Peak Discharge at Culverts

8/22/2019 Peak Discharge at Culverts

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Techniques of Water-Resources Investigationsof the United States Geological Survey

Chapter A3

MEASUREMENT OF PEAK DISCHARGEAT CULVERTSBY INDIRECTMETHODS

By G. L. Bodhaine

Book 3APPLICATIONS OF HYDRAULICS

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DEPARTMENT OF THE INTERIORDONALD PAUL HODEL, SecretaryU.S. GEOLOGICAL SURVEYDallas L. Peck, Director

First printing 1968Second printing 1969Third printing 1976Fourth printing 1982Fifth printing 1988

UNITED STATES GOVERNMENT PRINTING OFFICE : 1982

For sale by theBooks and Open-File Reports SectionU.S. Geological SurveyFederal Center, Box 25425Denver, CO 80225


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PREFACEThe series of m anuals on techniques describes procedures for planningand executing specialized work in wate r-resources investigations. The materialis grouped under major subject headings called Books and further subdividedinto sections and chapters; Section A of Book 3 is on surface water.Provisional drafts of chapters are distributed to field offices of the U.S.Geological Survey for their use. These drafts are subject to revision becauseof experience in use or because of aclvanccment in knowledge, techniques, orequipment. After the technique tlescribrd in a chapter is sufficiently developed,

the chapter is published and is sold by the U.S. Geological Survey Books andOpen-File Reports Section, Federal Center, Box 25425, Denver, CO 80225 (au-thorized agent of Superintendent of Documents, Government Printing Office).


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TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS OF THEUNITED STATES GEOLOGICAL SURVEY

The U.S. G eological Survey publishes a series of manuals describing procedures for planning and conductispecializedwork in water-resources nvestigations.The manuals published to date are listed below and may be orderby mail from the U.S. Geological Survey, Books and Open-File Reports, Federal Center, Box 25425, Denver, Colorad80225 (an authorized agent of the Superintendent of Documents, Government Printing Office).Prepayment is required. Remittance should be sent by check or money order p ayable to U.S. Geological SurvPrices are not included in the listing below as they are subject to change. Current prices can be obtained by writinto the USGS, Books and Open File Reports. Prices include cost of domestic surface transportation. For transmittoutside the U.S.A. (except to Canadaand Mexico) a surchargeof 25 percent of the net bill should be included to covsurface transportation. W hen ordering any of these publications, please give the title, book number, chapter numband U.S. Geological Survey Techniques of Water-Resources Investigations.TWI 1-Dl. Water temperature-influential factors, field measurement, and data presentation, by H.H. Stevens,Jr., J.F. Ficke, and G.F. SmoTWI l-D2. pages.TWI 2-Dl. Application of surface geophysics o ground water investigations, by A.A.R. Zohdy, G.P. Eaton, and D.R. Mab ey. 1974.116 pagTWI 2-D2. Application of seismic-refraction techniques to hydrologic studies, by F.P. Haeni. 19 88. 86 p.TWI 2-El. Application of borehole geophysics o water- resources investigations, by W.S. Keys and L.M. MacCary. 1971. 126 pages.TWI 3.Al. General field a nd office procedures for indirect discharge measurement, by M.A. Benson and Tate Dalrymple. 1967.30 pa geTWI 3.A2. Measurement of pe ak discharge by the slope-area method, by Tate Dalrymple and M.A. Benson. 1967. 12 pages.TWI 3-A3. Measurement of peak discharge at culverts by indirect methods, by G.L. B odhaine. 196 8. 60 pages.TWI 3-A4 Measurement of peak discharge at width contractions by indirect methods, by H.F. Matthai. 1967. 44 pages.TWI 3-A5 Measurement of peak discharge at dams by indirect methods, by Harry Hulsing. 1967. 29 pages.TWI 3-A& General procedure for gaging streams, by R.W. Carter a nd Jacob Davidian. 1968. 13 pages.TWI 3-AT. Stage measurements at ga ging stations, by T.J. Buchanan a nd W.P. Somers. 1968. 28 pages.TWI 3-A% Discharge measurements at gaging stations, by T.J. Buchanan and W.P. Somers. 1969.65 pages.TWI 3.A9. Measurement of time of travel and dispersion in streams by dye tracing, by E.F. Hubbard, F.A. Kilpatrick, L.A. Martens, andJ.F. Wilson, Jr. 1982. 44 pages.TWI 3-AlO. Discharge ratings at gaging stations, by E.J. Kennedy. 1984.59 pages.TWI 3-All. Measurement of discharge by moving-boat method, by G.F. Smoot and C.C. Novak. 1969. 22 pages.TWI 3-A12. Fluorometric procedures for dye tracing, Revised, by James F. Wilson, Jr., Ernest D. Cobb, and Frederick A. Kilpatrick. 1986.TWI 3-A13. Computation of continuous records of streamflow, by Edward J. Kennedy. 1983.53 pages.TWI 3.A14. Use of flumes in measuring discharge, by F.A. Kilpatrick, and V.R. Schneider. 1983. 46 pages.TWI 3-A15. Computation of water-surface profiles in open channels, by Jacob Davidian. 1984.48 pa gesTWI 3-A16. Measurement of discharge using tracers, by EA. Kilpatrick and E.D. Cobb. 1985.52 pag es.TWI 3-A17. Acoustic velocity meter systems, by Antonius Laenen. 1985 . 38 pages.TWI 3-Bl. Aquifer-test design, observation, and data analysis, by R.W. Stallman. 1971. 26 pages.TWI 3-B2. Introduction to ground-water h ydraulics, a programmed text for self-instruction, by G.D. Be nnett. 1976. 172 pages.lWI3-B3. Type curves for selected problems of flow to wells in confined aquifers, by J.E. Reed. 1980. 106 pages.TWI 3-B5. Definition of boundary and initial co nditions in the analysis of saturated ground-water flow systems-an introduction, by 0. LeTWI 3-B6.TWI 3x1. Flwial sediment concepts, by H.P. Guy. 1970 . 55 pages.TWI 3-c2. Field methods of measurement of fluvial sediment, by H.P. Guy and V.W. N orman. 1 970. 59 pages.TWI 3-a. Computation of fluvial-sediment discharge, by George Porterfield. 1972. 66 pages.TWI 4-Al. Some statistical tools in hydrology, by H.C. Riggs. 1968.39 pages .TWI 442. Frequency curves, by H.C. Riggs, 196 8. 15 pages.TWI 4-Bl. Low-flow investigations, by H.C. Riggs. 1972. 18 pages.TWI 4-B2. Storage analyses or water supply, by H.C. Riggs and C.H. Hardison. 1973. 20 pages.TWI 4-B3. Regional analysesof streamflow characteristics, by H.C. Riggs 1973. 15 pages.TWI 4-Dl. Computation of rate and volume o f stream depletion by wells, by C.T. Jenkins. 1970. 17 pages.TWI 5-Al. Methods for determination o f inorganic substances n water and fluvial sediments, by M.W. Skougstad and others, editor. 1979.6

1975. 65 pages.Guidelines for collection a nd field analysis of ground-water samples for selected unstable constituents, by W.W. Wood. 1976.

Franke, Thomas E. Reilly, and Gordo n D. Benne tt. 1987 . 15 pages.The principle of superposition and its application in ground-water hydraulics, by Thomas E. Reilly, 0. Lehn Franke, and GordD. Bennett. 1987.28 pages.

pages.

Spanish ti anslation also available.


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TWI 5A2.Tw 543.

TWI 5-A4.TWI 54.5.TWI S-A6TWI 5Cl.Twf 6.Al.TWI 7-Cl.TWI 7x2. Computer model of twodimensional solute transport and dispersion in ground water, by L.F. Konikow and J.D. Bredehoeft. 19790 pages.TWI 7-C3. A model for simulation of flow in singular and interconnected channels, by R.W. Schaffranek, R.A. Baltzer, and D.E. Goldber1981.110 pages.TWI 8-Al. Methods of measuring water levels in deep wells, by MS. Garber and F.C. Koopman. 1968. 23 pages.TWI 8.A2. Installation and service manual for U.S. Geological Survey monometers, by J.D. Craig. 1983. 57 pages.TWI 8.B2. Calibration and maintenance of vertical-axis type current meters, by G.F. Smoot and C.E. Novak. 19 68. 15 pages.

Determination of minor elements in water by emission spectroscopy,by P.R. Bamett and EC. Mallory, Jr. 1971. 31 pages.Methods for the determination of organic substances n water and fluvial sediments, edited by R.L. Wershaw, M.J. Fiihman, R.RGrabbe, and LE. Lowe. 1987. 80 pages.This manual is a revision of Methods for Analysis of Organic Substances n Waterby Donald F. Goerlitr and Eugene Brown, Book 5, Chapter A3, published in 1972.Methods for collection and analysis of aquatic biological and microbiological samples, edited by P.E. Greeson, T.A. Ehlke, G.AIrwin, B.W. Lium, and K.V. Slack. 1977. 332 pages.Methods for determination of radioactive substances n water and fluvial sediments, by L.L. Thatcher, V.J. Janzer, and K.WEdwards. 1977.95 pages.Quality assurance practices for the chemical and biological analyses of water and fluvial sediments, by L.C. Friedman and D.EErdmann. 1982.181 pages.Laboratory theory and methods for sediment analysis, by H.P. Guy. 1969. 58 pages.A modular three-dimensional finite-difference ground-water flow model, by Michael G. McDonald and Arlen W. Harbaugh. 198586 pages.Finite difference model for aquifer simulation in two dimensions with results of numerical experiments, by P.C. Trescott, G.FPinder, and S.P. Larson. 1976.116 pages.


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CONTENTSPreface__..._-.__.___~--__..___.__________._-Symbols and units-- __ _ ___ ____ _ ____ __ ____ __ _Abstract- __ ___ __ ___ __ __ _ ___ ____ ____ _ _ ___ __Introduction _ _ _ ___ __ __ __ __ __ __ ___ __ ___ ____ _Description of culvert flow-- __ __ _ __ __ ____ ___ _Genera l classification of flow- _ _ ___ ____ __ _Discharge equations--- ___ __ __ ___ __ _____ __ __Critical depth---_------___-_-----------Type lflow~___~___~~_~_~.__~~~~-~~~~Type Z~OW..________-___-__----_-..__-Flow with backwater-- _________________ _Type 3flow~____..___~~~_.~~_~~~~~~~_~Type4flow-_._--___-______----~----~Flow under high head- _ __ __ __ __ __ __ ___ __

Type ~Aow-________-_-_-.__-_____-__Type 6 flow- _ ___ __ __ __ __ __ __ __ ___ ___ _Field data- _ _ _ _ _ _ _ __ _ _ __ _ _ _ _ __ _ _ _ _ __ ___ ___ _High-water profiles _____ __ __ __ ___ __ __ __ _Headwater-- _ __ __ ___ ___ __ __ ___ _ ____ _Tailwater- _ _ __ __ __ __ __ ___ __ __ ____ ___ _Approach section--- __ ________ _ ____ _____Culvert geometry _____ _______________ ___Normal culverts- _ _ __ __ _ ____ ___ _ ____ _Skewed culverts- _ _ __ _ _____ __ ___ - __ __Mitered culverts-- _. _ _ __ __ ____ _ ___ __ _Photographs- _ _ _ __ _ ___ __ __ __ ___ __ __ __ __Special conditions --- _ __ __ __ __ __ ___ ___ __ _Debris_______--_-___---------~-------Breakinslope__~___~~~~~.~~__~~__~~~~Natural bottom- _ _ _ _ __ __ __ __ ___ ____ __Roughness coefficients- _ __ ___ __ _ ____ ____ __ ___Approach section- _ _ __ _ __ ____ ___ __ __ ___ _Culvert____-________------~------------Corrugated metal-- __ _ __ ___ __ __ ___ __ __Standard riveted section-- _- __ ___ __ __Multiplate section- _ __ __ __ __ __ __ ___ _Paved inverts- _ _ _. __ __ __ _ ____ __ __ __Concrete-- ___ __ _ __ __ __ __ __ ___ ___ __ __ _Other materials --- _ __ _ __ ___ __ ___ _ ___ __Natural bottom- _ _ _ __ __ _ ____ __ __ ___ __Computation of discharge _____ ___ _ __ ___ __ __ _Flow at critical depth- _ _ _ __ __ __ ___ ___ _ __Type 1 flow-- __ ___ _ __ ___ _ ___ ___ __ __ __Circular sections- __ _ ___ ___ __ __ ___ __Pipe-arch sections ________ __ __ __ __ __ _Rectangular sections- _ ___ _ _ __ __ ____ _Irregular sections- ___ __ __ ___ ___ ___ __Type 2 flow-s _ ___ __ ___ __ __ __ ____ __ ___Circular sections--- __ __ ____ _ __ _ __ _Pipe-arch sections _____ _ __ ___ _ __ __ __ _Rectangular sections- ___ __ ___ __ __ ___Irregular sections- _ _ __ ___ ___ ___ __ _ __

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VIII 1112334555566666777778899999101010101010101111,11112020212324252526292930

Computation of discharge-ContinuedFlow with backwater ____________________Type 3flow-_.____-________________-_Type 4flow______-_______.-----------Flow under high head- _ __ ___ _ ____ __ __ __ _Concrete culverts- __ __ ___ ___ __ __ __ ___ _Corrugated-pipe culverts ______ ___ __ _ ___Type 5flow__--__--___-__~__---------Type 6 flow-- _____________________ ___Routing method ________________________Unusual conditions ______ __ ___ __ __ _ __ __ __Multiple culverts- __ __ __ __ ___ __ ___ _ ____ _Coefficients of discharge- __ _____ __ ___ _ __ __ __ _Types 1, 2, and 3 flow--- _ ________ __ __ ___Flush setting in vertical headwa ll- _ _ __ __Pipe culverts- _ _ ___ __ __ ___ ___ __ __ __ _Box culverts- _ _ __ ___ __ ____ ___ __ _ __ _Wingwall entrance- _ __ ___ __ ___ ___ _ __ -Pipe culverts se t flush with verticalheadwall-----_--------------..----Box culverts- _ __ _______ __ __ __ - - _ -Projecting entrance- _________ __ __ _ __ __Corrugated-metal pipes and pipe-arches---------------------------Concrete pipes with beveled end- _ _ __ _Mitered pipe set flush with sloping em-bankment _______ __ __ __ __ _ _ ___ __ _ _Types4and6flow __________._____-___--Flush setting in vertical headwa ll- - __ _ -Box or pipe culverts ______ __ __ ___ __ _Wingwall entrance- __ ___ __ _ __ __ _ - _ __Pipe culverts se t flush with verticalheadwalL- _ __ __ _ ___ __ __ __ _ __ ___Box culverts- _ _ __ __ __ ___ __ __ _ - - - - -Projecting entrance.. ____ ___ _ ___ _ __ __ _Corrugated-metal pipes and pipe-

arches--__---_-------------------Concrete pipes with beveled end-- _ __Mitered pipe set flush with sloping em-bankment ______ _ ___ __ ___ __ __ _ - _ _Type Sflow_____~___-------------------Flush setting in vertical headwa ll- _ _ _ _Box or pipe culverts ________ _ __ __ __ _Wingwall entrance-- __ _ ____ __ ____ - - ---

Pipe culverts set flush with verticalheadwall _____ ___ __ _ _____ ___ _-- -- -Box culverts- _ _ _ __ _ __ __ __ _ _ __ - -- -Projecting entrance- __ _ ___ _ _ _ _ - -- - --Corrugated-metal pipes and pipe-arches_-----..--.-----------------Concrete pipe with beveled end --- - - - -

PIWe30303030313131313136363738383841

$4141414141424242424243434343434343434343444444444444

VII


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VIIICoefficients of discharge-ContinuedType 5 flow-ContinuedMitered pipe set flush with sloping em-bankment _____ ______._ -__--._.___.Unusual culvert entrances.. _ _ _ _ _. __ __.General remarks-- __ _ __- __ _ ____. _. _ __. _ _ __.Storage-------..-------....-..-----..---.-Stage-discharge relationships for culverts-.Ratings with transition between flowtypes-------.--...-----------------Typc4flow ___..__________ -___-___-__Typo ~Aow-_-...~~~-~-.--~-~~.--..--.Slope-area measurement within a culvert- _Verification of culvert flow. _ _ ____. _ _ _ _Wheretomeasure _________ ____________Pipes flowing full- ___ __ _ __ _ _. _ _. __ __ __ _Accuracy of culvert computations--- _. __ _ _Examples1. Type 1 flow through a corrugated-metalpipeculvert_______----------..----..-

CONTENTS( Examples-ContinuedPage 2.

44 3.4445 4.45, 54647 6.4848 7.4951 3.5151 9.51 10.

Type 1 flow through a concrete boxculvert- _ ___ _ __ __ _ __ __ __ _ __ _ __ _ _ __ _Type 2 flow through a corrugated-metalpipe culvert--- ________ ______ __ ____ _Type 2 flow through a concrete boxculvert- - - - - - - - - - - - - - - - - - - -- _ - - __ _Type 3 flow through a corrugated-metalpipe culvert--- ______ __ ____________ _Type 4 flow through a concrete pipeculvert- _ _ ___ _ __ __ _ __ _ __ _ _ __ __ __ __ _Type 5 flow through a corrugated-metalpipe culvert _______ _____ _ ____ ___ _ __ _Type 6 flow through a concrete pipeculvert- _ __ _ __ _ __ _ _ __ __ _ __ __ __ __ _ _ _Computation of flow by the routingmethod---___--____________________Computation of type 3 flow through anirregularly shaped culvert- _ _ _ _ _ _ _ __ __. -52 1 Selected references _____________ _____________

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5455565757585960

FIGURES1. Definition sketch of culvert flow ______________ ______________ ____________2. Classification of culvert flow-.. _____________ ______________ _____________-3. Relation between specific energy and depth _____________ ______________ ___4. Approach and culvert lengths for mitered pipe- _ _ __ _ _ ______ _ __ _ __ __ _- ---5. Depth-area curves for riveted pipe-arches,- _ _ ___________________________6. Depth-area curves for multiplate pipe-arches _______________ _____________ -7. Hydraulic properties o f the paved-invert pipe-arch-- _ _________-_-_--___--8. Dimensions of flared end sections for reinforced concrete pipe- _ __ - __ _ _ _ -9. Critical slope as a function of head for pipe and pipe-arch culverts, with freeoutfall-------------------____-___--___----------------------------

10. Relation between head and critical depth in pipe and pipe-arch culverts-----11. Critical slope for culverts of rectangular section, with free outfall--- __ _ - - -12. Relation between head and depth of water at inlet with critical depth at outletfor culverts of circular section ________ __ __ ___ _ ___ __ __ _ __ ______ __ _-- --13. Relation between head and depth o f water at inlet with critical depth at outletfor pipe-arch culverts- __ _ __ __ __ ___ ___ __ ___ _ ___ _ ____ __ ___ __ __ _- _ - --14. Relation between head and depth of water at inlet with critical depth at outletfor culverts of rectangular section- _ _ _ __ __ __ __ __ __ _ ___ __ __ _ ___ - - - - - - -19. Criterion for classifying types 5 and 6 flow in box or pipe culverts with con-crete barrels and square, rounded, or beveled entrances, either with or with-outwingwals-____--____--___--_-----------------------------------16. Criterion for classifying types 5 and 6 flow in pipe culverts with rough barrels---17. Relation between head and discharge for type 6 flow _______ ____ ___- -- - --- -18. Relation between outlet pressure lines and discharge for type 6 flow throughculverts of circular section ___________ _________--------------- --------

19. Adjustment to discharge coefficient for degree of channel contraction- - - - - - -29. Base coefficient of discharge for types 1, 2, and 3 flow in pipe culverts withsquare entrance mounted flush with vertical headwall-----..-------------21. Variation of the discharge coefficient wirh entrance rounding, types 1, 2, and 3flow in box or pipe culverts set flush with vertical headwall.-------------22. Variation of the discharge coefficient with entrance b eveling, types 1, 2, and 3flow in box or pipe culverts set flush with vertical headwall--------------23. Base coefficient of discharge for types 1, 2, and 3 flow in box culverts withsquare entrance mounted flush in vertical headwall- _ _ _ _ _ _ _ _ _ _ _ _ - - - - - - - -

Page124820212223

242526272829

323334353839394041


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CONTENTS IXPage

24. Variation of discharge coefficient with wingwall angle, types 1, 2, and 3 flowin box culverts with wingwall set flush with sloping emban kment--L _ __ _ __25. Variation of discharge coefficient with headwater-diameter ratio, types 1, 2,and 3 flow in mitered pipe set flush with sloping embankment---.. _ __ _ ___ _26. Variation of headwater with surface area of pond for determining reductionin discharge for various sizes of culverts _________________ ______________27-30. Rating curve showing transition from-27. Type 1 to type 5 flow in a box culvert ______ ____ __ __ ____ __ _____ __28. Type 2 to type 6 flow in a box culvert,- ___ __ __ ___ _ ____ _ ___ _ ___ :29. Type 1 to type 5 flow in a pipe culvert- _ ______ ____ ___ _ __ _____ ___30. Type 2 to type 6 flow in a pipe culvert- _ _ __ _________ ______ _____ _31. Rating curve for type 4 flow in a pipe culvert ________________________ ____32. Rating curve for type 3 flow in a pipe culvert--.. _ ___ _ ___ __ __ __ ____ _ ___ __ _

TABLES

4243454i4849505050

1. Characteristics of flow types __________________ _________________ _____-------2. Properties of circular pipes, riveted pipe-arches, and multiplate pipe-arches- - - - --3. Coefficients for pipe of circular section flowing partly full--- _ __ __ __ __ - - - - - - - - -4. Coefficients for pipe-arches flowing partly full _________________ _- __ _---_ ------5. Discharge coefficients for box or pipe culverts set flush in a vertical headwall;types 4 and Gflow-_______-_-_--______________________--~---------------6. Discharge coefficients for box or pipe culverts set flush in a vertical headwall withvariation of head and entrance rounding or beveling; type 5 flow- _ _ _ __ - - - - -7. Discharge coefficients for box culverts with wingwalls with variation of head andwingwall angle, 8; type 5 flow _________________ _________________ ----------

PW3121415424444


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SYMBOLS AND UNITS

D

D,d

4

4nF9Hohhch.bh.KK,Kok

DefinitionArea.Area of culvert barrel.Area of secsion of flow at criticaldepth.Width of contracted flow sectionfor box culvert.Coefficient of discharge; also,coefficient for computing variousculvert properties; subscriptsrefer to specific items, as a forarea, k for conveyance, m formean depth, p for wetted perim-eter, q for discharge, r for hy-draulic radius, and t for topwidth.Maximum inside vertical dimen-sion of culvert barrel, or theinside diameter of a circularsection. (For corrugated pipes,D is measured ds the minimuminside diameter.)Maximum inside diameter of pipeculvert at entrance.Depth of Aow measured from thelowest point in the cross sectionfor culverts.Maximum depth in critical-flowsection.Mean depth.Froude number.Gravitational constant (accel-efation).specific energy.Static or piezometric head abovean arbitrary datum.;1,+z for type 1 culvert flow.Head loss due to entrance con-traction.Head loss due to friction.Velocity head at a section.Conveyance of a section.Conveyance of critical depthsection.Conveyance of full culvert barrel.

Adjustment factor; subscriptsrefer to specific items, a8 afor skewed abutments withdikes, 15 or length, r and R forradius, w for length of wing-walls, and B for wingwall angle.

UnilIt?It*It*ft

rt

%t

tt/se@tttttttr/sects/sect3/sec

L

L,

L

mnn,PPPQRRo

DefinifionLength of culvert barrel, bridgeabutment, or broad-crested w eirin direction of flow.Distance a culvert barrel projectsbeyond a headwall or embank-ment.Distance from approach sectionto entrance of culvert, up-stream side of contraction,or crest of weir.Channel-contraction ratio.Manning roughness of coefficient,.Composite value of roughnesscoefficient.Wetted perimeter of cross sectionof flow.Wetted perimeter of the pavedinvert of a culvert.Total discharge.Hydraulic radius.Hydraulic radius of a culvertbarrel.Radius of entrance rounding.Friction slope.Bed slope of culvert for which thenormal depth and the criticaldepth are equal.Bed slope of culvert barrel.

Width of a section at the watersurface.Mean velocity of flow in a section.Full culvert velocity.Measure of the length of a wing-wall or chamfer.Length of partfull flow.Elevation of a point above adatum.Subscripts which denote the loca-tion of cross sections or sectionproperties in downstream order.Velocity-head coefficient.Acute anpie between a wingwalland plane of contraction orheadwall; and the bevel angle.Less than.Equal to or less than.Greater than.Equal to or greater than.

CJnirrt

ft

ft

ftftft*/secftfttt

tftlsecft/secrtItrt


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MEASUREMENT OF PEAK DISCHARGE AT CULVERTS BY INDIRECT METHODSBy G. L. Bodhaine

AbstractThis chap ter class ifies culvert flow into six types,gives discharge equations based on continuity andenergy equations, and describes procedures for meas-uring peak discharges using culverts in the field. Dis-charge coefficients for a varieby of geometries and flowtypes arc given. Ten examples detail step-by-stepcomputation procedures.

IntroductionThe peak discharge through culverts can bedetermined from high-water marks that definethe headwater and tailwater elevations. Thisindirect method is used extensively to measureflood discharges from small drainage areas.The head-discharge characteristics of cul-verts have been studied in laboratory inves-tigations by the U.S. Geological Survey, theBureau of Public Roads, and many universities.

The procedu res given in this report are based

on the information obtained in these studiesand in field studies of the flow through culvertsat sites where the discharge was known.Description of Culvert Flow

The placement of a roadway fill and culvertin a stream channel causes an abrupt changein the character of flow. This channel transitionresults in rapidly varied flow in which accelera-tion rather than boundary friction plays theprimary role. The flow in the approach channelto the culvert is usually tranquil and fairlyuniform. Within the culvert, however, the flowmay be tranquil, critical, or rapid if the culvertis partly filled, o r the culvert may flow fullunder pressure.The physical features associated with cul-vert flow are illustrated in figure 1. They arethe approach channe l cross section at a distanceequivalent to one opening width upstream from

Irade line-

-\ Entrance loss\ \

0I I--- ---_dz !Xa$r SUrface

I---_ VJ2---_

l:fm,,n,,m,---_ 29---_

1z Bottom culvert d;-p-Da&h-\- J12) ,(3) (4)

.-I .-.Approach Culvert Culv&rt Tailwatersection entrance outlet sectionFigure 1 .-Definition sketch of culvert flow. Note.- The loss of energy near the entrance is related to the sudden

contraction and subsequent expansion of the live stream within the culvert barrel. 1


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2 TECHNIQUES OF WATER-RESOURCES IINVESTIGATrONSthe entrance ; the culvert entrance; the culvertbarrel; the culvert outlet, the farthest down-stream section of the barrel; and the tailwaterrepresenting the getaway.channel.The change in the water-surface profile in theapproach channel reflects the effect of accelera-tion due to contraction of the cross-sectiona larea. Loss of energy ne ar the entrance is relatedto the sudden contraction and subsequentexpansion of the live stream within the barrel,and entrance geometry has an important influ-ence on this loss. Loss of energy due to barrelfriction is usually minor, except in long roughbarrels on flat slopes . The important featuresthat control the stage-discharge relationship atthe approach section can be the occurrence ofcritical depth in the culvert, the elevation ofthe tailwater, the entrance or barrel geometry,or a combination of these.The peak discharge through a culvert isdetermined by application of the continuityequation a,nd the energy equation between theapproach section and a section within the cul-vert barrel. The location of the downstreamsection depends on the state of flow in the cul-

TYPE I EXAMPLE1 Q=CA, 1/2g(hl-r+.$ - c+-hfl.2,

:RITICAL DEPTH * Lw-q 29

2 Q=CA 2g(h,+o&-d,-h - h ):RITICAL DEPTH k-Lw-+ c 2, f12 f23

3I

-- --Q=CA3 ~g(hl+.,c2hf23

rRANQUlL FLOW tclw-+j

vert barrel. For example, if critical flow occursat the culvert entrance, ttheheadwater elevationis not a function of either the barrel frictionloss or the tailwater elevation, a nd the terminalsection is located at the upstream end of theculvert.Information obtained in the field surveyincludes the peak elevation of the water surfaceupstream and downstream from the culvert andthe geometry of the culvert and approachchannel. Reliable high-water marks can rarelybe found in the culvert barrel; therefore, thetype of flow that occurred during the peak flowcannot always be determined directly from fielddata, and classification becomesa trial-and-errorprocedure.

General c lassification of flowFor convenience in computation, culvert flowhas been classified into six types on the basisof the location of the control section and therelative heights of the headwater and tailwaterelevations. The six types of flow are illustratedin figure 2, and pertinent characteristics of eachtype are given in table 1. From this information

TYPE 1 EXAMPLE4

SUBMERGEDOUTLETh!! 7 1.0Dh,/O al.0

--____

Figure I.


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MEASUREMENT OF PEAK DIWHARGE AT CULVERTS BY INDIRElCT METHODS 3the following general classification of typesflow can be made:1. If h,/D is equal to or less than 1.0 and(h,--z)/D is less than 1.5, only types 1, 2,and 3 flow are possible.2. If h,/D is greater than 1.0, only type 4 flow

is possible.3. If h,/D is equal to or less than 1.0 and(h,--z)/D is equal to or greater than 1.5,only types 5 and 6 flow are possible.Further identification of the type of flowrequires a trial-and-error procedure which isdescribed in a subsequent section of thischapter.

Discharge EquationsDischarge equations have been developed for

each type of flow by application of the con-tinuity and energy equations between theapproach section and the terminal section. Thedischarge may be computed directly from theseequations after the type of flow has been iden-tified. Discharge equations for critical depth ata section are used to identify flow types 1 and 2;thus, these equations are also included in thefollowing sections.

Critical depthFlow at critical depth may occur at either

the upstream or the downstream end of aculvert, depending on the headwater elevation,the slope of the culvert, and the tailwaterelevation. To obtain flow at critical depth, theheadwater elevation above the upstream invertmust be less than 1.5 times the diameter orheight of the culvert. Type 1 flow will occur if

r

the tailwater elevation is lower than the water-surface elevation at critical depth, and if thebed slope of the culvert is greater than thecritical slope. Type 2 flow will occur if the bedslope is less than the critical slope.Critical depth, d,, is the depth at the point of

minimum specific energy for a given dischargeand cross section. The relation between specificenergy and depth is illustrated in figure 3.The specific energy, Ho, is the height of theenergy grade line above the lowest point in thecross section. Thus,H,=d+$j

whereH,=specific energy,d=maximum depth in the section,V=mean velocity in the section, and9= acceleration of gravity.

It can be shown that at the point of minimumspecific energy and critical depth, d,,Q A3-=-,g T

and

where$=&,+

Q=discharge,A=area of cross section below the watersurface,T=width of the section at the water sur-face,d,= maximum depth of water in the critical-flow section, andd,= mean depth in section = A/I.

Table 1 .-Characteristi cs of flow types[D=maximum vertical height of barrel and diameter of circular culverts]

Flowtype Barrel flow Location ofterminal section Kind of control Culvert slope

Partly full _____ Inlet ________ ______ do ________ Critical depth--- _ __ __ _ _Outlet- __ ____ _____ do __________ _______ Steep- _ __ __Mild ____________ do ________ _____ do--- __ __ Backwater _____ _ __ _ __ _ __ __ --do--- _ _Full- _ __ _ _ __ _ _ __ __ do-- _ __ _ _ ___ _ d o-- _ ___ _ __ _ _ __ _ __ _ Any- _ _ _ _ __Partly full---+- Inlet--- __ _ __ _Full __________ Outlet- _ _ ____ Entrance geomdtry- _ __ __ ____ do -- _ _ _1Entrance and barrelgeometry. _____ do _____ II

2::;>l.O__---___--____-_--91.051.091.01;:;21.0


13/69

TECHNIQUES OF WATER-RESOURC ES XNVESTIGATIONS

Q =a constant=a constant

-d-d-Critical depthritical depth

4 6 ^ 8SPECIFIC ENERGY (Hu=d + c), IN FEETPECIFIC ENERGY (Hu=d + ti), IN FEET299Figure 3.-Relation between specific energy and depth.igure 3.-Relation between specific energy and depth.

For the condition of minimum specific energyand critical depth, the discharge equation for asection of any shape can be writtend,=maximum depth of water in the criti-cal-flow section, andD=inside diameter of circular section.

0) The two types of flow in this classification are1 and 2.Or

&=&hi& (2)The discharge equation can be simplifiedaccording to the shape of the sections. Thus,for rectangular sections,

Q=5.67bd,32, (3)and for circular sections,

Q= C$F2, (4)whereb=width of section,C,=function of de/D,

Type 1 flowIn type 1 flow, as illustrated on figure 2, thewater passes through critical depth near theculvert entrance. The headwater-diameter ratio,(hl--z)/D, is limited to a maximum of 1.5 andthe culvert barrel flows partly full. The slopeof the culvert barrel, SO, must be greater thanthe critical slope, S,, and the tailwater elevation,hp, must be less than the elevation of the watersurface at the control section, h*.The discharge equation is


14/69

MEASUREME NT OF PEAK DISCHARGE AT CULVERTS BY INDIRECr MErTHODS 5the culvert barrel flows partly full. The tail-water elevation does not submerge the culvertoutlet, but it does exceed he elevation of criticaldepth at the terminal section.The lower limit of tailwater must be such that(1) if the culvert slope is steep enough thatunder free-fall conditions critical depth at theinlet would result from a given elevation ofheadwate r, the tailwater must be at an elevationhigher than the elevation of critical depth at theinlet; and (2) if the culvert slope is mild enoughthat under free-fall conditions critical depth atthe outlet would result from a given elevation ofheadwater, then the tailwater must be at anelevation higher than the elevation of criticaldepth at the outlet.The discharge equation for this type of flow is

whereC= the discharge coefficient,A,= the flow area at the control section,V,=the mean velocity in the approachsection,(Y,= the velocity-head coefficient at theapproach section, andh ,,,=the head loss due to friction betweenthe approach section and the inlet=L(Q*/KIK~), andK=conveyance= (1 .486/n)R2A. (3)

Other notation is evident from figure 1 or ithas been previously explained. The dischargecoefficient, C, is discussed n detail in the sectionentitled Coefficients of Discharge.Type 2 flow

Type 2 flow, as shown on figure 2, passesthrough critical depth at the culvert outlet.The headwater-diameter ratio does not exceed1.5, and the barrel flows partly full. The slopeof the culvert is less than critical, and the tail-water elevation does not exceed the elevation ofthe water surface at the control section, h,.The discharge equation isQ=CA J( 2g h,+~~-d,-h,~-,-hl,,)r (7)where

h,,-,=the head loss due to friction in theculvert barrel= L(Q2/K2KJ.Flow with backwater

When backwate r is the controlling factor inculvert flow, c ritical depth cannot occur and theupstream water-surface elevation for a givendischarge is a function of the surface elevationof the tailwater. If the culvert flows partly full,the headwater-diameter ratio is less than 1.5; orif it flows full, both ends of the culvert arecompletely submerged and the headwater-diameter ratio may be any value greater than1.0. The two types of flow in this classificationare 3 and 4.

Type 3 flowType 3 flow is tranquil throughout the lengthof the culvert, as indicated on figure 2. Theheadwater-diameter ratio is less than 1.5, and

Type 4 flowIn this classification the culvert is submergedby both headwater and tailwater, as is shownm figure 2. The headwater-diameter ratio canbe anything greater than 1.0. No differentiationis made between low-head and high-head flowon this basis for type 4 flow. The culvert flowsfull and the discharge may be computed directlyfrom the energy equation between sections 1and 4. Thus,

[hl+h,,=h,+h,,+h,,_,+h,+h,,,+h,~_,+(h,,--h,,)l,where (

h,=head loss due to entrance contraction.In the derivation of the discharge formulashown below, the velocity head at section 1and the friction loss between sections 1 and 2and between sections 3 and 4 have been ne-glected. Between sections 3 and 4 the energyloss due to sudden expansion is assumed to be(ho,--hh,,). Thus,or

Q= CA, 2&---h,)29C2nTL (9)lf-------ROdI


15/69

6 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONSFlow under high head

High-head flow will occur if the tailwater isbelow the crown at the outlet and the head-water-diameter ratio is equal to or greater than1.5. This is an approximate criterion. The twotypes of flow under this category are 5 and 6.As shown in figure 2, part-full flow under ahigh head is classified as type 5. The flow pat-tern is similar to that downstream from a sluicegate with rapid flow near the entrance. Theoccurrence of type 5 flow requires a relativelysquare entrance that will cause contraction ofthe area of live flow to less than the area of theculvert barrel. In addition, the combination ofbarrel length, roughness, and bed slope mustbe such that the contracted jet will not expandto the full area of the barrel. If the water sur-face of the expanding flow comes in contactwith the top of the culvert, type 6 flow willoccur, because the passage of air to the culvertwill be sealed off causing the culvert to flow fullthroughout its length. Under these conditions,the headwater surface drops, indicating a moreefficient use of the culvert barrel.Within a certain range either type 5 or type6 flow may occur, depending upon factors thatare very diEcult to evaluate. For example, thewave pattern superimposed on the water-surfaceproflle through the culvert can be importantin determining full or part-full flow. Within therange of geometries tested, however, the flow typegenerally can be predicted from a knowledge ofentrance geometry and length, culvert slope,and roughness of the culvert barrel.

Type 5 flowType 5 flow is rapid at the inlet. The head-water-diameter ratio exceeds 1.5 as shown onfigure 2, and the tailwater elevation is belowthe crown at the outlet. The top edge of theculvert entrance contracts the flow in a mannersimilar to a sluice gate. The culvert barrel

flows partly full and at a depth less thancritical. The discharge equation isQ=CAc&(&i-). (10)

Type 6 flowIn type 6 flow the culvert is full underpressure with free outfall as shown in figure 2.

The headwater-diameter ratio exceeds 1.5 andthe tailwater does not submerge the culvert,outlet. The discharge equation between sections1 and 3, neglecting V12/2g and hllm2, is

Q=CA,~2g(h,--h,--h,,,). (11)A straightforward application of equat,ion 11is hampered by the necessity of determining h3,which varies from a point below the center of theoutlet to its top, even though the water surface isat the top of the culvert. This variation inpiezometric head is a function of the Froudenumber. This difficulty has been circumvented

by basing the data analysis upon dimensionlessratios of physical dimensions related to theFroude number. These functional relationshipshave been defined by laboratory experiment,and t.heir use is explained on page 31.

Field DataMake a transit survey of floodmarks andaccurately measure the culvert geometry assoon after the flood as possible. Use themethods of surveying previously described ;read elevations of highwater marks, hubs,reference marks, and culvert features to hun-dredths of a foot and ground elevations totenths. Obtain high-water profiles as well as acomplete description of the culvert geometry.Describe entrance and getaway conditionsif not evident from other data. Choose rough-ness coefficients (values of n) for the culvert aswell as for the approach section, and obtainstereophotographs documenting pertinent

features. Describe any unusual conditions atthe site. Appraise the possibility of entrance OIbarrel obstruction at the time of t,he peak;document evidence obtained from observers.Determine the elevat,ion of the low point oft,he crown of the road over the culvert, or makenote that there is a high fill. If there is apossibility that water flowed ncross the road-way, define a profile along the crown or highpoint of the road.High-water profiles

Obtain high-water profiles which adequatelydefine the headwater and tailwater elevations


16/69

MEASUREM ENT OF PEAK DISCI3ARGE AT ,CULVERTS BY INDIRECT METHODS 7in much the same manner as those for a slope-area or contracted-opening survey described inBenson and Dahymple (1967). If high-watermarks are available within a culvert, locate andlevel to them for use in checking computedelevations.

HeadwaterObtain the location and elevation of flood-marks along the embankment and upstreamfrom the culvert. For a definite approachchannel, obtain marks along the banks from theculvert entrance upstream for a distance of atleast two culvert diameters. Where pondedconditions exist, determine the headwater ele-vation from marks along the banks or upstreamfrom the opening where there is little or no

velocity. In doubtful cases of ponding, con-ditions approximating ponding can be assumedif high-water marks along the embankmentsapproach a level surface away from the culvertopening.Tailwater

Obtain tailwater elevations along the em-bankment or the channel close to the outlet,but not to represent the elevation of the issuingjet, which may be higher than the tailwaterpool. If marks cannot be found in the immediatevicinity of the culvert, extend the profile up-stream to the outlet on the basis of the existingprofiles.

Approach sectionAn approach section usually is necessary,but if the area of the approach channel is esti-mated as equal to or greater than five timesthe area of the culvert barrel, zero approachvelocity in the approach section may be as-sumed, and an approach section is not required.To avoid the possibility of the approach sectionbeing within the drawdown region, locate it oneculvert width upstream from the culvert en-

trance; or where wingwalls exist, a distanceupstream from the end of the wingwalls equalto the width between wingwalls at their up-stream end. If the wingwalls do not cause asignificant contraction, the approach sectionmay be closer than this, but not closer thanone culvert width. Take the cross section at

right angles to the channel. If high-water markscannot be found at the location specified for theapproach section, take the approach sectionwhere high-water marks can be found. Drivestakes at the ends of the cross section.One culvert width at a multiple culvert in-stallation may be considered as the sum of thewidths of the individual culverts.Select values of n and points of subdivision,if any, and record them clearly in the field notes.

Culvert geometryObtain complete details of culvert dimensions(measured by steel tape) including projections,wingwall angles, size of fillets and chamfers,degree of entrance rounding, size and shape ofopening, type of entrance, and length. Describethe material of which the culvert is made (con-crete, corrugated metal, iron, or other) as wellas its condition (new, fair, poor, or other).Record the value of n for the culvert. (See sec-tion below on roughness coefficients.)If dimensions of corrugated pipes, rivetedpipe-arches, and multiplate pipe-arches differsignificantly from design dimensions, the tabu-

lated property coefficients listed in the tablesmay not be directly applicable. For this reasoncheck in the field the pertinent dimensions ofevery culvert used.

In referring to culvert dimensions the usualpractice of highway engineers of specifying thehorizontal or width dimension first generallyshould be followed. For example, a 12- X lo-foot culvert has a barrel 12 feet wide and 10feet high.

Normal culvertsWhere the culvert opening is normal to the

axis of the culvert, measure the elevation ofthe invert at the opening or headwall. Forcorrugated pipes, measure the invert elevationat the top of the first full corrugation andfor concrete pipes, at the point of minimumdiameter (not down in the bell). For rectangu-lar shapes, obtain invert elevations usuallyat the center and edges, except in very widesections where they should be obtained every2 or 3 feet across the width. Elevations maybe needed at closer intervals for irregularsections. The elevation of the downstream


17/69

8 TECHNIQUES OF WATER-RESOURCES IXVVESTIGATIONSinvert is determined similarly. Always obtainthe elevation of the crown at both ends ofthe culvert. Also determine the elevations ofthe ends of the culvert aprons.Locate the positions of the culvert, wing-walls, aprons, and other features. Measure thelength of the culvert and length of apronswith a tape. Skewed culverts

A skewed culvert is one in which the head-wall is not normal to the centerline of theculvert or, in the event of no headwall, theend is not cut off squarely. Pipes and pipe-arches as well as box culverts are sometimesskewed. Where this occurs, measure the wing-wall angle as for a normal culvert, as the acuteangle at which the wingwall and headwall join.Measure the invert elevation for a skewedculvert on a line normal to the axis of theculvert and at the point where the full sectionof the culvert begins (minimum section).Measure the approach length, L,, to theinvert line described above. Measure thelength of the culvert, L, between invert lines,the shortest length of the culvert.

Mitered culvertsMany pipes and pipe-arches are mitered tobe flush with the highway embankment.Determine the invert elevations at the extremeends of the pipe. Often, the first section of amitered pipe is laid on a different slope fromthe rest of the culvert; therefore, obtain alsothe elevation of the invert at full pipe. Deter-mine the elevation of the crown at both endsof the full pipe section. Measure the totallength of the culvert to determine the slope(z is measured at ends of the invert). Alsodetermine the short length (the full sectionof the culvert) and the length of miter.For headwater-diameter ratios less than 1.0

measure the approach length from section 1 tothe point where the headwater elevation inter-sects the miter, figure 4. For ratios greater than1.0, L, is the distance from section 1 to thebeginning of the full section of the culvert. Foroutlet control, measure the length, L, to thepoint where d, or h, intersects the downstreammiter, or for a culvert flowing full, to the endof the full section.

1; lif Lw D )g 1.0orlh - z _______)(-

2 -5

3-4 L w- for (h1-2 ) < 1.0I= cl2 2-

d 1 I I I I I I I I I 11 2 3 4 5 6 7 8 9 10DISTANCE ALONG CHANNEL, IN FEET

Section 1 at station 0FLOW TYPES 2,3,4,5,AND 6

Figure 4.-Approach and culvert lengths for mitered pipe.


18/69

MEASUREME NT OF PEAK DISCZARGE AT CULVERTS BY INDIRECT METHODS 9For type 1 flow, d, is assumed to occur atthe point where the headwater intersects themitered entrance.

PhotographsObtain stereophotographs showing culvertdetails and all pertinent conditions upstreamand downstream from the culvert. These pic-tures are extremely important and may oftenavert a return trip to the site if certain dataare unintentionally omitted during the fieldsurvey. Good photographs are a required partof the data necessary before computations canbe completely reviewed.General views of the relationship of the cul-vert to the approach channel, to crest-stagegages if they exist, and to the getaway condi-

tions are useful. Take at least one closeup ofthe culvert entrance to show entrance detail.A level rod standing at the entrance furnishesa permanent record of culvert height and is agood reference for other details. Where roadoverflow occurs, include a view showing theentire overflow section.Spec-;al conditions

Hydraulic characteristics of culverts in thefield can be greatly different from closely con-trolled laboratory conditions. Before coeffi-cients 2nd methods derived in the laboratorycan be applied to field installations, considerany features that tend to destroy model-prototype similarity.

DebrisExamine d rift found lodged at the inlet ofa culvert after a rise and evaluate its effect.It is not uncommon for material to float abovea culvert at the peak without causing obstruc-tion and then lodge at the bottom when thewater subsides. However, if examination showsit to be well compacted in the culvert entranceand probably in the same position as duringthe peak, measure the obstructed area anddeduct it from the total area. Sand and gravelfound within a culvert barrel is often depositedafter the extreme velocities of peak flow havepassed; where this occurs, use the full area of

the culvert. Careful judgment must be exercisedbecause, in many places, levels before andafter a peak show virtually the same invertelevations even though high velocities occurred.Where dischaxge will be computed m anytimes through a culvert that has a shiftingbottom (natural bottom or deposited material),a cross section should be run after any severeflood, or at least once a year, and a record keptto evaluate the effect.In certain areas ice and snow may presentproblems. Ice very often causes backwaterpartly blocking the culvert entrance. Snowfrequently causes the deposition of misleadinghigh-water marks. as it melts.

Break in slope

Sometimes culverts a re installed with abreak in bottom slope. At other times a breakin slope will occur as a result of uneven settlinkin soft fill material. Determine the elevationand location of the invert at the break.A break in slope frequently occurs where aculvert is lengthened during road reconstruc-tion. In rare cases the size and shape of theculvert may be changed at this time.Natural bottom

Many culverts, especially small bridge-typestructures and multiplate arches, have naturalstream bottoms. The irregularity of the bottommay present difficulties in applying these dat,ato the formulas for certain types of flow. Com-pute slope using average bottom elevations.The determination of depth to the minimumelevation (definition of d) in the cross sectionor to the average elevation has no effect inflow types 1, 2, and 3 so long as h,, d,, andh, are measured at the same points. For flowtypes 5 and 6, use the average bottom eleva-tion to determine h,.

Because natural bottoms in culverts usuallycause nonuniformity in cross-sectional areas,special treatment must be given when theculvert is flowing full. An example is in type4, where the standard formula is not applicableand the routing method of computing dis-charge should be used.


19/69

10 TECHNIQUES OF WATER-RESO URCES INVESTIGATrONSRoughness Coefficients

Roughness coefficients for use in the Manningequation should be selected in the field for boththe approach section and the culvert at the timeof the field survey.

Approach sectionSelect roughness coefficients for the approachsection as outlined in the discussion of FieldData. These coefficients will usually be in the

range between 0.030 and 0.060 at culverts, be-cause stream channels are usually kept clearedin the vicinity of the culvert entrance. At timesthe approach roughness coefficient may belower than 0.030 when the culvert apron andwingwalls extend upstream to, or through, theapproach section.

Select points of subdivision of the cross sec-tion in the field and assign values of n to t,hevarious parts. For crest-stage gages where vari-ous headwater elevations are used, n and thepoints of subdivision may change. For t.hesesections, note the elevations at which thechanges take place.Culvert

Field inspection is always necessary before nvalues are assigned to any culvert. The condi-tion of the material, the type of joint, and thekind of bottom, whether natural or constructed,all influence the selection of roughness co-efficients.

Corrugated metalA number of laboratory tests have been runto determine the roughness coefficient for cor-rugated-metal pipes of all sizes.

Standard riveted sectionThe corrugated metal used in t.he manufac-

ture of standard pipes and pipe-arches has II2%inch pitch with a rise of $ inch. Accordingto laboratory tests (Neill, 1962), n values forfull pipe flow vary from 0.0266 for a l-foot,-diameter Iipe to 0.0224 for an S-foot-diameterpipe for the velocities normally encountered inculverts. Tests indicate that n is slightly smaller

for pipes flowing part full than for full pipe flow.The following are the results of tests by Neil1(1962)) and these values may be used :

A single value of 0.024 is considered satisfactoryfor bot,h partly full and full pipe flow for mostcomputations. This applies to all rivet,ed pipesand pipe-arches of standard sizes.Multiplate section

In multiplate construction the corrugationsare much larger, having a 6-inch pitch with a2-inch rise. Tests show n values to be some-what higher than for riveted-pipe construction.Average n values from various experiment,srange from 0.034 for a &foot-diameter pipeto 0.027 for a 22-foot pipe. A straight linerelationship of n values is assumed to exist fordiameters between 5 and 22 feet. Use the follow-ing roughness coefficients:

Pipe diamcfu(k.3t) 115-6___~--__________--------~---.- 0.0347-8____.-__-__--____~~-~~------.- .0339-11_----_-----------------.---.. .03212-13_---------------------------- .03114-15-------------.--------------- .03016-18----._-----------------..---- .02919-20_--_.___-~....___~-.~--~-~----- .02821-22_-_~--_~-~~~--~--~---~-.~--.- .027

A corrugated pipe with corrugations half thesize of those in multiplate construction, 3-inchpitch with a l-inch rise, is being made in bothstandard and multiplate sections. Until actualtests are run to obtain n values, use averageroughness coefficients between equal sizes ofstandard and multiplate sections-for example,use an n value of 0.028 for a 7-foot diameterpipe.Paved inverts

In many instances the bottom parts of cor-rugated pipe and pipe-arch culverts are paved,usually with a bituminous material. This re-duces the roughness coefficient to a valuebetween that normally used and 0.012. Thereduct,ion is directly proportional to the amountof paved surface area in contact with the water,


20/69

MEASUREME NT OF PEAK DWZL4RGE AT CULVERTS BY INDIRECT MEmTHODS 110r wetted perimeter. The composite valuefor standard pipes and pipe-arches may becomputed by the equation,

n,= 0.012P,+0.024(2-P,),P (12)where

P,=length of wetted perimete r that ispaved, andP= total length of wetted perimeter. IFor multiplate construction the value of0.024 must be replaced with the correct valuecorresponding to the size of the pipe.

ConcreteThe roughness coefficient of concrete is de-pendent upon the condition of the concrete and

the irregularities of the surface resulting fromconstruction. Sugges ted values of n for generaluse are:Condition ofconcretc nVery smooth (spun pipe) ______ 0. 010Smooth (cast or tamped pipe)-- . 011-O. 015Ordinary field construction---. _ 012- . 015Badly spalled _______ ____ __ _ __ _ . 015- 020

At times, sections of concrete pipe becomedisplaced either vertically or laterally, resultingin a much rougher interior surface than normal.Where this occurs, increase n commensuratewith the degree of displacement of the culvertsections. Laboratory tests have shown that thedisplacement must be considerable before theroughness coefficient is very much affected.Slight bends or changes in alinement of theculvert will not affect the roughness coefficient.However, the effects of fairly sharp bends orangles can be compensated for by raising the nvalue, as is done in slope-area measurements.Russell (1935) showed that for extreme ly sharpbends (90) the head loss may vary from 0.2 toto 1.0 times the velocity head, depend ing on theradius of the bend and the velocity. The lowervalue applies to velocities of 2 or 3 feet persecond and radii of 1-8 feet, and the highervalue to velocities of 15-20 feet p er second andradii of 40-60 feet. King (1954) stated that thelosses in a 45 bend may be about N as great,and for a 22% bend about M as great as thoseof a 90 bend.

Other materialsOccasionally culverts will be constructed ofsome material other than concrete or corrugatedmetal. Mannings coeffi%ients (King, 19.54) forsome of these materials are:

Ma&rid nWelded steel _________ ____ _ __ __ __ __ 0. 012Wood stave_--_.~-._~-___-..--~-~~ ,012Cast iron _________.___.._ - . ..__.___ 013Vitrified clay-- _ _ __ _ .__-_ _ __ _ __ _ 013Riveted steel---- ____ -.__-___-__--_ .015Culverts made from cement rubble or rockmay have roughness coefficients ranging from0.020 to 0.030, depending on the type ofmaterial and the care with which it is laid.

Natural bottomMany culverts, especially the large arch type,are constructed with the natural channel asthe bottom. The bottom roughness usuallyweights the composite roughness coefficientquite heavily, especially when the bottom iscomposed of cobbles and large angular rock.The formula used for paved inverts can be usedhere if the correct n values are substitutedtherein.

Computation of DischargeThe first step in the computation of discharge

is to determine the type of flow. Under lowheads, headwater-diameter ratios less than 1.5,type 3 flow will occur if the elevation of thedownstream water surface is higher than the wa-ter-surface elevation at critical depth. If the tail-water elevation is lower than the water-surfaceelevation at critical depth, type 1 flow will occurwith the bed slope of the culvert greater thanthe critical slope, or type 2 flow will occur withthe bed slope less than the critical slope. Type5 or 6 flow will occur with high heads, head-water-diameter ratios greater than 1.5, de-pending on the steepness of the culvert and theentrance conditions.Discharge coefficients are a vital part of eachculvert computation. These are discussed indetail on pages 37-45.Tables 2-4 have information that applies tocircular sections, riveted pipe-arches, and mul-tiplate pipe-arches. Figures 5-8 are graphs


21/69

12 TECHNIQUES OF WATER-RES OURCES INVESTIGATIONS

I-T

-


22/69

MEASUREMENT OF PEAK DISCHARGE AT CULVERTS BY INDIRECT METHODS 13

-5&XBi;

-


23/69

14 TECHNIQUES OF WATER-RESOURCES TNVESTIGATIONSTable 3.-Coefficients for pipe of circular section flowing partly full

[Coe&?Ienta for (1) tree, (2) wetted perimeter, (3) hydraulicrediae. (4) m~veysnce, (5) discharge for critical-depth flow, snd (0) top width](1) (2) (3) (4)-.---

d/o 1 A=C.D P-C,D R=C,D K=C,~-.---

c. G C. Ck-----0.8; 0. WI; 0.2003 0.0066 0.00006;. . 2838 .0132 .00030r: :: * z!:t : 3482 .0197 .00074;.05 : 0147 4027 .0262 .00137(:4510 .0325 .00222t$ * $4"; * 4949 .0389 .00328. . .5355 .0451 .00457: z: *X% : 5735 . 0513 ,006Ol.lO :0409 . 6094 .0575 .007756435 .0635 .00966

6761 .0695 .01187075 . 0755 . 01427377 .0813 .01687670 .0871 . 01957954 .0929 .0225. 16 . 0811 . 8230 .0985 .0257. 17 .0885 8500 . 1042 . 0291. 18 .0961 : 8763 . 1097 .0327.19 .1039 . 9020 . 1152 .0366.20 . 1118 . 9273 . 1206 . 0405: ;; . ;;g . 9764521 . 1259312 .04910446.23 : 1365 1: 0003 . 1364 . 0537.24 . 1449 1.0239 . 1416 . 0586.25 . 1535 1.0472 . 1466 .0634.26 . 1623 1.0701 . 1516 . 0685.27 . 1711 1.0928 . 1566 .0740.28 . 1800 1. 1152 . 1614 .0792: 309 . 1890982 1.. 1373593 . 1662709 .09070848.31 . 2074 1.1810 . 1756 ,096s.32 .2167 1.2025 . 1802 . 1027: 343 .22602355 1.2239.2451 . 1847891 , 1088155.35 .2450 1.2661 . 1935 . 1220: 376 .25462642 1.3078.2870 .20201978 . 1283350: 389 .27392836 1.3490.3284 .20622102 . 1421488. 40 . 2934 1.3694 . 2142 . 1561.41 .3032 1.3898 .2182 . 1631: 432 . 3130229 1.4101. 4303 .22202258 . 1780702: 454 .33283428 1.4505.4706 . 2295331 . 1854931.46 .3527 1. 4907 . 2366 . 2002 1. 190.47 . 3627 1.5108 . 2401 .2080 1.240.48 13727 1.5308 .2435 . 2160 1.291.49 .3827 1. 5508 . 2468 .2235 1.343150 .3927 1.5708 .2500 .2317 1. 396

(5)

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. :%.192;.214'. 237;

. 260!.285i

. xiii.3666

.395:

. t58i1 t2. XZI.628.666.704. E.825. 867. 910

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T= CJ,

C,

.475. 510. 543.572.600: xzi. 673. 694.714

. 925. 933. 940.947.954

. 960. 966. 971. 975.980

. 997. 9981: 20"1.000

(1) (2) (3) (4)----d/o 1 A-C& P=CpD R-C.D K=C&T

----C. G c. CI

0.510.4027 1.5908 0.2531 0.2394.52 .4127 1.6108 .2562 .2472.53 .4227 1.6308 . 2592 .2556. 54 .4327 1.6509 .2621 .263055 .4426 1.6710 . 2649 .2710. 56 .4526 1.6911 .2676 . 2791. 57 .4625 1. 7113 .2703 .2873. 58 . 4724 1.7315 . 2728 . 2955.59 .4822 1.7518 .2753 .3031. 60 .'4920 1. 7722 . 2776 .3115.61 .5018 1.7926 . 2799 .3192 2. 041.62 . 5115 1.8132 . 2821 .3268 2. 106. 63 . 5212 1.8338 .2842 . 3346 2. 172. 64 .5308 1.8546 .2862 . 3423 2.239.65 . 5404 1.8755 . 2882 .3501 2. 307.66 .5499 1.8965 .2900 . 3579:687 . 5594687 1.. 9177391 . 2917933 .37273658. 69 .5780 1. 9606 . 2948 .3805. 70 . 5872 1. 9823 .2962 .3874. 71 . 5964 2.0042 .2975 .3953. 72 . 6054 2.0264 . 2987 .4021.73 . 6143 2.0488 . 2998 .4090.74 .6231 2. 0714 .3008 .4157. 75 .6319 2.0944 . 3017 .4226. 76 . 6405 2. 1176 .3024 .4283. 77 . 6489 2. 1412 . 3031 .4349. 78 . 6573 2. 1652 . 3036 . 44151809 . 6655736 2.. 2143895 ..3042039 . 4470.4524.81 . 6815 2. 2395 .3043 .4578.82 .6893 2.2653 .3043 , 4630. 83 . 6969 2. 2916 ,304l .4681: 84,51 . 7115043 2.3186. 3462 .30383033 .47314768. 86 . 7186 2. 3746 .3026 .4816.87 .7254 2.4038 . 3018 .4851.88 . 7320 2.4341 .3007 .4884.89 . 7384 2.4655 . 2995 . 4916. 90 . 7445 2. 4981 .2980 . 4935. 91 .7504 2. 53221 2963 .4951

(5)2==C,D~

CV

(6)r=c*D

Cl

1.4491.5041.5601.6161. 674

1.000. 999. 998. 997.995. 993. 990. 987. 984. 980.975. 971. 966. 960. 954

2.3762. 4462. 5182. 5912. 666

. 947. 940. 933

. E2. 741; ~~8"2: 9783.061

---n 1----

I:Ei888: 67;

3. 1453. 2313.3203.4113. 505

. 854.842: iz. 800. 785. 768: 1'3":.714

4. 147 . 6944. 272 . 6734.406 . 6504. 549 .6264. 70 . 6004. 875. 065. 275. 525. 81

. 572. 543. 510. 475. 4366. 186. 677. 418. 83_-__-

. 392. 341. 280. 19!). 000* d=maximum depth of water in feet; D=diameter of pipe, in feet.


24/69

MEASURE MENT OF PEAK DISCHARGE AT CULVERTS BY INDIRECT METHODSTable 4.-Coefficients for pipe-arches flowing partly full

(CoetIlcients or (1) area, (2) hydraulic radius, (3) conveyance, 4) mean depth, (5) dkharge for critical-depth fbv]

15

(1) (2) (3) (4) (5) (1) (2) (3) (4) (5)---~ ----~d/D A= C.Dl R=C,D K=CkD; d,=C,D Q= C,Dsla d/D A = C.D R-C,D K,,ckE dm=C,D Q-C,OJ~n------ -----

c. c, Ck cm c, c. c, Ck C C.A. Nominal aIze6 feet 1 nch X 4 feet 7 nche s

0.005 0.016.009 .019.014 .025: 2 : E

::t2:. 10

.033.042r:%.068

. 11.12

.13. :t: ~~~.099,110. 120

. :7:::20

.131 . 109 .044 .114. 142 . 115 .050 . 122.I54 . 121 .056 .129.165 . 127 .062 . 137.176 . 132 .068 . 144:t;23:24.25

.189.201:22:63.238

324:338 .203.209: % : 2:.381 ,227,392.404:Z.438

,514.528

1-B I d=depth of water, in feet: D=riss, in feet.

O::.002,003.004 0.016.019.025: E 0.003.007:%,028.042.048: 23;

.006.008.Oll.014.017

.041 .038 56.048 .052 :57: ii; : :i; 2:.067 .099 .60

.075 .021082: 089

.025

.029.096 .034.102 .039

.076.084

.091.099. 106

,122.145.170:Z

2kl:282.314: 2:

.139 .075 .153 .418. 145 .082 . 162 458. 151 .090 . 170 : 499.157 .098 .178 .541. 163 .I05 . 186 .583

. 170 .115. 177 .125. 184 .135

. 191 .145197 .156

. 197: z.227,236

: E.188. 199.210

.246.256: 2;:,286

:%1.031. 091. 16: iii:238:241,245

.219 295 1.21.228 .303 1. 26.237 ,312 1. 32.246 .320 1. 37.255 329 1. 42.249252:256260:263

: ;ti:.285.295.305

.338 1. 49,347 1. 55.357 1. 61.366 1. 67.376 1. 74: %:,,342355:367

,388 1.82,400 1. 90.412 1.98,424 2.06,436 2. 14

0. 51.5224.55

61:6263: ;;

:t;.68.69.70.71::i.74.75.76:;i.z.81%::.t.86.87:tg

-I- .586.600:t::.643

0.289.292.296.300.304

0.380.393406: 419,431

.724.733

.743.752.762

.3212:.323

,505.512.519.526,533

.776.790.805.819.833

.327.330: %.341

.547.561.576.590.604.843.852: :7:.881

.341 .611.341 .619.342 .626.342 .633,342 .640.890.900.909.919.928

.343.345: z.349

: 2::.666.675.684

,936.944.951.959.966

.347.345: zig.341

2X 1: 88,694 1. 06.697 1. 10.701 1. 14,973.980.986.9931. 00

.338 .702,336 .704: xi; : 2;.330 ,709

1. 001.011. 011. 021. 021.031. 031. 041.041.05

,707.705.704,702.701: ;i:.288: %P:

168291 I_________._ _.673 _______..663 _-_-_-_.658 _------

:%.551.568.584

: Tit.803.822.841.864.889:Z.967

1. 181.231.291. 351. 411. 50 6.981. 60 7.231.71 7.521.83 7.822. 02 8. 2.i

_ _ _ - - - --_------_------_------_-e-s---

2.232.322.412.502. 592.692.792.892.993. 103. 173.253. 32:: :i3. 593.713.843.964. 994. 194.282%!4: 584. 704.814.935. 06.i. 18*i. 31.i. 435. .-ii.i. 705. 856.016. 186. 3.iI:E


25/69

16 TRCHNIQUES OF WATER-RESOURCES INVESTIGATTONSTable rl.-Coefficients for pipe-arches flowing partly full--Continued

0) (2) (3) (4) 6) (1) (2) (3) (4) (5)--P-P --~~~d/D A-CUP R=C.D KPC,C d,-C-D Q=C,Dn d/D A=C.D R=C,Dn KzCaF d,=C,D Q=CJW----- --~~~

c. c. Cb cm c* c. c, Ck c., c,B. Nominal m&e 7 feet 0 Inch X I fe et 1 inch

%:E.05:Z$4. 104:.::. 15.::. 18::t.21.22.23:;t:X!.2828.3123:;I!

:;: 48:it

0. 006 0. Oli.012 .02s.016 .02f.021 .02E.028 .03E.035.044.054: ii%

.04c:E:Xt:

.085.096.108.120

.131

.075.083:%. 103

.141.151.161: :::

. 108.114.I19.124.128.194.206.218.231.243

.I35.141. 147:%

:3$2.287.302.316

. 166 .115. 172 .125.179 . 135. 185 .146. 192 1156,330.344: E.386

g.215.221

.401: 2X.23

.226 .221.232 .234.238 .246: ;ts3 : 3;;

474: 486: ti:,521

:E259: 262.265.532 .268: x2 :%: XKi :3;t

0.001:i%.003.004

Y;;.026.029.035.006 .039:E : 2:.015 .061.018 .067

.076.084.092. 100

. 107

. 114. 120. 127. 133. 139.076 . 147.083 .156.090 164.098 : 172.I06 .I81

. 191:22::.222.232

.167. 177. 188:E

.242:ft!.281

281: 290.300:%.3292:;.357.366

0.004. 010: 8;:.029Gj.089.108.133.159:Ei.244

270: 298.326: izi

422: 461.502: Fit8: %.749.806.864.9219791:041. 101. 16

1.231. 301. 381.451. 531.591. 651.711.771.831.901. 962.032. 092. 16

0.283287: 292:%

0.380.394: t;:.437

0.447 2.25.462 2. 35.476 2.45,491 2. 55 ,.506 2. 65.303: %f.309.311

.447 .518 2. 72.457 .530 2.80.467 .542 2.89.476 .555 2.97.486 ,568 3. 05:E.748:8;:

.313.315.317: 2s

.497: %.528.538

.582 3. 14.597 3. 23. 613 3. 32.628 3. 42,644 3. 51

.784.798.811: PZS

.324.326.329.331.333

.662 3. 62.681 3. 74.701 3.85.721 3. 97.741 4. 09.848: :;x.883.895

.335 .608 .761 4.20.337 .619 .781 4. 31.339 .629 .801 4.43,341 .640 .822 4. -54,343 .65I .844 4. 66,905 .343.915 ,344.925 .345.935 .345.945 .346

.659: 6;;.684.692

,868 4. 78.892 4. 90.918 5. 03.945 5. 16.972 j. 29.956 .346.968 346.980 . 345.991 ,3451.003 .345

: 77::,717.725,733

1. 01:%1: 121. 16

1.009:. E1: 0271.034

.342 ,734 1.21 6. 30.340 .735 1. 26 6. 47.338 .736 1. 32 6. 6.i. 33.5 .737 I. 38 6. 84.333 .738 1. 44 7. 041.0391.0441.0501 0551.061

: 332370324.321,318

.737 1. j:!,736 1. 61.735 1. 72.734 1. 85734 2. 041.064 ,310 .724 __~_.._1.068 3021.072 : 295 ,715 _-__--_.706 __-_--.1.076 ,288 ,698 __-_--.1.081 .282 ,691 _ _ _ _ - _

-

I-i.:j-.L-

5. 4.;5. 615. 785.956. 13

7.2s7. 527. 828 1.i8. 59

_--___._-___-.___-.-- d-depth of water, in feet; D=rlse, in feet.


26/69

MEASUREMENT OF PEAK DISCHARGE AT CULVERTS BY INDIRECT METHODS 17fable 4.-Coefficients for pipe-arches flowing partly full-Continued-----------I ..___-

(1) (2) i (3) / (4) ) (5) (1) (2) (3) (4) (5)---.,-d_,--Y-e- P-P--d!D /I := c.D* REC!.U jKcc,F dm-C,D Q =CJW dIDI A-CJP R-C.D KpC,e d,= C,D Q=C&Pn----

c. I I-----

c, Ck cnl CP c. c, Cb CL G

0.007 0.015 0. 001 0.015.013 ,021 .002 ,021. 020 .026 .003 .026,027 .030 .004 .030.036 .037 .006 ,036

0.0052::: 821

.045 .044 .008 .042 . 052.063 .057 .014 .056 .085. 081 . 070 .020 . 070 .121.087 .073 .023 .073 . 133.093 ,077 .025 .077 .146

. 106 .085. 119 .094. 132 101145 109. 158 . 116

.030

. E

. 049.056

.086 .17?. 096 .209.105 .243,114 . 279. 123 .315

. 172.185198:211.224

.123 .063,131 . 071.138 .078. 144 .OS6. 151 .094

. 132.141. 149

. :z

.354. 394.434.476.519.23Y.254. fl. 299

. 159. 166,174181. 188. 2:.124. 135. 146

. 176. 186. 196.205.215

.570

. % t731.786.314 . 194.329 .201.344 .207. 359 .213,374 .218

,157. :E190. 201

.225,235.245,255

. 265

,845.9051: F1. 09.386 ,223398 227410 .231,422 .235.434 239

.211

. %Xi. 239,248

.273 1. 14282 1. 20. 290 1. 25299 1. 31.308 1. 36449 .244 260 .319 1. 44. 463 . 250 ,273 . 330 1. 51.478 .255 ,286 ,342 1. 59493 .260 299 .354 1. 66508 ,265 ,312 36.5 I. 74521:535.548.561.574

.268.2?2

.221;,281

.322 .376 1. 81.333 .38?, 1. 89,344 . 398 1. 96.355 409 2. 04366 .420 2. 11588.602,615

: 6::

,285 .3?8 433 2. 19.289 .391 .445 2. 28.293 ,403 457 2. 36296 .415 470 2. 45.300 428 483 2. 54

- --- --

--._

C. Nominal &a 3 foot 2 Inches X 6 feet 9 inches-- --- -- _0. 51.52

.E. 55

0.658 0.304 0.442 0. 497 2. 63.6?3 ,308 .456 .511 2.73,688 .312 .470 ,525 2. 83.?03 .315 .484 . 539 2. 93.718 . 319 . 498 . 553 3. 03. E,754.765.77?

.322 . 509 .566 3. 11,324 520 . 578 3. 20.326 .531 . 590 3. 29.328 .541 .603 3. 3i.331 .552 .616 3. 46.61

i:.64.65

.?89. 801.813

. E8

.333 .563.335 .574,337 .585

. 339 . 596.341 .607

.631: g.692

3. 563. 653. 7.i3. 8.i3. 9.5

:68Z. 6970

.849 . 342 ,618.861 .344 .628,873 .345 . 639.S85 347 . 649. 897 . 348 .660

.708.?24

. ~.z.774

4. lLi4. 164. 264. 3i4. 4x. :d.?3.32

. 909 .350. 921 . 352.933 . 354945 .355957 .357

.671.682SE. 716

.796 4. 60. 819 4. 73,843 4. 86,867 4. 99. 892 .i. 13.;;2.80

966 . 357. 975 .35?. 984 .3579931: 002

.357,358

.722.729.736,743

. 750

.916.940EE

1: 02

5. 24R. 365. 48.i. 61.i. 73

.81

.E.84.S5

1.0111.0201.029:: ii;

.357 . 756 1. 03 5. 83. 3.56 . 761 1. 05 .i. 3:j,355 .767 1. 07 6. 03,355 .?72 1. 08 6. 13,354 .??8 1. 10 6. 231.054:: %i1. 0781. 085

.YR2349.34?,345,343

.?SO. 783

. :ii. 790

1. 17 ti. 461. 24 G. 711. 32 G. 9i1. 41 7. 261. 31 7. .iS1.091 . 339 .789 1. 601.097 .336 .788 1. 601.103 .332 787 1. 821. 109 . 329 .786 1. 971.115 ,326 . 7&i 2. 171. 119 3181. 123 ,3111. 127 . 3041. 130 .2971. 137 . 291

. 775

.7:.?48. 739

_ _ _.___--.__ _ _ . _

--. -.-

__. .._________-_.___..__.--

d=depth of water, in feet; &&se, in feet.


27/69

18 TECHNIQUES OF WATER-RESOU RCES INVESTIGATrONSTable k-Coefficients for pipe-arches flowing partly full-Continued

(1) (2) (3) (4) (5) (1) (2) (3) (4) (5)----- ----d/D A = CJP R=C.D K=Cl$ d,=C,D Q=C.#n d/DC A = C.Dz R=C,D K=Cb$ d,=C,D Q=CJW

----- -----CL cr Ck C C, c. c. Ck C G

. it

.ii10

. id. 13

. :t

. :t. 18

.t:;;:23.24.25:;.282930

. ilk

. ;:3.53637zt. 40

.41::.444,s I

.46 1.47 !.4S j.49 !.50 1

0.007.013.020.027. 037

0.014. 021. 027: %

0.001. 002.003.004,006: 2;.027,032.038

0.004.Oll. 019.028041

0. 51. 52. 53. .54. 55

0.710 .0311 0. 484 0. 488. 724 .315 . 498 . 501. 739 . 31s . 512 . 514.754 321 . 526 527. 769 . 324 . 539 : 541,046. 057. 068: xi;;

. 044 . 009 .043 054.050 , 012 . 050 072056 .015 . 056 . 091. 063 .019 .063 . 113. 069 023 069 . 136. 56. ii

5:

. 783. 797.811: El?

. 327. 330333. 336339

. 553. 566. 580593. 607

_--. 300. 569. 584. 599. 614. 104 078 ,028 .078 . 165. 117 .085 .034 OS6 . 196. 131 .093 ,040 094 . 228. 144 . 100 .046 . 101 . 261158 107 ,053 109 . 296

. 61.15

. 6465

. 854 . 342 ,620 .630.867 . 344 . 633 . 647.881 . 347 . 646 . 664893 349 .659 .682909 351 673 700

173 . 115 .061 118 . 337I 188 . 123 069 . 127 . 380.203 . 130 . 077 . 136 424.218 . 137 . OS6 . 144 . 470,233 . 144 .095 . 153 . 517. tt. 68

;;

.921 . 352 .683 . 716934 . 354 . 694 . 733. 946 355 . 704 .750. 95s 356 .715 .767970 . 357 . 725 . 785.248.264.280. 295,311

. 151. 159

. :Ei180

105 . 162115 . 172126 181. 136 . 191147 . 200

. 569.622

. E789.273. 747.i

. 9821: E1.0171. 029

358 . 735 .806 5. 00. 359 . 746 . 827 .i. 13360 . 756 . 848 .i. 26361 766 .871 5. 30362 776 894 T,. .i2328 . 188 160 ,211 856. 345 195 173 . 222 . 924363 ,203 . 186 233 994380 .210 199 . 244 1: 07397 ,217 .213 255 1. 14

. :t

. :sx0

1. 039 361 . 7831. 04s 361 . 7901. 05s 361 . 7961. 068 360 . 8031. 077 360 810

918944,9719991: 03.411 ,222 .224 . 264 1. 20.425 .227 .235 274 1. 26,440 .232 ,247 ,283 1. 33,454 ,237 258 293 1. 39.468 ,241 269 302 1. 46

. :a. 83. 84. 8.5

1. 086 359 813 1. 061. 096 358 ,821 1. 101. 1O.i . 357 827 1. I31. 114 . 3.57 ,832 1. 171. 123 :?.i6 838 I. 22.4S4 247499 ,252513 .257,530 ,262546 ,267

. 2832963092%

.313 1. .54324: 335 1. 611. 69346 1. 77357, 1. 85, tE90

1. 1321. 1401. 1491. 1.581. 167

. 3.54 353 i3.52 3.50 /

. 34g I

x42846. 8.51. 8.55s.591. 331. 391. 461. .i3

.i61 ,272 349 369 1. 93 91 1. 173 346 S.58 1. 62. 37G .276 362 380 2. 01 92 1. 179 342 8.57 1. 71591 .280 376 ,391 2. 10 93 1. 185 339 8.56 1. 8.5,605 ,284 389 403 2. 1s 94 1. 191 336 8.j.i 3. 00,620 ,288 402 415 2. 27 95 1. 197 332 x.i4 2. 22,635 292 416 427 2. xi 96 1. 203630 .296 429 43!) 2. 44 97 1. 209665 300 . 443 431 2. 53 98 1. 215.6SO 304 457 463 2. 63 99 1. 220G9.i .308 ,471 476 2. 72 1. 00 1. 226

/

-

X24 .844317 83.5310 826303 ,818297 810

----I---- ---. ..-_...- ---------I---------_..___ --------__-_-------- --

D. Nominal sires 11 eet 5 inches X 7 feet 3 inches and 12 eet 10 nchen X 8 feet 4 inchen-

-_-

- - -72. 812. 913. 013. 113. 213. 313. 413. 523. 633. 733. 8.i3. 964. 084. 204. 324. 424. .i34. 6.14. 764. 88

5. 6.i5. 78.i. 926. O.-I6. 20;: ;*;6. 686. 8.57. 0.77. 247. 467. 697. RRx. 19X. 468. 750. 14!). 5i10. 1


28/69

MEASUREME NT OF PEAK DISCHARGE AT CULVERTS BY INDIRECT METHODS.Table 4.-Coefficients for pipe-arches flowing partly full-Continued19

(1) (2) (3) (4) (5) (1) (2) (3) (4) (5)---- -P-P-d/D A-CUB R=C,D KSCbD+n d.=CmD Q=CJW dIDI A= C.Da R=C,D K=CIF d,=C,D Q-C,DW

--~- -----c. c, Cb elm 0, c. c. Ck cm c,

E. Nominal aken 16 eet 7 inches X 1 0 eet 1 nch and 16 eet 4 inches X 9 feet 3 inches. and all riveted pipe-arches

0.0130. 27.040: 8::

5;:E. 10.080.0932;

. 11

. ii4

.::3;. 169. 182. 195

.:;.182:

.209.223238: 252.266.21:I:2:

.280 .162.294 . 168.308 . 173.322 .179.335 ,1852;.28.29.30

.351. 366: %.413

.31132f f: 35

.430.447: ii:.498

2;:%.40::i43: 44.45

--- -

-

-

0.0310. 43: 2;.069

0.0310.43.05I:81E

.076 . 021.082 .026: tt3 : 8::.098 .042

. 07E.082c: ;g.09E

.105. 110.116.121.I26

.048.054f y;

. 105.111. 117. 122. 128. 132 .081 . 135.139 .089 . 143. 145 .097 .151. 150 . 106 . 158. 156 .I14 . 16.5

. 124. 133142.152. 162

.173.184:;2.220

. 173. 181. 188:;i:

. 191. 197.203.209.215

.213.223.232,242.251.222 .234.229 .248.235 .262.241 .277_ 247 .292

,262.273.284: 31;

.252257: 2623;:.277.282:;2.296

.372: 2.408.420

.300: % i.311.315

.446.461475: 489.504

.432.444.456

.481

-

-

-

-

-

1,,

,

/

.

-

. 124150: 177.205.234:i: 59.60

.265 .61: 33: :E,362 .64.395 .65

::76::: 70

.661: 8x;.808.859

.71.72:2.75

: ii:1.041. 111. 17376:;0.80

1.251.331. 401. 481. 57

.81.82:E. 85

1. 641.72:%1:962.052. 142.232. 322. 41i* xi2: 692.792.88

-

/

-

0.747 0.318:E: z :

2;;: 330

.892.905.919: E

: E i.344.344.345.959: 2:9981: 012

1.0241.0361.0491.0611.0731.0841.0941.1051.1161. 126

: E: itt.363

1. 136:. :2;1: 1671.1771.1861.1951.2041.2131.222

.357.355,353: 2:

1.2281.2351.2411.2471.254

,346.343: E.333

1.2591.264:: 3;:1.280

.326.319.312.306.300

0.5172;: 571

.651659: 668.677.686

.772.783:%.814.821.829: EL.852.858: if:877: 883

: ::9.898.897,896.886,876: :2.848

0.494 2. 98.506 3. 07.518 3. 17.531 3. 26.544 3. 363. 473. 583. 69E

632,648: :;;.696

4.034. 144. 254. 364. 47.71429:Z

4. 604. 724. 854. 973. 11Fi. 235. 375. 505. 645. 77

:Ez9791: 011. 04

5. 91:z6: 366. 51

1.07 6.681.11 6. 861. 15 7. 041. 19 7.231. 24 7.431. 291. 351. 411. 481. 56

:%i8: 128. 378. 641. 64 8. 931. 74 9.251. 87 9. 642. 02 10. 02.22 10.6

____ _-__---______-_----Id~depth of water, in feet: D=rlse, in feet.


29/69

20 TECHNIQUES OF WATER-RESOU RCES XNVESTIGATIONS-------.s22iDmI56-------

-0.1 0.2 0.4 0.6 1 2 4AREA, IN SQUARE FEET

Figure S.-Depth-area curves for riveted pipe-arches.showing properties of certain size pipes, andpipe-arches. The purpose of these figures is toshow the general shape these curves will followas well as to show certain types of curves thatmay be of value for simplifying computationsof odd-shaped Culver&

Flow at critical depthAt first glance, it may not be possible to tellwhether type 1, 2, or 3 (a backwater condition)flow occurred. If the culvert is very steep andthe getaway conditions are good, the flow willbe type 1. For culverts set on zero grade withgood getaway conditions and no backwater,type 2 flow is well assured. In both cases the

type of flow must be proved. For fairly flatslopes and when backwater may be a factor,there is always the possibility of type 3 flow

--

------6

occurring. The following computational pro-cedures will identify the type of flow.Type 1 flow

The general procedure is to (1) assume thattype 1 flow occurred, (2) compute the elevationof the water surface at critical depth and thecritical slope, and (3) compare the critical slopewith the bed slope, and the water-surfaceelevation at critical depth with the tailwaterelevation. This will generally result in positiveidentification of types 1 or 3 flow or narrow thepossible flow conditions to types 2 or 3.If critical depth occurs at the inlet, the dis-charge may be computed with the applicablecritical-depth equations, 1, 2, 3, 4, and theenergy equation 5 as written between the ap-proach section and the inlet.


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MEASUREMENT OF PEAK DISCHARGE AT CULVERTS BY INDIRElCT MEmODS

l

0 20 40 60 SO 100 120 140AREA, IN SQUARE FEET

Figure &-Depth-area cun

In type 1 flow criticail depth nomally isassumed to occur at the inlet or upstream endof the culvert. However, a limited number ofcurren~meter measurements have showb that,for m itered pipes on steep slopes, this assump-tion will show less water than is actually flowingthrough the culvert. For mitered pipes, assumethat critical depth occurs at the point wherethe headwater elevation intersects the miteredentrance. For large culverts the difference inelevation be tween the inverts at each end of themiter may be several tenths of a foot. Computa-tions of type 1 flow for these two invert eleva-tions will show considerably difhxent discharges.Normally, a critical depth is assumed whichfixes the value of the remaining unknown terms.A good first approximation is d,=0.66(h1-z ).Successive approximations of d, will quicklyconverge toward the solution.To check the assumption of type 1 flow, thecritical slope for the culvert is computed asSe= (Q/K,)*. Here SC is the critical slope and K,

for multiplate pipe-arches.

is the conveyance of the section of flow atcritical depth at the inlet. If S,


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TECHNIQUEfi OF WATER-RESOURCES INVESTIGATIONS. .-.-- I I0.016 0.018 0.020 I I I I I I I

I- An--- ! I I /I /

PROPORTIONAL VALUES BAS ED ON FULL CONDITIONFigure T.-Hydraulic properties of the paved-invert pipe-arch.

Pipe-arch data for full flow are as follows:r-k-p-1.1 0.2301.6 .340;:i :Eii :%

1::lk3 :E1.0117.6 1.12

4. Type 1 flow can occur only if the criterionof step 1 is met and h,< (&+ z). If type 1flow is identified, compute the dischargewith equations 4 and 5 as outlined below.Type of flow must always be provedafter final computations are made.Computation steps:

1. Compute C, the discharge coefficient.2. Enter figure 10 with (h,--z)/D and selectvalue of d,/D from the appropriate curve.Compute d,.3. With this value of d,, enter equation 4 andcompute &.4. Compute a1V12/2g, hfl--), and A,.


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MEASURE MENT OF PEAK DISCHARGE AT CULVERTS BY INDIRElCT METHODS

Groove end on outletend sectionPLAN VIEW

k-Planned culvert length + End section+TYPICAL SLOPE DETAIL

Figure 8.-D lmensions of flared end sections for reinforced concrete pipe.Selected dimensions for various diameters of pipe

OvaraU length (D) of Iowa design is 3 It lti in for 24 in and 8 It 1% in for 30 in.NOTE.-SIO~B 3: 1 for aU sizes except 54 n. which is 2.4: 1.

5. Compute Q from equation 5. Generally this 1 Pipe-archsectionscomputed Q will closely check the as-sumed Q from step 3. If it does not, repeatsteps 2-5, using [hl+aIV12/2~-h,,~,] for[h,] in step 2.When the two discharges check within 1percent, the final result may be consideredsatisfactory.

23

Type 1 flow in -a riveted pipe-arch is com-puted in exactly the same steps as for a circularsection by using the pipe-arch data in figures9 and 10. Not all multiplate pipe-arches aregeometrically similar to rivet,ed pipe-arches orto each other. Therefore the curves of figures9 and 10 will provide less accurate values.


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24 TECHNIQUES OF WATER-RESOURCES lBVE8rMGATKNS

0.8

0.2 30 4.0 50 60 70 80

0.6 I 1I

Figure 9.-Critical slope as a function of head for pipe and pipe-arch culverts, with free outfall.

However, because the values from figures 9and 10 are only approximations, they aresatisfactory to use for multiplate pipe-archflow computation.Rectangular sections1. Compute the factors for the ordinate andabscissa of figure 11 for the culvert,

assuming d,=O.66@,- z), and plot thepoint. A point to the right of the lineindicates type 1 flow, and a point to theleft indicates type 2 flow.

2. Compare (d,+z) with h,.3. Type 1 flow can occur only if the criterionof step 1 is met and h,


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l

N 0.8,a-=I 0.6

Pipes

&!c-DFigure IO.-Relation between head and critical depth in

pipe and pipe-arch culverts.6. Compute Q from equation 5. Generally thiscomputed Q will closely check the as-sumed Q from step 4. If it does not, repeat

Step8 2-6, using[hl+a1V~/2g-hfJ for [h,] in step 3.

Computation of type 1 flow with pondedheadwater for rectangular box culverts setflush in a vertical headwall is simplified by thefact that C is limited to values from 0.95 to0.98. The factor 0.66 in the formula &,=0.66(WI-z) can be refined to give a final resultwith one computation. The following tablegives factors for various values of C:

C d 0 actor0.98_____-_____________---_-_______ 0.658.97---__--________________________ .653.96---__--__-_______-------~------ .048.95.---,----____-________,________ .643

irregular sectionsArches and all other culverts that have ir-regularly shaped bottom8 or tops (includingrectangular shape8 with fillets but excludingpipe-arches) are considered n this category. Thesame general procedure is used in computingdischarge for irregular shapes, except thatequation 1 or 2 must be used with equation 5to obtain the unique solution. For rectangularculverts with fillets, a variation of equation 3,in the form of Q=5.67Td,,,sJ2, may be used.If a number of discharge computations willbe made for a given irregularly shaped culvert,prepare graphs of area, wetted perimeter, andconveyance.

Type 2 flowIf type 2 flow is correctly assumed, thecritical depth should occur at the outlet. The

flow equations used for the computation oftype 1 flow are also applicable here, with thefurther provision that the barrel friction lossmust be accounted for in the energy equationsince the control section has shifted to theoutlet.The discharge and the critical depth mustbe computed by solution of equation 7 and theapplicable critical-depth equation 1, 2, 3, or 4.The solution is tedious, because to computethe barrel friction loss, h,*-,, the height of thewater surface at the inlet must be established.The complete equation for determining thedepth do at the inlet is

(13)Even though entrance losses actually are a func-tion of the terminal velocity rather than ofthe entrance velocity, the above equation maybe simplified for most computations by assum-ing Va=V2. Under average conditions this is IIfair approximation. Also, as a general rule,where ponded conditions exist above theculvert, or the approach velocity head and theapproach friction loss are compensa ting, thesefactors may be neglected. Thus, the equationis simplified to

(14)


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26 TEmQUJU3 OF WATER-REBOURCES lNVE#MGAITONS

C

1iti cal slope (SC;

Figure 11 .-Critical slope for culveti of rectangular section, with free outfall.

Figures 12 and 13 are graphical solutions ofequation 14 for circular and riveted pipe-archsections. Figure 14 is the solution for square orrectangular sections. These curves are basedon ponded approach conditions and the assump-tion that V3=V2. Similar curves may be con-structed for any given culvert shape, but thedevelopment is so tedious that it generally isnot worthwhile.In the event that approach velocity head andfriction loss cannot be neglected, the (hi-z)term should be increased by their algebraicSUIILIn long rough culverts Va is much larger thanVz; therefore,2gs


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,.0NIQ2s

0.9

0.8

0.6

0.4 0.5 0.6 0.7 0.8 0.9 1.04-DFigure Il.-Relation between head and depth of water at inlet with critical depth at outlet for culverts of

circular section.


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28 TECHNIQUES OF WATEFbF2ESOURCES INVESTIQATIONS1.4

1.2

1.0

0.8

0.6

0.4

0.2

0d2-ir

Figure 13.-Relation between head and depth of water at inlet with critical depth at outlet for pipe-archculverts.


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MEASUREM ENT OF PEAK DI&ZHARGE AT CULVERTS BY INDIRECT METHODS 29

/Square and rectangular

iioni I6 0.08 0.10 0.12 0.14 0.16922g(hlb??-Figure 14.-Relation between head and depth of water at

inlet with critical depth at outlet for culverts of rectangularsection.

used to compensate for the friction lossin the culvert.3. With this first approximation of d,, useequation 4 to obtain a trial value of Q.4. Compute Q2/2g@(hl-z)(D) and enter fig-ure 12 with (hi-z)/D to obtain dz/D.Compute dz.5. Having trial values of Q, dZ, and dt (whichis dJ , compute(a) ff ~V?Pg(b) h,,-,(c> bs3-

6. Compute H~hlt-culV~*/2y-h,,_,-hl,,.7. Use value from step 6 as numerator inratio H/D. Use this ratio as ordinate infigure 10 to read d,JD.8. From step 7, compute d,.9. Using value of d, from step 8 in equation 4,compute Q.10. Compute Q2/2g0(h,- z) (D), using Q fromstep 9.11. Use the value from step 10 in figure 12 to

obtain d,/D and compute dz.12. Compute the velocity head and frictionwith latest values of Q, d,, and dt. Alsocompute A, and K,.13. Compute Q from equation 7. The com-puted Q should closely check the as-sumed Q of step 9.

14. If the discharge computed with equation 7is not within 1 percent of the dischargecomputed in step 9, the assumed valueof d, is incorrect. The correct value of d,mu

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