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ENGINEERING MONOGRAPH

United States Department of the Interior

BUREAU OF RECLAMATION

\

No.

DISCII[ARGE COEFFICIEN’I’S

FOR IRREGULAR1

OVERFALL SPILLWAYS



United States Department of the Interior

Bureau of Reclamation

Engineering Monograph

No. 9

DISCHARGE COEFFICIENTS FOR IRREGULAR

OVERFALL SPILLWAYS

by J. N. BradlpJrEngineering Laboratories BranchDesign and Construction Division

Technical Information OfficeDenver Federal Center

Denver, Colorado I



On November 6.1979, the Bureau of Reclamation was renamed the Water and Power ResourcesService in the U.S. Department of the Interior. The new name more closely identifies the agencywith its principal functions-supplying water and power.

The text of this publication was prepared prior to adoption of the new name; ail references to theBureau of Reclamation or any derivative thereof are to be considered synonymous with theWater and Power Resources Service.

ENGINEERING MONOGRAPHS are publishedin limited editions for the technical staff of theBureau of Reclamation and interested technicalcircles in government and private agencies.Their purpose is to record developments, inno-vations, and progress in the engineering andscientific techniques and practices that are em-ployed in the planning, design, construction, andoperation of Reclamation structures and equip-ment. Copies may be obtained from the Bureauof Reclamation, Denver Federal Center, Denver,

Colorado, and Washington, D. C.



CONTENTS

INTRODUCTION..; .........................................

DEFINITIONOFSYMBOLS ....................................EXTENT OF INVESTIGATION ..................................

SPILLWAYSWITHFREE OVERFALL.. ...........................Method of Procedure ......................................Application of Results .....................................

Example 1: Spi llway with free overfall ........................

SPILLWAYS WITH OVERFALL SUPPRESSED. ........................Method of Procedure ......................................Application of Results .....................................

Example 2: Spillway with overfall suppressed ...................

DETERMINATION OF COEFFICIENT OF DISCHARGE CURVESpillways with Free Overfall .... .. ......... ...... : : : : : : : : : : : :Spi llways with Overfall Suppressed .............................Application of Results .....................................

Example 3: Coefficient curve for free overfall spillway .............Example 4: Coefficient curve for spillway with overfall suppressed .....

WATER SURFACE AND PRESSURE PROFILES .......................

LIST OF FIGURES

Identification of Symbols ...............................Spillways with Vertical Upstream Face .....................Spillways with Vertical Upstream Face .....................

Spillways with Vertical Upstream Face .....................Spillways with Vertical Upstream Face .....................Spillways with Sloping Upstream Face ......................Spillways with Sloping Upstream Face ......................Spi llways with Sloping Upstream Face ......................Spillways with Sloping Upstream Face ......................Spillways with Sloping Upstream Face ......................Spillways with Sloping Upstream Face ......................Spillways with Sloping Upstream Face ......................Spillways with Sloping and Offset Upstream FaceSpillways with Offset in Upstream Face ... .... : : : : : : : : : : : : : :Spillways with Offset in Upstream Face .....................Spillways with Offset in Upstream Face .....................Spillways with Offset in Upstream Face .....................Spillways with Offset in-upstream Face .....................

Elevation and Section American Falls Dam Spillway. ............American Falls Dam Spillway (Examples 1 and 3) ..............Spillways with Overfall Suppressed ........................Spillways with Overfall Suppressed ........................Spillways with Overfall Suppressed ........................Spillways with Overfall Suppressed ........................Spillways with Overfall Suppressed ........................Spillways with Overfall Suppressed ........................Spillways with Overfall’suppressed ........................Spillways with Overfall Suppressed ........................Spillways with Overfall Suppressed ........................Spillways with Overfall Suppressed ........................Spillways with Overfall Suppressed ........................

i



Number

:2334

35

LIST OF FIGURES (Continued)

Page

Plan and Section Kachess Dam Spillway . . . . . . . . . . . . . . . . . . . . . 37Kachess Dam Spillway (Examples 2 and 4) . . . . . . . . . . . . . . . . . . . 38Coefficients of Discharge for Other Than the

Design Head (Free Overfall Spillways) . . . . . . . . . . . . . . . . . . . . . 39Coefficients of Discharge for Other Than the

Design Head (Spillways with Overfall Suppressed) . . . . . . . . . . . . . 40

APPENDIX

Spillways with vertical upstream face ......................Spillways with vertical and sloping upstream faces ............. 4:Spillways with sloping upstream faces ......................Miscellaneous spillway shapes ...........................

2:

Spillways with irregular upstream faces ....................Spillways with offset in upstream face ...................... :87Earth dam spillways with shallow approach depth ..............Earth dam spillways with shallow approach depth ..............

ti

Earth dam spillways with shallow approach depth ..............Earth dam spillways with shallow approach depth .............. :iEarth dam spillways with shallow approach depth .............. 53

ii



INTRODUCTION

In 1948, the Bureau of Reclamation pub-lished Bulletin 3, Part VI, a Boulder CanyonProject Fir&Report, titled “Studies of Crestsfor Overfall Dams. ” This work was based on

an extensive series of experiments on weirswith sharp crests for the purpose of definingthe natural nappe shapes, both upper andlower, and determining the resulting dis&argecoefficients. These natural nappe shapes anddischarge coefficients, recorded in the abovebulletin, are termed “datum profiles” and“datum discharge coefficients” to distinguishthem from those which will be presented inthis monograph.

By datum shape is meant the shape ofspillway cross section which corresor coincides with the natural (basic P

onds toprofile

of the lower nappe surface for the design dis-

charge condition. This will be the smallestcross section, as well as the most efficientshape, on which no significant negative pres-sures wi ll exist for the design discharge.For discharges less than the design discharge,pressures on the face will be greater thanatmospheric and discharge coefficients willbe smaller than for the design discharge.For discharges greater than the design dis-charge, subatmospheric pressures wil l existon the downstream face and discharge coef-ficients will be greater. The terms “datumshape” and “datum coefficient” represent adefinite basis from which the designer maywork, even though he may deviate from the

datum shape in any particular designDatum shapes are included in this mono-

graph for the purpose of comparison. It issuggested that the reader become familiar

with Bulletin 3, Part VI, of Boulder CanyonProject Final Reports, because much of thematerial in the monograph is supplementaryto that in the bulletin

Coefficient of discharge information isquite Complete for the datum shapes. Thereis, however, much to be desired in the wayof reliable data on coefficients of dischargefor sections that differ from the datum shape.

The monograph deals with overfall spill-way sections which differ from the datumshape. For lack of a better descriptive term,these are referred to as “irregular” shapes.Irregular shapes are the ones most likely tobe encountered in practice. This is true forseveral reasons: (1) sufficient informationfor the design of datum shapes has not beenavailable until recently; (2) where radial orvertical slide gates are used for regulation,it has been customary to shape the overfallsection to fit-the trajectory issuing from asmall gate opening. This gives a broadersection than the datum shape. Such practiceis losing ground in favor of the datum shapes;and (3) where drum gates are provided on aspillway, a broad overfall section is usuallyrequired for structural reasons. For thesereasons, true datum shapes are not as com-mon in practice as the irregular shapes.

This monograph was written for the ex-

press purpose of providing the designer withexperimental information by which he maydetermine, with a fair degree of accuracy,the coefficient of discharge at any head forirregular overfall spillway shapes.

DEFINITIONS OF SYMBOLS

The symbols will be the same as thoseused in Bullet in 3, Part VI, Boulder CanyonProject Final Reports. Symbols appearing

F,this monograph are as follows: (See Figu~

A, total head for which spillway sectionwas designed (including velocity headof approach)

H any other total head measured abovehigh point of crest

& velocity head of approach

P + E the average depth of approach Channel

Co coefficient of discharge for the designedhead, Ho

C coefficient of discharge for other thanthe designed head, A

CM coefficient of discharge obtained frommodel at designed head

CD coefficient of discharge for corres-ponding datum shape at designed head

hd drop headwater to tail water elevation(low dams)

d tail water depth (low dams)

1



EXTENT OF INVESTIGATION

Tne Hydraulic Laboratory of the Bureauof Reclamation-has been continously experi-menting, collecting, and compiling data onflow over both high and low overfall dams

since its inception. It is now felt that suffi-cient information has been accumulated towarrant a compilation of coefficient data forspillways of irregular shape (those differingfrom the datum shape).

The information stems from model studiesperformed on spillways of dams designed bythe Bureau during the past 20 years, modelstudies of spillways for several TennesseeValley Authority dams, and model studies ofspillways for three dams for the Governmentof India, performed at the Colorado A and MCollege at Fort Collins. Coefficients of dis-charge are included for high dams with free

overfall, as well as for the shallow earth damtype of spillway where free flow is suppressedby insufficient getaway downstream.

Considering the information collectively,it will be found that, for high dams, Figures

2 through 5 pertain to spillways having ver-tical upstream faces; Figures 6 through 12represent spillways with sloping upstreamfaces; and Figures 13 through 18 are for spill-

ways having offsets, or corbels, on the up-stream face. Figures 21 through 31 apply toearth dam spillways. The charts on the fore-going figures will be referred to as stockshapes. All charts are plotted to the samescale, an ordinate or abscissa value of 1.0on any chart being equal to 100 of the small-est divisions on a 60 engineer’s scale. Thisscale will be referred to hereinafter as the“standard scale. ”

The discussion first shows how to obtainthe coefficient of discharge, at the designedhead, for a spillway section m question Thisis done for both the free overfall spillway and

for one in which free overfall is suppressed(earth dam type). Then it is shown how thecurve showing coefficient of discharge forvarious heads may be established from asingle point. Examples are included to illus-trate the procedures.

SPILLWAYS WITH FREE OVERFALL

Method of Procedure

The solid lines on Figure 2 represent two

spillway shapes with free overfall which weretested by means of hydraulic models. Thesecross sectional shapes and the ones that followare plotted to the same scale, which is dimen-sionless (both X and Y distances are dividedby the total designed head, Ho). By this meth-od of plotting, similar shapes with similarheads will coincide. The coefficient of dis-charge for each shape at its respective de-signed head (as determined from a model)is listed opposite the symbol CM. The modelcoefficient for the Wheeler Dam, CM is 3.99while the much broader section for the HooverDam shows CM is 3.58, Figure 2.

For the purpose of comparison, datum

shapes, computed for the same heads and ap-proaoh conditions, are also plotted on Figure2 for the two spillway sections and are identi-fied by the heavy dash lines. The datum co-efficient CD is 3.96 for the Wheeler Dam and3.93 for the Hoover Dam In making a com-parison of this kind, it is necessary to matcheither the upstream faces of the actual anddatum sections or their axes. Neither meth-od is altogether satisfactory. In this com-parison of free overfall shapes, however, theaxes of the actual and datum shapes are made

to coincide so that the crest, or high point, ofeach shape constitutes a common point. Thevalues H + (P + E) on Figure 2 indicate the

ratio of tl?e total designed head to the approachdepth.

The method consists simply of compar-ing an irregular shape in question with a cor-responding, or closely corresponding, shapefor which the coefficient of discharge is known.Considering the number of variables involved,the procedure is perhaps the best that can bedevised at the present stage of the study. Theaccuracy obtainable is well within the limitof practical design.

Dimensions and details have been omit-ted from the charts as it was desired to pre-sent these in as simplified a form as pos-sible. Prototype dimensions can be found inthe Appendix by observing the reference oneach chart. For example, the prototype di-mensions of the Wheeler Dam Spillway Sec-tion, shown on Figure 2, can be found in Fig-ure lA of the Appendix.

Application of Results

The most effective way fo explain the useof the charts on Figures 2 through 18 is topresent an example.

2



Example 1: Spillway with free overfall

From the elevation and section of theAmerican Falls Dam spillway, shown on Fig-ure 19, determine thecoefficient of dischargefor the designed head of 11.3 feet This spill-way has never been rated, so this serves as

a practical application as well as an example.First, all dimensions of the crest pro-

file, Figure 19, are divided by the total de-signed head which is 11.3 feet The resultingdimensionless values are then plotted, to thestandard scale, as shown on Figure 2OA, buttransparent paper shou ld be used so that thisshape may be readily superimposed on thestock shapes. As the shape in question hasa vertical upstream face, it should be super-imposed on the charts of Figures 2 through5 until a satisfactory comparison is obtainedwith an actual shape or a datum shape--eitherwill do. It is not necessary to match the axes

in this process, rather it is much more im-portant to match the upstream and downstreamfaces simultaneously.

The American Falls Spillway profilecompares favorably with the profile for theKeswick Dam Spillway, Figure 4. The modelcoefficient CM for the Keswick Spillway is3.50.

As the experimental work was per-formed in several laboratories by differentpersonnel over a period of years, inconsisten-cies in the results may be expected. There-fore, it is desirable to obtain as many com-parisons as possible. By checking with Fig-

ures 2 through 18. it is found that the shanefor the DavisDam Spillway (Figure 15) alsocompares favorably with the American Fallsshape. The model coefficient for the Davisshape is 3.59. It was previously demonstrat-ed in the Boulder Bulletin 3, that spillwayswith straight vertical offsets in the upstreamface perform very much the same as thoughthe upstream face of the offset was continu-ous. The Davis Dam Spillway can, there-fore, also be considered. From the two com-parisons, the coefficient of discharge for thetotal designed head of 11.3 feet will be cho-sen as 3.55 for the American Falls DamSpillway.

It is evident that a large variety of stockshapes is necessary in a compilation of thistype. It is to be understood that the chartsdo not include all spillway shapes that maybe encountered in practice; however, they doinclude the majority of cross sections usedby the larger design offices.

SPILLWAYS WITH OVERFALL SUPPRESSED

Method of Procedure

Earth dam spillways usually follow closelythe downstream profile of the dam; conse-quently, they are not steep and the approachdepth is shallow. ln the case of the free over-fall dam sections just presented, the onlyimportant factor affecting the coefficient.ofdischarge was the shape of the overfall sec-tion Three factors, however, affect the co-efficient of discharge on the earth dam typeof spillway: (1) the depth of the approachchannel; (2) the shape of the overflow or gatesection; and (3) the elevat ion of the floor ofthe channel or chute immediately downstream

from the gate section. The individual effectsof each factor are evaluated in Boulder Can-yon Bulletin 3, Part VI, but when combina-tions of the three factors must be consid-ered simultaneously, the following proce-dure is the best for determining over-all dis-charge coefficients.

From Figure 21, it can be seen that theefficiency of three flat spillways shown there-on can be increased considerably by makinguse of a small ogee, or overflow crest, at thegate section and providing a free getawaydownstream The solid lines represent the

actual shapes of the spillways, while the dashlines are datum shapes. The method of plot-ting is different than for the previous freeoverfall shapes, principally to illustrate apoint For fl&t spillways, the shapes are plot-ted with a common vertical axis, but due tothe better efficiency of the datum shape, itscrest has been elevated to show that eachspillway section will pass the same dischargefor the rmximum reservoir elevations. Shouldthe more efficient datum shapes on Figure 21be used, it would be possible to either reducethe height of the gates or,by holding the crestsat their original elevations, shorten the widthof the gate sections. The datum shapes, as

‘drawn, will have atmospheric pressure overthe face of the ove&.lls proper for the max-imum discharge condition, while the chutefloor downstream has been dropped to an ele-vation where it will have no effect on the dis-charge coefficim In actual design, the layoutof the gate section will depend on existing to-pography and other practical considerationsas well as efficiency.

Figures 21 through 31 all represent earthdam spillways in which the discharge is re-tarded by the position of the chute floor im-mediately downstream from the gate section

3



and by the skallow depth of approach Theseare dimensionless plottings in which the Xand Y distances are related to the total designhead. The scale is the same as in the pre-vious charts. The prototype dimensions forthese spillways can be found in the AppendixE~;.II,s of the reference number under each


ExamDle 2: Soillwav with overfallismressed

Determine the discharge coefficient forthe Kachess Dam Spillway, shown on Figure32, for the total designed head of 8.0 feetThis spillway has not been rated previously.

The procedure to follow to obtain thecoefficient of discharge for this flat profilespillway is the same as described in Example

1.

The dimensions of the overfall portionshould be divided by the designed head, andthe spillway in question should be drawn tothe standard scale on a piece of transparentpaper, A dimensionless plot of the KachessSpillway is shown on Figure 33A. The trans-parent plot is superimposed on the stockshapes of Figures 21 through 31 until one, orpreferably more than one, shape is found tobe col-rparable. Either actual or datum shapes

may be used, as the discharge coefficientsare listed for each. It will be found that areasonable agreement exists between the Ka-chess Spillway shape and the following:

Coefficient ofDam spillway Figure discharge

BocaScofield f; z:UnityDeer Creek 2”:

;:g

Keyhole 29 &6

Average 3.49

It will, therefore, be assumed that thecoefficient of discharge for the Kachess Spill-way for the total design head of 8.0 feet is3.50.

When using the stock shapes of Figures

21 through 31, it should be kept in mind thatthe flat portion of a chute immediately down-stream from a gate section can have a moremarked effect on the discharge coefficientthan the approach depth upstream Thus, itis more important to match the chute floorimmediately downstream from the overfallthan the approach floor upstream The gen-eral effect of the position of the chute flooron the coefficient of discharge can be read-ily observed from Figure 44 of the BoulderCanyon Bulletfn 3, previously mentioned.

DETERMINATION OF COEFFICIENT OF DISCHARGE CURVE

Spillways With Free Overfall

The coefficient of discharge curves ob-tained from the free overfall models of Fig-ures 2 through 18 are shown plotted in a di-mensionless form on Figure 34. The ordin-ate, II/Ho is the ratio of any total head to thetotal designed head, while the abscissa, C/Cis the ratio of the corresponding coefficien Pof discharge for the .head H to the coefficientfor the designed head, Ho A single curve wasdrawn through the mass of points, as therewas no logical order to those that scattered.The scattering is therefore considered ex-perimental error. When one considers thenumber of models involved, varying in sizeand scale, and considers that the testing wasperformed in several laboratories by a num-ber of individuals, the agreement is all thatcan be expected.

Spillways With Overfall Suppressed

The same method of plotting was used forthe earth dam spillways of Figures 21 through

4

31 and these results are shown on Figure 35.It was again possible to draw a single curvethrough the points. The curve is steeper thanthe free overfall curve and does not show asmuch variation in the value of C/Co. As thecoefficient of discharge is usually lower forthis type of spillway, it cannot vary as muchas for the free overflow. It can be noted thatthe curve doubles back for heads greater than1.2 times the design head and the maximumvalue of C/C is slightly more than 1.0. Thisis explained%y the fact that, as the head in-

creases over one of these flat spillways, thefloor effect downstream becomes more pro-nounced. The result is a decrease in the co-efficient of discharge.

As there is no particular order to thepoints on either Figures 34 or 35, there isno basis for drawing intermediate curves be-tween the two lines already established. Thus,it a-s that the discharge coefficients con-sidered in this monograph fall into one typeor the other. In attempting to classify a spill-



way as to type, it may be helpful to observethe values of

Ho and ( hd + d) actual

P (hd + d) experimental

tabulated in Figures 34 and 35.


.J=mDle 3. Co efficient curve for free

overfa&pillway

Determine the entire head versus co-efficient of discharge curve for the Ameri-can Falls Dam Spillway from the one pointobtained in Example 1, where Ho = 11.3 feetand Co = 3.55.

Values of C/Co for corresponding valuesof H/H, are read from the curve on Figure

34. These values are tabulated as shown inTable JA. With Ho and Co known, values ofH and C are computed. The resulting headversus coefficient of discharge curve is plot-ted on Figure 20B.

-mole 4: Coefficient curve for soillwayWith OVerfall SUDoreSSed

Determine the complete head versuscoefficient of discharge curve for the KachessDam Spillway from the one point determinedin Example 2, where Co = 3.50 for the de-signed head of 8.0 feet.

The procedure is the same as for Ex-ample 3 except that in this case the H/Ho andC/Co values were obtained from Figure 35.The computation is tabulated in Table 1B andthe resulting head-coefficient of dischargecurve is shown on Figure 33B.

WATER SURFACE AND PRESSURE PROFILES

Where the experimental information wasavailable, average water surfaces and pres-sures have been plotted on the charts of Fig-ures 2 through 18 and 21 through 31. Thewater surface and pressure profiles are forthe actual overfall shapes operating at theirrespective designed heads, Water surfacesfor the datum shapes are not shown as thesecan be computed from Bullet in 3, Part VI,Boulder Canyon Project Final Reports. Thewater surface profiles will be found useful

where the designer desires to locate gate pinsor counterweights in close proximity to themaximum water surface. They may also beuseful in determining the height of trainingwalls. One should be reminded, however, thata water surface profile is not nearly as easy

to define as the profile of the lower nappe,because piers and entrance conditions canproduce diagonal surface waves and fins ofappreciable magnitude.

Pressures are more or less indicative ofthe coefficient of discharge. Generally speak-ing, if the pressures are appreciable and posi-tive, over the overfall face, +he coefficient ofdischarge will be low. Conversely, subatmos-pheric pressures generally distributed over

the overfall face are conducive to high dis-charge coefficients, The pressures are plot-ted using the overfall face as a zero referenceline, thus pressures above the line are posi-tive and those falling below the line arenegative.

Table 1

COEFFICIENT OF DISCHARGE COMPUTATIONSFOR EXAMPLES 3 AND 4

A H/H, c/co H C

American Falls Dam %

0.843 2.26

Spillway . 0.900 4.52

2:0.940 6.79

33%

Ho = 11.3 2% 9.053:33

1’:;

3.46

co= 3.55 1:025 11.303.57 Ei

B

Kachess Dam Spillway

Ho 8.0

co = 3.50

H I c I

1.603.20 %

2%3:41

8:003.473.50

9.60 3.51

5



I

I

HO \

Ew----w----- m

i \ I

FIGURX 1 - Identification of symbols.

6



WHEELER DAMHEELER DAM

c, = 3.99 -, = 3.99 -Go = 3.96 ---o = 3.96 ---

APPENDIX-FIG. IAPPENDIX-FIG. IA

i HOOVER DAM1 SHAPE 3 MODEL M-l

I SE= .66C,= 3.56 -

I -c, =3.93 --

APPENDIX-FIG. 1C

I I

YHO

0 1.0 2.0

xHo

FIGURE 2 - Spillways with vertical upstream face.

SHEET I OF 4



HIRAKUD DAM

-1.0 ’

APPENDIX -FIG. 4A

0.5

0

u

HO

-I. 0

-2.0

fI

I\ \

I\\

.‘” \

I 2 \

I .

II

\

I

CANYON FERRY DAM

\p$ f 0.26

CM .70

Go= .96--

APPENDIX -FIG. I8

2.5

FIGURE3 - Spillways with vertical upstreaxu face.

SHEET 2 OF 4

8



KESWlCK DAMESWlCK DAM

-1.01.0 0, = 3.50 -, = 3.50 -

CD ~3.85-0D ~3.85-0

F1GUR.E 4 - Spillwaya with vertical upstream face.SHEET 3 OF 4



1.0

f--Ho

(HIGH CREST)c, = 390--.

CD 2 3.90--

APPENDIX - FIG. 48

0 I.0 2.0

?--n-T-

HOOVER DAMSHAPE 2 MODEL C-3

SE = 0.66 c,D 2 3.91.91 - - \ \APPENDIX- FIG. 1F

0 2.0

FIGURE5- Spillways with vertical upstream face.

SHEET4 OF4

10



0

Y

G

-1.0

- 1.5

MADDEN DAMADDEN DAM

c, = 3.71 -, = 3.71 -

CD = 3.97 ---D = 3.97 ---

APPENDIX - FIG. 2CPPENDIX - FIG. 2C

- 1.5 - 1.0 0

x

1.0

Ho

uHo

MARSHALL FORD DAM(INITIAL DESIGN )

CM = 3.96 -

FI(3KRE6 - Spillways with BlOpiZ lg U&JBtretiUIt face.

Ho

11 SHEET. I OF 7



I.0

0

Y

&I

-1.0

-1.5-1

MODEL C-8

GM = 3.76 -

CD =3.92 --

APPEND IX -FIG. 101

HOOVER DAMOOVER DAMMODEL C-8

GM = 3.76 -

CD =3.92 --

\\

\

\

‘--_

--.-.

j

Pressure-'

r..‘\\

‘\\\ \ \

\

1 =D.16CM 2 3.64 -

Go = 3.97 - -

APPENDIX-FIG. 2E

11\\

2.0 2.5

?‘Ix3uBE 7 - splllwap3 with dLoplm& upstmam face.

SHEET 2 OF ?



0

Y-

HO

-1.0

-1.5

Y

G

-1.0

-2.0-1.0

Pressure---“’

II

HOOVER DAMSHAPE 0 -FINAL MODEL C-6

GU = 3.85-

Go z3.92 ---APPENDIX - FIG. 28

//’/’

\, \, \

/

\

v,,

/

=c

,

/

r--

NORRISORRIS DAM

I

“0 -P+E -0.13 Co = 3.96---

APPENDIX- FIG. 3E\ ‘\

0X

I.0

G

FIGURE8 - Spllluaye with doplng lqls~eam face.

2.5

13SHEET 3 OF 7



-1.0 - G, : 3.76 -

c, = 3.64 - -

APPENDIX- FIG. 3C

-1.5 *

-1.0 0 Y 2.0 2.5

YiT0

-1.0

MOON LAKE DAM \C, = 3.80 -

CD f 3.89 - -

APPENDIX-FIG. $A

FIGUREg- Spillwsye with t3loplng upstre apn face.

SHEET 4 OF 714



-1.0

i-1.0

.O.SL‘

-1.01.0 0 I.0.0 2.0.0 2.5.5

X

6

Pressure

IMPERIAL DAM

CM = 3.75 -

co - 3.91 --

APPENDIX -FIG. 38

I

ii

// HGOVER DAMGOVER DAMSHAPE 4HAPE 4 MODEL M-3ODEL M-3

C,= 3.68 -

= 0.66 C,=, = 3.68.92 --, = 3.92 --

APPENDIX-FIG. 3FPPENDIX-FIG. 3F\

FIGURE 10IGURE 10 - spiuways with slopblg upstreaItl face.spiuways with slopblg upstrea m face.

2.5

15SHEET 5 OF 7



I HAMILTON DAM

-1.0 (

’ ‘\ ’

&.I6 GM=3.67 - \

CD = 3.90 ---\

APPENDIX -FIG. 3D

\

vHoo

-1.0

CEDAR BLUFF DAMGM’4.02 - -

CD = 3.88 ---

APPENDIX -FIG. 4C

CEDAR BLUFF DAM

= 0.96GM’4.02 - -

CD = 3.88 ---

APPENDIX -FIG. 4C

-2.02.0,

-1.01.0 0 1.0.0 2.0.0

xHoo

FIGURZll- Spillways with sloping upstream face.

SHEET 6 OF 7

16



0

.x

HO

-1.0

I

TRENTON

G, - 3.68- \.-CD = 3.76--

L

\APPENDIX -FIG. 4F

\

Outlet trashrocks interfere with flow \over spillway.

G, - 3.68 -CD = 3.76--

APPENDIX -FIG. 4F

Outlet trashrocks interfere with flowover spillway.

I I I-

2.0 2.5

HIWASSEE DAMHo

P3 so-'4G, = 3.82Go = 3.98- -

APPENDIX -FIG. 4E

FIGURE3.2 - SpilLways with sloping upstream face.

StiEEf 7 OF 7



-1.0

$0

-2.q

-2.2,

C

-1.c

Y

ii-,

-2.0

-2.5

CAPILANO DAM

\’ & ~0.23

C, =3.62 -GI, 3.95 --

APPENDIX-FIG. 68

I.5

f-

I-

-1.0 0 I.0 :

XG

BHAKRA DAM

Cy 13.66 -

co 23.95 --APPENDIX -FIG. SD

-1.5 -1.0 0 I.0 it.0

A

Ho

FIGURE 13 - spill~s with sloping and ofmet upstream face.

SHEET I OF G

18



0

Y

&I

- I.0

- 1.5

GRAND COULEE DAM

APPENDIX- FIG SA

I.0

0

Y

FT,

-1.0

-I .5

DAVIS DAMI (FINAL DESIGN)

$ : 0.64c u = 3.94

Go =3.95 --

APPENDIX -FIG. SF

FIGURE14 - spillways with offset in upstream face.

SHEET 20F 6

19



0

Y

Kl

-1.0

- 1.5

SHASTA DAM

APPENDIX- FIG 5C

0

v

HO

FlGUEB15- Splll~e 182th offeet In upetm8m face.

SHEET 3 OF 620



0

Y

Gi

-1.0

/-

-1.5

ANGOSTURA

CM= 3.88 - -CD= 3.97---

APPENDIX -FIG. SD

^- l.U cl

XI.0 2.0

K3

0.5

0

-1.0

-2.0

FRIANT DAM

CD= 3.%- -APPENDIX- FIG. 58

-1.0 0 I.0 2.0X

G

FIGURE 16 - spiuways with offset in upstream face.

.21

SHEET 4 OF 6



0.5

YIid

I-1.0

I

I

-2.0 .-1.0

\

co = 3.99- -

I I APPE NDIX -FIG. 6C I ‘\I \ I

I IFONTANA DAM

1 II APPENDLX - FIG. 60 I

0 1.0 2.0 2X

4l

FIGUREl7- spiuways with off set in upstream face.

SHEET 5 OF 6

22



/

\

<

\1

<

b

!DOS BOCAS DAMp$0.22

G,.95CD - 3.97 t

- p$=Q.22 G, - 3.95CD - 3.97

APPENDIX- FIG. 6A 1, APPET- FIG. 6A ,

0 1.01.0

- I.0

-2.0

Ho

APPENDIX -FIG. 6E

FIGURE 18 - spillways with off set in upstream face.

SHEET 6 OF 623



T----Upstream face of dam

-A,& ------------ 2,‘0’-----------;

PIER -SECTION

: -_-------- 21’-0” -_------

,-Normal W.S. El.4354.5

p---m--------, 5 Boys @ 36’0’ = 540’-O’------- -r--+--7

It I I

I I I I ’ I

I / Il- I I I I I

e$$-- End pier Intermediate pier --___Jtiii

UPSTREAM ELEVATION

/El.432129-_v_--

.,.:

.“.d,

0.’:

:

0”

,’ ‘o,

.‘;,

.v.‘D:

:o:

.+.,.

*:-.

_’ .‘.

.‘e..q. .

.’

.‘d. ‘. ‘,

:, :.

.:.‘.

v “. .,cf. .

:‘0 0 . .

6’;. .,. . ‘,.., ;:

.o’

..‘,a.,., :.0.’

. ...; :o-

0. “O.. :. ..::.’

.b ‘;

0. .”. ;,:; :, .;..

.SPILLWAY

I

I

!

I

300.42 I00’“..‘;.,, .:

.sfi0..;.a’ :.

‘0..

: .. . 10

SECTION .. .

FIGURE19 - Elevation and section American FaUs Dam Spillway.

24



0X

1.0 2.0

H,

A- OVERFALL CREST SECTION

14

I I I I I I I

I

Desion head: I 1.3’ 1 I /I

klWIL

lx I I I I I I I I I I I/ I0 I I I I I I I I A I t

Y

I I Ii I I III I I l/l I

II II II III1 I/ I

I I I I I I I I II/

iI l/l

/ I I I I IA I I

3.1 3.2 3.3 3.4 3.5 3.6

CinQ=CLH 4

B- HEAD- COEFFICIENT CURVE

2.5

F- 20 - AmericanFaYs ‘Dam Pi-W (‘-mles 1 ana 3).

25



*-1.0 0

Hxo

I .o 2.0 2.5

RYE PATCH DAM

H,- ‘7 C,:2.81 -

-+E 3.53 co53.77 --

APPENDIX- FIG. 7A

uHo

-\

\

\

\

\

h 3

s

AGENCY “AkEY DAM

Ho 17 GM- 2.73 --5P+E 3.23 Go= 3.78 --

CONTRACTION IN CHUTE D.S.

APPENDIX- FIG. 70

ii

PINE V&V DAM.

Ho 4 Cm= 2.74 -

P+E = 1.81 G0=3.86 --


APPENDIX -FIG. 7C

FIGURE2l- Spillways with overfall suppressed.

SHEET l OF II 26



Y

G

I.0 r

0 ’

-1.0 L

-1.5 *-I 0

YJ-Jo

Y \\

\‘\ . \ .

-.1

-.ALCOVA DAM

HO 8 = 2.85 -

PtE =

CM

2.81 GO = 3.80 --

APPENDIX - FIG 7E

I 1 I I

0X

1.0 2.0 2.5

Ho

.--

-1. 0 Ho 5.44 CM : 3.30- I

GE=3.17 Co = 3.78 - -

APPENDIX -FIG. 7F

-1.5 - 1

-1.0 0 1.0 20 2.5

1LHo

SHADOW MOUNTAIN DAM 1

F1GUR.E22 - spiu~ay13 with overfall s~pp3ss~a.

SHEET 2 OF11

27



L

HO

GREEN MOUNTAIN DAMHQ 5.5 C, = 3.21 -

P+E’ 3.16 CQ = 3.70---

CONTRACTION IN CtiUTE D.S.

APPENDIX - FIG. 78

U1L

1.v 2.0

Ho

ANDERSON RANCH DAMHg 3.80 GM = 3.40 -

-+E 3.46 GQ - 3.76---

APPENDIX- FIG. 8A

.^ --

HO

BARTLETT DAMHo 3.57

P+E= 2.64

CM = 3.40 -

C, =3.?6 ---

APPENDIX - FIG. BB

~~camz 23 - SpilLways with overfall suppressed.

SHEET 3 OF II

28



t?o

GRANBY DAMHo 5.0

“c”,= 3.20 -

m-3.1 = 3.7 I ---

APPENDIX- FIG. BC

-1.0 0 1.0--

X

?r,

VALLECITO DAMHo 3.8 C, = 3.42 -

Px ’ 3.0 Co = 3.720----


APPENDIX - FIG. 8F

-1.01.0 0

x

I.0.0 2.0.0 2.5.5

BOYS;: DAMOYS;: DAM(PRELIMINARY DESIGN)

HO 3.7 I -

PtE =

cy = 3.37

2.74 C, = 3.76 ---

APPENDIX - FIG. BE

(PRELIMINARY DESIGN)

HO 3.7 I

PtE = 2.74

cy = 3.37 -

C, = 3.76 ---

APPENDIX - FIG. BE

FIGURE 24 - Spillways with overfall suppressed.

29SHEET 4 OF II



SCOFI ELD DAM

-I .o “0 4.16CM = 3.44 - .

iTE = 3.14 CD = 3.72 --

lAPPENDIX -FIG 9A

I

-1.0

1.0 0 1.0 2.0 2

-1.0

-1.5

I IBOCA DAM

1“0 3.08 CM = 3.50 -

P+E = 2.52 CD = 3.81 --

APPENDIX -FIG. 8D

- I o 0 1.0 2.0

x

Ho

FIGURE25 - spillways with overfall suppresse d.

2.5

SHEET 5 OF II

30



-1.0

-1.5-I

-4- -

FRESNO DAM

“0 1.39

:

= 3.52

im 1.34 G, rJ 3.88

-

CD - -

APPENDIX-FIG 98#

0 1.0 2.0 2

\

‘.,..

I I

Ho 3.20

= 2.75

c,=3.48- .co = 3.79 --

UNITY DAMNITY DAMc, = 3.48-co = 3.79 --

APPENDIX -FIG. 9CI APPENDIX -FIG. 9C I I

0 1.0

FIGURE 6 - Spillways with overfall suppressed.

31

2.0 2.5

SHEET 6 OF II

i



0

uHo

-1.0

u

Ho

SHEET 7 OF II

\‘. ---a---

BULL LAKE DAM

Ho 2.75 CM = 3.58

P+E = 2.34 GI, - 3.04 --

APPENDIX-FIG. SOL

0 1.0 2.0

xHo

\

‘. A----

CABALLO DAMHo 2.62 CM = 3.48 -

P+E - 1.9 co :3.85 --

APPENDIX -FIG. SE

PIGuRE27- spillways with OverfdJ- sup~es~d*

32



-1.0 01L

1.0

M~n!*‘ki?AM

HO 4.0. G, 7 3.28 -

P+E ’ 2.57 ‘GQ = 3.80---

CONTRACTION IN CHUTE D.S.APPENDIX - FIG. 9F

HO

DEER CREEK DAMHo 5.0 h - 3.46 -

P+E = 4.22 CD = 3.61 ---

CONTRACTION IN CHUTE 0.S.

APPENDIX - FIG. 9G

--

-1.0 0

ALAMOGORDO DAM

& = ::282%I - 3.18 -

c,, = ?,.79---

CONTRACTION IN CHUTE D.S.APPENDIX - FIG. 9H

FIGURERS- spillways with overhll. suppre ssed.

SHEET 8 OF II

33



MEDICINE Cl&ii: DAM (LOW CREST)

HIJ 4.53

P+E’ 3.74

CN = 3.54

CQ = 3.73APPENDIX- FIG. IOC

0

&

0.5

\ A-r.

-1.0 0 r I.0 2.0 2

P+E=

4.0 Cu= 3.56

3.3 Co: 3.76APPENDIX-FIG. 100

-1.6 0X

1.0 2.0

DICKIN%N DAM

&= 2.75 CM=o =3.75.60APPENDIX -FIG. IOB

FIGURES- spiU.~ays with overfall suppressed.

SWEET 9 OF II 34



YHo

0

-0.5

-I

1.0

I

Ho

0

-0.5

YHo

-

\ \\

‘\

/-

I I I I

x 1.0 2.0 :

CACHlJitA DAMHo 5.0

FE= 3.55

Cu=3.42 -

CD ~3.76 --APPENDIX -FIG. IOA

?.& 1.0‘ 2.0

FALCON DAM

Ho 3.44

P+E= 2.50

c&=3.33 -

CD”3.78 --

r-1 I

APPENDIX-FIG. 110

1 I I I I I-1.0 0 X I.0

HORSE&E DAM

P+E=

4.75 Gu”3.20 -

2.54 --APPENDIX -FIG.

c‘, =3.74116

FIGURE 30 - Spillways with overfdl suppressed.

3.5SHEET 0 OF I I



Y

F.

0

-0.5

-1.0 0L

I.0 2.0 2.5

Ho

CASCADE DAMHO 6.67 c,” = 3.38 -

P+E ‘4.75 Go = 3.57 ---

APPENDIX -FIG. IIE

XI.0

zHo

TIBER DAM(WITHOUT CURTAIN WALL)

HO 3.49 CM = 3.49 -

P+E 2.77 c, = 3.77 - - -

APPENDIX- FIG. IIA

,I.0 0&

‘.O 2.0

HO

BOYSEN DAM(FINAL DESIGN)

“0 5.20 3.45 -

P+E =

cm =

4.5 I c, = 3.57 ---

APPENDIX- FIG. IIC

2.5

FIGURE 31- spillway6 With OV8l?fa SUp$W3668d.

SHEET II OF II

36



N01133S 13NNVHE- l 11x3 N01133S 33NVMlN3002522 13

00’69223,’.__...&+O~r(

: ;k ..p __., ooo(.~ ----j ^. _. : L .. .._ ........ l-ml......

-ipog F.. ........ .,gveg ..... ,_. _. ,~~.FZ 01. ’

NW-Id



0

Ho

A- PROFILE OF GATE SECTION

3.1 3.2 3.3 3.4 3.5 3.6

c in Q=CLH%

B- HEAD- COEFFICIENT CURVE

FIGURE 33 - Kachess Dam Spillway (Examples 2 and 4).

38



I I I I II 11 ” ’ “1

0 llllllllll~~ll

0.9 0.9 r 1.0 I.

vCO

-9-----r -----j

ha

SPILLWAY

I

FIGURE 34 - Coefficients of discharge for other than the aesign head(free overfall spillways).

39



I Ig SPI LLW --’Ihd+d (Actual)

P+EAl

I.3 Fresno I .64

3.7 Boysen (Prelim.) .852.6 Gob IOIIO .66 I

FXXRE 35 - Coefficients of discharge for other than the design head(spillways with overfall sup~essed).

40



APPENDIX

41



1 a1/ /I 1

/’/ /



A. M A R S H A LL F O R D D A M S P I LLWA Y,CINAL OESION,

M O D E L S C ALE 140 . 9RES. ELE”. 7420

PIE-9149'w, - 29.0 2: * . :09: -. o”*\v

8. HOOVER DAM SPl+LWAYSHIPE s- F lNlL MODEL c-6

MoatL 6Cbl .E 1:20MS. ELE”. IL32.0

: ; E = $&8:: :.“o: _z g:“r”,p

SPILLWAY S ECTIONS WITH VERTICAL IJPSTREAU FACF

c. MADDEN DAM SPILLWAYM O D E L S C & LE 1 : 72

R E S E LE V 265 . 4; : E : 1; ,z4,w C. . 3.71 - YOOEL

c.- 3.97--- OI,“Y

0. MARSHALL FORD DAM SPILLWAYUNlT lAL OESlCN,

M O D E L S C LLE 1 : 4oaRES ELE”. 670.0

: : E = ;$y’ C. - 3.96 -MODELc,- 3.9s---MTuY

E. ROSS,~D~A~QPILLWAY

M00EL”9C.LE I :60RE9 ELE”. 15450

‘H; E : h’b”os’ I&- 3.64 - MODELc.= 3.97 - -- o.,&al

SPILLWAY SECTIONS WITH SLOPING UPSTREAM FACE

FIGURE2 - Compewlaon of discharge coefficientsModel coefficient versub datum coefficient

for spillway sections with vertical endslapltq upstream faces


http://slidepdf.com/reader/full/coeficiente-de-descarga-para-vertederos 50/5945.



A. HIRAKUD DAM SPILLWAY 8. MEDICINE CREEK DAM SPILLWAY (HIGHCICST)

YOotL SCALE I ’ *0 YOOLL ,CALE 1’0 0“C, . LLCY. .10.0 ILS. ELL ”. *101.,0

He = 17.0’ cr= , .m-YODEL HO =2*7 c.. , ,o--YODELPtE-lOs ce= s.w-- -clAT”Y PtE-2e.2 co= I.‘)O-----D.T”Y

c. CEOAR BLUFF DAM SPILLWAY

YODEL SCALL , : .aR E S LLE Y 21930

Ho= !a?’ Cr’ +a*----YODELPtE”O8’ cs = 3.8~----DAI”Y

t? TRENTON DAM SPILLWAYYODEL SCLLE 1:s.RLI . LLE”. 21~100

FIGURE4 - Caqarieon of diecharge coefficienteModel coefficient versus datum coefficient

Mlscellaneou6 qd.llway shape6



0. ANGDSlURA DAM SPUWAY

UODEI. SCILC I : IL“ES. CLL”. II,,.,

g c : fff: C.. S.ss-YODcLc..3..7----Dm”Y

8. FRIANT DAM SPILLWAY

YODEL SC.LC , :soRES. LLL” . o, , .o

‘ .p : f ,qodp C. . S.SS-YODLL0,. s..s----DA,uy

E . D A V I S D A M S P H LWA Y

M O D LL S C A LE 1 : 100*Es. LLL V. WT.0

CIC . *o.o,“. 06000

CW S.WWDCL4. s.s.----0mn

IN FEE,

G. S H A S T A D A M S P I LLWA Y

F. DAVIS DAM SPUW

,FIWAl. Dtslo”,

YODLL *cALI ,:*o

FICURPj- Comparison of diecharge coefficlentr 3Model coefficient verma datum coefficientfor spillway with irregular upetream faces



I ’S

I A/I I s,.\ _

48



A. R Y E P A T C H D A M S P ILLWA Y

YODEL SOILL InsoRES. ELE”. 412, -o

” C.61% I

4. * . I , -YOOLL

14.1 4c, ,.71---UKnJY

t t .GREEN MOUNTAIN DAM SPILLWAY

,F lNlL DESIGN,

MODEL S0l l .E 1*40“ES. ELE”. 1950 0

%o ‘ : , ’( * . a. * , - YODEL0, . 3.76 - - -DATUM

19.76 6.96CONT”,OT,ON O.S. CROM SAT6 SECTlO”

E. A LC O V A D A M S P I LLWA Y

“00 s

RES ELE” ssoogP.C h.2 66 - UOOLL

C,., SO---DAWN53 s 11.5

FIGURES- Comparison of discharge coefficientsModel coefficient versus datum coefficient

for earth dam spillway sections with&allow approauh depth

c. PINE VIEW DAM SPILLWAY

UODEI. S0I l .E , * ,oRES ELE'A,6100

”I% ‘4’ E

0. . * . , . -MODEL

IL.9 1.1c..1.66---oLT"u

CONTRACTION D.S.FROM OATS SECTtON

F. SHADOW MOUNTAIN DAM SPILLWAY

M O D E L S C A LE b30RES ELE” 63610

Ho P.E Cr. ,.lO-MODELI9 1.0 G..3.76---OITUYI,., 1.4



A. ANDERSON RANCH DAM SPILLWAY

&lAtC:c~s~oi!:oI)El. CLEW .lS‘.O

E. BOYSEN DAM SPILLWAY,PRLLIMI”A”” OE6IONlYcmLL SCA‘L ,:oo

RES. ELE” 4711.6

c. QRANBY OAM SPILLWAY(FINrL OESlON I

WODEL SCILE I:.*RES. ELL”. SP76.0

FIGURE 8 - compcW1s0n of discharge coefficlerltsModel coefficient versus datum coefficient

for earth dam splllway sections withshallow approach depth



I .:

51



I I‘.w Oriqin ot cr55t oxir

I I Iii I I

A . C A C H U M A D A M S P t LLWA Y

YOOEL JCLLE I :60“LS. LLC”. 737.6

,“I.*1e.t

‘7$9.9’

o.= ,.*P--UOoELcD’1.7*--- DATUY

OISTANCL I” n-5,

B. DICKtNSON DAM SPILLWAY

UOOLL SCALL 1:3*ICI . ELE”. e. tmo

He P+Ete.4 4.5 C. - s.ts --YODELte.4 4. , C~=3.~0-- -oA7”Y

C. M~Dlc~~~~~f tE~~; “ ;A$ SPILLWAY (LOW CREST 1

IL, . CLE” L3¶*JO

3:sCtE

7.9. C”’ 5.84 “OOEL,I.* ..* co= ,.,I----DATUM

0 . K E Y H O LE D A M S P I LLWA YY O D E L S C A LE LP IREI. ELC”. 4lL1.10

2% ‘7Y C.=,.Se YOOLLCT.0 e.4 C~=3.,,---0*7”Y

FIGURE10 - Comparison of discharge coefficientsModel coefficient vt3rSus datum coefficient

for earth dam aplJ-lway sections with&allow approach depth



i I/ I III A

,o

--- -------- --_ ,$‘ F(I ____ I A! I

t i iir’i SI/ I I

n

T 4

53

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