

llml.ll~ IIC_",Dl~ l1J694llZ1~ HrUlIl.6lllI ~~ _m :l\T'..o.J.1l'l1 =- """" .~

llo;;<~m IHXOl(;o llJSiiilJlll l~I<iIO.jlll' }4Slll.l-ll oSi«J.'l!'4 :l\'JlIl~ =~ :3J1HH .~

lHillTm Illmm l~~<:;tI ,~~

.~- O/IlllJlll J9MZ.Il7o P..mOI. Nlol.6O'J .m1:l:i65'1.&9S ll'l'l:.ll.m l!o.!n102 lO!lt92.1l1l lltll<.ll2' 401V.m ~~ ="' 27Zt7816 .ml~.oaiI ,_m 11181HUi 11221lSlO6 lOml12 40661111 ~m' :mU."l V<'llll .~

l:l6ill'L'J!lt IUlll."'l ,,= 111201l1O SO!l~.ll2S ~~ =m lOl:ilJ12 V1l1.611 'm

Table 40 HGL Test for kaolin 10%Il.;.l~ .~ .= -Hili .0.621 Ul1t ,~ .~ "n ,m ...~... 0

".., ".., ".., ".., ".., ".., ".., ".., ".., .l........n-_

" ,. ,. ,. ,. ,. ,. ,. ,. (1.1.1lIW1.1l1 ~~. ~ _'E 'l9S2.!Ill ml.l90 lrno.11J.l moo. ""'= 0'",.."E 4i2'2.ll1i 170ll.J]t '1:lZlJ1O 1:5l7,7~ ""',. lr£19-"1i6 """" ""~ ".1i17\l!5l" -'" W1UJl "'~ lflJU'l 4ClJl'.'19 Et9.I81 J1Ul2'.l :Tn6l.oJl ~,

OIClJjJ 1191~.Ja2 "mm 5IJllUU ~~ ~11"'1 lI23.llll 1119111% 1l892.1iil ....67111492 !Q111T.! '''''''' .m... 11~.rn t15011..41n l;lll.il'1t Jl~l:l.1n l790tlll Lri'IJ

61!iI!2-~1l WJ!i!.JllJ ""'~ =,m oJ13:Hll m;son BI!l.184 Jl~l!! H12 ""'~ ""n~'" 03174.111 61C8lJ14 ll!1l9ilS'l1 omlD tl!l9O.m ~m ".,- """" unllm2H [lll2.'i61i lil~l\.l'" -"' ~m 11916.J6Ii :J901DD5ll J:mt17! 2'1liil.012 ,m7liS7HJ!! Iili'18IlJl'J 65119.Jll9 ~,~

-~'J:oll5il'l ~'" J2llODl ""'~

,~

1!3lIl.1l!l &8Liil.l9 "",. 62'l12471-~

.",,~ l1111.IJII :l:lll'.'BII VI.lll<t4 ,.,imll4Q!i TI.l9'1.l>1 _1.115 '."ill '~2LU1 ':&:3S9ll "l~.m ='" 2751t.l91 ,mtlJll.OJll -'" '1021Hl~ 00'T.l!-l'J ._n 1:§I.::ro .,~ mlillll 2'JtiaJj16 ,m

.. ~.m 1l"'1,1'\I!I ""'m 164C!l.1ll liJlp.an "'",,, 111116.1:i1l ll91liJll7 211Jll,05Q "0~,. UJlVYJ ""'m ,~~ nll:!..n ""'= 0/I11I.»1 JJIrIJ1! nm.E ".",.... -= ~l.m

_..ol'1lll!.Ili :!1ll':!J".)l ll.lWIrn )Jlnl9V "'''~ o~

lll!7!'JJ4 OOIll1£lI ."".. 1:Jl:l'lJ22 ~,171i """" lO7\IIJ!12 ""'''' Vmm om_m ~» ''j;)jl.111 4:Jlll!.ll'IIl ~.7Il ..~ :J<tlCl2O lllilU!IC 27'JIllf7 .'"

.. nmil'1t oJlD~ 'j2lS5<il 02;95'li1-~

3609UUl :l<ie:H12 2'l/iIUJl 1m'IJllt -~~ ~~ ..,....112 ":Jl1&l1 01<9<Jl!l .,."m '""'" m,... ....- C.l:lll

""'''' <iDI.m ~ ~"'" Illl'lE '!t9:lin:t lID<.1Il1 =,m 2l411.m ~m

';Il1:J25l1 ''l7n.nl 17'1J&~ U'l01.2'11J 4'''~"1 Jl611.U~ ~'" m.m !l411..'1~ om.mE 4791'2.141 1711e:9.m 15ilClJ:;S ,l!2!l,i1i J1\nll. lli\IlIjJl =m 2J617.111 .m_m nms 19l1'illl , ln0221~ 'll1l.:ill ...m _ill' ..... """" ""l7'ilJt11ll Ja75:l91 ...., 1?G6liJ91 t:l4U7:Jl :l&oI7~.J'Jlj l!ol:ll:m )l]9U16 1:'iilUD """"'"' "- IIE,J7j ll!"..HI6i:J _m ,.,,= 17121 (lJ!J llJ1]JT] 211711191 ~~

_1l1""'~

SIm.5l 182!1S.(IJIi «O'nJ71 ",,,m }l;I9O.IXl :mu.,: 11761.111 "..61l'lHIi> l<717m "'om ~111.11!l

_.,""'~ -~

:J19ll~ """'" o~

.. ~lDlZll ,mm tl!iJ<1l'l lm03lil <5Il1-621 -"' "",m ll4M.m ""'''' ~~

1111171i11 0%29]16 471'Q'i.m U2l1,81i3 111'9li.1:82 T>m.il' """" =.,. Z1ll24tl (Ul!

tl!]u.~ ~S!cr.nl ~. -- 411':1l-ll1 ""= :m... m "",m ""'m C,l~

"""" 1'lOl(!m2 """" 05L"U~1 '!%ljll mJolm ~"' ""'~rn,,~ Dm.

jJJ1un 19o.!j.D12 f11:i9.!i49 'lWJ": olll!ll.l;li J1!>liJOi l'&11l.1n ,..,ru """'" o~,

""'~ll.Illl231 41']7\1.;00 4.J3i!1.2l .~'" !7!iJ.D ~~ """" 27U3JJ2 0"....'" ""'~

....~ .SX6W oZl:36JJll T'$)llll m"", _m ""'''' ""


Appendix


72

,~

V....T,~

V"""1IO'",",,~_t

K

"'"~""l1l":

i>lft~'_]:

V.i?oJlCl'ii-I'i;oo~jlllll\l:

~T!I""

~"'J

,

.,....~PipeDim*[<I!!ll]:Ji.lI",WT!ft:

,

(.",;;".l~.

un'lQ.1IIl

"o.

IDUililolll%

lliiU

lOll!

II

0...

•

"'"IO.om

u.Jl

I~~· T .~ .,= ~zilii- .~ l.:sI 1Ul2 ,- ,- ,~

,~ ,~, """2 ~, ~. ~, ~. ~, ~. M ~_!""""-.. ,. .. .. ,. ,. .. .. ..

""'""6S5j!rn ,,.Ol;.m w.~ -= m'~$< lS'6lUD :r;"ll'I~

-~ =ru ,~

-~ '-u.:ll!5' '213:'27 lCI"li.iil:l JJlI1IDl m6S'll:l ~m ~m ~ ,~

'1~.5'IIl .3<OnI l::W':!Z 008;)77<; 3&lO:ll l/li!UIiIJ m1lJ.l:tO ,~~ ;:lIlll~ um!""'m '!!IB.'" 'l~~ "l~UlQl )17<1211 ~:l''il lnl<.1!l m:'OlIlJ =1"'- ,~

'7~.I7:Il1i «Q!OH .n~.1~ <ffi2'I:m 3l!r.'lOll """?J.7')l) :r.:n.l~1. , "51'S)l1J ,"",am ".<IIl"~I' ..J9I.lIl '::!Ill.':» , 411J17J1l :ll;• .,...26/i Ja;<.l1':! -= -., =>lil'::l ""l'1!llil:r.l!l WlSlm.:! ':521.,* 41!OlZllJ 3I!m.'''' ~ J2&lUD' ~~ 11125.511II ""<!4ill16:! _00 n14Hll '!:!l&.m :<'!/m_Ill ;0:17••:\0 ~m, m.l=

_m""-~ c.<6>'lU12 4Jl'IC.a16 '12:::5ll.! ~!J<1 ~., :nmm 1919<..m ;l!rnll<lil OD]

.~ .=m ':m9~~ OIllJ].I!!l-~

W16UIt :l:!!S!1. , l:IlOSllil ~,- ""-~ 'lll'l.1i6oI .~ .rm.r.;z,; "l\Im:~ 36':"'ZlIl~-

BSllm• ;:8:1:1<3'12 "".~~ 4S?HTI -- ~1512 ~., mo.. Dl7<TIl :ll:~!9l! -= O~._- "8J'I1 ~11 ..3lHlJ ~., ~7lI.m """" Ill.... )]l<l.l<.-~

O~

S11lS:!'.Il t1l .. r.:I UlSao 'I!9:!!ilIl <w.nr.I !1!3'.I17 ~,m "'i'DJ ;I!IJ66JlIC O~SJ0\;2S.1"lJ 11l01.0C/i .5<.\7.Q:l 4T0627'Ol &,.":llUiIS =~

_mlllta.1n ~= .=

!Z!:!ifJU .1C\= =~ ....m <C1tH:!l ~il..~ "",W ~= ~4.Il1 0.0;77mll266 <19<l.7H 4fi11.\.<al ':m;m 'C'lt~~ ~~ ~~ :JlWi.on ::z!<13lfl ,m1U>Il-711 ~'" ~ ..:at~l~ 't::ll_lli ='" =, =~ ;lIXU.f.! Q...l:'m_~ <l!JIL!.l'~ <lial!l'l _m= 'HnJ:Y :11<11..111 =m ))641,..1 m,~ ,~

-~ ~m ~J'l!l "~.I¥ or;)).):)9 )u1l.II) _m ))64111n :zs:!l'l.a:tl 0.1":UU2.~ ~ ..,.,5-13< ....... ""l 4t:m.:iilll _m l<J2'IIUlI l:l'l'1.'lI:l :il!r.!lJl'" ,mmn..'Illl cam.a1ll ~~ "'"m <.."'I5:l_ 1!M2_~. lI::.1LD :.5'900)81. ~n Vtlm.~ _LT.K

__119':1.'''0 '\11lUlJl _m )lJ~~ llJ21:m .112'9:1.<0: ,~,=, <l&6O.410 <101• .16< >4t:21Jl16 fl'lJ8.9'12 -= )OJM:.0Q2 11l6:J<a ::5011.l'' ,m

S]mr.!ill-~ 411t:J.l1ll 44llJlin '1:60 :09 J11ll.lz:l .~~ }l~_nI ;227Htl ".

~1/ill.;m :;llllUOlI 'iI2n-l~ '5WlI2i .Zl5B-"J~ ~" ~.1a:i 11SllJ.1rn =~ ,~

:'<1::95<] -,~ -'" 'lbt:B ';lJ~.:17_.,

:lO"'19!O Jl6JII.lW =~,m

S<lilUll ~~ _.<t, '~Ol& •_m lM.U\• J<"l:nlll llSTUll ~ I.U;

Table 42 HGL Test for kaolin 10%Iw"";';;;- .~ _1.41 .'''' 1 -J.nl 'lli 4Ql] I.. 1 ,.. ,oo,..... a

~, "''' ~l , ~. ..., .... '" , .... ..., '-""'-'" ,. ,. ,. ,. ,. '" ,. ,. i'Jol...

.>I764~ mB4Zf ""'''' ~mtlJJ5 'JZl).m 36657:» ~J7Ll:l JIl6i~)6 ""'.. """"'''' m'illliI2 ""',. ~,.!m ,O}(!l'1( ~11_7!l Jm!Wi m". 34>1Wl am57"1l1141 ".","" ~"3U; ~1!l_~~ 44m.m 396)J~ ""'~, """" 29lnH2 omm",,, "mm! illSiS'll ".cm "294hZl """" >:mill ,

:J25lljIJlC ll4>U\9 om

""'''' S6!IlH:<6 DllUlI .,,"" ~"-.a:!l tOO66.!/j( :l66!6.l92 1!1!l641 1't~1.36S ""'<klQ491 5O.m.M8 """" ...n ..,,,,, -emlll l!/il.l.1I2J mlo.m 19SJ1&1 ""..0= ""'" "'~.. 4989Ul& ~lO,JID """" J6lill.ll2l !lllo:m 29511.611 am

"""., 117m'j'g ."". "'"'" lS42!!.fllJ ilIlS1!I'm_.,

"""" 36~ln ''''_...S71lJ99 .""" ~H6 l~~l!4 40414.'laS ..,m mm 2!l61L6!J 1018

J9:m.71!l mn~, 542IH.!l11 ""'''' 4S44HB ~,IO ""'.m ""'''' ~.516 IOn


I"" ..... I .,,, I "'" .19ll -I'" '''' '''' ... w, "",..... a

"'" 1 ...,"'" "'" "" ... ""

..., .., j,..... 1br.

'" P. P. ,. ,. ,. P. ,. P. :L'11i1a1Z1 ".,"s "".lJl '6"'" .,,,'" ""'-'" Dllll ""'" ""'.. lill

""'JZl ~31hA8 6ll£l1l 56ml~ ~~I (jl.am J.Thl.36J ."". -" lilliisa-m ~_491 51ooH14 1 "'lll tliIiIj!.1r84 49115 lHl'l.1~ 14519.912 "'''.\ll lill61m.'iJJ ~~UiS l51\Ilm ll>'!l.9!2 06ill!<l 0441..l7a !lJii5li 1411l1~ -.. '1516li!6J14 ...'" i'i1114i ""'''' ..,m 43m.m m"l" XJIj\146 ..... ".6l?8UliI '''''''' ",,,'" S2«Ljjj, "'"'" 43734219 J1~18.m -'" 2I"illU9l ''''s::m.m /ilI189"di lIWlJJ ""'''' %m.m 001,. -,. """. """" ,>11

6ni!99 ""'''' Sil131.E !Z:1:9m 46761J\6 mlU~ 11111'" D1lJj16 """. 1>11

""'>11 !i!4mm "!lWl -'" "",.m ""'''' mJ6.«J """" """. ll~.....

61437«S !/lllill.ID ,..'" mn.X1 ~ml 4ll1*.!SJ """" EJJ60"_.,

'1106llmn m~.559 S!ii11.1n Slr,lDl ~7f11J11 tJlrnw Jl4l.9.1I!l TIl3Hll 29i-lU',(J ,mEll4lJ 434 &;4$.411

_..""'''' ~m O];;9.:m mll.m 112lf.35'5 Dl19'~ W!

1il.<;4Jj:l!l Slll1'" l6lI!~1 1 S11ll'" l/i!7S.l81 *zmJW mOUl) m~.22 2%lHIl8 'l19634l!1.1ID 1ir763.m smnn 52'1.\227(l l/iS1OP,8] """. J11l1TI9 32!l'l/iUl lO!O1 """"'.. .""" m(J.l~ I l1l6JJZl 46W-n:l aIllS12 ..,'" I m", alhlO ,..mmll ""'01 """" 1 sum 111 46!~3'J) 005.m _HI. l21J14(1 "'"'" ""~:mm ~lmS8 S'i'Ju.:m llEl'l ~J!& ms,us "'.,lE" "'"'" """" "11"'00 ~1416MS """" I m{2.iJ'1 ~:r;.m cnam J6II~ji6 ""'''' 1<l1llOl ,,'"


Appendix


73

,~

V.... Tvo..,<100-"';..,],~

F.poO;"...w.n.;.j7_

,K

•

17J81X(1O

i_r"""...... """""'...:...Ji ..... ,.,,""'"l?ow-.

D~

•o~

"'""""'11r-',

I.cbaUI'T.115H

!G7Q3

"..

I.................. I m I -H1 .,,> I -I·m ,'" I ].llll I 'W 'w .~.~ •)',,<1 ..., ..., .... ..., .... ." .... '"" .- --e. .. e. e. .. .. .. .. .. r...;

I 1i1!:J1lT.:1 -" f>l'llQ:5S S6oI"Ii08O ~'M ,""W :lD!Ii:.CJl "'"~ ""'~ ''''-~ ' ..n!>lll 6117il.m '€m 1<3 400C<l;1 '5:"1-<77 :l89!I:l61 "'".. ~)'JI ''''I Ii7:li1UIJ ~412 1,000..1' !IIiI'~lm ~.4!' <llnl.m ...... JoI~IHIl ::r.&.l...m ,~,

6lSl1.$1ll 1')4il.ll.l =l:'!:l 11>ll!l2l =~ 'l«7.S1I "l7~}<l J<j(Q.... ...~ ,,,,m~3<4 5W.A"", )><111146 ~Hl'l ""'m f'.:msn "".. -,~ ~"

,..'1~!611 ~'D ~:!l1I I<#\-'J4 <67n6ll4 nr:~11j :mll.ln -... OWl: ~5Cl ""r;:l41U:l2 I£llllr.6 _ill 522!l.n.a 061Zl.'1! ..",.

-~ ""'~...~ ,~

Q)l1:9'J ~1~.'26 'Ailli-m ml~m ..,fIN U!lU:B mlJalj E'llJ.l16 I ~l~ ,m~m 6ll~!C.m ;M11.!:ill

-~ ."'m ",",w lTl16<lll J3S11D1 21'116.... ""6241H<S 6Oi6Q:rn ~~ >:lO!I.llI2 48i:S.lll 0:!8<.161 n!.l.l1Ol""'~

YJq."Il "l1:l4&DIl.m

~'''' 5o!lnJ!l ilm..X!l 411161Im fjiCJN :J1'Ol~.1l.!l J..'DI6IJ :lW(1170 1-1:!1fill4C;_~l4 ~m

""'~ -~~_m UW.:181 :J7ll1.7l! mt'.!I'i'l lllli':l4 un

'll<112Sl ~~ S!~"'I =~ 06111.:!IlI .m~11a "l7Wt111

_...~lll. un

0J00ll].!ID ""'.~ mow~"'" ~lUllI3 t;!f]•.l/il :l7111.719 ~rll ;slO\Iill7 'M

=us ,,",S S1l4USli ""'ill .....m 4~UC:Z

_m-~

318'17'I~ '"'Dmllll -~, YIlTlIl.w SJlilJJ.ll7 <61«)Cl fJ6I~.I52 JlI&'Hlf ll7l1 ..7 -.. ,m..2Jlm m'l'l3ill ml~;m =,., OimJ16 <m<n ~

""'~Zil9a2.II;J ,m

iQI.Ot1 ~lfl~_ '"'"'" s:nQ.5:J5 thlJJ.m t1nI.fn )!lIl~J!6 mo•• ""'M' ,m'


HGL Test for kaolin 10%(w~...,;," I ..". ::i..\26' ,. ( ·u, ~'" '''' ,W, l' l.66t ,... ,..". ,.., .., .., .... .., ... .., ... '"" • --e. ,. .. .. e. .. .. .. .. ..

l48Illt:l1 =~ 41.1:li:C8 m.~ <11l'!-MlI J9111UT1 )ll7!~ JI7W-7t5-~

,~,

j<oJ.lrm ",,,= flm.6<r f!:m.Dr .~= ]fU;13ll ."'~ 1I5l/1'6f! J9OI'P.t;.f ,..}<'i'n.lilli 5OtJ1.m t8ll:lsrf f15't.11la <<lm98ll ~~ ..... ll62<1m 1Il17J.:m ,m'"'0 _m 'II1P~ "~S fl~!lhlJ ~~l _"' I JlliO'l3l:i ~.~ 1.<3<

''''H" ='m m4J.<lI.! Ci61l!.lMl frsr.lS2 3!".Hl ,,",c m6t:'~1 ...~ UCO~10'}Ylf

""'~ tr.lill05! ·_m fns..lJ2""'~

:ltI$.fSJ )1""'910 JIl<16tll 11:1_wJImt.'191 _in .~~ 4.,m!ilJ2 -,= 3<~.91' ,,"'"" _.,

,~

illl:;1lJ9 5U6:iaJ!l1 _m .=rn ·2Joll.Jl'l )9)qlQ )01'*11:;'<1 J1IDllll ~"m ,m""'~ ""'~ Ollllll~ .=~ ':lliIlJI1 JIO(l:l.m:l 'l«:@!l 19~ 11S1:l.t'L ~~ Ulf:;:;;lSl19l ~~, 4811!,16 t6l!lL.lW f2:al6nl :m9U.52 3<71~Jlli lL5f(].'i9!l :l>IC:HH l.ml:>\:Ulf

""~ <!DO.1OCI WZI.toSol tlt2UJl l\lf16.2j.< J<lJ4.S1 lL:ll:l1'!1 :n;l16 Ull

=~ =~ ""J9i11l ~ro fifi'Jrlll mU.a< :J<m.r.=t ,,~~ ;tU/!7J!'2 HIQ

""'.. llGOij6i ~,~ -= .;..IU), -,~ l'I1JlJ16 11~.12l =~ "n~ ..

~,,~ _m '""'" 4lil1l.!lill ·2l:II.m 1911Ul~ .m~ 31<7I5lIl ;/Il1!:!IIS ,rn-," lllllillot1 ..,~ ~SUS7 '2t9l.<~ JJJl:l.1'I"I ...~ ll"!HlIl m."" ,m~m llt!2J16 _Ill -l6J1I,J91 'ill<m '""~

.,.~ l1<2e:m ""'m lCllI_m 5J1U1.l11 """" -~

<mUIIl BOIJ,~ .,"~ 3144H16 ~;m 1.IJi

=~ ,=m .,"'" ""'m O21lUlS ~'m l<8<1.'}7 llIDm-~ ".nlMIi.6<1 l!:l!l!l.t31 ffll2.?Cll ~lllB <:1<11.»1 "'"'"

_rnJI17f.l)l. ll<Ol-111 ,~

~~ Ilm31l fflUl.m <6<lQ.sI~ '<66)001 ~m l<8J4.lIlIJ ll36CQl O&<l'l<ll ,m_m SI&3li2& """" 4661U1] .~= ~,~ ....... ll)/oCliI1 ~~ ,.,=~ SUM2)f """" 4<!m.$If m"~ ~,~ J<;llU'J:l lll\l(lli'll ;l&<1/;Jl. ,.,_m l11-\jJ04 """" 46oi1IS/li <:;on1Jl

-~l'Ii<6.'111 llDlllll ~11il'i l<17

""'~lllU_ ~1'l'1lI1 <66SI6'll t24lHISIl ~;'!Il ~m ll~m ~f2;/. >Q

smlc"" ll~IJJI6 '0'''' -,'" tlStalJ-~

:;m3.lfl 112!l!llJ'l ..... ~

-loSlil.ltl SLIlG.«1 ...~ 016920;'>1 <15liSm :lSll~56J :lC><11J1ll Jllllm _.m ,m~m =,. ~ll:l~ P.l7J5Iil! .=... :lll'117.':liI

-~llDJl'I-I 1Il2:.9:'fll 'Q

.. lM71:m ~m 'mlQJ9S ~lJ~ t~J]]

_on"""" J1X!:l.5U6 ""'"' ,~

~.h(l ~~ ""'" 476.1lm .""m mum l<I!/;.6lJ )lJ2.l.JloIJ 2!2J!IllIiI ,m

-~W6<SlII ~n 4':.19 It1 tn.<Io 38iIlCUO:; ,.,,,.. llllij;!ll .,,,,, ,m

... s;:nHm nom.m ~m <7OJtm t:<lil:l_ ".,~ ~L<~ l1X1:l3lli =.m ,.,".,~ mlJ.C2 """~, <i!.671!J1 t2Ul.71l :llB7tJll '>on Jll5Illl'n .,"'" ,~

...,'" "'''~ lll/lnii tiIiiJIll'O! ......m Ui6o.111 1l«lHS7 Jltl(wa ~= 2913_m l..-~.746 SI2'li.-f2li ..... '0 Gm.719 Oil16<S mn,'lli Jllll1l;ll1 2lWIJ Itl ,"'moUI.:l ~.'Ia l:~.IJot _371 t:Jrnlll

_.•"""" 111.l11t1 ""',. ,,,

"""m ""'''' 5l....,~ ol84"/lJHO '::6Oim Gll.4!l2 ~m 3mO'9 2Im6:9lI 1017

~Ullll fllill7L """'" om., t:""H75 ..."" lllll.:lll 1114.'l.l(/g :l1Wi1.1.. lOll

~.'az J1JBJl6 =~ ...Inll ) <J.I:§.<11 fO<)~ =UJl' ,=~ JlI1'I'J-llt ,~

5S72U·.\ mnm 11!l6[l.l1ll Glintn '3<O'i.o13 ClOnJ!ll ~~ llntl:l'l :lalll/i.hll l.lll

""'= mtl-..:l llL7I.,S ~jl~ t:l'lIJ~'" o.m =om llt9ll6ll ...~ l,l11

""~lJlllill!7 'jJn.1li6 ;

_m.0041; ...1 4Of4.1.V1 1lOl7il1 11:ll:J~ ZSlillHll ll1l

...,m ~~ ~m~ ~"S '::-'ill.:lll «lOl'JO:f )<%1.6o!lI llt9~:lJl' ZS116.:m ".~,. n96-tt)< ,,~ _1t9 •~la.tl1

_..l'I';6Jm lHiJn... 2lI11l1.lI'Il ''''5'l'\6i!.:Il1 l28!1\.%1 ~\~l~ ~I" 4Jt9JJ!l:l o"~ J<m~ 112!a """"C1S6 ,~

","B' -~Iln~11 mtlHl7t ·l.llIlliJl «J<9:J.£6 llli2JII 1lOUll llll/i<.ID ''''...~ _ill .llnltLt •ran t:ID3Jll

-~lllJ2ll.n1 nw.JI.] 21U:lJO• ,m


Appendix 74


,,-V':"T

Vobo~""'1

v_ ..........Fi,oe-...r_~,

O''''''r('....''''J

"K

e.L.>l3lJl\".

llli3,4

IO.1!Il

"

lbal ...i-. r ..'f.~ .. ar.~ , .:l9ll5 , <rn ,~ ,~,. ,a ].'116 .~

i_l~ ,~, lhiZ W ~. ~, M ~; ~. ~, 4_ .........,. ,. ,. ,. ,. ,. ,. ,. ,. "..~, ll!P:!:'1 :lj<l:\,Oll 41~j1' , 'I<IlIJ:.2>ll 41llP.n. <Cm,l" _m J7'l11:r:'1 JIll'lUl..l ,m

rrm07l :C.q]~ '~.!!' ..m.5O!! 1l7J2El'1 'llJIUJI> JII>JII.DI !7illl1n_m

~m

$366<.811 If./!::L':";3 nlIl1nJ ...'IIU<ll 4113'1= -,m J\IC.':li.4J1 1l~1:m JCWS:' ,n.~"' ll:'l"'..<l'S "m6~ "~.'I\' 4:U:SO OC<:lIB~! ~m J761~~ :l&:'!lCrn ~,

lJM'."lI'I ~17.J:l7 qr.'.:~ll 4!l<:ll.Ylli .=~ ~ll.'l Jll:::.m ~"' ""'~11'l

l3ilo'i<l1"i7& =., '=375 4JCil.:l6] 'lTfU'&I 4Qll..l.::ll )IlCII].1l.l 11<lSl.'!6i >oJ6i71>! .J:')

:i<looJ.2IIl lBl:l-!O! ~lJ.l'l[l .=~ 'Jl7Jl1£9 ~.m :lIl.'l)~ _0' ~"= ,-54n~'l!! 11:!!ll.:MQ <lr.l&.'.l"I '!26"''>n '~l'S tIlIi!lVl :u.>lI1 ,,~ ]7107.'::01 ''''''" ,~

.~n .I1lla3", -= .~~ 4l1Clll.m oWl:';.'''''_.,~

-~1,1(l8

}<OIl::':: !lJl':.lJSl "l41-1.,"", • .,..,.371 421:l:\r.!J oonlHiO F ....m J'J':;tS.110 lkn.?>, ]]71

~.'71 lllJl.:l61 <ll541.1ill 45(,[J1,l!I:l '~.691 ~= :)'1J9'l.7!l ~.371 .".~ ,,'5<5i!l.47"l !L~"'611 q:l69.~ '.lTI9.n. .:noo.W! <lItJ 1:15 J93lr:'j:llJ :r1Ol.'llJJ "",= ]~

.~~ jj71l)Jj.< _m .=7.<.1 .nIilBI .1QllJtlS JlDl..-~ -~

,~

~llI:.6n 1~").tC5 -,. <:l!!4<.m .== 'IQ!I1HO!' 11411.a~2 -", _,n Jol.

.. m'ill.m 2111.2Z1 ~n .,;eIl.il7 <2UO.m CQ9!;~.JQl :!l~.'TI 18!lll9l J66<6.L'< '0'~I]lll.611 ro:-:.w. _n <63766 '2076.496 ']WUOII Jilll.<'n ""m351 -= ,m1!466.<Cll llmS46 _m ~~, .== '1]:1-'%1 J919~_'lO :lII''l2.3:rl J01~lI:l' ,W~5il!ll'l IDI.m ......,'6< ~~ C'~Jm <]jJ7HJJ l7<l76J2!I 18'8II.Jll ~,= ,~

~E l].'n,llI 4'illlIJ<4 ~~ .~~ 4t:lOll.:lIl_m

ll:m.:D J$<.Ols.! ,ml~..slf ~= 0'1<[7.:19 <6l.:i75'l1 ~_'ll "161.9<1 m.= =m :l6t.'7fIll ,,.-~

m17:!)01 ~ ~"ZIl .== .~~ ~m ~m J6f:lJCll '.IJ.o

... =":;12 =.1191 ....lIII116 "65llIl-1!l 4261lEIl <I)\tI,m l!I'J5ol,1i'll ~~

-~Hf1

S~52J(l 5:'676~ ~ -= <1m.:m ":m.m :M'!~ -~, ""'," .m-= Wl1.E2 ~_4.17 "66£!.617 .== ~I:SZ-= 3Y7J',191 -= ""'," ..,~JI~ D4J:l.'1'!i -., <11l~JIll Olj6~ 'l~n.'1.l7 -.0.12 l8lU,m

_.,'m

~,. =.1')] :llI311l11!l '''7JililSll .~1l.219 'l.~. :IlI1 ~.l"lll E'~.J!'! 3'll2L.'IC .mS7IG:)rJ: n93,HD !I:llI1~l 477'.!1!.ltIJ 'l!1J,m '161l'.LJJS <ll116.161 ~911 J1l0!ll<'16 <n.S7l&l8<a r!'Il•.''i] mJJ5«l f7O\1C1,m '11'1_~ '10'.s.- «lUl.l!l:'l :lti:I!'n l7I!1.a:n .mS:~1l.1'.!! J.orti.'118 I~O!H3l'i ~IH1R ,nn.J:i9 '1:'U.~ W~~ :l871'-- mi6D .wS'15olJ2:19 !'~215 l\C11I~ '"'%'5<1 O!J3ll= '[",",HE <cr.lIU71

-~=,~ .~

SilO<i."~ ~'" JlSoOlW ~"a '~913 'j~.!lOl '""11510 lM'IIJl'l '""'" '"'ill:l!l.7'll ~7:Ull ll~".:Il!1 4IO'~.m .~~.•n '1!r.J.DIi -,~ 3Iiil1.fm l1Ul.:z.2 H1~

SClIJ."5 lltn_ 11%9Ul -,~ .:l6l:lllJl .212.....17 ~= ~ln mllllll ~rn

.~~ 1l1~nl 11;.JL1:l'l _,m .16991111 '11:)6511 ""'~.m _m :J7~..m ,~

'iIIW.&OO -= mU.m .9LlII'IZl .J9J6.'.Il '2108.201 _m :MW.l1II :m..u:;:t ,m~,,, ,~ == -= ':l71l,r.ll 42.1\IlILll ~~ -,- ~94, ,~

S9m.91' ~ U60,9! _ill _m ~lJ'i!I.llIIJ «Tl'J.II7' ~~ """. ,m~JlIIJl 1}Il~ 15lll Q60Hll 0!I1llW ....:nl.:Il1 'l:!lill:l ..mJ.l41

-~ -= ,w-- lSl-\lJ::'IlI .\<6;!-'6!l ~.= _9 ,=,~ _m J>IJHiSll "!1l;\7i19 .-l\Il911~ 1>681 ID ~.l/iill 194J4211 ':5'~,m .~ -= lIml.crlll l7&!l.:Il1 ,m-- =,- -"lIl!I.62 '1I7!l.<l3' _m '~.WJ 4i!llll./JI/ ~= J9!S3f/J ,m5<17.l.1ll' lllllJZT] <8IOUI3 .~m .l2<6.l1ll

_m~.~ :J/IlISlm 1619\:l!9 'd

JliIJ13l1 ~~ ''!W.76li ..>60311 '19J6.B17 01».' 171 1lI111711M _a ~m ,~,

5:lJOl19l 5lIlJD7I 4·.....Ml _1l~ '19l1.n~ ~~ _m "rn~ =,- I.'HI

.Ill~a& =T_ O.,H.Il "1lO~ll .1741!m "",= :U'~oIlIIl l7811:3ll J6UJ.H7 ,mJJmJ6il =~ 4lwm ...'46J<l1 .I'.l~ tQJ)7.'71 ~= l1WT.J JO<IO.27l ,~

mlllW _0' '="")J _.9 '101'-629 -~_m :J7MIl:'5 :)6llJ= ,m

.Il126.l?tI ~.:Jl\I O.71J:Ji ...m.ll4 4l771.7D _.- _T' )1:'><1641 )l;ll1.l.1 ,m-= ..~ d= ~m ..~, J519<D.;,J ~~ 3nM.240! '-"'= 'ill-= =- '"l'JJ7.1J1 ~~ ~16IUS' -= )I!>:lIl.766 ~ ""'~,m

-~ ~-.">161.,56 ..m.l56 '1621UllI ~.l.'

_,.11:»...\< ~,m ,~

119l21IS '!II3U.:a

_. -- _m :l96EI,'" JIIl'I09Il :lIi92J,"'~ :mtll.nIl 1.191

J1lllllm '!II3'Ii.m ~~ .~'" -~, J"jl1.n ~m J619].i.o-~

IlllJD!7!;.lQl <lJl7.1n .s.og-!Jl .Z166<l -~, -= ~~ l6<C.9I~ -= ,m-- i4-<49.'J:l _w <l6'.lll.1ll1 )9JlHM l816i.•l' _0' ~m -- 'EJiJlJ!'2<1 <lIll:l3o! '5646.:tI1 l:JJZl.lJl ~~ ""'~. l1!iIil.1ll1 360<)0.910 =,~ ,.'lllJOOl2 .ml,llS lSlD<.m ~m _.m

-~~

_.,l3l!lOiSl .~

Table 47 HGL Test for kaolin 10%1"",';;"- -

.LIl9 ""-- ,,,,, ,m ,., , ".-'.ill .., -10'

V.MI'- a

"" "" "" "'. "" "', "" "" "" .l~~,.

P. P. P, P, p, h h p. p, nlI]

~lll:H)J 4928j16 (/51148:1 tjlJ:6&j 4J71L281 mJl160i l!lllOOi """" lQllO ,,<1$44181 ~7Ul29 (l]lU1\ 4(J516!l1 mU.m Tl441ml JmJJDl -~, Jlli6~

,.,.

SlOllJI6 ~lWJlJl fl45U411 45C-4L19! 416llE.66a 376laJlJ 3J99500 ml9171 1I!;9,lli W,

5!(IjlN 'SOlll.~ (/S4\l.i1l ! 41119411 m34.668 i7m._i1 ~l1.li6 mm 11111!l6li Wl

~. 51611.m ''IoiJl#9 48'J).t.ill I 4U9715 m'J133l rt117.iD1 ~Lm llJJl~' lJVln ""jl9"~.J86 ~,~J24 t8t5iJSl 4.)j4ol45'J 41Dl.367 :l8JTJ.aa lL"4ll.1'Jl mlJ~ mn:~ Hr.!

5l1~.m ';0"''' q~ 4~16S 4l00lll.blS ..run ".H" 121:H19 llll1m la

SIl7691B ""',. ""'.... %2~lS/i U4(~:/)( J8l'17%5'.l :l6'll3ln m,,,. "">11 UTI

~Jl6 SC88'l.1'66' ~}Q ""'« .13%:311 ~r.~!! ~llJ J1Z9S111 l!t'1~ ,m""'" 51145li.631 I ~19J')IJ 471Q541 416J8£i/i J&C7]Q 36ffi\.i:IJ J1«r.:m llmJ64 '01

-l>ilJll mOI.4(5 (9'1£645 I ~?OODJ1 41238.262 :!¥t6a.lCl/ ""'.. ",.m ~Jl7 ,~,

""'., 5l!1l'..'£i 49al.m """m 4l221,461 ..mo )007.1111 lmlOlI lJU~' ,m..

5lE516 m62£2 :mom ! mlllB8 4~ma 3B64L~ ~1142 :Jl."Tilll """' 1ltO

""'''' "m.. ,..., 4798L'1JI 4llliJS2 Ja&4!Ja4 ...'" -'" ""~, ''''

•...17!iGflJ4vm.-Tl'l'":VWt~lIIIIl]:

,m.~

Fi;I!~["",,~

Jia.mlT~_1 1I],4}

""'"1I6H

f, 1000

~~~----t[±l


Appendix


75

'''''''y"", Tntv.... · ...j

YJ,..~

FipoDW-,..[_J;1(.....:.1,-"

"K

1::10Lo!;..lO%

U.,,~

,~

lholl:i>,_ 1 ",m ... 1 _"I 1 ·15:'J I ,m ,.. 1 l:!n 1 8M1 1 U'>t'f....~ 0, i'ooi, "" "" "'. "" "'. "" l'ooi.1 "" 1.."",fbo'",. ,. ,. ,. ,. ,.

" ,. ,. r"143fio»!l26 'mlJl. 41?l!:.12 <:Im 156 Ji:ea.l~ Jlli'97!lJ :;"'«<:3 Jl56::ill ~T!2 ,~

4ft4.I7.Z!:l ·!168.•41 4i([JJ471 _liS;,. JXl89.5'14 ~7tO m:rJ.lS T,£:,~ ,10169lJ ,.~

""'m 'n<7.445 ~)01~ , 4:lSi.~ .\5'1911;8 'S:2"illOll :i577E60 !:-4()U:6 ;ISO-,,", uoo4&rn."Ill 41186)88 ...'" tJ1~.:1il ltn.!!l'H Jr2S1'JJS ~6<.~'1 :nJ:;]Sl JP......l L·l/&~3Il1 4"-l61~ ,,:mm <.\1'iH45 , 1<wJ':9 3$C:.581! !:'lSB7!1 , ~EO ~719 1."'2_..

tis<ll:l] 46605'7l 1OCi'i.348 It%JtJ4 Ul571 l'11Jil.1<l !)5l;;11r! ;)W..m ,~

== .""" "1l':i.i/ItJ ~3'J JI£ ~.. _..'17t1?m "',,'" =- ,.,

I '~2!1:! ~m.2JJ Hm1ll1 I ...m ftl<HM 3e9Si.m Jr.'XU67 ~m """:l>'Jo!i lmI """. 411lLID <lilllLt.!:l , lll513" n58!i7lU ~'1I :ml:!.nJ '"" "' l:'n6<tl ~lS1

«~1I1m .,,41,;$1 t~m!l/ill , <U:8.1m !Jill.n& :l41>tJlll 1<..<';:.<64 ~n.m ;~j566 '.m. -"47:':o:rl 'n'iColCl mS:l.li3 , -Illl..m 3?36ol~Ja 3U'I!.>61 :l<T:JI5llJ1

-~ "'Io:lil~ 6:154S5S02!ll' «ml5J~ .~11ill ""',. '''''" ""'ill !llISHJ6 mOli.'lJol ""'''' J1SJ~I1 ''S3JJJl 4:l!126m 41lillO(! 3IlJllI!1.l<! ]~IGj;srA nm1T1 , J<mo:1 MH" l!lll4JmSI41 "7li8.r~ 42roHlo ~JIJ 1i9JIOiCl 34'1"..6J'11 :nT<1&l ,

""'~ :!SOOli.'~ J.m


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Volftpao;n,lt:

Fi;oeo;."r..,.C=lIWcri.olTJ'lI'!

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J.

K

42.12......,'"1214

1'i.1Dl

'"

'bW&.~ ,,'" _>7n _1,985 '.m "" JflJ5 '''' un, ""'fbopJ- ,,... , ,.., ..., .... ..., "" ..., "'" .... A_f"""wo

'" ". &, &. '" &. ". &. 6P.,. ,. ,. ,. ,. ,. ,. ,. ,. "","m """" l<m8.m 2421S_~ n?5&066 4462un ~i86_iffl 634.5311iO 7'Zl7H61 ,,,,"m lJ72S:m 2IJ1't1 Q59 2ll:l2S,;&l J.I.[F)S,418 4~m S71Il2691 !\£l64J3IS 15lnl.7!ll o.n,'" 15619612 til768 !27 251%924 34g.;2i!71 ..-m,~ lins~ 6oQ84781 7491ICt7ll ,,~

1-- ''''' 14813.058 1".diCl_~ ""'''' :J~ill:!l 483'JQo!7 :ill66..!,m "''''~ iCll'lll37S 0,149,.. 1:lS'1.11D: 1955£',01 ""'''' J.ID4S.53 4l!JSlJJJ6 Sl16jH2ll 61tl'JH'T.! m14S7ll ""''''' 1ll1l4211 _m 2li'!:JL81i9 ]S1Il.U18 .sO:llU72 6l12.44n ,,,,,m 79121213 ".,.. 15352.J1l1 1!l:l12M:i 266%.385 """" 4956J,m """" 5>':;,0.1)1 7!l94S.111S a,m

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Appendix


76

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Appendix


77

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Non-Newtonian Losses Through Diaphragm Valves DM Kazadi

Appendix 78

Table 53 HGL Test for kaolin 13%IWo;,!!!al I ·1.41 .,'" ·Ul .ll.1'Il I 1l..'7 Hi1 I ''" I ''" I HS'I!ft!lm ,

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9&l2Jl~ 1l'J57Il111ll 811l•.'AJ lIm.'i15 .""n ".., l1219DJ "..." )C,81911 n.!17l0lJ52 9lllDB/;1 Dl25.SS "A>'" =. mn.:l6Ii .mBJ.172 4JS:!10!l :l65lH.ll H'91J'.2.648 9I117!l1.l1 .""" 7.l654484 ~m 611~.l.1l7 17i11J1014 O12!J:18 ](6il8;W,l 2416

97'i61JJ:1.l 9l!11L'13 mJi" 1.di1a91 WIll.%>' 61/il128:! l7'i61.113 ~:m~1~ _~l ll.mU664 9Q51.1J!il Sm5i.'9' ""'" 'a9~J6J 6!7!ilJ!16 mI'lI.l~ 4-4llfIm J6ilI!l.'i11 l.lli9Ilm.953 ""'," !ll2!l.3'll ."un 6a17llD 6191lJ11 ffi6U84 44184lJ1 :m3J.l "Ill_..

!llJm604! ""'.. 16:Jl~1I71 6'ltluOJ 611'%.'iD Slll'i61r.! 442497)( TmLJll B'm1!.%> ""'''' rnl1'!64 m9'7.1lS 6S41~96j 6!lli4lQ .l75l1.T.!7 .m.Jll ,,,,,,. ".f1~lJ.T.iJ """" ml6J16 1507lJ13 6D-!33Q mnm l1SS1l5(l {j6JJm ""'.. "";)11].417 ""'" ..",. 1~3H16 ""'~I m~Hll m21'8B ~:::64'.ll6J "",.re lID'_.DJ ...'" I2ln~S3 15e1l.6ll 6!l1311IN 6lJ1Ull ~m 41S1.1!!l1 :l6J>/iJS l[]}j

mam 'lUl2lI.7:-4 ='" 1616041~1 &i4!I.\lI!!l 6l112jJ;lJ JWlm ...,,, :!6XlIii! ltm9Il1llilm6 "..,," "",m 76:5'lloa ",n", 6!mm .li'll7S.13C ,,"',. :iOl19.'ii& lm9litil.1.! """" S!lEmI 7J.'S'?861 6OZ2fJ1ol1 S8!115.l4l1 mu !Ill ....~, !r.:i.fo!l 1419

%219oq ll364a.H!l i:l36.m 11.143672 M34i.ltl5 mJj.Yl1 lllS.. 4um.12'l !JI!75(1 .....!1tIl!l'!l.7Bi ~m Ilfl'i!l mu. "'.'" >mm =~I 41001CBl Dr.h~ ..~,!l64,!m'\ ""'.. m'Ul1 13'>'i6OJ 6612H11 1!mi.?:Il 54E18J 4ilDlHi/ilI If<C111l l'"

""'''' "'~I 1;413.513 ""m ...'" 'IOU< ""'"' ""m mlm ""... !j!"H64 !lM':l.JiIl I'm.m ,."m """n JJOmll j]ffill4 "",m 3f.4I"Jl:l 39Sl

97l6'1.as2 ...'" "'"'" 14&12$ ..,'" .l961TII ''''''" 4ll:ll.'1l ""'~, ..n... 91142219 .mm """" 7.>655U 61llID'JJII ..".. J:Ql:+49 I ""'" ",,., H4'


Appendix


79

r_V i"'", ~-JVaioo_l'ip:~[_l

IW..alT~:

Dt=niP'j

"K

V<ioe~=l

i.m~

~o-..{-'""'l.

K

<..k:i.1J%".,"""''''

•0.,iHl

!o:IiII:lY.mOl

.11JJ

''''

-rwbi;'" ! .= -4s:m .m> r "" r "'" ". ~.9I~ I un I ~o 156,..~~ 0!'oil "" "" "'. "" ""

,.., "'. rn;~ 1_9;;""", ,. ,. ,. ,. ,. ,. ,. ,. ,1'71i31l7J as507.1J9 1Illll1.l41 .,,,'" ""'''' ,.,'" l.J...'7!l.G5 I lIIm!lJl !ll!3J14 Hm]i5mw j·ll714.25! !1ZJI!JOO , ll<UO!I!4 1648HU 5nlJ.789 ""'"' (SJG.m 4:~J36

,..,J(l;4€J!J6J l'lllP'Zi mnm """... nlI7'J072 67'JIllITJ:l Ii:'ru.'" I 43s.l566 .mHO ~.l'IJ

j[5olq.7O:J lJ!1!J.I-lli 9J1::6--!l!I Ijti0336 151SUfl 5a5"1i!:lS 6ol'lllM ."'"" """" ""115511.m mmm >J!697'i1 i 1j!J71ll11 7S14J il1 5S'J1l0ll6 o<aII4ll 4Sli1SOIil 1:.mMl ,~,

!f57lo.:!l!! ImZlOm !l34'..a.152 1 !U::!!I0iS3 7m2:; 69I!l'1>61 6<l:n:Jl 4<1S4 :41 4im.l.~ H"!~l 1~1J8llS45 !l341U36 I Imf73l3 761l5:D SIlOlJ ~""1.93t '''"''' li4;1" ""llCl6.l11l2 Im!l~.94j ~79'lli "m", T/{lI'.E.l/i 1 m27.l4! 65"".:£I.!ll1 4~~_,41 11l4J1]] ...llriBID I:!m4SS ""'..,, 1 lIOlil!21l """., 69!il.l.n c;lSJn 1%0 156 mum '~I

JJJ!J7l!25 )!!2!il9J15 9<.l6iJ.:>3' a.w;m m51m ~U9j £oil7m ""'''' fll3' 1Ij ....LJl45lID IU2Ir.... f1}J ~JL1([l lI6:m_l~ 177l&.5:6 ""'.. ""''' 41'a4!i:!Z'l U&J.J!'/ 4&11lllSD28 IIllIJl_~l ~jl9'}11i ""''" ~Jl2 i!ll9LSJI ""'.. SIlll.34! 41961l301 ..,

.. m:"JlJ 1!Im2.0C2 lr.m5M a75'7.l1:i 78.1001lli1 7(lJjHn !iliI!ll'J:l ().I2'>I::. Il:8i£l ..,ll:5iLm 1iTI6511rtl. """" lIIl1C!!.-Ioll ""ill 1tll.t.64 "'lHoll .;mm 1!L'-lit4 '"112lW;.4IlIi 1:J4(lJ4.G5J Il5IUiIYl 87l11H18 ..,,'" 1Ol:H~1 56iljm ..l("ID 4;'l'llJ.~ l(lll1ElHl~ 11ill%.ID !l6Q;4111 "".. 7'JTJl1G/i 1l!llllZl 5mtJ21 i:6JI.!ll (lllllE ""113l!<.714 1~3S.m >5JO.Ifll 5IlC1sm ""'''' llTll:')lI /4mj60 , Sll$071 12l..<HlII m1134eJID l:JSl'i1l656 >67T1111 ""'''' ?9ol1lnl 11:liUC1l ",mm 1 (i421j«)

""'~,m

1I313.rm 1a'i9lGJ(J 90951.78.1 lIIl76l!74t ""'.. l1(1S1911( rnn.iW mnne ,,.iSm H.sa11J(1n6ll ~13l1 111~1J(7 al:i411!i!l ",.". M567 53J mUll , """m -o678ill1 ""1r0:J43.1!ll IlZllUlII 0«41.760 ,.,,'" 6.li1iH14 BSH8( ffii'l.!lJ1 (15l1.T.Il >mm ,..,0'(5127] j:iD:.7lil mQ!>Il """" 7ll1Ill1ll 534"-01 ii2'll.ttl , (1I5l8ll :m22.t:!1 Hl~

HJj(11:!!7 !mM,iD1 3291iL"78 1IJ7l..!.9l1 719J15>1i 6T.'a1.C!1a ..,... (::wm ms.m l."10710Ul5 mllIj7j .,.'" """. mm" ""'.. """ :!>1!l1~ llil6'm "'"

Table 56 HGL Test for kaolin 13%Iw'mi_ I ·U12 I ... .j1i! I .1.!i'I'J ~.1U7 I HID lm I 8.~1 I ,,.'''"Id 0

"" PoiJ "" "" Poll Pol' "" "'. "" 1~n:.:ilt,. ,. ,. ,. ,. ,. ,. ,. .. [,os]roS,U22 ""'J!J rn54~ ~.!ll jJJ11lli C6JJJ.79J 00110 J056J6J ill'iiJal a1".."". 6534-1.%5 rnJ1J" .", OJ HJJl,m 4638'.m C4Iil.!!J ~mm mhl.(TI om

""'" ill&!l:8 ElJn:J43 :m~l ""m C6!jj(J4(I roll> :Am.S']) TI1ClI.1i1 ",'..... ... ""'JXll "",m "'J2S\3 5l:9J.l~ ~7r.t1 1671J63 Clill.m )7121iOl ]]1924 1.'];lJ

.... ••7511 ~H14i 007::E1 5SIli9922 ""'''' ....,. olilmc l7li'!I.861 ""-'" I",

"'~I 66a7IJJ44 .- S:..(l.121 ~llUJ2 '''''''' ...TIHoll JI~111 3':GlJ8li I.,.eam:,14I 5J957969 6!!99Jl3 ""'.. m,,,," ~Zl.5S "",no :l64ZWO mlW Lil1

&ll27227 66317,7!ii "."" !2!911 lliI!O %!}HS1 o;[l9_182 ..."" m34~ ''''ea-m.m .J"'" .",m , $""".4:1'" 00"" 46)>6.141 CC';6,lcl i '""'" 1rnlil lJI!ilS6:'.76S 6S51(ll4 "JlJ.m n4ill. ""'.. C667llgl "",no I liS9UH Il23UJl ''''

......... 6mlE 6«%.4lJ2 l']I\1Ull =.. 46a9i164 4JI~.m :lWrO.m nmoo ""!nl!I1D 67S2l?S1 ~~~ SOIl'S ~19UJ rnJ711J 00)0> J&5C1 [fl'.l lDP,i;l ,.,

...mllOJ 681114-15 ~mlD ".... joIj]8E12 4741[7)1 414lHSJ :mJJ([Jl mr7Dll lJll1!~14e aJ14.221 """" .- ~Hl'1.91 W.:S.all 4-Ijj'1.2). J1OCIJ.96..I )flmIl JjJj

..._.. 1I45tUI =1Ill ""'''' 61151.m %lHJJ """" "'}(IA:l ,mu" ""'.. 10lllLTIllll gm~ fIJn'J}l 61651891 ""',. li6BJID'I ..... JlllUlO OOUjj '.IBJm9~7 om" 66]95i1 6lSl.115 .iSllHi4 Hi19lli #BB,[;l] -l7176JJJ m41.4O:l ''''ml.8Il 7Ol'R711 ""Jli "",:m "",ms fJ858142 l4:a!J12 m". "0"" ,.,7ll£l£i6 6'JI4IJ.1ll frJ9Dl! 61i~~ """" 13110,T.lt »m,. , J12llID nm" ,..mnl> ltl9S.'1Jii f1mSliI ""'" l5J1:WS 4~.J}!i .\47l),aEJ JllY.!lll m9J75< 5m31(JXU2i 115l11J!i 6i4)lJzjj a<7l812 illlH88 482:ll.s4ll tml112 mll'" ''''91' ""


Appendix 80

Table 57 HGL Test for kaolin 13%Iw~

,".41l .m -HI I ·10 I om ,m ,m ,

'"' I ".,- ,0

~, ~, ~, ~. ." ~, ~; ;;.;.! ~. "_1'"_-,. h .. ,. h .. ,. , .. .. :..\T'~3m S:1l2!!l 6ru:).:56J ,

m:!J~:~ m1>B<ll ''!!l:l>.'l +l.!1<1Zl , ~11!!:!l100i =:;:1 liI"1'9T.l?Hlll ~.m 661C!.:56J 0iJS9l.i'..l ".....,.64< 17:'19 '26 ....1:l.I1~ JWl;~ no1~'::~~ ::-11<5

I n:IlI_~ ~:50;)<7 663!l! ~:n 6l~'7 'al J~ij."'''1 41::l:lJ$ "~!7\I,

J""~ ..l =c:J ,~

"'=17:3 691;].154 00]'l1....S ~:0i<I! l~1WO. ...~'I<'I "1I>l.t.J ~n~ TI'l\\<m ,~

='E ~,m 667:J.:J'7~ &mll~ llD1.m 47'J9~1 "7~~l J6<W!l6! _m ,.,~m i;l911~ !~311J !!"l~ ~~l.'il'f '''6:n~7 "'.1::-<6'1 ~- ~~ J.:\.9

7:!615211 1llIl5IMS 6"nt:4 ?IS illl:io\lM ~j.- ~~ ..;q.~ ~a .= m1<\'.\'12 lm~...~ ~m

~" I ~l.lo'\ ~.~ '=.:m 'Yll!~,:i) 1l,lo::m ,m15'!O.m 1161!.El 6i4'.l.'.l1 om,.. .l66IlW 4Z!lln 06:"':.7511 ~~ :'<mOO ,m14WIW 71634.91 6367J:m U/TJ16C 5/;lll.;m 6<'.:.3111 o,sSll!Jl JD)~m }4.$<91511 ,~

T.1:M 1:6 ~,nl ~o~... 6!il"Im iJIPJ.·~ m;a,illI 4U1~B«l J1[!7lilllO ~,~ <I.1WJ~' ~:!~ ~,<06 ,

51LlZ.~ S<111:::J t1201.!lIl 4URa:n ;.u:C.&l!l _n '.1l1li

=a 1iS<:llli I167ISSII-~

!Y.!fI.J!il _,m ....17E ;re! III ~,~ '.:JI17Jj9~ IJ.i ...m ~,i'3I , 61B7'JOO4 ~}Ol.9<1 '1'9'SlI<n _.,t. :m;;o JOWl.m .~

71\5<1<. $E14J;"i !~,:m &;D] III 5SD: .. l HlSOLli5 ~,>\,C36 m1,~<-~

H\'1;

~15\ 'i'l<:'Jl,411 1m\«71 ~'n'l; \~\ '&I01':{,(, ~\,W ~5:!Y ='00 ~~ ,=71"'J~ 7IJUHJJ 6741<.:113 6Z!1~:I<~ S1C1!11

-~..>.:1....1 TAi;lS2l ~~ .~

71l!~,<n mJ1JM' 67166::9< 6"""',.0, i! ~ 10 ClI OIiHI92n-~

:l'J.Il!l,'illl ~,~ .~

1<T.5J.541""'~ 6"/<;l1.1S6 .~~ "",n OCtJU11 .=~ J'J64lO6ll

-~...

7rr.:lI,.:X; ';lldJ.2J) 6"/ID'l'l1 !i.':>l)l:lll $.J<7j-l>4B , OIiIlI2.Dl ":/C':l6 l1O;4S4 _m .~

":.1<1:15 Jl;41'l1ill 6??l'>,:;60 6X~"'l 1:l<7l-lll 0IiZi6,!lII] "mm J7'~1!i8t ~'0 lm1<411.2.Sl

""~!76'i'.L"Il =m ~m. 481;!]9S ~~ 115<1(lXl ~:>4,m H:a

""

, m"'lSll 71e'J I~S _m -,. ~l.l<l oa:.<lJ .. l5".til,1rn ~,rn j«59JD ''''n:tM~SJ ~1q:;<Jl/i ~= =rn =<= =n "?illl,1 , ~Wi ~"9,~

15«~-5ilIl 7!:!TIJI« 6C6~.SO':l o::""",:m ~,77J ~ 4l::Jl,2ll'l J76X:!l1 )O(109,Jl! ,m'SllI4.'TI 1l7l!J::'6 ~m ~:ll,IJ~ ~,"9 4Iolnm 1~.I611 JTl')l-991 }I(l]11lJS H77TtI&!.""5 1'tIl1U:S 676&4>04S ~rn :lO,~~.:m 0190\506 .== :JJ:l!IJ4U !J!nIJCI ll;J'1«29,166 "",m _m 1iJ:;sl)1!J "6«J,ll:6 0Iilil9121 <lH14lit ml~1:l1 JclJUIIJ ,.,n~= ~9~ 6761l11D1 OXllU lJ~jlll Ulllnl _,4[< !161~ :01 .u~ .m=rn :talJ.., f16019656 =rn "'"~, ~oo 4<8ln~l 11~1lI1 J<21~m ""-~ '""'~ mlU61 li:.:<9<m '~<acl _m <llJ11m 11611l(m )1:<6:<61 Hl1,Un4lll Jl;ilnl 6=16 ru:E:l:ia i!..'<G39S -=119 "m-:.61 :I77".6m l4:~ HJI-= SI~55 005;~"2 6111115'111 :lO%H,n ..~ "'J1.r.lO :JJJJ1:4l D7l1.J111 ,~

=m o;:l)1.106 OoIJ"'-:1lII 61161[12) ~j969 nlla~ "12Ii:rT1 ~~ !1?'l816ll ,mJ01~.l.1.' 6mlID 641Jll2!!:

_ml]8<j.9!ll\ <Q!<i:66 Oitl'lll! J6I,lJ:1Jl nll2~'"

,~

_.1'1 6UI''*' 6J641,:JJ!I 19IJl.106 TI:la1j11 <O'..l1719 =,. JU."'l1r.lJ nnl-9l1 ,~

~I 0..IIB3

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n"""v.... Tn-:v':"~-J

v.:..eitiot<F;p."",,"",.. _~

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Non-Newtonian Losses 1brough Diaphragm Valves DMKazadi

Date post:	31-Mar-2023
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NON-NEWTONIAN LOSSES THROUGH DIAPHRAGM VALVES

Documents