Dam Design

HYDRAULIC DESIGN CRITERIA

SHEETS 111-16TO 111-16/2

HIGH OVERFLOW DAMS

CREST PRESSURES

1. Hydraulic Design Charts 111-16to 111-16/2presentcrest pressures for H/~ values of 0.50, 1.00, 1.17, 1.33,

plots ofand 1.50.

The charts are based on recent ES 801 test data* for crests with and with-out piers: Chart 111-16represents pressures on crests without piers;Chart 111-16/1,pressures midway between piers; and Chart 111-16/2,pres-sures adjacent to piers. Piezometers used for measuring the last conditionwere located immediately adjacent to the pier face.

2. The data shown are applicable to high overflow dams with standardcrests. Data are plotted in terms of the dimensionless factors, pressuredivided by design head (hp/Hd) and horizontal distance divided by designhead (X/Hal),to permit ready conversion to any selected design head. Pres-sures for intermediate head ratios can be obtained by plotting hp/~ ver-sus H/Hal for a given X/Hal .

3* It is recommended that the spillway design head ~ be selectedso that the minimum crest pressure for the maximum expected head H be nolower than -20 ft of water to ensure cavitation-free operation.

-—

* U. S. Army Engineer Waterways Experiment Station, CE, Investigations ofVarious Shapes of the Upstream Quadrant of the Crest of a High Spillway;Hydraulic Laboratory Investigationz by E. S. Melsheimer and T. E. Murphy.Research Report H-70-1, Vicksburg, Miss., January 1970.

-

111-16to 111-16/2Revised 3-55Revised 9-70

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)3 -02 -o I o 01 02 03 0.4 05 06 07 08 09 10 11 1.2 1.3HORIZONTAL DISTANCE X

DESIGN HEAD [1~

F’=2H’85Y

NOTE. DATA BASED ON ES801 TESTS

HIGH OVERFLOW DAMSCREST PRESSURES

NO PIERS

HYDRAULIC DESIGN CHART 111-16

PREPARED BY u s ARMY ENGINEER w#. TERw AYS Experiment sTATION, VICKSBURG, MISSISSIPPI REV 3-55, 9-70 WES 9-54

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-1 0-03 -02 -o I o 01 02 03 0.4 05 06 07 08 09 10 II 1.2

HORIZONTAL DISTANCE

()

&

DESIGN HEAD Hd

1.3

HIGH OVERFLOW DAMS

CREST PRESSURESNOTE. DATA BASED ON ES801 TESTS

CENTER LINE OF PIER BAY

HYDRAULIC DESIGN CHART 111-16/1

PREPARED BY u s ARMY ENGINEER WATERWAYS EXperiment STATION, VIc K5i3u RG, MISSISSIPPI REV 9-70 WES 3-55

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1)

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DESIGN HEAD Hd

TYPE 3A PIER

AXIS BOTH QUADRANTS (CHART 111-51

w

HIGH OVERFLOW DAMSCREST PRESSURES

NOTE DATA BASED ON ES801 TESTS ALONG PIERS


PREPARFD BY U S ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISS15SIPP( REV 9-70 WES 3-55

.- HYDRAULIC DESIGN CRITERIA

●SHEET’111-17

HIGH OVERFLOW DAMS

PRESSURE RESULTANTS

1. In certain stability problems it is desirable to determine theactual pressure forces acting on the upstream face of the dam rather thanto assume straight-line pressure distribution near the crest. HydraulicDesign Chart 111-17 presents a plot of experimental data showing pressuredistribution in terms of the design head. The data pre ented are based on

rCW 801 tests for crests without piers and on USBR tests 1, of pressures ona sharp-crested weir for H/Hal= 1.00. The location and magnitude (in termsof the design head) of three resultants based on integration of the pres-sure plot between the limits of O < y < 1.5 Hd are also shown. The cross-hatched area (RI) is a pressure reduction to be applied to the normallyassumed pressure acting on the vertical face of the dam. Sufficient pres-sure data on the vertical face are not available to allow computation ofthe resultant (Rl) for H/Halvalues of 0.50 and 1.33. R2 is the verticalpressure resultant effected by flow over the curved surface of the crest.R3 is the horizontal pressure resultant effected by the flow downstreamfrom the spillway crest.

‘L.

(1)“Studies of Crests for Overfall Dams, Boulder Canyon Project,”

Final Reports, Part VI, Bulletin 3, Bureau of Reclamation, 1948.

‘—

111-17Revised 8-58

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———_—.—

HYDRAULIC DESIGN CRITERIX

SHEETS 111-18 TO 111-18/5

SPILLWAY ENERGY LOSSES

1. An estimate of the loss of energy on the downstream face of ahigh overflow spillway may be important in the design of energy-dissipatingdevices at the foot of the spillway. If the losses are substantial, theirevaluation is desirable in order to design an economical stilling basin orto estimate the throw of a jet from a flip bucket. The problem is twofold:(a) determination of energy loss during development of the turbulent bound-ary layer, and (b) determination of energy loss in the fully developedturbulent flow. For a large head on the crest with the spillway designflow, usually only (a) need be considered. HDC 111-18 to 111-18/5 applyto the condition of turbulent boundary layer development.

2. Previous Design Criteria. It has been common practice to use theManning equation or some other open-channel equation to determine spillwayenergy losses. Gumensk~ based an analysis on the Manning equation and pub-lished a graph which has been widely used. Jansen2 proposed an empiricalequatio

fbased on Randolph’s3 observation on Madden Dam. Bradley and

Peterka published a graph which reflects spillway losses as indicated bytests on Shasta and Grand Coulee Dams. In general, the results obtainedby these methods do not agree.

3. Boundary Layer Theory. The concepts of displacement thicknessand momentum thickness of the boundary layer are discussed in modern fluidmechanics textbooks.5 The concept of energy thickness, which is useful inthe spillway energy-loss problem, has appeared in the literature onlyrecently. Schlichting6 makes reference to the use of the energy thicknessby Wieghardt.7 The decrease in energy flux in the boundary layer causedby friction is found by:

where b is the boundary

/

6

*P $0 u ( - U2)dY (1)

layer thickness as indicated in the definitionsketch in HDC 111-18, u is the velocity at a distance y from the bound-ary, and U is the potential flow velocity. By definition, the energythickness 83 is the thickness of a layer of fluid with velocity U whichrepresents the loss of energy flux in the boundary layer:

(2)

(3)

111-18 to 111-18/5

If 63 can be estimated, the energy flux loss upstream from any point onthe s~illway face can be found from:

Division of equationthe specific weight,of head:

3km‘L=2 3

(lb/see)

4 by qy , where q is the unit discharge andresults in defining the energy loss in terms of

2

6.UJ

%3

= 2gq(feet of head)

where g is the acceleration due to gravity. The evaluation of bU is discussed below. 3

(4)

y isfeet

(5)

and

4. ‘Turbulent Boundary Layer Investigations. During spillway dis-charge, the turbulent boundary layer continues to develop until it reachesthe free-water surface or until ~he flow enters the energy dissipator atthe toe ofcorrelatedroughness.reanalyzed

the structure. Bauerb>g made extensive laboratory tests andboundary layer thickness and development length (X) with surfaceHis analysis included limited protot~e data.lo KeuleganllBauer’s data and proposed the equation

6 ()++

Y = 0.96 ~

where X is the distance from an assumed origin and k is the absolutesurface roughness height.

(6)

839 data, Keulegan s5* Spillway Energy Losses. A study of Bauer’s , 11

reanalysis, additional prototype dat ,128

and photographs* has been made bythe Waterways Experiment Station13~1 to develop design criteria for esti-mating spillway energy losses. This study resulted in the curve given inHDC IH-18 which is applicable for estimating the boundary layer thicknessin flows over spillways. The equation of the curve is:

6

()

-0.233

c= 0.08 ; (7)

where L is the length along the spillway crest from the beginning of thecrest curve (HDC 111-18). A roughness k value of 0.002 ft is recommendedfor concrete.

* Unpublished photographs by the U. S. Army Engineer District, Vicksburg,Miss., of flow over the spillway of Arkabutla Dam, Coldwater River,Mississippi.

111-18-tO111-18/5

6. The relations between boundary layer thickness b , displacementthickness 51 , and ener~ thickness 53 , based on Bauer’s data for screenroughness, have been found to be:

5 = 0.2253

(9)

The use of these relations in conjunction with the potential flow depth andequations 5 and 7 are recommended for estimating spillway flow depths andenergy losses. Modifications to equations 7, 8, and 9 may prove desirableas additional data become available.

7. Application.

a. Case 1. The boundary layer thickness 5 , the flow depth—, and the spillway energy loss HL for design heads of

~0, 30, and 40 ft can be estimated directly fromHDC 111-18/2and 111-18/3 for the standard crest shape defined byHDc 111-1 to 111-2/1. The use of HDC 111-18/2and 111-18/3is applicable to spillways with tangent face slopes of 1:0.7and a surface roughness k of 0.002 ft. HDC KL1-I-8fl illus-

trates the required computations. The computations indicatethat the boundary layer has not reached the free-water sur-face. Therefore, no bulking of the flow is to be expectedfrom air entrainment caused by turbulence generated at the.spillway face.

b. Case 2. For the standard crest shapes with face slopes other—than 1:0.7, HDC 111-1, 111-18, and 111-18/I- and equations 5,8, and 9 should be used in the manner illustrated by the sam-ple computation given in HDC 111-18/5. If the computedboundary layer thickness is indicated to become greater thanthe summation of the displacement thickness and the potentialflow depth, the intersection of the free-water surface andthe boundary layer, sometimes called the critical point, canbe located. This can be done byand boundary layer thickness 6length as shown in HDC 111-18/2.yond the critical point, and thewell understood.

plotting the flow depth das functions of the boundaryAir entrainment begins be-energy-loss mechanism is not

c. Case 3. For other than the standard crest shape, the curved—crest length Lc is determined graphically or analytically.The computation procedure is then similar to that for Case 2.

8. References.

(1) Gumensky,ing walls

1949), PP

D. B., “Air entrained in fast water affects design of train-and stilling basins.” Civil Engineering, vol 19 (December831-833, 889.

111-18to 111-18/5

(2) Jansen, R. B., “Flow characteristics on the ogee spillway.” ASCEHydraulics Division, Journal, vol 83 (December 1957), pp 1452-1 to1452-11. ._.

(3) Randolph, R. R., Jr., “Hydraulic tests on the spillway of the MaddenDam. “ Transactions, American Society of Civil Engineers,(1938), pp 1080-1112.

Vol 103

(4) Bradley, J. N., and Peterka, A. J., “Hydraulic design of stillingbasins.” ASCE Hydraulics Division, Journal, vol 83, HY 5 (October1957), pp 1401-1 to 1406-17.

(5) Rouse, Hunter, Advanced Mechanics of Fluids. John Wiley & Sons, Inc.,New York, N. Y., 1959.

(6) Schlichting, H., Boundary Layer Theory. English translation by

J. Kestin. McGraw-Hill Book Co., Inc., New York, N. Y., 1960.

(7) Wieghardt, K., “Ueber einen Energiesatz zur Berechnung laminarerGrenzschichten (Concerning an energy principle for calculation oflaminar boundary layer).” Ingenieur-Archiv, vol 16 (1948), p 231.

(8) Bauer, W. J., The Development of the Turbulent Boundary Layer onSteep Slopes. A dissertation submitted to State University of Iowa,August 1951.

(9) “Turbulent boundary layer on steep slopes.” Transactions,American S~ciety of Civil Engineers, vol 119 (1954), pp 1212-1233.

.—

(10) Hickox, G. H., “Air entrainment on spillw~ faces.” Civil Engineering,vol 15 (December 1945), pp 562-563.

(11) U. S. Army Engineer Waterways Experiment Station, CE, TurbulentBoundary Layer Development on Spillways, by G. H. Keulegan. Miscel-laneous Paper No. 2-587, Vicksburg, Miss., July 1963.

(12) Michels, V., and Lovely, M., “Some prototype observations of airentrainment flow.” Proceedings, Minnesota International HydraulicsConvention (August 1953), pp 403-414.

(13) U. S. Army Engineer Waterways Experiment Station, CE, A Study ofSpillway Energy Losses During Development of the Turbulent BoundaryLayer. Miscellaneous Paper No. 2-642, Vicksburg, Miss., April 1964.

(14) Office, Chief of Engineers, Department of the Army, Engineering andDesign; Hydraulic Design of Spillways. Engineer Manual EM 1110-2-1603,Washington, D. C., March 1965.

111-18-tO111-18/5 .

‘-----

L

0.100

0.080

0.060

0040

0.020

&L

0010

0.008

0.006

0,004

0.002

0.0012 x 10” 3 4 6 8 104 2 3 4 6 8 10=

~K

—

L

DEFINITION SKETCH

PREPARED BY U, S ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG MISSISSIPPI

6= BOUNDARY LAYER THICKNESS, FT

L= SURFACE LENGTH, FT

K= ABSOLUTE SURFACE ROUGHNESSHEIGHT, FT

OVERFLOW DAMSHIGH

SPILLWAY ENERGY LOSSBOUNDARY LAYER DEVELOPMENT


WES 1-66

3.5

NOTE CURVE APPLICABLE TO CREST SHAPE

DEFINED BY HDC Ill-1 TO 111-2/1.

3.0

i

2.5 i ‘

/ ‘

2.0 / ‘

r

/ ‘

1.5

/ ‘

A

{

1.0

/ ‘

/ /

/

1-

0.5 A

UPsr REAM WAD RANT LENGT H = o.3f 5 #(i

DEFINITION SKETCH1 , t , , t

0.00.0 0.5 1.0

+1.5 2.0

x2.5

~

NOTE: Lc = LENGTH ALONG CURVED CREST, FT

x = HORIZONTAL COORDINATE, FT

Hd = SPILLWAY DESIGN HEAD, FT

HIGH-OVERFLOW DAMS

SPILLWAY ENERGY LOSSSTANDARD CREST LENGTH

HYDRAULIC DESIGN CHART 111-16/ I

PREPARED SY u s ARMY ENGINEER WATERWAYS EXPERIMENT s7AT10N, VICKSBURG, MISSISSIPPI wES 1-66—

30

20

I [ I I I I I I I I

I

<a#>+++..*________k-----i

r—‘}--#--- ‘“- --‘wI I I I I I I I I NJ [,.—. — -——-

4.-+- . ..

+ I 4-- -w !-- ,x ----- ..-

. . . . . - . .

3 l-+! 1 1 1 1 1 s I 1 1 1 1 1%

—.——. —. .—-.

f I I [ I I I [ I— .—. — .—— —- —...—— —. .—.

I / I I [.-_. —_ —.— _— _ . .

-.,1 I 1,

1/1 -_-_---t-–---+ “---- P++ -tt-- ‘-- -

dOR

61

I .-.— ,

I .—+ ...-— 1

I f—.—— —— . .

{ .—-t x

2 -“: I /,.—-——.

I ./ 1---T L 1 1

—-

- +—-—— -–- – - -–

—.—. . ——.—

,1 1 I P- I I

I_iiiiiiiii iiiI

1’ I A I

‘-

---- .,- ,., -.OW DEPTH, FT

e = BOUNDARY LAYER THICKNESS, FT

6, = DISPLACEMENT THICKNESS, FT

U ❑ POTENTIAL VELOCITY, FPS.,. -

~ = POINT VELOCITY, FPS

3

L = TOTAL LENGTH TO SECTION, FT ‘~~ :

HA = SPILLWAY DESIGN HEAD, FT

I I I I I

~ -+--—” ‘1-- ,- .--- .,,_- - _,, - .,--------. -1

Ibllt *f! I I I [ [ 1 1 1 1 ‘ tF+--+ “—---i ‘ K = AM> WLUIL KVUbli NL3>, t I . . i

L

NOTE: CURVES APPLICABLE TO STANDARD

1SPILLWAY CREST CHDC II I-I TO 111-2z I)WITH 1:0.7 TANGENT FACE SLOPE.

DEPTH (d) IS POTENTIAL FLOW DEPTHPLUS DISPLACEMENT THICKNESS.

d

t6 L HIGH - OVERFLOW DAMS

SPILLWAY ENERGY LOSSSTANDARD CREST

t 6 LOCATION OF CRITICAL POINTDEFINITION SKETCH


PREpARED BY u s ARMY ENGINEER WATERWAYS EXperiment STATION, VICKSWURG, MISSISSIPPI WES I -66

----

HL

L

LEGEND

HL=ENERGY HEAD LOSS, FT

L =TOTAL LEN GTHTOSECTION, FT

Hd ‘SPILLWAY DESIGN HEAD, FT

HIGH- OVERFLOW DAMS

SPILLWAY ENERGY LOSSSTANDARD CRESTFACE SLOPE 1:0.7

HYDRAULIC DESIGN CHART II 1-18/3

PREPARED BY U 5 ARMY ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG, MISSISSIPPI WES I -66

GIVEN:

Hd = 30 ft

H = 250 ft

k = 0.002 ft (Surface roughness)

Face slope = 1:0.7

COMPUTE:

1. Boundary Geometry

a. Length of curved crest, L ~

x,—= 1.67 (HDC 111-1)Hd

Lc—= 2.50 (HDC 111-18/1)Hd

LC = 2.50Hd = 75.0 ft

b. Length of tangent, L~

Y,—- 1.32 (HDC 111-1)Hd -

Y, = 1.32Hd =39.6 ft

Y2 -Y, =250 -39.6 =210.4ft

x2 -X,=%(Y2-Y, ) = 147.3 ft

!Hd

H 11

Y

0.7

2. Hydraulic Computation

a. Spillway energy loss, H~

For L = 331.9 ft and Hd =30 ft

H~ = 20.0 ft (HDC 11 1-18/3)

b. Energy head entering stilling basin, Hb

Hb=H+Hd-HL

=250+ 30-20 =260ft

c. Depth of flow, d, and boundary layer

thickness, 8, at PC of toe curve

d = 5.30 ft (HDC 11 l-18\2)

8 = 1.62 ft (HDC 11 1-18/2)

LT = ~(210.4)2 + (147.3)2

= 256.9 ft

c. Total crest length, L

L= LC+LT

= 75.0 + 256.9 = 331.9 ft

Note: Computed H ~ is satisfactory and no

bulking of flow from air entrainment

since 8< d.

HIGH OVERFLOW DAMS

SPILLWAY ENERGY LOSS

SAMPLE COMPUTATIONFACE SLOPE I :0.7

PREPARED BY U S ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISSISSIPPI

HYDRAULIC DESIGN CHART I II -18/’4

WES 1-66.

GIVEN:

Hd ==30 ft\ H = 350 ft

k = 0.002 ft (Surface roughness)

Face slope = 1:0.78

COMPUTE ENERGY HEAD

ENTERING STILLING BASIN:

1. Boundary Geometry

a. Length of curved crest, LC

$= 1.47 (HDC 111-1)

d

; = 2.15 (HDC 111-18/1)d

LC = 2.15Hd = 64.5 ft

b. Length of tangent, LT

Y,

~ = ‘“04 (HDC “’-’)

Y, = 1.04Hd =31.2 ft

Yz -Y, =350 -31.2 =318.8ft

Tana. ~. 1.2821

sin a= ().7885Y* -Y,

LT =Sin Ct

= 404.4 ft

c. Total crest length, L

L= LC+LT

= 64.5 + 404.4= 468.9 ft

2. Hydraulic computation

------

a.

b.

c.

Boundary layer thickness, 8

L 468.9~=~= 2.344 X 105

U -0.233

& 0.08 ; (HDC 11 1-18)

= 0.08 (0.0561)

= 0.00449

8=2.loft

Energy thickness, 83

83 =0.228(Eq 9, sheets 111-18 to 111-18/5)

==0.462 ft

Unit discharge, q

q = Cti~’2C = 4.03 (HDC 111-3)

q = 4.03 (30)3/2 = 662 cfs

Note: Computed Hb satisfactory and no bulking

of flow from air entrainment since 8< d.

L- PREPAREDBYuS ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISSISSIPPI

d.

e.

f.

9

I ‘d

1H IY 1

0.78

x

Potential flow depth

PC of toe curve

dP and velocity U at

H .d COSU+UJTp 2g

COS a= 0.6150

HT=H+Hd =350+ 30=380ft

By trial

upu —

2g

(ft) l–(ft)—

156.0 377.9

155.9 377.4

(ft)

2.1

2.6

(jP =

-’---upH -—

T 2g

0.6150

(ft)—

3.41

4.23

(Cfs)

532<662

659 = 662

Spillway energy loss

8 usHL= fi(Eq 5, sheets 111-18 to 111-18/5)

0.462 (155.9)3 = A, ft.64.4 (662)

Energy head entering sti Iling basin

ti#-i+tid-ti L

=350+ 30-41 =339ft

Depth of flow, d, at PC of toe curve

d=dp +8,

8, = 0.188 (Eq 8, sheets 111-18 to 111-18/5)

= 0.18 (2.10) = 0.38 ft

d =4.23 + 0.38 =4,61 ft

HIGH OVERFLOW DAMS

SPILLWAY ENERGY LOSS

SAMPLE COMPUTATIONFACE SLOPE I I0.78

HYDRAULIC DESIGN CHART I I I - 18/5

wES 1’66

.—

HYDMUTJC DESIGN CRITERIA

SHEETS 111-19To 111-19/2

HIGH OVERFLOWDAMS

-

SPILLWAY CREST WITH OFFSETS

Cl%lLSTSHAPES

AND RISERS

10 Purpose. Use of spillway crests with offsets and risers mayeffect appreciable economies in the construction of concrete gravity spill-ways provided the concrete mass eliminated from the standard crest shapedefined in HDC 111-1 to 111-2/1 is not required for structural stability.The scheme has also been adopted for the high arch dam Monteynard.lHDC 111-19 to 111-19/2 shotid serve for developing crest shapes for prelim-inary economic studies. It is suggested that the final spillway shape bemodel-tested.

2. Background. A laboratory study of overhanging crests produced byan offset in a sharp-crested weir was reported by the U. S. Bureau of Rec-lamation (USBR).2 A recent analysis of unpublished USBR test data was madeby the Waterways Experiment Station (l?ES). In this study the dimensionlessquantity of the ratio of the riser height to the head on the rounded crestM/Hd was selected as the basic shape variable. The offset dimension Ndoes not appear to be very effective until the ratio M/Kd becomes verysmall ● One limiting case is the offset weir with no riser (M = O), whichforms a 45-degree backward-sloping weir. The lower nappe of the flow overa 45-degree backward-sloping, sharp-crested weir may extend initiallyslightly upstream of the sharp crest. The other limiting case is a highspillway with no offset (N = O) described in HDC 111-1 to 111-2/1. Thetest data selected for the WES study were from experiments with negligiblevelocity of approach, a condition representative of a high dam for whichsubstantial savings in concrete would result from undercutting the upstreamface. These data were for M/lid test values of 0.240 to 0.396 havingN/Hd values of 0.079 to 0.240. The resulting M/’N values are 1.0 to 5.O.Sections having Mm values less than 0.5 are not recommended.2 The re-sults of this study are summarized in HDC 111-19 to 111-19/2 and generallydefine spillway crest geometry for riser-design head ratios ofo <M@d <1.().

3. Crest Location. The USBR lower-nappe coordinates are in terms ofthe head on the sharp-crested weir and have their origin at the weir. Fordesign purposes, it is more convenient to have the coordinates in terms ofthe head Hd on the round crest with their origin at the crest apex.HDC 111-19 gives curves for estimating the distance Xe of the round crestfrom the sharp crest and the height Ye of the round crest above the sharpcrest. The curves are in terms of the design head Hd on the round crest

and are plotted as a function of the ratio of the riser height to designhead M/Hd . The values of Xe/Hd and ye~d were feud to be 0.287 and0.166, respectively, for the limiting case of M/Hd=O. HDc 111-2/1

111-19tO 111-19/2

gives values of 0.2T0 and 0.126 for Xe~ and

the case of M/Hd ~ 1.0 . These limiting casesand were used as guides in defining the generalin the chart.

ye~ , respectively, forare plotted in HDC 111-19shape of the curves given

4. Downstream Quadrant. The standard form of the equation for thedownstream quadrant with the head on the round crest is:

Yn

()—=K$‘d d

(1)

Values of the constant K and the exponent n for various ratios of M@dwere determined graphically and by electronic computer. Values of n andK resulting in best correlation with the basic data are plotted in graphsa and b in HDC 111-19/1. Data points appropriate for the limiting casesdiscussed in paragraph 3 are also shown. The vertical-face spillway de-fined in HDC 111-1 has n and K values of 1.85 and 0.50, respectively.It is reasoned that the values of n and K shotildapproach these limitsasymptotically as the riser height M becomes larger in relation to thedesign head Hd .

5. Upstream Quadrant. The standard form of the equation defined inHDC 111-1 to 111-2/1 for the upstream quadrant of the vertical-face weirwas used as a basis for the case of weirs with offsets and risers:

(2)—

The subscript w refers to the sharp-crested weir. The conditions estab-lished for developing the exponents and constants of the equations included:

a.

b.

c.

d.

dYwCurve slopes — of zero at the round crest and of infinity

%

at the sharp-crested riser for the selected values of ‘e/Hdand ye/Hal “

For M@d values > 0.24, the exponent nl of the first termhas the value of 0.625developed for the vertical-face weirusing relaxation data of McNown and others3 discussed inHDc 111-1 to 111-2/1.

The exponent n of the second term is the same as thatdeveloped for the downstream quadrant.

The constants K1 and ~ developed to provide a reasonablefit to the experimental data.

6. Computed values of exponents and constants for equation 2 basedon the selected USBR data are plotted in graphs a and c in HDC 111-19/1.The plotted points meet the conditions established in paragraph 5.

111-19 tO 111-19/2 -—

‘=.-

7. Application. The crest shape defined in HDC 111-1 to 111-2/1should be applicable to overhanging spillways having riser heights~o.6~ . Use of the curves in HDC 111-19and 111-19/1is suggested forpreliminary design purposes should there be design reasons for making theriser smaller than 0.6~ . The curves on these charts should be used inthe reamer indicated by the sample computation given in HDC 111-19/2. Thefinal design should be model-tested. The use of a curvature of appreciableradius to connect the riser to the sloping overhang is recommended if modeltests indicate pressure pulsations on the crest resulting from flow separa-tions around the riser.

(1)

(2)

(3)

8. References.

Bowman, W; G., “French high arch dam is all-in-one (MonteynardDam).”Engineering News-Record, vol 169 (25 October 1962),pp 30-37.

U. S. Bureau of Reclamation, “Studies of crests for overfall dams.”Boulder Canyon Project Final Reports, Part VI, Hydraulic Investiga-tions, Bulletin 3, Denver, CO1O. (1948).

McNown, J. S., Hsu, En-Yun, and Yih, Chia-Shun, “Applications of therelaxation technique in fluid mechanics.” Transactions, AmericanSociety of Civil Engineers, Vol 120 (1955),pp 650-6690

‘“—

1w19 tO m-19/2

___

------

Hd

Iw

1r

Ye

M

DOWNSTREAM QUADRANT UPSTREAM

x~

iq

0.2

Ye

~ \

o. I0.0 0.2 0.4 0.6 0.8 1.0

M.

BASEDON UNPUBLISHED USBR DATA

BASEDON PUBLISHED USBR DATAHDC ill-2/l

NUMBERS ON GRAPH ARE VALUESOFN/Hd.

Hdis DESIGN HEAD BASEDON LOWERSURFACE OF NAPPE FROM SHARP-CRESTEDWEIR WITH NEGLIGIBLE VELOCITY OFAPPROACH,

PREPARED 8Y U 5 ARMY ENGINEER WATERWAYS EXPERIMENT 5TATION, VICKSBURG, MISSISSIPPI

HIGH-OVERFLOW DAMSSPILLWAY CRESTS

WITH OFFSET AND RISER

CREST LOCATIONHYDRAULIC DESIGN CHART 111-19

WESI -66

.

___

-—

-.

n

1.85

1.80 (

1.750.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.54

(

0.52

k

0.50

0.48000. I c

k,

(

0.6

E0“5\

0.4

0.30.0 0.1

M~

a. EXPONENT 17, DOWNSTREAM QUADRANT

.0. /57

0.079

●0.126

, ,0.132

2 0.3 0.4 0.5 0.6 0.7 0.8

Mm

COEFFICIENT K, DOWNSTREAM QUADRANTb.

:9 1.0

AZ

0.132.00.079

I0.240 ●

●0.126

g 0./57

‘l 0.240 .0.132~o.12 6 fi 0.079 . . .—— -—— ——

-0. /57

0.2 0.3 0.4 0.5

M1+~

c. COEFFICIENTS AND EXPONENTS,

LEGEND

● BASED ON UNPUBLISHED USBR DATAO BASED ON PUBLISHED USBR DATA■ HDC SHEETS 11l-1 TO 111-2/1 AND HOC II I-2

NOTE: NUMBERS ON GRAPHS ARE VALUES OF N/Hal.

Hd IS DESIGN HEAD FOR NEGLIGIBLE VELOCITYOF APPROACH.

PREPARED BY u 5 ARMY ENGINEER WATERWAYS EXPERIMENT 37 ATt0N, VICKSBURG, MISSISSIPPI

0.6 0.7 0.8 0.9

UPSTREAM QUADRANT

HIGH-OVERFLOW DAMS

SPILLWAY CRESTSWITH OFFSET AND RISER

1.0

0.9

kz

0.8

0.7

n,

0.6

0.5

1.0

CREST SHAPEHYDRAULIC DESIGN CHART I I l-19/l

WES I -66

GIVEN:

N

q= 0.25 ft

Negligible velocity of approach

COMPUTE:

1. Downstream Quadrant Equation

()

;=K + n

d d

K ==0.508, n = 1.825 (HDC 111-19/1)

()

1.825

; = 0.508 ;d d

2. Upstream Quadrant Equation

i= K+5’-KwK, = 0.405, K2 = 0.730

, = 0.6252 n = 1.825 1(HDC 111-19/’1)

n

Y ()0.625

— = 0.405 ;()

1.825

Hw-0.730 +

w w

3. Check for Zero Slope at Crest

x~= 0.282, & 0.130 (HDC 111-19)

d d

Hw=Hd+Ye =Hd+o.130Hd =l.130tid

x, x,

Hw =‘-0.250> $= , ,;; H

1.130Hd = 1.130-=0.115

jf]=Kln(~~’-1_K2~(~)nd

w

l—

k fit

4. Solve for Values Of K, and K2 Giving

xZero Slope at the Crest for & = 0.250

w

%= KG$’-KG)n0.115 = K, (0.250 )0”625 - K2 (0.250)

0.115= 0.421K, - 0.080K2

()d;w

0.625K, (0.250)-0-375x=

()d~

w

- 1.825K2 (0.2.50 )0”825 = O

1.05K, -0.583 K2=0

K, =0.554K2

1.825

(1)

Substitute Equation 2 into Equation 1

0.115 = 0.421 X 0.554K2 - 0.080K2

K2 =0.752, K, =0.416

Upstream Quadrant Equation

Y ()0,625

()

1.825

iTw= 0.416 ; -0.752 f

w w

(2)

_ 0.405 x 0.625— 0.730 x 1.825 (0,250)0825

(0.250)0$375 -

0.253

-0.5941.331 (0.319) = 0.002 * 0.000

HIGH-OVERFLOW DAMS

Note: For final design greater accuracy of

computations is recommended.

SPILLWAY CRESTSWITH OFFSET AND RISER

CREST GEOMETRYSAMPLE COMPUTATION

HYDRAULIC DESIGN CHART I I I -19/2

PREPARED BY u 5 ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MIsSISSIPPIWES I -66


SHEETS 111-20 TO 111-20/1

ELLIPTICAL CREST SPILLWAY

COORDINATES

1. Previous Crest ShaDes.

a. Downstream Quadrant. The U. S. Bureau of Reclamation(USBR) (reference 6) conducted extensive experiments onthe shape of the falling nappe over a sharp-crested weir.Using these data, the U. S. Army Corps of Engineers recom-mended that the 1.85 power of X be used to define thedownstream quadrant for a high overflow spillway withnegligible approach velocity (see Chart 111-2). Again,based on USBR data (references 6 and 7), Charts 111-7through 111-10 present coordinates from the best fit of

the general equation: Xn n-1

= KHd Y for 3V on 3H, 3V on

2H, and 3V on lH upstream faces. For low ogee spillwaycrests (with 45-deg upstream face only) Charts 122-3 to122-3/5 present plots of X , Y , n , and K forvalues of the ratio of velocity head divided by designhead ha/Hal of 0.08 and 0.12 where X = horizontal coor-

dinate positive to the right; Y = vertical coordinatepositive downward; n = variable, however usually setequal to 1.85; and K = variable dependent on approachdepth.

b. Upstream Quadrant. It has long been known that, forcurving flow of the type encountered in overflow spill-ways, conditions at any point in the flow are dependentupon influences directly upstream. Early attempts to fitcircular arcs to the profile of the lower nappe of flowover a sharp-crested weir produced surface discontinuitiesat the weir crest. This problem was partially remediedthrough the use of a combination of relaxation techniquesand data fitting (references 1 and 2). Another method,the fitting of a third, short-radius arc tangent to thevertical face and the intermediate-radius arc, was modeltested at the U. S. Army Engineer Waterways ExperimentStation (WES) (reference 4) and is incorporated in Chart111-2/1. No additional criteria were available for highoverflow spillways with other than a vertical upstreamface. Curves and factors for a 45-deg upstream face lowogee crest are given in Charts 122-3/1, 122-3/4, and122-3/5.

111-20 to 111-20/1

2. Elliptical Up,stream Quadrant Model Tests. In the late 1960’s,WES conducted a study to compare performance of four commonly used up-stream quadrant design procedures (reference 4). Of the four tested,the short-radius arc method (Chart 111-2/1) and an elliptical formula ofthe following form

(1)

where A and B are the major and minor axes, respectively, of theellipse, appeared to yield the most acceptable results. In 1973 WESpublished results (reference 5) of preliminary studies done to verify adesign procedure incorporating an elliptical upstream quadrant developedfrom the USBR data of reference 6. The procedure was verified for highspillways during these tests. A comprehensive test program with a widerange of approach velocities, upstream face slopes, and head ratios wasconducted at WES from 1977 to 1982 (reference 3). For these later ex-periments P/Hd , where P is the approach depth, ranged from 0.25 to2.0, H /Hd ranged from 0.4 to 1.5, and upstream face slopes rangedfrom ve~tical to 2V on 3H.

3. Spillway Crest Coordinates: Downstream Quadrant. For highspillways where the velocity of approach can be considered negligible

(ha/Hal< 0.06), the downstream quadrant equation is that given is Chart

111-2. As the depth of approach decreases, approach velocities increaseand the spillway should become flatter to match the partially suppressedvertical contraction of the nappe. Data for sharp-crested weirs were

found to be closely fit by maintaining the form of the equation (Xn =n-1

KHd Y) with n = 1.85 and varying K with approach depth (refer-

ence 5). The K value can be determined from Chart 111-20.

4. Point of Tangency: Downstream Quadrant. Chart 111-1 is aplot of coordinates for the tangent points X/Hd and Y/Hd versus

slope function u (l/slope) for K = 2.0 . Coordinates of the down-stream tangent points, X/Hd and Y/Hd , for other K values can bedetermined from Chart 111-1 values by multiplying those values by

(K/2)1/0.85

Alternately the coordinates of the downstream tangentpoint can be”determined directly from

1/0.85

-()

X=K(2)

‘d1.85a

and

111-20 to 111-20/1—

Y ()1 x 1“85—=iziq‘d

(3)

or

()YIK1.85/0.85

‘=~ 1.85a‘d

(4)

5. Spillway Crest Coordinates: Upstream Quadrant. Model studiesindicated that the quadrant of an ellipse in which the axes systemati-cally varied with depth of approach would fit the measured data exceptthat the ellipse quadrants would extend upstream of the position of thesharp-crested weir used to generate the nappe form to become tangent tothe vertical (reference 5). This extension is more pronounced for lowervalues of P/Hd . The general equation for the elliptical upstreamquadrant is given by

(5)

where the origin of the coordinates has been translated to the crestapex and the positive y-direction is downward (see definition sketch onChart 111-20). Solving for Y , equation 5 becomes

(6)

Graphs to determine A and B , normalized by the design head‘d ‘ ‘or

various ratios of approach depth to design head P/H are given inChart 111-20. For P/Hd z 2.0 ,

dA and B become constant with values

of 0.28Hd and 0.164Hd , respectively.

6. Point of Tangency: Upstream Quadrant. If a sloping upstreamface is desirable (normally P/H= < 1.0), then the elliptical upstreamquadrant is designed for a verti~al face as discussed above and-thesloping upstream face is attached tangent to the ellipse. The coordi-nates of the upstream point of tangency (PT) are determined by differ-entiating equation 6 with respect to X and setting it equal to theupstream face slope F and solving for the X coordinate, i.e.

s

-— 111-20 to 111-20/1

where F is equal to the slope LY/flX of the upstream face. Substi-tuting f& X in equation 6 and solving for the Y coordinate gives

Y=’-* (8)

Chart 111-20/1 illustrates the computational procedure for determiningthe

(1)

(2)

(3)

(4)

(5)

(6)

(7)

coordinates of a spillway with an elliptical upstream quadrant.

7. References.

McNown, J. S., Hsu, En-Yun, and Yih, Chia-Shun, “Applications ofthe relaxation technique in fluid mechanics,” Transactions, Ameri-can Society of Civil Engineers, vol 120 (1955), pp 650-669.

Office, Chief of Engineers, Department of the Army, Engineering andDesign; Hydraulic Design of Spillways, Engineer Manual EM1110-2-1603, Washington, D. C., March 1965.

U. S. Army Engineer Waterways Experiment Station, CE, GeneralSpillway Investigation; Hydraulic Model Investigation, by S. T.Maynord, Technical Report HL-85-1, Vicksburg, Miss., March 1985.

Investigations of Various Shapes of the Upstream Quad-rant of th~ Crest of a High Spillway ; Hydraulic Laboratory Investi-gation, by E. S. Melsheimer and T. E. Murphy. Research ReportH-70-1, Vicksburg, Miss., January 1970.

, Spillway Crest Design, by T. E. Murphy. MiscellaneousPaper No. H-73-5, Vicksburg, Miss., December 1973.

U. S. Bureau of Reclamation, U. S. Department of the Interior,Boulder Canyon Project, Hydraulic Investigations; Studies of Crestsfor Overfall Dams, Part VI, Bulletin 3, Denver, Colo., 1948.

U. S. Bureau of Reclamation, U. S. Department of the Interior,Design of Small Dams, Washington, D. C., 1973.

—

111-20 to 111-20/1

.10.0.

8.0

6.0

4.0 ‘

u

x 2.0

nauxz0:1.0 “n

0.8 “

0.6

0.4

0.2

0.15+0.21 0.23

51GN POOL

//

-—

0.25 0.27 0.29

A/Hd0.12 0.14 0.16 0.18

B/Hd

I

I

I

I

—.1

J1.90 2.10 2.30

K

/COORDINATE

PT

/

J Fs

1.0

REFERENCE: WES, SPILLWAY CREST DESIGN, BY

~cREsTAx\

T,E, MURPHY, MISCELLANEOUSPAPER H-73-5, DECEMBER 1973

(REFERENCE 5).

DEFINITION SKETCH

Hd = TOTAL HEAD

F~ = UPSTREAM FACE SLOPE


COORDINATES

COORDINATE COEFFICIENTS


PREPARED BY U S ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISSISSIPPI WES 11-87

-_-

U.S. ARMY ENGINEER WATERWAYS EXPERIMENT STATION

COMPUTATION SHEET

JOB GS 801 PROJECT JOHN DOE SPILLWAY SUBJECT ELLIPTICAL DESIGN

COMPUTATION SPI LLWAY DESIGN

COMPUTED BY AJR DATE 10/26/82 CHECKED BY BJB DATE 11/20/82

GIVEN:APPROACH DEPTH P = 15 FT

DESIGN HEAD Hd = 25 FT

4V ON 1H UPSTREAM FACE

2V ON 3H DOWNSTREAM FACEREQUIRED:

SPILLWAY SHAPE WITH ELLIPTICAL UPSTREAM QUADRANT

COMPUTE:

1. COORDINATE COEFFICIENTS

p/Hal = 15/25= 0.6

FROM CHART 111-20 A/Hal= 0.25 B/Hal = 0.146 K = 2.04

A = 6.25 B = 3.65F~ = V/H = 4/1 = 4.0a= H/V =3/2=1.5

2. TANGENT POINTS

UPSTREAM:

A2 Fsx ‘-(AZF~Z + BZ)112

(6.25)2(4.0) = -6.184FT= ‘[(6.25)2(4)2 + (3.65)2] li2

B2= 3.65-

(3.65)2 = 3.123FTy = B - ~A2F~2 + B2)1/2[(6.25)2(4)2+ (3.65)2]lD

DOWNSTREAM:

)( +&),0s5Hd = ((1:5~1,5)’’025,25, = 17.41FT

y=(.:)8,=_l_&!)l&5= ,2,FT

3. EQUATIONS:

UPSTREAM :

‘=BWTI‘3651-(1-6:2)”?DOWNSTREAM:

)(1.85 x’ “85Y=——

x’”,,

K Hd0s5 = (2.04 )(25)0”85 = 31”469ELLIPTICAL CREST SPILLWAY

NOTE: ATTACH UP- AND DOWNSTREAM COORDINATESFACES AT TANGENT POINTS.Y POSITIVE DOWNWARD.

CREST DESIGN

HYDRAULIC DESIGN CHART 11 1-20/1

F+!EPAREDOY11S A*Y ENGINEERWATERWAYSCWElilWNT STAIION VlCK581J@G,W5SISSIPPI WES 11-S7


SHEETS 111-21 TO 111-21/1


DISCHARGE COEFFICIENTS

1. General. Discharge over an uncontrolled spillway crest iscomputed using the equation

Q = CL H3/2e

where

Q= total discharge, cfs

c = discharge coefficient (Chart 111-21 and 111-21/1)

L= effective crest length, ft (Hydraulic Design Sheet 111-3/1)

He = energy head on crest, ft

2. Test Data. Tests were conducted at the U. S. Army EngineerWaterways Experiment Station (wES) in 1970 (reference 1) and 1977-1980(reference 2). The later set of tests was conducted in a 2.5-ft-wideflume with a design head of 0.8 ft. Because of possible Reynolds numbereffects, measurements were not made for He less than about 0.3 ft

(He/Hal= 0.4, where‘d

is the design energy head on crest in feet).

Instead, curves were extrapolated to the theoretical value of about C =3.09 , which is the coefficient for critical flow over a broad-crestedweir (reference 3). For P/Hd = 0.25 , where P is the crest heightabove approach channel invert in feet, measurements were difficult aboveH /Hd = 1.0 due to upstream turbulence associated with a Froude numbern~ar 1.0. The kinetic energy correction factor a was assumed to be1.0 for all tests. .

3. Two separate plots of the three variable groupings involvedare provided for ease in interpolation. The curve marked 3.4 on the Cvs He/Hal plot in Chart 111-21 is identical with the curve for high

overflow dams presented in Chart 111-3. It can be considered to be the

limit above which the relative spillway height has little or noinfluence.

‘—

4. Application. Although there is a general tendency for flatterupstream slopes to result in lower discharge coefficients, ellipticalcrest data for all upstream slopes fall into two distinct envelopes:slopes less than lV on lH and slopes greater than IV on lH. See

111-21 to 111-21/1

Sheets 111-20 to 111-20/1 for a discussion of slopes used. It is recom-mended that the two families of curves shown in Charts 111-21 and111-21/1 be used directly for slopes greater or less than lV on lH, re-spectively. Charts 111-21 and 111-21/1 should also be used to developrating curves in lieu of Chart 111-3/3 which was found not to fit ex-perimental data for elliptical crest spillways. The concept of under-designing for H ~ Hd is also applicable to elliptical crest spillways

esince discharge coefficients increase beyond He/Hal= 1.0 , especiallyfor values of P/H2 above 1.0.

(1)

(2)

(3)

u

5. References.

U. S. Army Engineer Waterways Experiment Station, CE, Investiga-tions of Various Shapes of the Upstream Quadrant of the Crest of aHigh Spillway; Hydraulic Laboratory Investigation, by E. S.Melsheimer and T. E. Murphy, Research Report H-70-1, Vicksburg,Miss., January 1970.

s General SDillwav Investi~ation: Hvdraulic Model Inves-. 4 J w dtigation, by S. T. Maynord, Technical Repo~t HL-85-1, Vicksburg,Miss. , March 1985.

Brater, E. F., and King, H. W.,Solution of Hydraulic Problems,N. Y., 1976.

Handbook of Hydraulics for the6th cd., McGraw-Hill, New York,

—-

111-21 to 111-21/1

.—

‘-.

10

:76

5

4

3

2

IL X“

1.0$:0.70.6

0.5

0.4

0.3

0.2-.—3

0.8

0.6

Iz“ +’

0.4

0.2

0

~1 I I I I I3.2 3.4 3.6 3.8 4.0 4.2 4.4

D

1.8

I

1.6

I ~ IA ‘“p/Hal= 0.25 05 1.0 ~o 3.4

F,. Ill/l/

C=Q/

IISCHARGEVERS

VERTICAL UP

A’!ZT DEFINITION SKETCH

Hd = DESIGN HEAD

b

I 1 1 1 1 I I I 1 I 1 I 1 J

3.0 3.2 3.4 3.6 3.8 4.(

C = Q/LHe3/2

REFERENCE: WES, GENERAL SPILLWAY INVESTIGATION;

HYDRAULIC MODEL INVESTIGATIC)N, BY

S.T. MAYNORD, TECHNICAL REPORT HL-85-1,

MARCH 1985 (REFERENCE 2). ELL

I 4.2 4.4

PTICAL CREST

SPILLWAYDISCHARGE COEFFICIENTS

VERTICAL UPSTREAM FACEHYDRAULIC DESIGN CHART III-21

PREPARED BY U S ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISSISSIPPI WES 1147

.—109876

5

4

3

X“ 2

1.:0.80.70.60.5

0.4

0.3

0.2

1 I i I

L

3.0 3.2 3.4

0.8

0.6

II@x?’

0.4

0.2

0

—

I 1 1 1 1 1 I I I1

, , ,I I I I I I I I

I I Ii

I I I 1 1 I i I I

3.6 3.8 4.0 4.2 4.4

C = Q/ LHe3J2

DISCHARGE COEFFIC

VERSUS P/Hal

III UPSTREAM FACE

+0

0/

1.8

F

1.68Q.

1 I / /— ‘i

q i I 3.4

Q 05 1.0 2.0 ‘//

1.4

\

I\ I/l/

11 1

Ii1

II I ,

4. b_lJ—u4

‘1 II /Y/@-

:IENT

/I1.0 “

1

4 4

0,0

—

DEFINITION SKETCH

Hd = DESIGN HEAD

1 I 1 1 I I 1 I I I I I

3.0

REFERENCE:

3.2 3.4 3.6 3.8 4.0 4.2

C = Q/ LHe3/2

WES. GENERAL SPILLWAY INVESTIGATION:

HYDRAULIC MODEL lNVESTIGAT1O-N, BY -

S,T, MAYNORD, TECHNICAL REPORT HL-85-1 ,

MARCH 1985 (REFERENCE 2).

ELLIPTICAL CREST

SPILLWAYDISCHARGE COEFFICIENTS

1:1 UPSTREAM FACE


PREPARED BY U S ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISSISSIPPI WEs 11-s7

--


SHEET 111-22

GATED ELLIPTICAL CREST SPILLWAY

PIER CONTRACTION COEFFICIENTS

1. Previous Criteria. See Charts 111-5 and 111-6.

2. General. See Sheets 111-20 to 111-20/1 for a description ofmodel studies conducted at the U. S. Army Engineer Waterways ExperimentStation (WES) to test elliptical crest spillway design concepts.* TwoType 3 piers were located as shown in Chart 111-22. See Chart 111-5 fora description of Type 3 pier geometry. For a vertical upstream face,the pier nose was located in the same plane as the face of the spillway,and this same horizontal distance was maintained upstream of the axis ofthe spillway crest for a lV on lH face. Measurements were taken forP/Hd = 0.25 , 0.5 , and 1.0 over a range of He/Hal values where P is

the crest height above approach channel in feet,‘d

is the design en-

ergy head on crest in feet, and H is the energy head on crest infeet.

e

3. Application. Chart 111-22 provides an estimate of pier con-traction coefficients for an elliptical crest spillway. Curves aredrawn for clarity purposes and should be used with caution since coef-ficients depend greatly on approach conditions. Further data may benecessary to confirm trends and values indicated by this figure.

-——.—.—

* U. S. Army Engineer Waterways Experiment Station, CE, General Spill-way Investigation; Hydraulic Model Investigation, by S. T. Maynord,Technical Report HL-85-1, Vicksburg, Miss., March 1985.

111-22

L.

. .

He/Hal

I

1.6

I.4

I .2

I,0

0.8

0,6

0,4

0,2

0,0

P/Hal ~erf. 1:1 CURVE

I

——

0.25 A*—

A 0 —-—0

9 u ‘–—

●o

!A D @

B q Q

\

\

\

1 t 1 I

-o. I 5 -o. I -0.05 0.0 0.05 0. I 0.15Kp

~CRESTAX/S I REFERENCE:

Ito.s’

r. I

I 1;I 2s’

I II 0.s’

I

DEFINITION SKETCHTYPE 3 PIERS (CHART III-5)

WES, GENERAL SPILLWAY INVESTIGATION;

HYDRAULIC MODEL lNVESTIGATlON, BY

S,T. MAYNORD, TECHNICAL REPORT HL-85-1 ,

MARCH 1985

ELLIPTICAL CREST

SPILLWAYPIER CONTRACTION COEFFICIENTS


PREPARED BY U.S. ARMY ENGINEER WATERWAYS EXPERIMENT STATiON, VICKSBURG, MISSISSIPPI! WES 11-87


SHEETS 111-23 TO 111-23/3


WATER SURFACE PROFILES

1. General. See Sheets 111-11 to 111-14/1 and 122-3/9 to122-3/10 for discussion of previous criteria and other availableinformation.

2. Model Tests. See Sheets 111-20 to 111-20/1 for general modeltest details (reference 2). Tests were conducted for both gated and un-gated crests for P/Hd values of 0.25, 0.5, and 1.0 and H /Hd valuesof 0.5, 1.0, and 1.5, where P is the crest height above ap~roach chan-nel in feet,

‘dis the design energy head on crest in feet, and H

is the energy head on crest in feet.e

3. Chart 111-23 is applicable for ungated elliptical spillwaycrest design. Charts 111-23/1 through 111-23/3 depict upper nappe pro-files along piers and in gate bay center lines for the three differentP/Hd values. See Chart 111-22 for a description of pier placement.

4* Application. Upper nappe profiles were found not to vary sig-nificantly with change in upstream face slope over the range of slopesand P/Hd values tested. For values of P/Hd other than those given,P/Hd may be plotted versus Y /Hd for constant X/Hd as demonstrated

by Rouse (reference 1). Ungated flow values of X/Hd to about 0.8 andcentral values of X/Hd for gated flow may be interpolated linearlywithout significant error.

5. References.

(1) Rouse, H., cd., Engineering Hydraulics, John Wiley and Sons, Inc.,New York, N. Y., 1951, p 530.

(2) U. S. Army Engineer Waterways Experiment Station, CE, GeneralSpillway Investigation; Hydraulic Model Investigation, by S. T.Maynord, Technical Report HL-85-1, Vicksburg, Miss., March 1985.

111-23 to 111-23/3

He

T~

-1.0

-0.8

-0.6-0.4

-0.20.0

0.20.4

0.60.8

1.01.2

1.4

-1.0-0.8-0.6

-0.4-0.20.0

0.20.4

0.60.8

1.0

1.2

1.4

P— = 0.25Hd

y_Hd

-0.452-0.452

-0.446-0.435

-0.414-0.378

-0.319

-0.233-0.120

0.0200.188

0.375

0.578

D

—= 1.0id

-0.768-0.759

-0.750-0.735

-0.712

-0.678

-0.629-0.550

-0.453-0.331

-0.172

0.0080.212

T-Y_Hd

-0.479-0.472

-0.462-0.445

-0.419-0.377-0.318

-0.219-0.102

0.0410.218

J

0.412

0.629

-0.897-0.879-0.857-0.829

-0.792-0.742

-0.677-0.579

-0.465-0.328

-0.1600.033

0.243

-1.0

-0.8

-0.6

-0.4

-0.20.0

0.2

0.40.60.8

1.0

1.21.4

P— = 0.5Hd

_lP--0.467-0.463

-0.452-0.436

-0.409-0.365

-0.297-0.199

-0.0760.071

0.244

0.4450.661

-0.849-0.840

-0.822-0.796

-0.764-0.714

-0.647-0.557

-0.449-0.307

-0.140

0.0590.278

/ UPPER NA PPE

SEE CHART 111-20 FORVALUES OF K.

DEFINITION SKETCH


HYDRAULIC MODEL INVESTIGATION, BY

S.T. MAYNORD, TECHNICAL REPORT HL-85-1,

MARCH 1985 (REFERENCE 2)


WATER SURFACE PROFILESUNCONTROLLED CREST


PREPARFD BY U.S ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISSISSIPPI WES 11-87

.._

L.

‘d

CENTER LINE OFGATE BAY

-1.0-0.8

-0.6-0.4

-0.20,0

0.20.4

0.60.81.0

1.2

1.4

ICEYiij

-0.469-0.469

-0.464-0.454

-0.438-0.405-0.358

-0.260-0.151

-0.0180.135

0.3150.528

-0.850-0.848

-0.839-0.823-0.796

-0.758-0.715

-0.640-0.553

-0.448-0.303

-0.135

+0.045

DEFINITION SKETCH



S.T, MAYNORD, TECHNICAL REPORT HL-B5-1 ,


ALONG PIERS

=_FF-1.0

-0.8

-0.6-0.4

-0.20.0

0.20.4

0.60.81.0

1.2

1.4

-0.469-0.469

-0.466-0.469

-0.488-0.414

-0.286-0.175

-0.066+0.061+0.209

+0.378

+0.577

-0.838

-0.835-0.833-0.835-0.894-0.900

-0.756-0.615

-0.471-0.311-0.139

+0.044

+0.250

LEGEND

— ~ OF BAY

---- ALONG PIERS

7.85 y

WATER SURFACE PROFILESCONTROLLED CREST

P/Hd = 0.25



-—

CENTER LINE OF GATE BAY ALONG PIERS

H

~0-5 I 1-0I 1-5Ipl 0-5I 10I 1-5

YHd

-1.0-0.8-0.6-0.4-0.2

0.00.20.40.60.81.01.21.4

-0.483-0.479-0.471-0.454-0.429-0.388-0.329-0.241-0.123+().()19+o.198+().394+o.613

-0.894-0.886-0.871-0.851-0.824-0.783-0.728-0.655-0.570-0.458-0.300-0.104+().119

-1.254

-1.244

-1.229-1.208-1.183

-1.149

-1.099

-1.034

-0.951

-0.856

-0.753

-0.631

-0.426

-1.0-0.8-0.6-0.4-0.2-0.15

0.0

0.2

0.40.60.81.01.21.4

-0.483-0.481-0.477-0.480-0.467-0.450-0.356-0.252-0.159-0.0550.0810.2560.4770.672

-0.889-0.880-0.869-0.880-0.917-0.910-0.825-0.677-0.541-0.414-0.258-0.0890.1050.319

-1.257-1.248-1.233-1.243-1.338-1.373-1.324-1.176-1.029-0.885-0.735-0.566-0.383-0.188

.

I TYPE 3 PIER

(CHART ill-5)I

LEGEND

— Q OF BAY

--- ALONG PIERS

Y

DEFINITION SKETCH



S.T. MAYNORD, TECHNICAL REPORT HL-85-1 ,


ELLIPTICAL CREST SPILLWAYWATER SURFACE PROFILES

CONTROLLED CRESTP/Hd = 0.5


PREPARED BY U.S. ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISSISSIPPI WEs 11-87

..—

CENTER LINE OF GATE BAY ALONG PIERS

-1.0-0.8-0.6-0.4-0.2

0.00.20.40.60.81.01.21.4

0.5 1.0 1.5

-0.494-0.488-0.483-0.476-0.445-0.403-0.335-0.240-0.116+0.029

0.2010.4030.626

-0.939-0.925-0.913-0.888-0.855-0.808-0.743-0.666-0.573-0.454-0.291-0.086+(3.150

-1.311-1.300-1.275-1.248-1.210-1.162-1.102-1.029-0.938-0.833-0.707-0.562-0.395

TYPE 3 PIER

(CHART 11 1-5)

H

< 0.5 1.0 1.5

-1.0-0.8-0.6-0.4-0.2-0.150.00.20.40.60.81.01.21.4

-0.489-0.483-0.475-0.488-0.463-0.438-0.369-0.264-0.170-0.0630.0690.2340.4310.651

YHd

-0.933-0.925-0.918-0.931-0.935-0.915-0.829-0.695-0.571-0.441-0.298-0.1280.0650.278

-1.311

-1.300

-1.280

-1.313

-1.375

-1.383

-1.315

-1.171

-1.023

-0.882

-0.730

-0.555

-0.362

-0.140

I>

.-\

UPPER NAPPEN

‘d<

<N

\ LEGEND\

— ~ OF BAY

--- ALONG PIERS

..

REFERENCE:

PREPARED BY US

DEFINITION SKETCH

WES, GENERAL SPILLWAY INVESTIGATION;


S.T. MAYNORD, TECHNICAL REPORT HL-B5-1 ,


ELLIPTICAL CREST SPILLWAYWATER SURFACE PROFILES

CONTROLLED CRESTP/l+d = 1.0


ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISSISSIPPI WEs 11-87

.—


SHEETS 111-24 TO 111-24/10


SPILLWAY CREST PRESSURES

1. Hydraulic Design Charts. Charts 111-24 to 111-24/8 presentplots of crest pressures for He/Hal values of 0.50, 1.00, 1.17, 1.33,and 1.50 and P/Hd values of 3.4, 1.0, 0.5, and 0.25 for crests withand without piers, where P is the crest height above approach channelin feet,

‘dis the design energy head on crest in feet, and H is

ethe energy head on crest in feet. Piers for P/Hd = 3.4 were Type 3A

(see Chart 111-5) with the test arrangement depicted in the insets ofCharts 111-24/7 and 111-24/8 (reference 3). Piers for all other p/Hal

values were Type 3 with the same test configuration except flume widthequalled 2.5 ft (reference 2).

2. Application. These charts apply to spillways with and withoutpiers over the given range of P/Hd values which are designed in accor-

dance with references 2 and 4 and Chart 111-20. Pressures for interme-diate head ratios can be obtained by plotting H/Hd versus He/Hal fora given X/Hd“

3. It is recommended that spillway design head‘d

be selected

so that minimum crest pressure for the maximum expected head is lessthan -20 feet of water to ensure cavitation-free operation and avoidpossible pulsating and inefficient spillway operation (reference 1) (seeChart 111-25). Chart 111-24/9 provides a suggested minimum allowablepressure design curve for an elliptical spillway crest without piers.It was constructed using maximum negative pressures for P/Hd values of0.5, 1.0, and 3.4 for vertical and lV on lH upstream faces. Chart111-24/10 provides a data summary curve for the case of an ellipticalspillway crest with piers designed as described in paragraph 1 above.Note that maximum negative pressures along the pier control the designhead limit in all spillway crest designs with piers.

4. References.

(1) Bauer, W., and Beck, E., Handbook of Applied Hydraulics, McGraw-Hill, 1969, Section 20.

..-


111-24 to 111-24/10

(3) U. S. Army Engineer Waterways Experiment Station, CE, Investiga-tions of Various Shapes of the Upstream Quadrant of the Crest of aHigh Spillway; Hydraulic Laboratory Investigation, by E. S.Melsheimer and T. E. Murphy, Research Report H-70-1, Vicksburg,Miss. , January 1970.

(4) Spillway Crest Design, by T. E. Murphy, MiscellaneousPaper H-73:5, Vicksburg, Miss., December 1973.

—

111-24 to 111-24/10

I

11’111~111-0.10 *

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-QS -0,4 -0.3 -Q2 -m @ QI Q2 0.3 0.4 0.5 OS 0.7 OB Q9 Ig 1,1 1.2 1.3 14 1.s

HORIZONTAL DISTANCE x

DES!GN HEAO ~

IV ON IH UPSTREAM FACE

0.60

MOd

a4 o

00

0.20 — — — I

alo

0.00 k

I Illlr%lli I T 1 >1 I I I

-0.10 ~ , \

- Q20

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-0.5 -0.4 -0-3 -02 -Q1 Qo m 02 0.3 a4 0> 0.6 0.7 0.8 0.9 10 I.1 I .2 1.3 1.4 1.5

HORIZONTAL DISTANCE XDESIGN nEAO ~

VERTICAL UPSTREAM FACE

NOTE NuMBEREO CURVES REFER TO ELLIPTICAL CREST SPILLWAYVALUES OF lie/tid

SPILLWAY CREST PRESSURES


HYDRAULIC MODEL INVESTIGATION, BYS.T. MAYNORO, TECHNICAL REPORT HL-S5-1 ,MARCH 19S5 (REFERENCE 2)

NO PIERS

P/Hd = 0.25


PREPARED BY U.S. ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISSISSIPPI WES11437---

Mo .

030

Q20 r

0.00

-0.$0

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HORIZONTAL OISTANCE xDESIGN HEAO ~

IV ON lH UPSTREAM FACE

0.60 t

0s0 ,[1 I

10.40

1

a30 ,I

0.20

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HORIZONTAL OISTANCE xOESIGN HEAD ~

NOTE, NUMBERED CURVES REFER TO VERTICAL UPSTREAM FACEVALUESOF H/H~

REFERENCE WES, GENERAL SPILLWAY INVESTIGATION;

HYDRAULIC MODEL INVESTIGATION, BYS.T. MAYNORD, TECHNICAL REPORT HL-S5-1 ,MARCH 19S5 IRE FERENCE 21 ELLIPTICAL CREST SPILLWAY

SPILLWAY CREST-PRESSURESNO PIERSPIHd = 0.5

IHYDRAULIC DESIGN CHART 11 1-24/1

PREPARED BY U.S. ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISSISSIPPI WEs 11-s7‘..

—

Obo

050 ~

040 t

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020 .9

010 ,

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HORIZONTAL OISTANCE 2

DESIGN HEAO ‘d

IV ON II+ UPSTREAM FACE

0.60-

050 ~1

0.40

0.30

020 .

0.10

, 0.00

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4

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-lglo~-0,s -0,4 *.3 -0.2 -01 09 0.1 0.2 a3 a4 03 !28 a? OD Q9 10 1.1 1.2 1.3 1.4 1..5

REFERENCE. WES, GENERAL SPILLWAY INVESTIGATION;

HYDRAULIC MODEL INVESTIGATION, BYS.T. MAY NORD, TECHNICAL REPORT HL-B5-1 ,MARCH 19S5 (REFERENCE 2)

NOTE NuMBERED CURVES REFER TOVALUES OF H#id

HORIZONTAL OISTANCE x

DESIGN IiEAO 7d

VERTICAL uPSTREAM FACE

ELLIPTICAL CREST SPILLWAYSPILLWAY CREST PRESSURES

NO PIERSP/Hd =1.0


PREPARED BY U.S ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISSISSIPPI WES 1147.—

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-----

4.3 4.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 ().8 0.9 1.0 1.1 1.2 1.3

HORIZONTAL DISTANCEGN HEAD +

f

PIERREFERENCE:

1

---

ELEVATION VIEW

WES. INVESTIGATIONS OF VA RlflllR ~l+ApE!j

OF THE UPST{EAM QUADRANT OF TUE CRESTOF A HIGH SPILLWAY; HYDRAULILINVESTIGATION. BY E.S. ME LSHEIME

.,,-P LABORATORYER AND T.E. MURPHY,

RESEARCH REpORT H-70-1, JANuARY 1970

(REFERENCE 3).


ALONG PIERP/Hd = 3,4



PREPARED BY U S ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISSISSIPPI WEs 11-07

.

-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3

HORIZONTAL DISTANCE ~DESIGN HEAD Hd

PLAN VIEW

REFERENCE: WES, INVESTIGATIONS OF VARIOUS SHAPESOF THE UPSTREAM QUADRANT OF THE CREST

OF A HIGH SPILLWAY; HYORAULIC LABORATORYINVESTIGATION, BY E.S. ME LSHEIMER AND T.E. MURPHY,RESEARCH REPORT H-70 -l, JANUARY 1970

(REFERENCE 3).

ELLIPTICAL CREST SPILLWAYSPILLWAY CREST PRESSURESCENTER LINE OF GATE BAY

PIHd = 3,4




c-’

-..-...

Xa

0.0

-o. I

-0.2

-0.3

-0.4

-0.5

-0.6

-0.7

-0,8

-0.9

\

o<$ iJGGESTEl ) DESIGN

CURVE

●

\

8

\

\

(

I .0 1.1 I .2 I .3 I .4 1.5 1.6

He

Hd

LEGENDREFERENCE: WES, GENERAL SPILLWAY INVESTIGATION;

O VERTICAL UPSTREAM FACEHYDRAULIC MODEL INVESTIGATION, BY

S.T. MAYNORD, TECHNICAL REPORT HL-85-1,● IV ON 1H UPSTREAM FACE MARCH 1985 (REFERENCE 2)

Hp = PRESSURE HEAD ON CREST, FT ELLIPTICAL CRESTHd = DESIGN HEAD, FT

SPiLLWAYHe = ENERGY HEAD, FT MAXIMUM NEGATIVEP = AVERAGE APPROACH DEPTH, FT PRESSURE VS l+e/Hd

UNCONTROLLED CREST (P/Hal > 0.5)HYDRMULIC DESIGN CHART Ill - 24/9

PREPARED BY U.S. ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISSISSIPPI WEs 11-87

I

.. - 0.0

-0.1

-0.2

-0.3

-0.4

In ZU -(3.5

-0.6

-0.7

-0.8

-0.9

u~A

\ \

A CENTERLIN E

k

A

●

c>

\

●

ALONG PIER

LEGEND \dO CENTER LINE, VERTICAL UPSTREAM FACE

– A CENTER LINE,lVON IH UPSTREAM FACE

● ALONG PIER, VERTICAL UPSTREAM FACE

A ALONG PIER,lV ON IH UPSTREAM FACE *

-1.0I .0 1.1 I .2 I .3 I .4 I .5 1.6

REFERENCE WES, GENERAL SPILLWAY INVESTIGATION;


S.T. MAYNORD, TECHNICAL REPORT HL-85-1 ,


Hp = PRESSURE HEAD ON CREST, FT

Hd = DESIGN HEAD, FT

He - ENERGY HEAD, FT

P = AVERAGE APPROACH DEPTH, FT

He

Hd

ELLIPTICAL. CREST SPILLWAY

MAXIMUM NEGATIVE PRESSURE VS He/Hal

WITH PIERS (p/Hal > 0.5)


PREPARED BY U S ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISSISSIPPI WES 1147

0.6

0.5

0.4

0.3

0.2

0.1

0

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a<: -0.2

z

: -0.3UJn

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-0.7

4.8

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/,= 1 17~

-0.3 -0.2

REFERENCE:

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

HORIZONTAL DISTANCE X

DESIGN HEAD —Hd

WES, INVESTIGATIONS OF VARIOUS SHAPES

OF THE UPSTREAM QUADRANT OF THE CREST

OF A HIGH SPILLWAY; HYDRAULIC LABORATORY

INVESTIGATION, BY E.S. ME LSHEIMER AND T.E. MURPHY,

1.0 1.1 1.2 1.3

RESEARCH REPORT H-70-1, JANUARY 1970

(REFERENCE 3).


WITHOUT PIERS

P/Hd = 3.4





SHEETS 111-25 TO 111-25/1


CAVITATION SAFETY CURVES

1. General. Sheets 111-20 through 111-24/10 describe variousdesign aspects of elliptical crest spillways. For a description ofmodel test data to support these sheets, see reference 2 and Sheets111-20 to 111-20/1.

2. Cavitation Safety Curves. Charts 111-24/9 and 111-24/10present plots of the function Hp/Hd = F(He/Hd) where H is the pres-

Psure head,

‘dis the design total head on crest, and H is the

eactual total head on crest. This formulation is versatile and can beused for any value of the pressure head H . However, vacuum tank

Pobservations by Abecasis (reference 1) indicated that cavitation on aspillway crest would be incipient at an average pressure of about-25 feet. For safety purposes, it is recommended that spillway crestsbe designed so that the maximum expected head will result in a pressureno lower than about -20 feet. Chart 111-25 is taken from the data ofMaynord (reference 2) for H = -20 feet and a crest without piers.

PCurves of -25 and -15 feet are also presented. The -25-foot curve cor-

~ responds to the lower portion of Abecasis’ measured envelope of valuesfor incipient cavitation. Chart 111-25/1 presents the same curves for acrest with piers located as described in Charts 111-24 to 111-24/10.These pressures were measured at a point 0.02 foot from the pier edge ina model with a design head

‘dof 0.8 foot. The two -20-foot curves

can be approximated by the following equations:

(without piers)‘d

= 0.277(He)l”2585 (1)

(with piers)‘d

= 0.309(He)1”2186 (2)

3. Design Examples. Depending on the available data, economics,and other design restrictions, there are many different approaches tothe proper sizing of a spillway for preliminary design.

4. References.

(1) Abecasis, F. M., “Discussion of ‘Designing spillway crests forhigh-head operation,’” by J. J. Cassidy. Journal of the HydraulicsDivision, American Society of Civil Engineers, vol 96, No. HY12,December, 1970.

111-25 to 111-25/1


111-25 to 111-25/1 —

‘-._

L

90

80

70

60

1?

50

40

30

20

NO CAVITATION ‘

ZONE

CAVITA

NOTE: Hd = DESIGN TOTAL HEAD, FT

He = ACTUAL TOTAL HEAD, FT ELLIPTICAL CREST SPILLWAY

CAVITATION SAFETY CURVESNO PIERS

HYDRAULIC DESIGN CHART III-25

PREPARED BY U S ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISSISSIPPI WEs 11-87+

1.1 1.3

I+e/ Hd

ION ZONE

\

1.5

.-90

80

70

60

1?

50

40

30

201.1

Cavitation ZONE

NO CAVITATION

ZONE

1.2 1.3

NOTE: Hd = DESIGN TOTAL HEAD, FT

He = ACTUAL TOTAL HEAD, FT

1.4 1.5

I+el Hd


CAVITATION SAFETY CURVESWITH PIERS


1.6

PREPARED BY U S. ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISSISSIPPI WEs 11-87


—

SHEETS 112-1 AND 112-2

SPILLWAY STILLING BASINS

HYDRAULIC JUMP

1. General. The principle of conservation of linear momentum re-sults in the classical hydraulic jump equation

%=’8+/%$Tables for the evaluation of D2 may be found in the Corps of EngineersHydraulic Tables, 2d Edition, 1944.

2. Spillway Stilling Basins. The purpose of Hydraulic DesignCharts 112-1 and 112-2 is the determination of the elevation of the apronor stilling basin floor when headwater and tailwater elevations are knownfor a given discharge. The form of the graphs was devised by Irwin.*On each chart families of D1 and D2 curves are shown for various dis-charges per foot of basin width and heads. Chart 112-1 covers a headrange of 5 to 500 ft and a discharge range of 10 to 250 cfs. Chart 112-2covers a similar range of heads but has a discharge range of 100 to 2500Cfs ● The head (H) as defined by the sketch at the foot of each chart isthe difference between the headwater and tailwater elevations. In thedevelopment of these charts friction losses were neglected. Recent ex-periments at State University of Iowa* for the Waterways ExperimentStation indicate that friction losses in accelerating flow down the faceof a spillway may be considerably less than the normal friction loss inwell-developed turbulent flow. Two lines depicting the Froude numbersquared (F2 = 3 and F2 = 12) are shown to define the jump characteris-tics. The line F2 = 3 marks the boundary between jumps of the undularand shock types. Model studies indicate that a strong hydraulic jumpforms in the region above the line F2 =12.

* R. L. Irwin, “Diagram for hydraulic jump,” Civil Engineeri~ (June1942), P 335.

* W. J. Bauer, “The Development of the Turbulent Boundary Layer on SteepSlopes,” Dissertation, University of Iowa, Iowa City, August 1951.

“L.

112-1 and 112-2Revised 1-68

.—

10 15 60 70 80 90 100 150 200

q = :;CHfR;E ~;R FOO;~F 8A;N WIDTH IN CFS

250

FORMULA: H =2 q* D2

[r

0 q2

~———— T– gDs [l- ]’+~—~+ 1-lgD2

-Da


HYDRAULIC JUMPIo<q <250

HYDRAULIC DESIGN CHART 112- I

WES 4-I-53

‘L.

ko 150 200 300 400 500 600 700 SOO 9001000 Iwo 2000 2500

c1 = DISCHARGE PER FOOT OF BASIN WIDTH IN CFS

SPILLWAY STILLING BASINSHYDRAULIC JUMP

100<q <2500HYDRAULIC DESIGN CHART 112-2

WCS 4-1-53

HYDRAULICDESIGN CRITERIA

‘----

SHEET 112-2/1

SPILLWAYSTILLING BASINS

HYDRAULICJUMP

VELOCITY DISTRIBUTION

1. The balance of pressure-plus-momentum upstream and downstreamfrom the jump is the basis for the theoretical equation of the hydraulicj-• This equation is given in HDCllz-s. When an end sill or bafflepiers are added there is an additional force i the upstream direction.U. S. Army Corps of Engineers EM ll10-2-1603(B~ suggests that a sa_Msfac-tory jump will occur for 0.gd2 by the use of an end sill and bafflesalthough more shallow basins have been demonstrated to perform satisfac-torily in the laboratory.

2. If the drag force of baffles is to be estimated, the effectivevelocity against the baffle and the drag coefficient must be known. Thedrag coefficient of the isolated cube referred to in HDC712-1 has beenestimated to be 1.33 based on State University of Iowa air lmnnel tests. (1)

The drag coefficient of~

single cube in open channel flow has been com-puted to be about 1.5. 7 Tests at Massachusetts Institute of Technol-0~(3) ind,ica-te that the drag coefficient is about 0.7 for a single row ofstepped iers and about 0.4 for a double row of Bluestone Dam type baffle

7piers.(G

3. HIX 112-2/1 can be used as a guide in selecting baffle pierheight and location as well as in estimating the velocity in the vicinityof the baffles. HDC 112-2/1 presents vertical velocity distribution curvesin the hydraulic jump at X/d2 stations of 1, 2, and 3 from

(t?e toe of

the jump. The curves resu t from experimental data by Rouset

and Mahon-ing Dam model study tests. 5) Curves for Froude numbers of entering flowof 2, 32 h, 6} 8} and 10 are given. The local velocity V is expressedin terms of the entering velocity V1 . The distance y above the flooris in terms of the depth downstream from the jump d2 .

4. The force exerted on the baffle piers and the resulting reductionin total downstream pressure and momentum can be estimated by use of HDC112-2/1 and an estimated drag coefficient. Available data indicate thatthe pier spacing as well as pier size and geometry has an effect upon thedrag coefficient. The designer is also sometimes concerned with the forceexerted on baffle piers by logs and other debris passing through the basin.

5* References.

(1) Chien, Ning, Fing, Yin, Wang, Huang-Ju, and Siao, Tien-To, Wind TunnelStudies of Pressure Distribution on Elementary Building Forms. Iowa

112-2/1

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Institute of Hydraulic Research, for Office of Naval Research, 1951.

Harleman, D. R. F., “Effect of baffle piers on stilling basin perform-ance.” Journal, Boston Society of Civil Engineers, vol 12, No. 2(April lgyy), pp84-gg.

Newman, J. B., 111, and La Boon, F. A., Effects of Baffle Piers on theHydraulic Jump. M.S. thesis, Massachusetts Institute of Technology,1953.

Rouse, H., Siao, Tien-To, and Nagaratnam, S., “Turbulence character-istics of the hydraulic jump.” Transactions, American Society ofCivil Engineers, vol 124 (1959), pp 926-966.

U. S. Army Engineer District, Pittsburgh, CE, Report on HydraulicModel Studies on the Spillway and Outlet Works of Mahoning Dam, onMahoning Creek, near Punxsutawney, Pennsylvania. Case Institute ofTechnology, May 1936.

U. S. Army Engineer Waterways Experiment Station, CE, A LaboratoryDevelopment of Cavitation-free Baffle Piers, Bluestone Dam, New River,West VirRinia. Technical Memorandum No. 2-243, Vicksburg, Miss.,

.

March 19~8.

, unpublished data. 1957.

U. S. Army, Office, Chief of Engineers,EM 1110-2-1603, March 1953.

—. —.

Hydraulic Design, Spillways.

—

112-2/1

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‘=I

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1


SHIWIW112-3 TO lU-5


SEQUENT DEFTH CURVES FOR RECTANGULAR CHANNEL

1. The conventional hydraulic jump equation is based on the prin-ciples of conse~ation of momentum and continuity of flow. The equation is

II 2 Dl Dl2

‘1+ 2V1‘2 =-F g ‘T

where Dl and D2 are sequent depths upstream and downstream, respec-tively, from the jmp. V1 and V2 are the corresponding sequentvelocities.

2. Tables have been published by King(s) and the Corps ofEngineers(6) that give the Dp value when the D1 and V1 values areknown.

3* A log-log graph, devised by E. W. Lane(5) and published by theNational Resources Committee(k), is given as Chart 112-3. It maybe usedto determine D2 and V2 when D1 and V1 are known.

4. A graph on Cartesian coordinates was devised by Doma(2) and re-published by Abbett(l). This graph gives the solution for D2 when D1and VI are known. The graph was prepared for a range of values of10 CVl < 100 in Chart 112-4 and of 6 < V1 < 10 in Chart 1X2-5.

(1)

(2)

(3)

(4)

5* List of References.

Abbett, R. W., American Civil Engineering Practice. Vol II, JohnWiley & Sons., Inc., New York, N. Y., sec 17, p 56.

Douma, J. H., Hydraulic Model Studies of the Wickiup Outlet WorksStilling Basin, Deschutes Project, Oregon. U. S. Bureau of Reclama-tion, Memorandum to Chief Designing Engineer, Denver, Colo., 30 June1939, Appendix 1, fig. 17. (Available on loan only)

King, H. W., Handbook of Hydraulics. 3d cd., McGraw-Hill Book Co.,Inc., New York, N. Y., 1939, table 133, p. 444-4-45.

National Resources Committee, Low Dams. Washington, D. C., 1938,p. 105.

112-3 to IJ2-5

(5) U. S. Bureau of Recl~ation, Drawing No. X-D-931. lJOctoberlgss.

(6) War Department, Corps of Engineers, Hydraulic Tables. 2d cd.,U. S. G. P. O., Washington, D. C., 19X4, table 3, p. 16-56.

----

112-3 tO 112-5

1.4

1.6

1.8

2V

ALU

ES

OF

V21N

FT

/SE

C

___

2.5

33

.54

56

78

10

12

14

16

18

20

25

30

35

40

>-

IL 0 to

0.I

0.2

0.3

0.4

0.50.6

0.8

1.0

23

45

VA

LU

ES

OF

DI

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BA

SIC

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UA

TIO

NS

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Iv2

=—D

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10

WH

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BO

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LO

CIT

YB

EL

OW

TH

EJU

MP

,F

TZ

SE

C

9=

GR

AV

ITY

CO

NS

TA

NT

,F

T/S

EC

/SE

C

20

30

40

50

60

80

I00

SP

ILLW

AY

ST

ILLI

NG

BA

SIN

SE

QU

EN

TD

EP

TH

CU

RV

ES

RE

CT

AN

GU

LA

RC

HA

NN

EL

S3<

VI<

IO0

HY

DR

AU

LIC

DE

SIG

NC

HA

RT

11

2-3

T—

,T

RE

V1-6

4W

ES

8-5

8

‘—

1-IL

z—

ONL0cou

3<>

60

55

50

45

40

35

30

25

20

15

10

5

0“o I 2 3 4 5 6 7 8

VALUES OF D, IN FT

SPILLWAY STILLING BASIN

SEQUENT DEPTH CURVESRECTANGULAR CHANNELS

Io<vl<loo


WES 8-58

I

---

-—.

24

22

20

18

18

14

12

10

8

6

4

2

n“o I 2 3 4 5 8 7 8

VALUES OF 0, IN FT

.— ——_———

————————————— L ‘2 —

t v] — &j/ 1

SPILLWAY STILLING BASIN

SEQUENT DEPTH CURVESRECTANGULAR CHANNELS

6< VIC40


WES 8-58


SHEET112-5/1


END SILL

TAILWATER REDUCTION

1. An end sill is commonly used as the terminal wall of a stillingbasin. Where a tailwater deficiency prevents satisfactory hydraulic jumpperformance and accompanying energy dissipation, the stilling basin flooris set lower than the riverbed and an end sill forms a step, or rise, tothe elevation of the bed of the channel. Hydraulic Design Chart 112-5/lcan be used to determine the relation between the Froude number of theentering jet, the sill height, and the downstream depth required forstabilizing the hydraulic jump when baffle piers are not used.

2. The effects of end sill height upon the reduction of flow depthdownstream from a sill have been investigated experimentallyby Forster andSkrinde.* Chart 112-5/l reproduces the data and curves published byForster and Skrinde. The ratio of the depth d3 over the end sill to theentering depth dl is plotted against the Froude number F1 of theentering flow. The curves represent various ratios of sill height to theupstream depth h/dl for basin lengths of 5(h + d3). The dashed linelabeled h/all= O is the theoretical hydraulic jump curve for sequentdepths.

3* The design criteria above apply to a stilling basin that requiresa vertical end sill or downstream channel invert sufficiently high to pro-duce the tailwater required for formation of the hydraulic jump. The endsill may act as a critical-depth control, and flow into the downstreamchannel may be very turbulent with supercritical velocities. Excessivewave action, surges, and supercritical velocities may require that in-creased protection be provided for 100 ft or more downstream of the still-ing basin to prevent channel erosion. Careful consideration should begiven to the need for increased riprap protection downstream of the still-ing basin. In extreme cases lowering of the basin elevation and use of astandard-type stilling basin may be more economical than extensive riprapprotection.

* J. W. Forster and R. A. Skrinde, “Control of the hydraulic jump bysills.” Transactions, American Society of Civil Engineers, vol 115,paper 2415 (195o), pp 973-987.

.—

112-5/1Revised 9-70 c

.

9 -(

//

/ ‘/o ‘ f f

8 A / ‘

r A

7

AJ/

6P {

o0

45

/ r r o

/ o

- , , . L #

‘o r r

/0 LOWER LIMITOF EXPERIMEIV m

i

/ /

/f I

/’/

I _/kr- 14

3I

\= lJ- THkO@CAL:CUR@ !

FROUDE NUMBER, F,

LEGEND

v, NOTE : CURVES AND DATA BY FORSTER AND SKRINDE.l’=

d== CRITICAL DEPTH

//////////1///////// [Iillll llllllllflllr’1

L .(,+------rDEFINITION SKETCH SPILLWAY STILLING BASINS

END SILLTAl LWATER REDUCTION

HYDRAULIC DESIGN CHART 112-5/!

PREPARED ❑ Y U S ARMY ENGINEER WATERWAYS ExPERIMENT STATION, VICKSBURG, MI SSISS!PPI WES 1-66

.


SHEETS 112-6 to 112-6/2

HIGH OVERFLOW DAMS

BUCKET-TYl?EENERGY DISSIPATOR

1. Bucket-t~e energy dissipators are used where excessive tailwaterdepths prevent adequate energy dissipation by means of a hydraulic jump ona horizontal stilling basin floor. HDC 112-6 and 112-6/1 can be used toestimate probable roller and surge heights for preliminary design purposes.

2. The design curves shown in the charts were developed by McPhersonand Karrl from extensive laboratory tests wherein the discharge was dis-tributed uniformly over the bucket. The test data have been omitted fromthe charts in the interest of clarity. The data points shown are fromWaterways Experiment Station (WES) studies2-6 and are in reasonably goodagreement with McPherson’s and Karr’s curves for q parameters ~ 26 x 10-3.The agreement is less satisfactory for higher q parameters. The chartsare therefore not considered applicable for q parameter values> 26 x 10-3, and the final design for large structures should be developedby hydraulic model study.

3. The streambed was generally at the same elevation as the bucketinvert in the McPherson and Karr tests. In the WES tests, the streanbedelevation varied from bucket-lip elevation to below the bucket-invert ele-vation. However, it is believed that the channel-bed elevation has neg-ligible effect on roller and surge heights.

4. The discharge parameterthe Froude number of the entering

q =Vd

of thejet in

and V

design curves can be related tothe following manner:

Then

and

*=*

where F = Froude number of entering jet

q = discharge per ft of bucket width, cfs

112-6 to 112-6/2Revised 1-66

‘1 =d=

v=

available energy head (pool to bucket invert), ft

depth of flow entering bucket, ft

velocity of flow entering bucket, fps

5* HDC112-6/2 illustrates application of HDC 112-6 and 112-6/1 forthe preliminary design of bucket-type energy dissipators. The sample com-putation is for a specific spillway discharge. The full range of spillwayflows should be investigated.

6. The WES model data shown in HDC 112-6 indicate that good energydissipation is obtained when the bucket roller depth hb is between 75 and90 percent of the tailwater depth ~ . For this condition, the surgeheight is 105 to 130 percent of the tailwater depth.

(1)

(2)

(3)

(4)

(5)

(6)

7. References.

McPherson, M. B., and Karr, M. H., “A study of bucket-t~e energydissipator characteristics.” ASCE, Hydraulics Division, Journal,vol 83, paper 1266, No. HY 3 (June 1957); vol 83, paper 1348, No.HY 4 (August 1957), Corrections, PP 57-64; VO1 84, paper 1832,No. HY 5 (October 1958), Closure, pp 41-48.

U. S. Army Engineer Waterways Experiment Station, CE, Model Studiesof Spillway and Regulsting Sluices for Wolf Creek Dam, CumberlandRiver, Kentucky. Technical Memorandum No. 201-1, Vicksburg, Miss.,January 1944.

, Model Studies of Spillway and Bucket for Center Hill Dam,Caney Fork River, Tennessee. Technical Memorandum No. 202-1,Vicksburg, Miss., August 1946.

, Model Study of Spillway and Bucket, Stewarts Ferry Dam,Stones River, Tennessee. Technical Memorandum No. 2-239, Vicksburg,Miss., September 1947.

, Spillway for Osceola Dam, Osage River, Missouri; ModelInvestigation. Technical Memorandum No. 2-261, Vicksburg, Miss.,October 1948.

, Spillway Design for Whitney Dam, Brazes River, Texas;Model Investigation. Technical Memorandum No. 2-263, Vicksburg,Miss., October 1948.

—

112-6 to 112-6/2Revised 1-66

I

--0.9 I II II I Ill I I [1 I I I I I I I I I J .J. .-1

I 1 I I I I I I 1! I I I I I I I II Mtdlltww

.~ljf~+~~+~f#l+]\ll. .- .- . .*

LEGEND 1

Mc PHERSON

WES AND KARR ++

qh,

qI?l

SYMBOL PROJECT x 103 —x 1033/2

viih,R 3/2 K

viih, —o CENTER HILL (TYPE 1 -HIGH) 14-53 3.94.4 5 6

❑ CENTER HILL (TYPE 1 -LOW) 1348 4.1-4 7 10 6-7

0.7

Bil

A OSCEOLA (ORIGINAL)

v oscEoLA {TYPE11■ STEWARTSFERRY(TYPE11

El3C-1C6 1.7-2.1

30-106 2.1-26

13

26

24-75 2.7-32

0.6

0.5

0.4

0.3

0.2

0.1

nn---0.0 0.1 0.2 0.3 0.4

h2

~

DESIGN CURVES SHOWN DEVELOPED BY McPHERSON ANDKARR FROM EXPERIMENTAL DATA. THESE DATAOMITTED TO SIMPLIFY CHART.

POOL

1

L-

/“

ROLLER

[

- SURGEhl i

H s +’ TW4

0,5 0.6 0.7 0.8

RANGES OF VARIABLES

SPILLWAY SLOPE

LIP ANGLE

H/h,

hi/R

q/~h13z2 X103

McPHERSONWES AND KARR

141-167 I 1’1

45° 45°

068-093 >0.75

SEE LEGEND

SEE LEGEND

HIGH OVERFLOW DAMS

i L,+h~ h2

;s e BUCKET-TYPE ENERGY DISSIPATORt -t 1

ROLLER DEPTH

DEFINITION SKETCH HYDRAULIC DESIGN CHART 112-6

PREPARED BY “ S ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISSISSIPPIREv 1–66

WES 5-59

0.9 rI II I I 1111 I 1[1 I I Ill I

I II I I I I I I I I I I I I I [1 I I I

LEGEND t

+ *7 t. 7

II!“lit

0.7

0.6

Mc PHERSON

wES AND KARR

“ h, “ h,SYMBOL PROJECT ~g;,, ,’ 103 ; ~g;,, ,’ 103 ;

l~]FIGURES SHOWN ARE VALUES ~W+~

HH4’HH

0.5

0.4

0.3

0.2

0. I

0.000 0.1 0.2 0.3 0.4 0.5 06 0.7 0.8

NOTE:

POOL

hs

~

DESIGN CURVES SHOWN DEVELOPED BY McPHERSONAND KARR FROM EXPERIMENTAL DATA THESEDATA OMITTED TO SIMPLIFY CHART

RANGES OF VARIABLES

SPILLWAY SLOPELIP ANGLE

H/h,

hi/R

q/~hl 3/2x lo3

McPHERSON~ AND KARR

141–1.67”1 1:1

45° 45“

068-093 >0,75

SEE LEGEND

SEE LEGEND

v‘1

I’I.l...:!!tfifw,HIGH OVERFLOW DAMS

BUCKET-TYPE ENERGY DISSIPATORSURGE HEIGHT

DEFINITION SKETCHHYDRAULIC DESIGN CHART 112-6/1

PREPARED WY U. S. ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISSISSIPPIREV 1-66 WES 5-59

f06

’06

COMPUTATION FOR PRELIMINARY DESIGN

-.

GIVEN:

Discharge (q) per ft of

basin width = 450 cfs

Pool elevation =765ft

Tai Iwater elevation z 650 ft

Radius of bucket z 50 ft

Slope of bucket lip = 45 deg

Spillway slope = 10:6.1

Ratio of H to hl >0.75

POOL

ASSUME:

Bucket invert elevation H 550 ft

COMPUTE:

1.

2.

3.

4.

5.

hl = pool elevation - bucket invert elevation 6.

= 765-550= 215 ft

hz = tailwater elevation - bucket invert 7.

elevation

= 650-550 = 100 ft

h#hl = 100/215 = 0.465

Discharge parameter

450 x 103=5.68 x 3153

= 25

From Chart 112-6 read hb/hl = 0.42

for hz/h 1 = 0.465 and

x 103 = 25G ;1312

Note: Good energy dissipation is indicated if

the roller height (hJ is between 75 and

90 percent of the tai Iwater depth (hz).

PREPARED BY u s ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VI CKSBUF!G M, SS, SS, PP,

8.

9.

10.

hb =0.42x hl

=0.42 x215=90 ft

From Chart 112-6/1 read h,/hl = 0.52 for

hb/h 1 = 0.42 and

q X 103 = 25

G hlslz

h,=0.52xh1

=0.52 x215= 112 ft

Compute hb and h~ for full range of

spillway flows.

Determine maximum elevation of bucket

rot Ier and surge.

HIGH OVERFLOW DAMSBUCKET-TYPE ENERGY DISSIPATOR

SAMPLE COMPUTATIONHYDRAULIC DESIGN CHART II2- 6/2

REv I-68 WES 5-59

—


SHEET 112-7

HIGH OVERFLOW DAMS

ENERGY

FLIP BUCKET AND

DISSIPATORS

TOE CURVE PRESSURES

1. Hydraulic forces acting on high, overflow spillway flip bucketsand toe curves are of interest in the structural design of these devices.Theoretical studies and model and prototype data indicate that the bottompressures change continuously throughout the curve and are influenced bythe curve radius, the total head, and the unit discharge. It has alsobeen shown that the pressures immediately upstream and, in the case of thetoe curve, downstream of the curve are influenced by the curvature.

(Rouse 3) illustrates the application of the flow net solution to thisproblem.

2. Flip Buckets. Approximate techniques, including use of thecentrifugal force equatiorl(pland a vortex ana.logy,(1~2)have been sug-gested for computing the pressures on spillway flip buckets. A recentWES study~7) using a theoretical approach similar to vortex analogy sug-gested by Douma(2) indicated that, for relatively high dams, bucket pres-sures could be expressed as:

%= f(*’%)where

hP

= pressure head against boundary, ft

‘T= total head (point to energy gradient), ft

q= unit discharge, cfs

R = radius of curve, f’t

g = acceleration due to gravity, ft per sec per sec

(2= angle of rotation from beginning of curve, degrees

%= total deflectio~.angle, degrees

The term ~j~ defines the relative position along the curve.

3* HDc 112-[7

resents dimensi nless flip bucket pressure curves7based on Pine Flat 4 and Haz%well(j model spillway data analyzed in

.—— 112-7Revised I-64

accordance with the preceding expression. Spillway energy losses were as-sumed negligible in the analysis. The plotted data for al% from 0.25to 0.75 indicate that the pressure in the middle portion of the bucket isnearly constant. Therefore, the pressure distribution through the bucketcan be adequately defined by the four curves shown in the chart. The curvefor ~/~ = 1.0 coincides with the axis of the chart ordinates since thepressure on the lower nappe of the jet leaving the bucket is atmospheric.The Pine Flat(G) prototype data plotted on the chart indicate satisfactorycorrelationwith the model data. Allowances were made for spillway energylosses in computing the total head HT for the prototype data.

4. Toe Curves. The available data(8)

from model tests conductedunder the Corps of Engineers Engineering Studies Item 801 which are plottedin HllC112-7 indicate that for a high dam the flip bucket pressure dis-tribution curves generally apply to spillway toe curves. However, the datashow that the pressure at the end of the toe curve approximates that at thebeginning of the curve if the toe curve is not submerged.

5* HDC 112-T can be used to estimate the pressure distribution onspillway flip buckets or toe curves associated with high overflow dams.However, for design purposes, allowance for spillway energy losses shouldbe included in the computations of HT required for use of the chart.The user is cautioned that the curves are not applicable to toe curves af-fected by submergence.

6. References.

(1)

(2)

(3)

(4)

(5)

(6)

Balloffet, A., “Pressures on spillway flip buckets.” Journal of theHydraulics Division, American Society of Civil Engineers (September1961), pp 87-96.

Douma, J. H., discussion of paper, “Design of side walls in chutes andspillways,” by D. B. Gumensky. Transactions, American Society ofCivil Engineers, vol 119 (1954), pp 364-367.

.—

Rouse, H., Engineering Hydraulics. John Wiley and Sons, Inc.,New York, N. Y., 1950, p 47.

U. S. Army Engineer Waterways Experiment Station, CE, Spillway andConduits for Pine Flat Dam, Kings River, California; Hydraulic ModelInvestigation. Technical Memorandum No* 2-sl”j,Vicksburg, Miss.,December 1953.

, Sluice Outlet Portal and Spillway Flip Bucket, HartwellDam, Savannah River, Georgia; Hydraulic Model Investigation.Technical Memorandum No. 2-393, Vicksburg, Miss*, August 1954.

, Prototype Tests of Spillway Crest and Flip Bucket,Pine Flat Dam, Kings River, California. Technical Report No. 2-511,

-—-

Vicksburg, Miss., June 1959.

112-7Revised 1-64

\.

(7) U= S= ArmY Engineer Waterways Experiment Station, CE, An Investigationof Spillway Bucket and Toe Curve Pressures. Miscellaneous Paper No.2-625J Vicksburg, Miss., February 1964.

(8) } unpublished ES 801 data.

112-7Revised I.-64

--- -

0.40 -

0.35 –

0.30 –

0.25

0.20 –

0.15

0.10 –

0.05

0.00 d

—ala ~=/. o(FLfPBu CKETS)

x 94

/

4

0

}

o

/g/“&>%x

85 # 38

NOTE: NUMBERS ARE VALUES

OF (a/a T)x 102 FOR

DATA POINTS.

-- --- ---0.00 0.10 020

DEFINITION SKETCH

—

—

0.30 0.40 0.50 0.60 ().10

>HT

LEGEND

A PINE FLAT MODELx HARTWELL MODEL

A PINE FLAT PROTOTYPE

n ES 801 (TOE CURVE)

HIGH OVERFLOW DAMS

ENERGY DISSIPATORS

FLIP BUCKET AND TOE CURVE PRESSURES


REV 1-64 WES 10-61

..—

HYDRAULIC DESIGN CRITERM—- ....-—-—_____

.— SHEET 112-8

HIGH OVERFLOW DAMS

ENERGY DISSIPATORS

FLIP BUCKET THROW DISTANCE

1. For economy, flip bucket or ski-jump energy dissipators are some-times used when spray from the jet can be tolerated and erosion by theplunging jet will not be a problem. Flip buckets have caused trouble inclimates where spray from the jet resulted in icing of nearby roadways orelectrical equipment. The major amount of energy dissipation occurs inthe region where the jet plunges into the tailwater; a minor amount occursas the jet frays after leaving the bucket.

2. Factors affecting the horizontal throw distance from the bucketlip to point of jet impact are the initial velocity of the jet, the bucketlip angle, and the difference in elevation between the lip and thetailwater.

3* HDC 112-8 presents throw-distance curves for lip angles of O to45 degrees. The horizontal throw distance X and the vertical drop fromthe bucket lip to tailwater Y are expressed in terms of the jet velocityhead Hv . The following expression based on the theoretical equations forLtrajectories was used for developing the curves:

_—— ———----X/Hv = sin 20 + 2 cos 0&in2 0 + Y/~

where

x = throw distance, ftY= vertical drop from lip to tailwater surface, ftHv & velocity head of jet at bucket lip, fte = bucket lip angle, deg

4. HDC112-8 is a guide for judging the point of impact of the jet.The throw distance may be substantially less than indicated, depending uponspillway energy losses. Prototype measurements of spillway energy lossesare needed to permit a comparison of theoretical and actual throw distances.

‘— 112-8Revised I.-64

.—

-—

I .0

0.8

0.6

e

0.4-

0.2

* /

0.00.6 I .0 1.4 I .8 2.2 2.6 3.0

EQUATION

vx -slN2e+2cose slN e+Hv

~-

WIIERE:X = THROW DISTANCE, FT

e ❑ BUCKET LIP ANGLE

Hv= vELOclTY HEAD AT BucKET

LIP, FT

Y = VERTICAL DROP FROM LIP TOTAlLWATER SURFACE, FT

.\-——-‘\’\ \\

‘, \ HIGH OVERFLOW DAMS\ \,_

4 ENERGY DISSIPATORSx F LIP BUCKET THROW DISTANCE

DEFINITION SKETCHHYDRAULIC DESIGN CHART 112-8

pREpAREO 8V u s ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKS9URG, MISSISSIPPIWES 10-61

Dam Design

Documents

technical

asce hydraulics

turbulent

boundary layer

potential

hydraulic

maximum expected

boundary layer