CJ >­::c

I ~ v BHP.EAU OF RECLAMATION C, I'...--' ~~ cf' HYDRAULIC LABORATORY,

OFFICE /4~t.-~ ;;)_ I .R. '2. 2-Tu FILE CflPY . UNITED STATES T

DEPARTMENT OF THE INTERI<l'i¥EN BORROWED RE'l'URN PROMPTLY BUREAU OF RECLAMATION

PROGRESS REPORT III

RESEARCH STUDY ON STILLING BASINS, ENERGY DISSIPATORS, AND ASSOCIATED APPURTENANCES

SECTION 7

SLOTTED AND SOLID BUCKETS FOR HIGH, MEDIUM, AND LOW DAM SPILLWAYS

Hydraulic Laboratory Report No. Hyd-415

DIVISION OF ENGINEERING LABORATORIES

COMMISSIONER'S OFFICE DENVER, COLORADO

July l ,1956

Summary

The slotted bucket developed in this study for use as an energy dissipater at the base of a spillway is particularly suited to installations where the tail water is too deep for a hydraulic jump apron, or where a bucket structure is preferable to a longer hydraulic jump stilling basin. Charts and curves are presented in dimensicnless form so that a bucket may be designed for most combinations of dis­charge, height of fall, and tail water range. The resulting bucket will provide self cleaning action to reduce abrasion erosion in the bucket arc, protection against undermining of the bucket and apron as a result of scour, and good vertical distribution of the flow leaving the bucket. The water surface downstream from the bucket may, for the lower tail water elevations, be somewhat rougher than desirable, however, making it necessary to consider the effects of possible riverbank erosion.

A schematic diagram of a spillway and slotted bucket containin, definitions of' the important dimensions is shown below:

.. ' . .. .

.... . ..... . . Bed may be level or ;

sloping ( see text)._.,

A simplified version of the seven steps required to design a bucket is given below:

1. Determine Q, q (per foot width), V1 D1; compute Froude V1

number from F = "/ gn1 for maximum flow and intermediate flows. In some

cases Vi may be estimated from Figure 25.

2. Enter Figure 19 with F to find bucket radius parameter R

V12 from which minimum allowable bucket radius R may be computed. D1+-2g

R

3. Enter Figure 21 with D + V1 2 and F to l 2g .

minimum tail water depth limit may be computed.

find Tmin from which D1

4. Enter Figure 22 as in Step 3 above to find maximum tail water depth limit, Tmax.

5. Make trial setting of bucket invert elevation so that tail water curve elevations are between tail water depth limits determined by Tmin and Tmax. Check setting and determine factor of safety against sweepout from Figure 24 using method~ of Step 3. Keep apron lip above riverbed, if possible.

6. Complete design of bucket using Figure l to obtain tooth size, spacing, dimensions, etc.

7. The sample calculations in Table VII, page 48, may prove helpful in analyzing a particular problem.

The procedures outlined above summarize the main considerations in the design of a slotted bucket. Other considerations are discussed in the report, however,-and the entire report should be read before attempting to use the material given above •

CONTENTS

Introduction. ............ • • • • . . . . . . General Performance . . . . . . . . . . . . . . . . . . . Performance . . . . . . . . . . . . . . . . . . . . . . .

Slotted Bucket Development Tests. . . . . . . . . . . . . . .

1

1 2

2

General • . . . . . • • • . • . . • . • . • • • • • . . • 2

Development from Solid Bucket • • • • • • • • • • • • • • 6 Tooth Shape, Spacing, and Pressures • • • • • • • • • • 9 Apron Downstream from Teeth • • • • • • • • • • • • • • 11 Slotted Bucket Performance. • • • • • • • • • • • • • • • 12 Summary of Slotted Bucket Development Tests • • • • • • • 12

Generalization of the Slotted Bucket. . . . . . . . . . . . . . General •••••••••• . . . . . . . . . . . . . . . Test Equipment ••••••• Bucket Modifications Tested

. . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . General . . . • • • • . • • • • • • • • • • . • . • • • Tooth Modification I ••••••••••••••••• Tooth Modification II ••••••••••••••••• Tooth Modification III ••••••••••••••• TootnModification IV ••••••••••••••••• Angostura Bucket with Teeth Removed •••••••••• Solid Bucket • • • • • • • • • • • • • • • • • • • • •

Summ.ary • • • • • • • • • • • • • • • • • • • • • • • •

Determination of Radius and Tail Water Limits . . . . . . . . General • • • • • • •• Six-inch Radius Bucket.

Lower Tail Water Limit Upper Tail Water Lim.it Maximum Capac 1 ty • •

. . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ . . . . . . . . . .

Nine-inch Radius Bucket •••••••••••••••• Twelve-inch Radius Bucket • • • • • • • • • • • • • . • • • Eighteen-inch Radius Bucket • • • • • • • • • • • • • • • Larger and Smaller Buckets. • • • • • • • • ••••• Data Analysis • • • • • • • • • • • • • • • • • • • • • •

12

12 14 14

14 16 16 18 19 19 19 20

20

20 25

25 25 28

28 32 36 36 39

CONTENTS--Continued

Safety Factor • • • • • • • • Evaluation of Variables •••

• • • • • • • . . . . . . . Practical Applications •••• • • • . . • • •

• • • • • • • • • • • •

• • • • • •

Tail Water Requirements for Bucket Versus Hydraulic

39 39

45

Jump • • • • • • • • • • • • • • • • • • • • • • • • 53

Summary of Bucket Design Procedures. • • • • . . • • • • • • 55

FIGURES

!2:. ~

1 Submerged Buckets. • • • • • • • • • • • • • • • • . • • • 3 2 Performance of~Solid and Slotted Buckets • • • • • • • . • 4 3 Diving Flow Condition--Slotted Bucket. • • • • • • • • • • 5 4 Solid Buckets Tested . • • . ·• • • • • • • • . • • • . • • 7 5 Tooth Shapes Tested for Slotted Bucket • • • . . • . • • . 8 6 Erosion Test on Angostura Spillway . • • . . • • • . . • . 13 7 Test Flume and Sectional Spillway. . • • • • . • • . . . • 15 8 Slotted Bucket Modifications Tested. . • • • . • • • • • • 17 9 Di·scharge Calibration of the 5-foot Model Spillway . • • • 21

10 Six-inch Bucket Discharging 1.75 Second-feet Per Foot. • • 22 11 .Tail Water Limits and Bucket Capacities • • . • • • . • • . 24 12 Flow Currents with Fixed Bed . • . • • • • • • • • • • . • 27 13 Nine-inch Bucket Discharging 1.5 Second-feet Per Foot. • • 29 14 Nine-inch Bucket Discharging--Tail Water Depth 1.85 Feet. • 30 15 Average Water Surface Measurements--9- and 12-inch Bucket. 31 16 Twelve-inch Bucket Discharging with Tail Water Depth

2.3 Feet • . • • . • • • • • . • • • • • • • • • • • • • 34 17 Eighteen-inch Bucket Discharging . • • . • • . • • . • . • 37 18 Definition of Symbols. • . • • . • • • . • • • • • . . • . 4o 19 Minimum Allowable Bucket Radius • . • • • • • • . . • • • . 43 20 Maximum and Minimum Tail Water Depth Limits . . . • • . • • 44 21 Minimum Tail Water L:IJni t • • • . . . . . . • • • • • • . . 46 22 Maximum Tail Water Limits • • . . • . • . • • . • • . . • • 47 23 Dimensionless Plot of Sweepout Depth . . • • • . . . • .. • 48 24 Tail Water Sweepout Depth. • • • . . • . • . • • • . . • • 49 25 Velocities on Steep Slopes . . • • . • • . • • • • • • • . 52

ii

No. -I

II III

IV V

VI VII

VIII

CONTENTS--Continued

TABLES

Pressures on Tooth Design III--0.05R Spacing •••••• Pressures on Tooth Design III--0.035R Spacing ••••• Data and Calculated Values for 6-inch Radius Bucket •• Data and Calculated Values for 9-inch Radius Bucket •• Data and Calculated Values for 12-inch Radius Bucket •• Data and Calculated Values for 18-inch Radius Bucket •• Examples of Bucket Design Procedures •••••••••• Comparison of Tail Water Depths for Bucket and

Hydraulic Jump • • • • • • • • • • • • • • • • . . • •

111

Page

10 11 23 33 35 38 50

54

Foreword

This report, Progress Report I~I, is the third in a series ot progress reports-on research subjects included under the general title ot this report. Progress Report II, published as Hydraulic Laboratory ReportHyd-399 which superseded Progress Report I, Hyd-380, contains~ sections covering the following subjects:

Section 1--General Investigation of the Hydraulic Jump on a Horizontal Apron (Basin I)

Bectio~ 2--Stilling Basin for High Dam and Earth Dam · Spillways and Large Canal Structures

(Basin II) Section 3--Short ·stilling Basin for Canal Structures,

Small Outlet Works and Small Spillways (Basin III)

Section 4--Stilling Basin and Wave Suppressors tor Canal Structures, Outlet Works and Diversion Dams (Basin IV)

·section 5--Stilling Basin with Sloping Apron (Basin V) Section 6--Stilling Basin for Pipe or Open Channel

Outlets--No Tail Water Required (Basin VI)

Section 7 is contained in this report and covers Items 11 and 12 given in the "Scope" of the research program as originall1 planned and given in Progress Report II. Other numbered items will be completed and reported in future progress reports as time and funds permit.

The bucket tests described in this report are of recent origin, however, bucket tests in general have been made since about 1933. Some of the early tests were valuable in this study in that they helped to point the'way for the later tests and eliminated certain bucket schemes from further consideration. These early tests were conducted by J. H. Douma, c. w. Thomas, J. w. Ball, and J. N. Bradley. Later tests were made.by R. c. Besel, E. J. Rusho, and J.M. Bradley under the laboratory direction of J. E. Warnock. The final tests to develop the slotted bucket and generalize the design were made by G. L. Beichley under the supervision of A. J. Peterka and J. N. Bradley and laboratory dir_ection of H. M. Martin. Most of the material contained in this report was· submitted as a thesis tor the degree of Master of Science, University of Colorado, by G. L. Beichley. All tests and analyses were· conducted in the Bureau of Reclamation Hydraulic Laboratory, Denver, Colorado. This report was written by A. J. Peterka.

UNITED STATES DEPARTMENT·OF THE INTERIOR

BUREAU OF RECLAMATION

Commissioner's Office--Denver Division or Engineering Laboratories Hydraulic Laboratory Branch .. Hydraulic Structures and Equipnent Section Denver,·Colorado July 1, 1956 · ·

SECTION 7

Laboratory Report No. Hyd-415 Compiled by: G. L. Beichley

A. J. Peterka Submitted by: H. M. Martin

SLOTTED AND SOLID BUC.KErS FOR HIGH, MEDIUM, AND LOW DAM SPILLWAYS (BASIN VII)

INTRODUCTION

General

The development of submerged buckets has been in progress f'or . many years and many types have been proposed, tested, and rejected f'or one reason or another. The bucket used at·the start of' these tests, the Grand Coulee bucket, therefore, was the result of' many trials and experiences, both in models and in ~he field. The bucket was turther developed for use at Angostura. Dam by· adding slots in the bucket and a · short sloping apron downstream. After extensive laboratory tests showed that the Angostura bucket could not be improved in a practical way, tests were conducted to generalize the design so that proper bucket dimensions and limiting conditions could be determined for any installation. Some of' the limits established during the tests had no sharp line of demarca­tion between acceptable and undesirable·perf'ormance, consequently, the results of' the tests reflect the judgment of' the testing engineers. Every attempt was made to set the limits from a practical viewpoint so that.the resulting structure would be economical to construct but would still provide safe operation for the extreme limits and satisfactory or better performance throughout the usual operating range. Strict adherence to the charts and rules presented will therefore result in the smallest possible structure consistent with good performance and a moderate factor of' safety. It is suggested, however, that confirming hydraulic model tests be performed whenever: (a) sustained operation near the limiting conditions is expected, (b) discharges per foot of' width exceed 500-6oo second-feet, (c) velocities entering the bucket are

appreciably over 100 fe~t per second, (d) eddy effects at the ends of the spillway result in poor flow conditions, and (e) waves in the downstream channel would be a problem •

. Performance

There are two general types of roller or submerged buckets for spillways; the solid type developed tor Grand Coulee Dam, Figure lA., and the slotted typ~ developed tor Angostura Dam,. Figure lB. Both types are shown operating in FigQ.re 2 and are designed to operate submerged at all times with the maximum tail water elevation below the crest of the spillway. Both types also require more tail water depth (D2) than a hydraulic jump basin.

The hydraulic action and the resulting performance of the two buckets are quite different. In the solid bucket the high velocity flow, directed upward by the bucket lip, creates a high boil on the water surface and a violent ground roller that deposits loose material from downstream at the bucket lip. The constant motion of the loose material against the concrete lip and the fact that unsymmetrical gate operation can cause eddies to sweep material into the bucket may make this bucket undesirable in some installations. In the operation of the slotted bucket both the high boil and violent ground roller are reduced, result­ing in greatly improved performance. Since only part of the flow is directed upward the boil is less pronounced. The part of the flow directed downstream through the slots spreads laterally and is li:rted away from the channel bottom by the apron extending downstream from the slots. Thus, the flow is dispersed and distributed over a greater area providing less violent flow concentrations than occur with a solid bucket.

The tail water range over which the buckets will operate satisfactorily is less, however, with the slotted bucket than with the solid bucket. Sweepout occurs at a higher tail water elevation with the slotted bucket, and if the tail water is too high, the now dives from the apron lip to scour the channel bed as shown in Figure 3. With the solid bucket, diving is impossible except perhaps in rare cases. In general, however., the slotted bucket is an improvement over the solid type and will operate over a wide range of tail water depths.

SIDTTBD BUCKET DEVELOPMEifl' TESTS

General

The basic dimensions for the slotted bucket were determined from tests made to adapt the solid bucket for use at Angostura Dam.

2

437

. . . ' .

A. GRAND COULEE TYPE SOLID BUCKET

See Figure 5 for tooth detail

0.05R radius~-

->: r:- 0.05 R I I I I I I I I

' I I

B •. ANGOSTURA. TYPE SLOTTED BUCKET

SUBMERGED BUCKETS

FIGURE L

FIGURE 2

437

A. SOLID TYPE BUCKET

' . . ..,..-------:-~~ ,,--, ~ - -~ ........_ ____ _ ·.'d: . . ~,~-------~-;' //. . ~ ---> -. . . , ~ - ( ~ "',1/ ,1t -->-. o .. ~- . .. A . I ..- ~

... -~"'"' J ./ -;r ~ ~"' o_.: ~-. ~ ~ /1/1/~ c r'~ ' ~-~ ~ • • • '-'A.. __, :r {' ~ p ........ ~~~ ? ~- ... , ,...__ - 4/) ~ "--->

· · o· · ·o · < ' · .. . ·-:.·. . . ~ . ·o. O·o· .. . . . . . . o· . . .

B. ANGOSTURA TYPE SLOTTED BUCKET

Bucket radius = 1211 , Discharge (q) = 3 c.f.s., Tailwater depth= 2.31

PERFORMANCE~ OF SOLID AND SLOTTED BUCKETS

4

i

en

437

Tailwater surface-, ~

·Note: The diving flow condition occurs with the slotted bucket only when the tailwaJer depth becomes too great.

DIVING FLOW CONDITION

SLOTTED BUCKET

-----

"Tl

Ci)

C ::u fTI

(IJ

This study is reported in Bureau of Reclamation Hydraulic Report No. Hyd-192 and is summarized in the following paragraphs.

Development from Solid Bucket

The first stage in the development was to determine the radius of' bucket required to handle the maximum. design flow and to determine the required elevation of the bucket invert for the existing tail water conditions. Solid type buckets shown in Figure 4 were used in the model to determine these approximate values since the slotted bucket had not yet been anticipated. The 100- and 63-f'oot radius buckets were found to be unnecessarily large for a discharge of 11010 second-feet per toot of width and a velocity of about 75 feet per second. The 42-foot radius bucket was found to be the smallest bucket which would provide satisfactory performance.

The tail water depth was not sufficient f'or good performance when the bucket invert was 45 feet below tail water ele~ation. Per­formance was better with the invert 69 feet below tail water ele~ation, but tor all invert elevations tested a ground roller occurred which moved bed material from downstream and deposited it against the bucket lip.

The second stage in the development was to modify the bucket to prevent the piling of' bed material along the lip. Tubes were placed in the bucket lip through which jets of water flowed to sweep away the loose material. Results were satisfactory a~ low discharges, but for the higher flows the loose material was piled deeply over the tube exits, virtually closing them.

Slots in the bucket lip were then used instead of' larger tubes. The slots were found to not only keep the bucket lip free of' loose mate­rial, but also provided exits for material that became trapped in the bucket during unsymmetrical operation of' the spillway.

In order that the effectiveness of the bucket in dissipating the energy of' spillway flows be maintained, the slots were made no larger than necessary to prevent deposition at the bucket lip. The first slots tested were l foot 9 inches wide, spaced three times that distance apart. The slot bottoms were sloped upward on an 8° angle so that the emerging flow would not scour the channel bottom, and were made tangent to the bucket radius to prevent discontinuities in the surface over which the flow passed. The spaces between the slots then became known as teeth and were 5 feet 3 inches wide. Three tooth designs, shown in Figure 5, were tested.

6

' -------i--.. :.-·_::_:·.·.. l-EI. 3157.2 . . ....

. . .

. . .

. . Bucket segment .-. : ·. :··:. · typical joint-~·:·.·:.·.·:· .. . .

' • • • I.• I • ·,. • • • •

FIGURE 4

. . . . . . · ..... -:.·.:: . . . . . . .

I • • • • • I

: . ·.·. \ ~~~-;:_E·-·,-·-3:___0. ·-4·.:.·_6 . .:.0--:. ·. ·.-. ·.·.·.·.· ... -:: :,-::·: ·. ·.·. · .. _-. :::: .. : . \;_.. ~ ~ . . . . . . . . . . . .... . . . . . . . . . : . . . . . . . . . . . . . . . . . . ' . · .. : . , . . . . . . . . . . . •· . . . . . DESIGN I

DESIGN 2 -j-----

1 \

.. <i.-· ·1 \ C'\, I ,,,. . I 0

/ I I 'I.~

I - \""' '

:~;-;-~·.+ f:· .. ·: .·: ·· . , . . . . . . . ·: : -:-El.3070.0· •II e • • I • I • • • •

I • • • • . . . . . . . . . ~ ', • • • I•

DESIGN 4

DESIGN 3 -i, -/ \ ,,,._. \

.. ,- • \ 0

. f I \f(,,,f:, . I ->j \

• • • I \

·.·;:--·,·-:-·-:--:-. ... ... : . ( . . . . . . . . : .. •. · . ·.,El. 3070.0::

" I I 9 I • I " . . . . . . . . ... • • e • • • I

• I I I • I • I I •

• .• I • o •

• I I • • • I I • • • • •.

~ . . . . . . . DESIGN 5

SOLID BUCKETS TESTED

7

FIGU-'R E 5

'

4).

[ D TOP

END SIDE

DESIGN I

: [ TOP

END SI DE

DESIGN II

.....,..!!!!!!!!!==~~~2=0=~,,=x__,_(t=:~~~~j~=,~~=~~1~7-~~Jl 0.05R rad.-! 0.J25R :

- •TOP ~ t<-0.05R 1 -------- 1

\ \

,, Reduce 0.05 R corner ~ radius to 0 at ,- - .. \ bucket P.T. - --"' ' I

\ \

~ \

i 8° SIDE

: I I 15 . '13 _s _____ _

'vL--' 14 ', ;·Radial • o,~

16 - 0c':J

END

------------1 (.., .. P.T. • DESIGN m - RECOMMENDED

TOOTH SHAPES TESTED- FOR SLOTTED BUCKET

8

Tooth Shape, Spacing, and Pressures

Tests using Tootp. Design I were encou,rag~g. The energy dissipating action of the bucket and the elimination of piled material along the bucket lip were both -satisfactory. However, small eddies, formed by the jets leaving the slots, lifted loose gravel to produce abrasive action on the downstream face of the teeth. Therefore, a sloping apron was installed downstream from the teeth to help spread the jets from the slots and also to keep loose material away from the teeth. The apron was sloped upward slightly steeper than the slope of the slots, to provide better contact with the jets. The apron was found to perform as intended; however, the best degree of slope for the apron and the shortest possible apron length were not determined until after the tooth design and the tooth spacing were determined.

Pressures. observed on Tooth Design I at the piezometer loca­tions shown in Figure 5 were, in general, satisfactory. Undesirable subatmospheric pressures were found on the downstream face, however.

The profile of Tooth Design II, Figure 5, conformed to the radiu~ of the bucket, eliminating the discontinuity in the flow passing over the teeth. Energy was dissipated more readily and a smoother water surface occurred downstream from the bucket. Pressures were sub­atmospheric at seven locations, the majority of' which were located on the downstream face. The necessary rounding of the edges of the teeth was determined by testing model radii ranging from 0.l to 0.3 inch. The larger radius (12.6 'inches prototype) was found to be the most desirable.

Tooth Design III, Figure 5, was shaped to improve pressure conditions o~ the sides and downstream face of the teeth and the radius for rounding and edges was increased to 15 inches prototype. Subatmos- · pheric pressures still occurred on the downstream face at Pi~zometers 3,. 4, and 5, but the subatmospheric pressures were above the·critical. cavitation range.

Preliminary tests had shown that pressures on the teeth varied according to the tooth spacing. The most favorable pressures consistent with good bucket performance occurred with Tooth Design III, tooth width 0.l25R and spacing 0.05R at the "downstream end. Table I shows the pressures in feet of water at the piezometers.

9

Table I

Pressures on Tooth Design III o.o~ Spaciy

Piezometer: Pressure :Piezometer: Pressure lo. : ft of water: No. :ft of water

• . • • • • l . +l to +16: 9 • +58 • •

• . . • . • 2 • +5 to +13: 10 • +42 • •

• . .. • • •

3 • -2 to +15: ll • +68 • • • • • • • ..

4 . -13 to +16: 12 +49 • • • • .

5 • -9 to +11: 13 +11 • • • . •

6 . +8 to·+16: 14 +13 . • • • .

7 • +22 • 15 +21 • • • • . .

8 • +62 • 16 +34 • • • . • • • • 17 • +39 . • •

Piezometers 1 through 6 showed fluctuations between the limits shown. Piezometers 3, 4, and 5 showed negative or subatmospheric values, but since these piezometers are on the downstream face of the teeth it is unlikely that damage would occur as a result of cavitation. According to the pressure data the teeth are safe against cavitation for velocities up to about 100 feet per second, i.e., velocity computed from th• · difference between headwater and tail water elevations, and Jll81' be sate tor even considerably higher velocities.

Reducing the tooth spacing to o.035R raised the pressures on Piezqmeters 3, 4, and 5 to positive values. Pressures on the tooth are s~ in Table II.

10

Table· II'. "' I ~ • ,'

Pi'essures ·.on Tooth, :Design III 0.035R Spacing

Piezometer: Pressure :Piezometer: Pressure No. : ft of water: No. : ft of water

1 ... :· . ;:.. ,' ·• ·• . ·-

.. ,, ·.: .: .·.;" .:··· ·: :-

+36 ·: · •9-'· -• ..

· :. : ,. 2 : ': .. ,: .. +27'' ' · -: -10

3 -. -

• • • • :- :-_.

:'..·>: ;4 .. ; :: ··· -:--_.

. 5.

. 6'

.. .. • • -·. . . . . • ·­. . , •.

+30

+26

+14

+27

+39

: : 11

. . -:.-. _ _.

.. ·.· • . . . :--• .. . .

13'-.

i4···

15

-8 ·- -·: - +64 -. -: __ ; 16 · · . . . • . .. ,.

• • . • 17

. : .

-: +62= • . ... .. +57 · . .. • • • +71 • . .. . -+63 • • • .. --+21 . • •

. . +28 • . . : +l;io· -· • .. +47 • . . . +58 .

With 0.035R spacing the teeth should be safe against cavitation for veloc-ities well over 100 feet per second., - However, f'or small buckets the openings between teeth ma'i be too small· for easy·_ c·onstruction and the slots ·may also tend-to clog with :debris.· -In other respects the bucket performance with o.035R tooth- spacing is satis:f'acitory. ·

.. -. ~ : ~ . . . . . •'

Apron Downstream from 'Teeth ·-- . -·.-_·: ... : f. ·: . ~.

The slope and- length -of' -the · apron -- downstream from· the teeth were the remaining bucket dimensions to be determined. Since the apron served to spread the Jets from the slots and also improved the stability of' the flow leaving the bucketi, ·Jt: ri.t iD.lporbt.nt.:.thli.t ·the apron. characteristics be investigated.

A 16° upward sloping apron was found to be most satisfactory. With a~·12° ·slope the f'iov-·was- ·unstable, intermittently· diving from the end of' the apron ··to scouJt the riverbed~ ·, Uslng· a 20° slope the spreading action of' the 'flow was c·ountera:cted ·to some degree by the directional effect_ of tlle ·st-ee.p apron·." · · · ·

Two apron lengths, one 10 feet and one 20 feet, were tested to determine the minimum l.e,ngth required for satisfactory operation. The

11

longer apron, o.5R in length, was found necessary to accomplish the spreading of the jets and produce a uniform flow leaving the apron. Ttle

· 20-foot apron on a 16° slope was therefore adopted tor use.

Slotted Bucket Performance

The slotted bucket, shown in Figure 1, operated well over the entire range of discharge and tail water conditions in the sectional model, scale 1:42. The bucket was then rebuilt to.a scale of 1:72 and tested on a wide spillway where end effects on the bucket could also be observed and evaluated.

In the 1:72 model minor changes were made before the bucket was constructed and installed. The bucket radius was changed from 42 feet to an even 40 feet, and the bucket invert was lowered from 69 to 75 feet below maximum tail water elevation. Figure 6 shows the 1: 72 model in operation with 277,000 second-feet (1,010 second-feet per toot), erosion after 20 minutes of operation, and erosion after l-1/2 houre of operation.

Performance was excellent in all respects; was better than tor any of the solid buckets or other slotted buckets investigated. For all discharges the water surface was smoother and the erosion of the riverbed was less.

Summary of Slotted Bucket Development Tests

Reviewing the development of the slotted bucket three factors were involved: (1) the radius of the bucket and elevat;l.on of the invert with respect to tail water tor the given flow conditions; (2) the shaping and spacing of the teeth; and (3) the pitch and length of apron downstreaii from the teeth. All three factors are important in obtaining the desired energy dissipation, a smooth water surface, and a minimum amount of river channel erosion. Dimensions of the buc~t teeth, slots, and apron are expressed in terms of the bucket radius ·in Figure 1.

GENERALIZATION OF THE SIDrl'ED BUCI<Er

General

The tests made on the Angostura bucket indicated that a satis­factory design could be developed tor use at a particular site. It was also evident, however, that generalization of the design would be desirabl so that bucket dimensions, proper elevation of bucket with respect to tail water elevation, and the capacity of the bucket could be determined for any installation~

12

The general features of the bucket, shown in Figure 11 were believed to be satisfactory but before starting the generalization tests possible :f'urther improvements in the bucket teeth were investigated. When it was found that the tooth s:tze developed for the .Angostura bucket provided best hydraulic performance, tests were then directed toward generalization of the design.

Test Equipment

An entirely new sectional model was constructed and tested in Flume B, Figure l of' Progress Report II, and also shown in Figure 7 of this report. The flume was 43 feet 6 inches long and 24 inches wide. The bead bay is 14 feet deep while the tail bay is 6 feet 3 inches deep and has a 4- by 13-foot glass window on one side. The discharge end of the flume was equipped with a motor driven tailgate, geared to slowly raise or lower the tail water so that continuous observations could be made.

The sectional spillway model was constructed to completely till the flume width, 24 inches, with an ogee crest at the top of a 0.7 slop­ing spillway face. The bucket assembly was made easily detachable from the spillway- f'ace. Four interchangeable buckets having radii of 61 91

121 and 18 inches, constructed according to the dimension ratios shown in Figure 11 were designed so that they could be installed with the buckets inverts located 5 feet below the spillway crest and about 6 inches above the floor of thF flume. All flow surfaces were constructed of galvanized sheet metal with smooth Joints. The downstream. channel was a movable bed molded in pea gravel.- The gravel analysis:

Retained on. 3/4-inch screen Retained on 3/8-inch screen Retained on Ho. 4 screen Retained on Pan

6 percent 66 percent 25 percent 3 percent

Flow was supplied to the test flume through a 12-inch centri­fugal pump and was measured by one of a bank of Venturi meters permanently installed in the laboratory. Additional water., beyond the capacity of the 12-inch pump., was supplied by two vertical-type portable pumps equipped with two portable 8-inch orifice-Venturi meters. All Venturi meters were calibrated in the laboratory. Water surface elevations were measured with hook gages mounted in transparent plastic wells.

Bucket Modifications Tested

General. To determine whether practical modifications could be made to improve the performance of' the Angostura slotted bucket the 12-incb radius bucket, constructed according to the recommended

14

.... (II

4!7

-Flume :~:.~~-~~~·1· ~:~:~:- :::~.~ flares·· '

,,2-12"Supply Pipes !

-- , -1-12"Supply pipe l

---- Flume width 23t./' from here 1odownstream end-------->>-

__ _:: ___ -------- 7!.:.4!12-;-_-.:.. __ ~--:-:-- - - ------ -4'-10" . ' ----

I I I I

I I I I I I I I I I I I I I I I I

l I I

,;b ~

I Removable crest--....,

-.,, -,!..

I

~------- - 81-5"-.,..--------+l I

I

i I l

l I I -T,-----~

!~-:r~ I:<-..;_--:-:-;-------·----- , ···li---21/2' ---- 13'-a"

;-- ·----------------. --- -~ I

'lb 'l'

rHead\l'Qter \ I gage tap ~.

' ·--i:-;·

I =,;,;. .;.t;

' ~; I:

I I I

! I I I I I I I I I ,· I I !

I I I I bl ~)

"' ~

l

----1-Fi~ed Spillway Face

' +I

...,.!z , ./rRemavable bucket '-Glass Window--.,><_,., . 0

I I

,-·Folse · Floor

! Toil water. Control Gate--,,

',. -..,

I -.,,

i 10 I

------------------r-------------~::~~~~::~:~~=::~:-~~~'-0"--------c------~~---=3'-6" ------------------------------------

I ,..._ ------'

r··--,~ .1 '·1 i s'-o"-----'----i+-------4'-ft' '-------,4.,.----3co•c ___ >-J _

. l-----s'-6"-----~r · ,' I • ' . I

-----------------------------------------------~ • I

SECTION ON i OF TEST FLUME

TEST FLUME AND SECTIONAL SPILLWAY ,, Cl C :u rrr .....

dimensions in Figure 1, was first tested. The purpose in repeating the test was to obtain data for generalization and to establish a performance standard with which to compare the modified buckets, all to be made on the 12-inch radius bucket.

To provide a standard bucket test, which was necessary to reduce the amount of testing required on each bucket modification, the 12-inch Angostura bucket was thoroughly investigated. The bucket capacity was estimated to be about 6 second-feet. Best performance tor this flow occurred with the tail water 2.3 feet above the bucket invert, Figure 2B. These conditions were used tor the standard bucket test. Also., as part of the standard test the movable bed was molded level, Just below the bucket lip, at the start of a test.

In retesting the Angostura bucket it was noted that muc,h of the energy dissipation occurred as a result of the spreading action downstream rather than in the rolling action in the bucket. Flow passed through and over the teeth to emerge at the water surface some 3 or 4 feet downstream from the bucket, Figure 2B, producing a boil at this point and waves on the water surface downstream. In some installations action of this type might be objectionable since bank erosion could occur or powerhouse operation could be affected.

It was concluded from these tests that if improvements could be made in the. bucket performance, reduction in wave action in the downstream channel should be given first consideration since energy dissipation and bed erosion. were entirely satisfactory. Four modifications of the bucket teeth were tested; the bucket with teeth removed was also investigated. Also, a solid bucket was tested to indicate the relative advantages of the two types. Only a brief description of these tests is given since none of the modifications are recommended for general use. However, to indicate the scope of the testing a SUllllll&rY of these tests is given.

Tooth Modification I. In the first modification the teeth were extended in height from 456 to 60° as shown in Figure 8. The spacing of the teeth and the shape and length of the apron were not modified since these bad been carefully determined in the early development tests.

In operation with the standard test the bucket performed much the same as the original. The boil occurred about 6 inches farther upstream and was higher than for the Angostura bucket. Waves were also as high or higher, and since the sweepout point was about the same no further testing was done.

Tooth Modification II. In both the Angostura and modified buckets tested it was noted that the water surface directly over the

16

"

"i' // ', II II ,, , 0 72->' l<--6 -->I ., I ' • I I I ,,.-- I ', , 1 I

. ,.," ', - : : ·- --· ... : ," O ii, I I . f

C:." , I~ 6.o I. ,<--A'-J . '·' I I ', I

I I I

ANGOSTURA TYPE SLOT,J'ED BUCKET

15'!.>1 ~ . ,, , ' I I

. .,,.---.----, _____ II

,/ I ," . • I

,.,," ~· . ,· ./ ·,," 0 ,,,,"' ,q, :· __ ,

SLOTTED BUCKET MODIFICATION n

SLOTTED BUCKET MODIFICATION Ill:

SOLID BUCKET

FIGURE 8

SLOTTED BUCKET MODIFICATION I

k--611-->1 I I

I I I I

16!, : ' \ I

SLOTTED BUCKET MODIFICATION m

ANGOSTURA TYPE BUCKET WITHOUT TEETH

· Dimensions applicable to all designs­'Bucket invert to downstream edge

of structure = 15.21 11• •

Approach chute slope= 7: 10. Bucket radius = 121:

Where shown; tooth width = 1.5 11 and space between teeth = 0.721~

SLOTTED BUCKET MODIFICATIONS TESTED

17

bucket was lower than the tail water downstream. It was believed desirable to move the boil upstream directly over the bucket, consequently, the teeth were extended in height to an angle ot 90°, as shown in Figure 8. It was realized that the teeth would be too tall to be structurally stable in any but a small bucket but the trend in performance was the real purpose 1n making the test.

Performance of' this modified bucket was excellent for the standard test. A large portion of' the flow was turned directly upward to the water surface where it rolled back into the bucket. The tail water depth directly over the bucket invert was about the same as the depth downstream. A slight boil could be detected over the teeth, but it was not nearly as great as for the two previous slotted buckets tested. The flow passing between the teeth also provided fairly uniform distribution of velocity from the channel bed to the water surface 1n the c~l downstream. The water surface was quite smooth and the channel bed was not-disturbed.

The bucket also performed well for high and low tail water elevations. The tail water could be raised to a higher elevation than for the two previous buckets before the flow pattern changed to scour the channel bed; and it could be lowered to a lower eievation before the now was swept from bucket. Thus, the range of tail water depths for which the bucket operated satisfactorily was increased.

The performance of this bucket was very good in every respect; however, cavitation could occur mor~ readily on the surfaces of the tall teeth. Cavitation pressures or the possibility of eliminating such pressures were not invesiigated because the teeth were considered too high f'or practical use on large structures. Therefore, this slotted bucket modification is suggested for possible use with small buckets where cavitation pressures cannot occur, i.e., velocities near the teeth below 50 feet per second.

Tooth Modification III. In the third modification a tooth radius half' that of' the bucket radius was used, as shown in Figure 8, to curve the teeth to a height of 9()0 • This modification was made to determine whether the height of' the teeth, or the 90° curvature of the teeth, provided the improved performance.

Tests showed that the shorter teeth were not effective in lifting flow to the surface. Flow passed over and through the teeth to form a high boil dc?wnstream similar to the first modification. In addition, o~servation of' the flow passing over the tops of the teeth indicated that cavitation pressures were a likely possibility. Pressures were not investigated since performance was not as good as for the Angostura slotted bucket.

18

:,.,:

;•.· ',l'ootb Mod.i:ficati-on rv· .. Modification iv u-t.ilized the same tooth as Modificat_ion -Il;I., but· the t~eth were1_;placed qn the ap:ron 'at -the down• stre':Jll e~d of the 't>ucket,,- a1:1· sh~ -in F+guz:e 8. :Ct W$.S anticipat.ed that· the teeth, placed farther downstream and at a slightly higher elevation, would turn a portion of the now directly upward to the-water surface as for Modification II. Performance tests showed that the teeth turned .. more of the f'low upward but the performance was no better than f'or the_ Ango~tlµ"&:, design.

' ; . ' . -

: Angg1:1tur'1 bucket with .teeth removed. - The Angostura buc~t without teetb_-is SQ9Wll in-F_;Lgure 8. Tb.is design was not expected t~ perform: _as we:t.i as .the _sl,otted Angostlll'a bucket, but: was. ·testeq to · indi:ca.te t.lle v:al~ of the teeth and slot1:1 in dissip11.t:l,ng -ttie -e:r;iergy- of the spillway flow. Operation was quite satisfactory for flows .cOf'.-3 .. and 4 second-feet but performance was poor for 6 second-feet. For the higher tl°"s.ot 5to 6second~f'eet,the1:'low leaving the bucket.was u~stal:ll,e and the wat!!r sur~e was rough. For.a few seconds.the boil would: be. quite high then suddenl-Y: -,,ould ,become quite low. _Erqsion. of the. riverbec3.: was negligible fo::r,- all fl.ows, however •

. ·· ... . . .

Th~ tests without -teeth in th~ b:ucket indicated t~t-t~e prill'.J.arY funct-fon of the teeth is to stabil-ize the flow and reduce water surface fluctuations ~ the. channel downstre-•. _Tbe-~ests. also suggeat_ed .the fact that should the teeth in the Angostura bucket deterior•te oyer. a . period of time in a prototype structure, the 111 effects of the deterio­ration could be easily observed and evaluated. Discharges up to about half maximum wo~d .be sa~isfaeto-ey. "'.1th tbe- teeth _gone. .

.- . . . .

Solid bucket. _The solid bucket design, shown in Figure 8, was . tested to compare the action with that of a slotted bucket. Figure 2 shows, th~. bucket performing ~d~r similar discharges and t,11 water elevations •. For the solid bucket, all of t_he flow is directed :to the water sµrtace a short,distance downstream from the bucket,_resulting in a ver., high boil. Part of the flow rolls back into the bucket while part, continues on downstream. Since there are no slots to provide flow C'lll'.rents in .a downstream.direction un~::r,- the'b9111 a.v,iol~nt undercurrent flowing upstream, -or _ground roller, exists at all ti~es. It is the .. ground roller that moves _gravel upstream and deposits it at the bucket. lip. Currents passing over the. lip then pick up the. material and move it downstream, :restµ.ting in_ a cont_inua;L circulation of bed material. The action itself is. harmlesi:, except that the l:iP is- exposed.t~. ab~sive ... action 11,11d with '11;!,Symmetrical oper(l.tion of' the spillw&Y: gates the ... material . is often swept into. the buc.ket. O:nce the . material is i.n the

.~ucket,. it is trapped and causes erosiqn ·ot ~he concrete. su,r.fa.ce·s -as _it is moved about both. laterally and lpngitudinally insi-de the bucket arc. Therefore, a solid bucket, without slots, has certain disadvantages where loose material may be carried into the bucket or where the high boil might be objectionable.

19

Some advantages, however, were found for use of a solid bucket. A lower tail water elevation is required to sweep the flow out of the bucket and the flow could not be made to dive from the bucket lip to scour the channel bed. However, in general, the slotted bucket performed better than the solid bucket.

Summary

The Angostura bucket performed better than any of the modified forms.of the bucket except Tooth Modification II. However, the high teeth in Modification II were considered to be impractical for most prototype construction and the possibility of cavitation at high velocities is great. For small structures the relatively high teeth might be practical in which case the use of Tooth Modification II should be considered.

The Angostura slotted bucket with or without modifications, in general, is considered to be superior in performance to the solid bucket, The Angostura slotted bucket also provides more stable flow and better energy dissipation than did the Angostura bucket with teeth removed; how­ever, with the teeth removed fairly good energy dissipation occurred without disturbing the channel bed. The Angostura slotted bucket without modification is, therefore, recommended for use on spillway structures where tail water depths are within the limits required for use of a bucket type energy dissipater.

Determination of Radius and-Tail.Water Limits

General

The investigation to determine the minimum bucket size and tail water limits for a range of structure sizes, discharges, and overfall height was accomplished with the testing of 6-, 9-, 12-, and 18-inch radius buckets, tested in that order.

For each bucket installation, a range of discharges was passed over the spillway. The head on the spillway was measured and recorded. The relation between head and discharge on the spillway is shown in Figure 9. For each discharge, the tail water depth was lowered slowly until the flow swept out of the bucket, as shown in Figure 10. Since the bucket study did not include flip-type buckets, the depth at sweepout was considered too low for proper performance of the bucket. The tail water sweepout depth, measured above the bucket invert, was recorded in Tables III to VI and plotted in·Figure 11. Figure 10 also shows the bucket operating with tail water depth Just safely above the depth required for

20

FIGURE 9 ..

,. 6 .---,--~r--~.----.----.--------,.----,.----,.-----------1.5 t---t---1-------if-------f------f----t---+---+---+---+---+---+---+---t

....... ' t.4 1-.---+----+---+---+---+---'--+---+---+---,--+---'-'-+--+--+--+-'--I

/ 1.3 1----~------1--~,..._---1----1---+--+--+--+--+--+..;....;;.-+_;_-+_.,.,,,.'----i ·---···. -···-··· ······· -- .. .-:.: .. ,. . .... -... . ... , /v. ,.2 .,__--+--+-'---.-+-~~.,;......,+,___,;_..,,--i-'---,-+..,+;--+-~f---+---/-,,_;..+-v_..,.'l----+-----I

I. I t---+---1-------if-------1------1----t---+---+---+---+.----+---+--+----t

/" .J

~ ~:t----t--,-+---+---+---+--t-----t1: -/_:~v __ ·t------ir---t-----,..--:-;--------i

z I/' = :c o.e J'-. ...;.· .,;,.,;· --+----+---+---+---+---#----+---+---+---+----:-c-+--+--+-'--1

= V C ...... , . . . ·:J· ·.-., . •! ,. ··., ,·1

<I o. 7 t----'--l---l-----'11---'----'l__,;_~__:..____,,_.;....,;1,._; ......... _._-+--+--+--+--+---I

~ ~~~- ~Desig.n head,.;0.587 0.6t---+------,l-------if--...,,.,"+-fty1F----+----.------,-----,----t----t----i---;---;-------i

437

/__ OSt---1-----1--·""'··A-l~~>--+--+---+-------+---+-,---+---+---+--+---t---t------t V ~

!::;

~4 " .. _/ f . .o.3 r "fi

/ ut.

0.2 t-/---#--+----+-----t : • .2'

0.1 ------ : f C

2 3 . 4 -5 DISCHA.RGE II II IN' SECOND FEET q .

. ,, · · . PER FOOT OF WI 0TH

·o.lSCHARG.E CALlBRAT•oN OF: THE 5-FOOT MODEL SPILLWAY

~··' ~ ...

.. •.

·21

7

FIGURE 10

A. Tailwater below minimum. Flow sweeps out.

·-.. ~ . . -----: :·.·.. /7-)--::5'~ :---. -::::::;--~---~ =-->, Iii> -

· .. : =. ·:.. ( ' ~-~ ~ --- Di- _ _____,,.. l> .,. .. :.-.. ~'-.-1/~- )~ ~ ~ > l>

.•. · . . :.··\.."-.A ,: <- .) ~ -----------------. . . . . . . ----•• •.; •: ;·:.-::::: o--ir--~-

B. Tailwater below average but above minimum. Within normal operating range. ·

--------------------·:. v------------- ",/ ------- ---· .. = ··" ~ - "" r -c.- .c. / __... - I> -- ... >-: •• ·: ,' ~ \.. <;: ) ( <::> • / / / ~ - ... > ... · : . _., - 1/ /. / ,,,,.-:=: ::---- -· .. : : : : ~ -------- ~~~_;°./-................ (> .> -> ~ --- >-

• • • • : • ~ ____..,. ,P, ·"A .,. '-, -- I>--

..... : ,: •: ;: :·::;~ ~ !¥~'?(' -- -------

C. Tailwater above maximum. Flow diving from . apron scours channel

/2-_;:::;::-- ...... - ---- - ----------: .... : . ' -c.-: <-3- . --:-- -- ----.... : ~ ""\ ~- --- --- --> . . . ~ -:__ ~ --- -- ____..

__ ,.. ..... ·t~ /. ~ ____ . -- ;, --- ~ . . . . . . . .'- . ,,,,.,,,,. - - --- ? .,,........_..,,__ "' ~ - 0,,. ...... ··-7' -~,,.. ~ -;;> --- ....... ~ -- ~ . . • . .. . < C ,.....,,, ___ _,,,,.. ........_ ___ __. ...____, ____ _ .. · .. -:.:::-:-::: ... _/ . .

D. Tailwater same as in C. Diving jet Is lifted by ground ~ roller. Scour hole backfills similar to B. Cycle repeats. -..

~

( Bed level 0.3-inch below apron lip at start of test)

6-INCH BUCKET - DISCHARGE. (q) = 1.75 C.F.S.

Table III

DATA AND CALCULATED VALUES FOR 6-INCH RADIUS BUCKm'

Bed was a roximatel 1 2 J

Sweepout Conditions

1 H 0.198 0.274 0.352 o.413 o.48o 0.481 0.526 0.581 0.678 .. :

2 T ( sweepout depth ) 0.767 0.765 0.826 0.943 1.023 1.0~1 : 1.139 1.203 1.403

3 q 0.31 0.54 0.81 1.03 1.30 1.30 1.50 1.75 2.25 . 4 ; Tmin 0.967 0.965 1~026 1.143 1.223 1.281 1.339 1.403 1.603

v12 5 2g = X + H - Tmin 4.231 4,309 4.326 4,270 4.257 4.200 4.187 4.178 4.075

6 V1 16,50 16.65 16.70 16.58 16,56 16.45 16.42 16.41 16.20

7 : D1 0.019 0.032 o.048 0.062 0.078 0.079 0.091 0.107 0.139

8 V1

21.2 16.31 13.36 11.72 10.42 10.31 9.50 8.85 7.65 F "'-ygi>, :'.Ew.n 1

51.43 29.78 21.10· 18.40 15.57 16.21 14.66 13.16 11.54 9 : Di

10 D + V12 4.245 4.341 4.374 4.332 · 4.335 4.279 4.278 4.285 4.214 1 2g

R 11 v12

D1 + 2g 0.12 0.12 0.11 0.12 0.12 0.12 0.12 0.12 0.12

Diving Flow.Conditions

12 T (diving depth) 2.565 2.576 2.435 2.464 2.439 2.397 2.043 2.200 2.213

13 Tmax 2.065 2.076 1.935 1.964 1.939 1.897 1.543 1.700 1.713

14 v12 2g=X+H-Tmax 2.133 2.198 2.417 2.449 2.541 2.584 2.983 2.881 2.965

15 V1 11.72 11.89 12.47 12.55 12.78 12.90 13.86 13.62 13.81

16 D1 0,026 o.045 0.065 0.089 0.102 0.101 0.108 0.12'8 0,163

17 V1

12.67 9.84 8.62 7.40 7.cx; 7.20 7.42 6.70 6.02 FV@i

18 : Tmax 1

77.92 45.72 29.76 21.62 19.06 18.82 14.26 13.23 10.51 :Ti"" : V12

19 D1 + 2g 2.159 2.243 2.486 2.538 2.643 2.685 2.983 3.009 3.128

R

20 v12 D1 + ""2g

0.23 0.22 0.20 0.20 0.19 0.19 0.17 0.17 0.16

R = bucket radius (ft) H = height of reservoir above the crest (ft) T = depth of tail water above the bucket invert (ft)

Tmin = minimum·tail water depth for good performance (ft)= sweepout depth+ 0.2 ft Tmax = maximum tail water depth for good performance (ft)= diving depth - 0,5 ft

q = discharge per foot of model crest length (cfs) X = height of crest above bucket invert= 5 feet

V1 = velocity of flow entering the bucket computed at tail water elevation (ft/sec) Dl = depth of flow entering the bucket computed at tail water elevation (ft) F = Froude number of flow entering bucket computed at tail water elevation

Maximum capacity of bucket estimated to be 1,5 to 1.75 second-feet· per foot of width.

23

l ,-

~,

1.5

1.4

1.3

1.2

I .I

1.0

i-: 0.9 LL

E 0.8 ::c -0 0.7 <t w :::c. 0.6

0.5 I

0.4

' 0.3

0.2

0.

a

Approx. Cop. of 911 -Bucket J/ with bed approx. o.05R /

below apron lip-- .... / ' ' Approx. Cop. of 6"-Bucket with z ./

bed approx. 0.05R below apron lip- -- l/u {\ \ -, n/

f?1 V v·, /

L~-.;,< ~ - .,. Sweepout depth with be_d ___ ...

½ 1/ Y; v'1 approx. 0.05R below apron lip. --.c:.::; ~- .......... ·v 'Q.1' I

~ v~ .P ~ ~ I

7 CY- ' " I

/ '"-I

~

v~ Minimum depth for satisfactory/, perform once of the bucket.-"

cf

FIGURE 11

--8

7

6

5

4 (/) LL 0 --E

3 CT -lLJ (!)

I\ /' i-Approx. Cop. of 18"-Bucket --

with bed approx. o.05R t:.

7 I I below apron lip. -Maximum depth for satisfactory I ~ / --

~/ y I I performance of bucket when bed

> I is approx. o.05R below apron lip. _, I I

'

/ J:(' I,' --/ -Approx. Cop. of 12"-Bucket

~/· - t:. ,," with bed approx. o.o5R ,, I below apron lip. I fl x· I I --

I I I f, ! 4.-. I

0 ~ .... ' r--~ -

/ 1 I\ 0 --,. ~ l1 -j---_ , v-,. ~-.. ___

/ r--~ \ / ~-- • / r---._

a:: <t

2 ::c 0 (/) -0

/ p l 0 -- , ,I A -,, -"/ 1 r--.- / / r-- r--..

~ 0 0 / ~ / • / -- /~ .... -

I / / ~

~ / "·-< r--.-.. ••Cle r--;,. .... , / --r--- , / 0 -x

'·..........._, - .,_ /

• ,., -~ r----I 0 /

"'-..... ,, ,. ( --~ • 1 - --a-_

< ·- I r---r---~ 0 \ -_,, -~

--~ ,., --........... '

' ' -- •·Minimum ta itwoter depth for

I ,., .. diving to occur when bed is

I "a.... 'Z~ I approx. 0.05R below apron lip. \ ' '--Minimum tailwater depth for diving to occur

when bed slopes up from apron lip.

0.4 0,5 0.6 0.7 0.8 0.9 1.0 I.I 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 TAILWATER DEPTH (T) FEET

BUCKET CAPACITY IN TABLE TEST BUCKET BUCKET C.F.S. PER FT. OF WIDTH RADIUS

BED APPROX. BED SLOPES (R) INCHES 0.05R BELOW UP FROM

APRON LIP APRON LIP 6 1.5 TO 1.75 -9 2.0 TO 2.5 1.5

-------.,2 3,25 TO 3.5 2.0 TO 2.5 18 5.0 TO 5.5 -

NO DATA RADIUS BED ARRANGEMENT DESCRIPTION OF TEST DATA SYMBOLS SYMBOLS CR} INCHES

m 0 6 Bed approx. o.o5R below apron lip. Tailwater sweepout depth and Min. toilwater depth at which diving occured

nr 0 9 Bed approx. 0.05R below apron lip. Tailwater sweepout depth and Min. tailwoter depth at which diving occured

'JZ: fl 12 Bed approx. 0.05R below apron lip. Tailwater sweepout depth and Min. tailwater depth at which diving occured.

n 0 18 Bed approx. 0.05R below apron lip. Tailwater sweepout depth

'Q. 18 Bed approx. 0.05R below apron lip. Est. Min. toilwoter depth for satisfactory performance of the bucket

• 9 Bed approx. 0.05R below apron lip. Est. Mox. tail water depth for satisfoftory performance of the bucket. A 12 Bed approx. 0.05R below apron lip. Est.Max. tailwater depth for satisfactory performance of the bucket.

m • 9 Bed sloped up from apron lip. Min. tailwoter depth at which diving occured.

'lr X 12 Bed sloped up from apron lip. Min. tail water depth at which diving accured.

TAILWATER LIMITS AND BUCKET CAPACITIES

24

Q >­::c:

, JI,,,_. I ,_,,_.A.J__,,,,"_, // BHP.EAU OF RECLAMATION v...,... ,,,, _______ cJ' HYDRAULIC LABORATORYi

f~ :ii~'Z-2- omcE UNITED STATES FILE COPY .

DEPARTMENT OF THE INTERidiEN BORROWED RE'I'URN PROMPTLY BUREAU OF RECLAMATION

PROGRESS REPORT III

RESEARCH STUDY ON STILLING BASINS. ENERG . .1f DISSIPATORS, AND ASSOCIATED APPURTENANCES

SECTION '7

SLOTTED AND SOLID BUCKETS FOR HIGH., MEDIUM, AND LOW DAM SPILLWAYS

Hydraulic Laboratory Report No. Hyd-415

DIVISION OF ENGINEERING LABORATORIES

· COMMISSIONER'S OFFICE DENVER, COLORADO

July 1, 1956

Swmnary

The slotted bucket developed in this study for use as an energy dissipater at the base of a spillway is particularly suited to installations where the tail water is too deep for a hydraulic jump apron, or where a bucket structure is preferable to a longer hydraulic jump stilling basin. Charts and curves are presented in dimensionless form so that a bucket may be designed for most combinations of dis­charge, height of fall, and tail water range. The resulting bucket will provide self cleaning action to reduce abrasion erosion in the bucket arc, protection against undermining of the bucket and apron as a result of scour, and good vertical distribution of the flow leaving the bucket. The water surface downstream from the bucket may, for the lower tail water elevations, be somewhat rougher than desirable, however, making it necessary to consider the effects of possible riverbank erosion.

A schematic diagram of a spillway and slotted bucket containin. definitions of the important dimensions is shown below:

. . ··.· .... Bed may be level or ) sloping ( see text)._.,

A simplified version of the seven steps required to design a bucket is given below:

1. Determine Q, q (per foot width), V1 D1; compute Froude V1

number from F = "/ gn1 for maximum flow and intermediate flows. In some

cases Vi may be estimated from Figure 25.

2. Enter Figure 19 with F to find bucket radius parameter R

V12 from which minimum allowable bucket radius R may be computed. D1 +-2g

R

3. Enter Figure 21 with D + V12 and F to 0 l 2g .

minimum tail water depth limit may be computed.

find Tmin from which D1

4. Enter Figure 22 as in Step 3 above to find maximum tail water depth limit, Tmax.

5. Make trial setting of bucket invert elevation so that tail water curve elevations are between tail water depth limits determined by Tmin and Tmax. Check setting and determine factor of safety against sweepout from Figure 24 using method!:! of Step 3. Keep apron lip above riverbed, if possible.

6. Complete design of bucket using Figure 1 to obtain tooth size, spacing, dimensions, etc.

7. The sample calculations in Table VII, page 48, may prove helpful in analyzing a particular problem.

The procedures outlined above summarize the main considerations in the design of a slotted bucket. Other considerations are discussed in the report, however,-and the entire report should be read before attempting to use the material given above.

CONTENI'S

Introduction. . . .. . . . . . . . . . . . . . .. . . . . . . . . General Performance •••••••••• Performance • • • • • • • • • • • • • •

• • • • • • • • • •

• • • • . . . . Slotted Bucket Development Tests . . . . . . . . . . . . . . . .

General • • . • • . • • • • • . • • • • • • • • • • • • • Development from Solid Bucket • • • • _. • • • • • • • • • Tooth Shape, Spacing, and Pressures ••••••••••• Apron Downstream from Teeth ••••••••••••••• Slotted Bucket Performance •••••••••••••••• Summary of Slotted Bucket Development Tests • • • • • • •

Generalization of the Slotted Bucket . . . . . . . . . . . . . . . General •••••••••• Test Equipment • • • • • · • • Bucket Modifications Tested

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

General . • • • • . • • • • • • • • • • • • • • • • • • Tooth Modification I ••••••••••••••••• Tooth Modification II ••••••••••••••••• Tooth Modification III •••••••••••••••• Tooth-Modification IV ••••••••••••••••• Angostura Bucket with Teeth RelllOved •••••••••• Solid Bucket ••••••••••••••••••••• Summary • • • • • • • • ' • • • • • • • • • • • • • • •

Determination of Radius and Tail Water Limits • • • • • • • •

General •••••••• Six-inch Radius Bucket •

Lower Tail Water Limit Upper Tail Water Limit Maximum Capacity ••

• • . . . . . . . . . . . . . . . • • • • • • • • • • • • • • • • •

. . . ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ . . . . . . . . . . Nine-inch Radius Bucket ••••••••••••••••• Twelve-inch Radius Bucket • • • • • • • • • • • • • . • • • Eighteen-inch Radius Bucket • • • • • •. • • • • • • • • • Larger and Smaller Buckets •••••••••••••••• Data Analysis • • • • • • • • • • • • • • • • • • • • • •

1

l 2

2

2 6 9

11 12 12

12

12 14 14

14 16 16 18 19 19 19 20

20

20 25

25 25 28

28 32 36 36 39

C0NTENTS--Continued

• • • • • • • • • • • • • Safety Factor •••••••• Evaluation of Variables ••• • • • • • • • • • • • • •

Practical Applications •••• . . . • • • • • • • • • • •

Tail Water Requirements for Bucket Versus Hydraulic

39 39

45

J'lllllp • • • • • • • • • • • • • • • • • • • • • • • • 53

Summary of Bucket Design Procedures. • • • • • • • • • • • • 55

FIGURES

!2.:.. !!s!. 1 Submerged Buckets. • • • • . • • • • • • • • • • • • • • • 3 2 Performance of~Solid and Slotted Buckets • • • • • • • . • 4 3 Diving Flow 0ondition--Slotted Bucket. • • • • • • • • • • 5 4 Solid Buckets Tested • • • . ·• • • • • • • • • • • • . • • 7 5 Tooth Shapes Tested for Slotted Bucket • • • • . • . • • . 8 6 Erosion Test on Angostura Spillway . • • . . • • • . . . . 13 7 Test Flume and Sectional Spillway. . • • • . . • • . • . • 15 8 Slotted Bucket Modifications Tested. . • • • . • • • • • • 17 9 Discharge Calibration of the 5-foot Model Spillway . • • • 21

10 Six-inch Bucket Di-scharging l. 75 Second-feet Per Foot • • • 22 11 .Tail Water Limits and Bucket Capacities • • . • • • . • • • 24 12 Flow Currents with Fixed Bed . • . . • • • • • • • • • . • 27 13 Nine-inch Bucket Discharging 1.5 Second-feet Per Foot. • • 29 14 Nine-inch Bucket Discharging--Tail Water Depth 1.85 Feet. • 30 15 Average Water Surface Measurements--9- and 12-inch Bucket • 31 16 Twelve-inch Bucket Discharging with Tail Water Depth

2.3 Feet . . • • . • • . • . • • • • • . • • • • . . • • 34 17 Eighteen-inch Bucket Discharging . • • • • • • • • . • • • 37 18 Definition of Symbols. • . • . • • • • • • . • • • • . • . 4o 19 Minimum Allowable Bucket Radius. . • • • . • • . • • • • . 43 20 Maximum and Minimum Tail Water Depth Limits • • • • • . . • 44 21 Minimum Tail Water LjJnit • • • • • • . . . • • • • • • • . 46 22 Maximum Tail Water Limits • • . . • . • . • • . • • . • • • 47 23 Dimensionless Plot of' Sweepout Depth • . • • . . . • • • . 48 24 Tail Water Sweepout Depth. . . • • . • . • . • • • . • • • 49 25 Velocities on Steep Slopes . . . . • . • . • . • • • • • • 52

11

No. -I

II III

IV V

VI VII

VIII

CONTENTS--Continued

TABLES

Pressures on Tooth Design III--0.05R Spacing •••••• Pressures on Tooth Design III--0.035R Spacing ••••• Data and Calculated Values for 6-inch Radius Bucket •• Data and Calculated Values for 9-inch Radius Bucket •• Data and Calculated Values for 12-inch Radius Bucket •• Data and Calculated Values for 18-inch Radius Bucket •• Examples of Bucket Design Procedures •••••••••• Comparison of Tail Water Depths for Bucket and

Hydraulic Jump • • • • • • • • • • • • • . . . . . • •

111

Page

10 11 23 33 35 38 50

54

Foreword

This report, Progress Report rrr, is the third in a series ot progress reports·on research subjects included under the general title of this report. Progress Report II, published as Hydraulic Laboratory Report Hyd-399 which superseded Progress Report I, Hyd-38o, contains~ sections covering the following subjects:

Section 1--General Investigation of the Hydraulic Jump on a Horizontal Apron (Basin I)

Section 2--Stilling Basin for High Dam and Earth Dam Spillways and Large Canal Structures (Basin II)

Section 3--Short Stilling Basin for Canal Structures, Small Outlet Works and Small Spillways (Basin III)

Section 4--Stilling Basin and Wave Suppressors for Canal Structures, Outlet Works and Diversion Dams (Basin IV)

·section 5--Stilling Basin with Sloping Apron (Basin V) Section 6--Stilling Basin for Pipe or Open Channel

Outlets--No Tail Water Required (Basin VI)

Section 7 is contained in this report and covers Items 11 and 12 given in the "Scope" of the research program as originally planned and given in Progress Report II. Other numbered items will be completed and reported in future progress reports as time and funds permit.

The bucket tests described in this report are of recent origin, however, bucket tests in general have been made since about 1933. Some of the early tests were valuable in this study in that they helped to point the'way for the later tests and eliminated certain bucket sr.hemes from further consideration. These early tests were conducted by J. H. Douma, c. w. Thomas, J. w. Ball, and J. N. Bradley. Later tests were made by R. c. Besel, E. J. Rusho, and J. N. Bradley under the laboratory direction of J.E. Warnock. The final tests to develop the slotted bucket and generalize the design were made by G. L. Beichley under the supervision of A. J. Peterka and J. N. Bradley and laboratory direction of H. M. Martin. Most of the material contained in this report was· submitted as a thesis for the degree of Master of Science, University of Colorado, by G. L. Beichley. All tests and analyses were conducted in the Bureau of Reclamation Hydraulic Laboratory, Denver, Colorado. This report was written by A. J. Peterka.

UN:tTED STATES DEPARTMENT OF THE INTERIOR

BUREAU OF RECLAMATION

Commissioner's Office--Denver Division of Engineering Laboratories Hydraulic Laboratory Branch ..

Laboratory Report No. Hyd-415 Compiled by: G. L. Beichley

A. J. Peterka Submitted by: H. M. Martin Hydraulic Structures and Equip~nt Section

Denver, · Colorado July l, 1956

General

SECTION 7

SLOTTED AND SOLID BUCKETS FOR HIGH, MEDIUM, AND LOW DAM.SPILLWAY$ (BASIN VII)

INTRODUCTION

The development of submerged buckets has been in progress tor . many years and many types have been proposed, tested, and rejected tor one reason or another. The bucket used at·the start of these tests, the Grand Coulee bucket, therefore, was the result of many trials and experiences, both in models and in ~he field. The bucket was further developed tor use at Angostura. Dam by· adding slots in the bucket and a · short sloping apron downstream. After extensive laboratory tests showed that the Angostura bucket could not be improved in a practical way, tests were conducted to generalize the design so that proper bucket dimensions and limit-ing conditions could be determined for any installation. Some of the limits established during the tests had no sharp line of demarca­tion between acceptable and undesirable·performance, consequently, the results of the tests reflect the judgment of the testing engineers. Every attempt was made to set the limits from a practical viewpoint so that.the resulting structure would be economical to construct but would still provide safe operation for the extreme limits and satisfactory or better performance throughout the usual operating range. Strict adherence to the charts and rules presented will therefore result in the smallest possible structure consistent with good performance and a moderate factor of safety. It is suggested, however, that confirming hydraulic model tests be performed whenever: (a) sustained operation near the limiting conditions is expected, (b) discharges per foot of width exceed 500-6oo second-feet, (c) velocities entering the bucket are

appreciably over 100 :f'e~t per second, (d) eddy e:f'fects at the ends of' the spillway result in poor flow conditions, and (e) waves in the downstream channel would be a problem.

.Performance

. There are two general types of roller or submerged buckets for spillways; the solid type developed for Grand Coulee Dam, Figure lA, and the slotted typ~ developed for Angostura Dam,. Figure lB. Both types are shown operating in Fi~e 2 and are designed to operate submerged at all times with the maximum tail water elevation below the crest of the spillway. Both types also require more tail water depth (D2) than a hydraulic jump basin.

The hydraulic action and the resulting performance of the two buckets are quite different. In the solid bucket the high velocity flow, directed upward by the bucket lip, creates a high boil on the water surface and a violent ground roller that deposits loose material from downstream at the bucket lip. The constant motion of the loose material against the concrete lip and the fact that unsymmetrical gate operation can cause eddies to sweep material into the bucket may make this bucket undesirable in some installations. In the operation of the slotted bucket both the high boil and violent ground roller are reduced, result­ing in greatly improved performance. Since only part of' the flow is directed upward the boil is less pronounced. The part of' the flow directed downstream through the slots spreads laterally and is lif'ted away from the channel bottom by the apron extending downstream from the slots. Thus, the flow is dispersed and distributed over a greater area providing less violent flow concentrations than occur with a solid bucket.

The tail water range over which the buckets will operate satisfactorily is less, however., with the slotted bucket than with the solid bucket. Sweepout occurs at a higher tail water elevation with the slotted bucket, and if' the tail water is too high, the flow dives from the apron lip to scour the channel bed as shown in Figure 3. With the solid bucket, diving is impossible except perhaps in rare cases. In general., however, the slotted bucket is an improvement over the solid type and will operate over a wide range of tail water depths.

SroTTED BUC:ml' DEVELOPMENT TESTS

General

The basic dimensions for the slotted bucket were determined from tests made to adapt the solid bucket for use at Angostura Dam.

2

437

A. GRAND COULEE TYPE SOLID BUCKET

See Figure 5 for tooth detail

0.05R radius~-

->: r:- 0.05 R I I I I I I I I

' I I

B. ANGOSTURA TYPE SLOTTED BUCKET

SUBMERGED BUCKETS

3

FIGURE L

FIGURE 2

437

-----' _.;- '- . '\. I., ~\ . ,.,..., ..... ~ ~- . ,,.,,,. / / .,......---:.. ............ .. --- -.._.,,,,;---

. c· ~ "Y-------.../ ~) ~ .. ·-.-~·-. ~ r r ) J / ?~ ~ ---:. ... . ·.·.-:·\~ "'--:/&? Q .. ~~~ --

0 • -~,~ - -{~'- o--- o--- ;;..} .. ,~ ~'· ---..__ · •• c;:,. ..........__,,, 0 0 0--~ _, 0 ~ • • • • . 0· I-,' . • . 6' . . . . . --~ .....,.,,, ~ ' • 0 • • O•

. · .. ·o· .. . . .

A. SOLID TYPE BUCKET

" -------·.0-. ,, . ,,,-,,,.,- ----~ ............._ ____ _ .. :"\..'\...~ _,/ /..,,.. ·.o:. -~~/'------~ /' . ~ . ~ ---> -. :_o·\ '}~ ( r,. ~) 1/1' / --->- -----.

.. -~"''"' __J ,. ~ ;-,-~ ~ o.·:6--~~ .//1/1// ( r> '\ ~'---> ·.·· ~~_.,., -:r,~ ~"' •• --- t-'r. ..........

•• 0:; • • :r ~ e -<- , '- <- "'./ ) ~ ,____> · . · o· ·. · .. · .·c _.,Jfll~~--~~'-~~ ~~bi ·. ··o ·. ~·o· ..

. . . . . . o· . .

B. ANGOSTURA TYPE SLOTTED BUCKET

Bucket radius = 1211 , Discharge (q) = 3 c.f.s., Tailwoter depth = 2.31

PERFORMANCE~ OF SOLID AND SLOTTED BUCKETS

4

c.n

437

i

·~:-:ti:.. ~ To 11 water surface \ ·o,:r:,: ·o·· 3 _ ····11·.·o t ~~ -,.v.· .·." .. ·. ---------------::: ,~ ~ ~ - __ ,... --.~: __ 1?~.·n:.~ ,r.~ - - - ~ ~'l// ~ __.__.+- - ---+- _ --.o 'V· V , • · ...-:= ~-'- -- ',1./;-., / ...,. __ .,_ --~l/{~~- ~ ::::-~~NJ:',/// /Channel bed ofter fiow dives -fl,., , 0, ,._., ~ I~_.- '( ~ --.. \!%/// , --+-•t?_ ", • ',• •...., , I ~ ~ I - . -

~-~:-:.: -:'~ .':-.' -~:: b.\.~ '1, ~ ~ \... J J.j I// ~~~}}J{!~ ... ---Channel _bed before flow dives ... (). t> . c::.. . d. I>~'( - ~ ~ ../~/ / -~0°ogi0:c:.s~~ois4. ..... _ •.O • '' 'O· •. , • • •• ~ _ ~ o.a.8-2!'~.s!S'~U:>a&>~~"'II.ID-.-------------I\. • • • ~ (J • d ,.._ • D• ~ ~~: ~ ooooe>goooooooocoooooeooo.,oooc>o~.,,oo~c,c,oo'&"o ~o0 o0 • o ~D °'o"o~ :v,• ··.•i&,,I" •• • • •V• 0 C:::S •• • ;,_ • 0 '-..,_~ go0 03:0 ,.o0 G o0 o~g$g:31>00 0 0c;.igJ>ooo ooo ao.o oo 0010 0 0000 0 i.fo"Q",

.,,Flow dives from apron .llp':"'-:--::;,-p. 0t,~ cour hole ~'l.~c:,\::::0is~,Jt.r.r.~cff!U0°::0 f>eR, 0 9rovel bed 0° ...... 0-:,,~~ .. :ij.rJi.a . v·c:,; .• : • ·•· .•Of," ' ••• • , • '~ ,O: o ~ 000o-oooooou1 o tt'o0o¥ooo 0000000 o o o o ooOa,~Or.Do aonoo.o..,. -

Note: The diving flow condition occurs with the slotted bucket only when the tailwa~er depth becomes too great.

DIVING FLOW CONDITION

SLOTTED BUCKET

"Tl

Ci)

C :::0 ITI

(IJ

This study is reported in Bureau of Reclamation Hydraulic Report No. Hyd-192 and is summarized in the following paragraphs.

Development from Solid Bucket

The first stage in the development was to determine the radius of bucket required to handle the maximum. design flow and to determine the required elevation of the bucket invert for the existing t~il water conditions. Solid type buckets shown in Figure 4 were used in the model to determine these approximate values since the slotted bucket had not yet been anticipated. The 100- and 63-foot radius buckets were found to be unnecessarily large for a discharge of 11010 second-feet per foot of width and a velocity of about 75 feet per second. The 42-foot radius bucket was found to be the smallest bucket which would provide satisfactory performance.

The tail water depth was not sufficient for good performance when the bucket invert was 45 feet below tail water elevation. Per­formance was better with the invert 69 feet below tail water ele11&tion, but for all invert elevations tested a ground roller occurred which moved bed material from downstream and deposited it against the bucket lip.

The second stage in the development was to modify the bucket to prevent the piling of bed material along the lip. Tubes were placed in the bucket lip through which jets of water flowed to sweep away the loose material. Results were satisfactory a~ low discharges, but for the higher flows the loose material was piled deeply over the tube exits, virtually closing them.

Slots in the bucket lip were then used instead of larger tubes. The slots were found to not only keep the bucket lip free of loose mate­rial, but also provided exits for material that became trapped in the bucket during unsymmetrical operation of the spillway.

In order that the effectiveness of the bucket in dissipating the energy of spillway flows be maintained, the slots were made no larger than necessary to prevent deposition at the bucket lip. The first slots tested were 1 foot 9 inches wide, spaced three times that distance apart. The slot bottoms were sloped upward on an 8° angle so that the emerging flow would not scour the channel bottom, and were made tangent to the bucket radius to prevent discontinuities in the surface over which the flow passed. The spaces between the slots then became known as teeth and were 5 feet 3 inches wide. Three tooth designs, shown in Figure 5, were tested.

6

---

-

-; --

--

-

7

' -------!--.. ::.::-. t-EI 3157.2 . . . . . . : . : . . .

. . .

. . Bucket segment :_ :-. ·_·::. · typica I joint-~ · :·. ·: .'- ·:· .. . .

I I

I

-+, -I ' I '

/ I ', I '

I ' I '

I ' I '

I ' I ', ~- ',

~ ',

FIGURE 4

00 /-f', 0 ,,, '

"'-ii; '!, .,,., ', / __ A ',

I -- ' . . ... . . . . ... -: ... ::

• • • • 0 0 • • I • 0 o O O I

0 o o I f ·o I t • • • • I

: . :·- \~~~-=:_E·-·,---:;-0· ._4·.:.·_6 . .:.0,.,·.·.- ..... ·.·:·-··:-·::::· :·.·.·. ·. ·.·-:::: • f ,• I~-- ~ ~ ·' I I I I • I t t e I I f I 1 1 . . . . ... '. . . . . : . . . . . . . . . . .- . . . . . . ' . . · .. :

0 • 0 0 • f O O e t O O • I t I

DESIGN I

·r, -I ' I ', .

I ' I '

I ' ~- ',

(o O ,',,, h) l' ',

c::...,, '

. . .

,,,...., '. --- .. . . . . .

~-: f __ .:._•_.:.~_:....__ ·:: -: : . ·.-:-:-:-: --~ :: .. -.~1~394~.~-·- .. · .... ·: . . . . . . . . . . . . . . . . . . . . . . . . . .

DESIGN 2 -r-, \

.. ti:· 1· \

(\, I

"" . I 0 / I I '\~

I - \,-(."" '\

:~:-=--~·~::-.. ·: .·:··' • I • • • • . • • ••

: ':'El. 3070.o: .. . . . . . . ' . . .. . . . . . . . . . . . . . . ~ ·. . . . . . DESIGN 4

. . . . . . ·. . . . . . .. · . . . . . . . . . . . ·. ~:.·. · .. ~ .. DESIGN 5

SOLID BUCKETS TESTED

7

FIGU'RE 5

43.

[ D TOP

END SIDE

DESIGN I

: -----

[ TOP

END SI DE

DESIGN Il

:=:=:=&::::::2:0:~,,::-+-:1::~~-:~;:j::1~~~:~:!:rn:7-:::J- 0.05R rad. ->I 0.125R :-

- •TOP ->t :<-0.05R ~- : \

\

l Reduce 0.05 R corner \ radius to O at .,.- -, \ bucket P.T. - _.,,

\ \

~ \

I I I

,-_ 8° SIDE

I I

15 " '13 'vL---

14 ', ;-Radial • o,<t..

16 ~ 0c':J

END

------------1 < .... P.T. • DESIGN m - RECOMMENDED

TOOTH SHAPES TESTED FOR SLOTTED BUCKET

8

Tooth Shape, Spacing, and Pressures

Tests using Tootp. Design I were enco~agi1;1g. The energy dissipating action of the bucket and the elimination of piled material along the bucket lip were both satisfactory. However, small eddies, formed by the jets leaving the slots, lifted loose gravel to produce abrasive action on the downstream face of the teeth. Therefore, a sloping apron was installed downstream from the teeth to help spread the jets from the slots and also to keep loose material away from the teeth. The apron was sloped upward slightly steeper than the slope of the slots, to provide better contact with the jets. The apron was found to perform as intended; however, the best degree of slope for the apron and the shortest possible apron length were not determined until after the tooth design and the tooth spacing were determined.

Pressures. observed on Tooth Design I at the piezometer loca­tions shown in Figure 5 were, in general, satisfactory. Undesirable subatmospheric pressures were found on the downstream face, however.

The profile of Tooth Design II, Figure 5, conformed to the radiu~ of the bucket, eliminating the discontinuity in the flow passing over the teeth. Energy was dissipated more readily and a smoother water surface occurred downstream from the bucket. Pressures were sub­atmospheric at seven locations, the majority of which were located on the downstream face. The necessary rounding of the edges of the teeth was determined by testing model radii ranging from 0.1 to 0.3 inch. The larger radius (12.6 'inches prototype) was found to be the most desirable.

Tooth Design III, Figure 5, was shaped to improve pressure conditions o~ the sides and downstream face of the teeth and the radius for rounding and edges was increased to 15 inches prototype. Subatmos- · pheric pressures still occurred on the downstream face at Pi~zometers 3, 4, and 5, but the subatmospheric pressures were above the critical. · cavitation range.

Preliminary tests had shown that pressures on the teeth varied according to the tooth spacing. The most favorable pressures consistent with good bucket performance occurred with Tooth Design III, tooth width 0.l25R and spacing 0.05R at the "downstream end. Table I shows the pressures in feet of water at the piezometers.

9

Table I

Pressures on Tooth Design III O. 0 2 Spac ie_s

Piezometer: Pressure :Piezometer: Pressure Ro. : tt ot water: No. :tt of water . • • • 1 +l to +16: 9 • +58 • . • • • 2 +5 to +13: 10 +42 • • . ..

• • 3 -2 to +15: 11 • +68 •

• . • . 4 • -13 to +16: 12 . +49 • • . • : • • 5 • ·9 to +11: 13 • +11 • .

• • . . • • 6 . +8 to·+l6: 14 • +13 • • . . . • . • 7 • +22 • 15 . +21 • • •

• • • . . • 8 • +62 • 16 • +34 • . •

• • • • • . . • 17 . +39 • • •

Piezometers 1 through 6 showed fluctuations between tbe limits shown. Piezometers 3, 4, and 5 showed negative or subatmospberic values, but since these piezometers are on the downstream face of tbe teeth it is unlikely that damage would occur as a result of cavitation. According to tbe pressure aata tbe teeth are safe against cavitation for velocities up to about 100 feet per second, i.e., velocity computed from th• · difference between bead.water and tail water elevations, and may be safe for even considerably- higher velocities.

Reducing the tooth spacing to 9.035R raised the pressures on Piezometers 3, 4, and 5 to positive values. Pressures on the tooth are shown 1n Table II.

lO

· ·· ·· :• ... · Table· II'· ;·, ..

Pressures ·.on Tooth·-'Design III· 0.035R Spacing

Piezometer: Pressure :Piezometer: Pressure No. : ft of water: No. : ft of water

~ (··.. f • : • ..

.- ·,

t -· ....

_.,;.,_. : ... '. ~ ,-, ·.·.

"":•;· •• .••• I:"' •

·1 • . -- . .· ;:.. i: ·• ...

: : '. . .. . ..... . -· ·,; .. ..

• • ..

·2 , '.; ... -: .. +27 .,, ' . · : 10

3 • • • • :· -:·: .

+30

: ; 4, · · , :: +26 . ... ...

• • : 11

I -: ••• ,, •

•· • . 5.

6

: +14 '· · : 13 · .

i4

15

... . . . . • +27

7 ·; : . +39 ., •...

. . . . • .. . . :: .

· 8 :_ - : · · . +64 · '· · · : •" 16 • . • • •

• • . . 17

. : .

: .. +62: • • . . •.. +57 ·. . . • • • +71 • ... .. . +63 ..

-·: . . ·.+21 . ·• •

. . ·+28 . . . . : -+l;l-0. .. • .. +47 • . • . . . +58 •

..... .. - '

With 0.035R spacing the teeth should be safe against cavitation for velocities well over 100 feet per second.; However, tor small buckets the openings between teeth may be- too small· for easy· construction and the slot's · may also tend· to clog -with 'debris.- · In otlier respects the bucket performance with o.035R tooth -spacing is satis:f'acitory. · ·

. ,:., : :.• ..

Apron Downstream froiif Teeth · · .. -...

. ~ . _: c_ :;. . ;,~ -_.

The slope and lerigth-of--the apron- dovnStream from·the teeth were -the remaining bucket dimensions to be determined. Si12ce the apron served to spread the jets from the slots and also improved the stability of the flow leaving the bucke:e; . .-Jt,: ri.t -1iaportant.:.:tbilt · t;be :apron. c baracteristics be investigated.

A 16° upward sloping apron was found to be most satisfactory. With a ·'12·0 . Slope the .fiow ·'WaS· 'unstable, intermittent1y· diving from the end of the apron ·to sco~ the riverbed~ ·, Using· a 20° slope the spreading action Of'the'flOWW&S cotmter&:ted·to some degree'by the directional effect. of t~e ste~p apron·. · · ·

Two apron lengths, one 10 feet and one 20 feet, were tested to determine the minimum le,ngth required for satisfactory operation. The

11

longer apron., 0.5R in length., was found necessary to accomplish the spreading of the Jets and produce a uniform fiow leaving the apron. The

· 20-foot apron on a 16° slope was therefore adopted tor use.

Slotted Bucket Performance

The slotted bucket., shown in Figure l., operated well over the entire range of discharge and tail water conditions in the sectional model., scale 1:42. The bucket was then rebuilt to. a scale of 1:72 and tested on a wide spillway where end ettects on the bucket could also be observed and evaluated.

In the 1: 72 model minor changes were made before the bucket was constructed and installed. The bucket radius was changed trom 42 feet to an even 40 feet., and the bucket invert was lowered trom 69 to 75 feet below maximum tail water elevation. Figure 6 shows the 1: 72 model in operation with 277,000 second-feet (1.,010 second-feet per toot)., erosion a:tter 20 minutes ot operation., and erosion a:tter 1-1/2 houre ot operation.

Performance was excellent in all respects; was better than for any ot the solid buckets or other slotted buckets investigated. For all discharges the water surface was smoother and the erosion ot the riverbed was less.

Stmary ot Slotted Bucket Development Tests

Reviewing the development of the slotted bucket three factors were involved: (1) the radius ot the bucket and elevation ot the invert with respect to tail water for the given flow conditions; (2) the shaping and spacing ot the teeth; and (3) the pitch and length ot apron downstreali from the teeth. All three factors are important in obtaining the desired energy dissipation., a smooth water surface., and a minimum amount ot river channel erosion. Dimensions ot the buc~t teeth., slots., and apron are expressed in terms ot the bucket radius in Figure l.

GENERALIZATION OF THE SIDrTED BUCKE!'

General

The tests made on the Angostura bucket indicated that a satis­factory design could be developed tor use at a particular site. It was also evident., however., that generalization of the design would be desirabl so that bucket dimensions., proper elevation ot bucket with respect to tail water elevation., and the capacity of the bucket could be determined for any installation~

12

Erosion Test on Angostu.ra Dam Spillway 1:72 Scale Model

Recommended Slotted Bucket

13

Figure 6

Maximum discharge . 1010 second feet per foot of width ,

Erosion after 20 niinutes

Erosion after 90 minutes

The general features of the bucket, shown in Figure 11 were believed to be satisfactory but before starting the generalization tests possible further improvements in the bucket teeth were investigated. When it was found that the tooth s.he developed for the Angostura bucket provided best hydraulic performance, tests were then directed toward generalization of the design.

Test Equipment

An entirely new sectional model was constructed and tested in Flume B, Figure l of Progress Report II, and also shown in Figure 7 of this report. The flume was 43 feet 6 inches long and 24 inches wide. The head bay is 14 feet deep while the tail bay is 6 feet 3 inches deep and has a 4- by 13-foot glass window on one side. The discharge end of the flume was equipped with a motor driven tailgate, geared to slowly raise or lower the tail water so that continuous observations could be made.

The sectional spillway model was constructed to completely fill the flume width, 24 inches, with an ogee crest at the top of a 0.7 slop­ing spillway face. The bucket assembly was made easily detachable from the spillway- face. Four interchangeable buckets having radii of 6, 9, 121 and 18 inches, constructed according to the dimension ratios shown in Figure 11 were designed so that they could be installed with the buckets inverts located 5 feet below the spillway crest and about 6 inches above the floor of th1! flume. All flow surfaces were constructed of' galvanized sheet metal with smooth joints. The downstream channel was a movable bed molded in pea gravel •. The gravel analysis:

Retained on. 3/4-inch screen Retained on 3/8-inch screen Retained on No. 4 screen Retained on Pan

6 percent 66 percent 25 percent 3 percent

Flow was supplied to the test flume through a 12-incQ centri­fugal pump and was measured by one of a bank of Venturi meters permanently installed in the laboratory. Additional water, beyond the capacity of the 12-inch pump, was supplied by two vertical-type portable pumps equipped with two portable 8-inch orifice-Venturi meters. All Venturi meters were calibrated in the laboratory. Water surface elevations were measured with hook gages mounted in transparent plastic wells.

Bucket Modifications Tested

General. To determine whether practical modifications could be made to improve the performance of' the Angostura slotted bucket the 12-inch radius bucket, constructed according to the recommended

14

.... CII

40,

·Flume width 4'-o'f' ' --Flume width flares-- 1

4!.o'!.----- ------ 51-011

,,-2-12"Supply Pipes

-- l 1-12"Supply pipe

---- Flume. width. 23!11' from h~re 1o downstream end-------- .,.:>-I

--------------t:~~. -~--------4' 1011 . : ----

I I I

I

.r 'b ~

' O>

i!.

J ~;;,-c-7-------------- ,3·-a~· ...; ___________________ .:,. ____ _,

rHeaclJrclter J4_~09efop

II 11· ~· ; ! ,;

I ,· I I

'

I ,;.·•:•·.'•',•. IJ! I

i:?\lt)~. · · -+Fixed Spillway Face

f rJ.I¥llif ~I:0:b~~. . .. 0 ,, .,. __ "- · Window----,,.., -Glass · · 0

.,·-False · Floor

<+-------- s·-s··------~

I

'I!. ,i.

! Tail water, Control Gate--.,

I =··. t - - ··---r-- ; . ,-., I f -1 . . t

'l---:~=-------------10'-o" -~------c----------J co. ~------- 5'-o" ---:-t-~=~::;::_~·~s~------.+----3~0~---, .

.----------------~------ · ------.... ; ------ ·--------,---------- 43' s• ------------------------------------------- .. --------- · _____ ' ___ · __ · t ___________ ~

SECTION ON t OF TEST FLUME

TEST FLUME AND SE.CTIONAL SPILLWAY

.,., G) C: ::u f'TI .,.

dimensions in Figure 11 was first tested. The purpose in repeating the test was to obtain data for generalization and to establish a performance standard with which to compare the modified buckets, all to be made on the 12-incb radius bucket.

To provide a standard bucket test, which was necessary to reduce the amount of testing required on each bucket modification, the 12-inch Angostura bucket was thoroughly investigated. The bucket capacity was estimated to be about 6 second-feet. Best performance tor this flow occurred with the tail water 2.3 feet above the bucket invert, Figure 2B. These conditions were used for the standard bucket test. Also, as part of the standard test the movable bed was molded level, Just below the bucket lip, at the start of a test.

In retesting the Angostura bucket it was noted that muc,h of the energy- dissipation occurred as a result of the spreading action downstream rather than 1n the rolling action 1n the bucket. Flow passed through and over the teeth to emerge at the water surface some 3 or 4 feet downstream from the bucket, Figure 2B, producing a boil at this point and waves on the water surface downstream. In some installations action of this type might be objectionable since bank erosion could occur or powerhouse operation could be affected.

It was concluded from these tests that if improvements could be made in the.bucket performance, reduction. in wave action in the downstream channel should be given first consideration since enera dissipation and bed erosion.were entirely satisfactory. Four modifications of the bucket teeth were tested; the bucket with teeth removed was also investigated. Also, a solid bucket was tested to indicate the relative advantages of the two types. Only a brief description of these tests is given since none of the modifications are recommended for general use. However, to indicate the scope of the testing a SUllllllary of these tests is given.

Tooth Modification I. In the first modification the teeth were extended in height from 456 to 60° as shown in Figure 8. The spacing of the teeth and the shape and length of the apron were not modified since these had been carefully determined in the early development tests.

In operation with the standard test the bucket performed much the same as the original. The boil occurred about 6 inches farther upstream and was higher than tor the Angostura bucket. Waves were also as high or higher, and since the sweepout point was about the same no further testing was done.

Tooth Modification II. In both the Angostura and modified buckets tested it was noted that the water surface directly over the

16

'i' // ', II II ., , 0 72->I l<--6 -->I .,,, I ' • I I I ---- I ', I I I ,,/ , 11 I

· _, ' I I,. ·· ·· I ,,· O ~, I I . f

A,'o'· ',I~ 16! I .. ,<--"" ,I I ' I I I I

ANGOSTURA TYPE SLOTJED BUCKET

1511>1 . I' . • - I ~ ,--------;t _____ I I

;,-' I .,. I

,,,, . • I

.,.,' ~, ., .· o/ ·.,-- 0

,,"' ,OJ:· __ ,.

SLOTTED BUCKET MODIFICATION n

SLOTTED BUCKET MODIFICATION :m

SOLID BUCKET

FIGURE 8

,i'-- i<--6"-->1 .,,, ', I I ,,, ',, I I

_, ' l II .,./ • ...... >t 1<.-0.625 / -;,-J I: I ,,,,,.;,_ ,, r''"'' ., 1-

00/ I 16~ I I!.' ' I. r< __ ,...'1 \ \ I

SLOTTED BUCKET MODIFICATION I

l<--6"-+i I I I I I I I I

I

16!, : ' \ I

SLOTTED BUCKET MODIFICATION m

l<-'-6"-->t I I I I I I I I

: 16~,: I ' I

ANGOSTURA TYPE B·UCKET WITHOUT TEETH

Dimensions applicable to all designs­'Bucket invert to downstream edge

of structure = 15.21 11• •

Approach chute slope = 7: 10. Bucket radius= 121:

Where shown; tooth width = 1.5 11 and space between teeth = 0.72'~

SLOTTED BUCKET MODI Fl CATIONS TESTED

17

bucket was lower than the tail water downstream. It was believed desirable to move the boil upstream directly over the bucket, consequently, the teeth were extended in height to an angle of 90°, as shown in Figure 8. It was realized that the teeth would be too tall to be structurally stable in any but a small bucket but the trend in performance was the real purpose in making the test.

Performance of' this modified bucket was excellent for the standard test. A large portion of the flow was turned directly upward to the water surface where it rolled back into the bucket. The tail water depth directly over the bucket invert was about the same as the depth downstream. A slight boil could be detected over the teeth, but it was not nearly as great as for the two previous slotted buckets tested. The flow passing between the teeth also provided fairly uniform distribution of velocity from the channel bed to the water surface in the cha.:rmel downstream. The water surface was quite smooth and the channel bed was not-disturbed.

The bucket also performed well for high and low tail water elevations. The tail water could be raised to a higher elevation than for the two previous buckets before the flow pattern changed to scour the channel bed; and it could be lowered to a lower e~evation before the flow was swept from bucket. 'lhus, the range of tail water depths for which the bucket operated satisfactorily was increased.

The performance of this bucket was very good in every respect; however, cavitation could occur mor~ readily on the surfaces of the tall teeth. Cavitation pressures or the possibility of eliminating such pressures were not inves~igated because the teeth were considered too high for practical use on large structures. Therefore, this slotted bucket modification is suggested for possible use with small buckets where cavitation pressures cannot occur, i.e., velocities near the teeth below 50 feet per second.

Tooth Modification III. In the third modification a tooth radius half that of the bucket radius was used, as shown in Figure B, to curve the teeth to a height of 90°. This modification was made to determine whether the height of the teeth, or the 90° curvature of the teeth, provided.the improved performance.

Tests showed that the shorter teeth were not effective in lifting flow to the surface. Flow passed over and through the teeth to form a high boil downstream similar to the first modification. In addition, ob.servation of the flow passing over the tops of the teeth indicated that cavitation pressures were a likely possibility. Pressures were not investigated since performance was not as good as for the Angostui-a slotted bucket.

18

\ j1.•:

" 'l'ooth Mod.ificati-on IV. -Modi.ti-cation iv util{zed the same tooth as Modifi~at_ion I:U, but ttie teeth were,.:.placed o,n the apron ·at the down­stre~ en:d of the: ~ke'.t,· a.,· sho'.'ffl -in F+gur,e 8. J:t W$.S anticipat.ed that· the teeth, placed farther downstream and at a slightly higher elevation, would turn a portion of the flow directly upward to the-water surface as for Modification II. Performance tests showed that the teeth turned more of the flow upward but the performance was no better than for the_ Ango~tlµ'a .. design.

-: Anf?!!tur~ bq.cket with .teeth .removed. -- The Angostura· bucket -without te~tb .-is sh~ in ·F.i,gure 8. This design was not _expected t~ _ perform _as- weii as the .slotted Ango!!ltura bucket, but was. te,ste4 to · · indi:ce.te t.he .v:al~ of the teeth and slot!!I in dissipe.t:l,n-g -t~e -e11ergy of the spillway flow. Operation was quite satisfactory for flows,.of.,3 and 4 second-feet but performance was poor for 6 second-feet. For the higher ;tlo1rs.of 5 to 6second'.9feet,theflow leaving the bucket.was ~sta~le and the water sur~e was rough. For a few seconds the boil would: ))e qui'.te hi_gh then sudd.en'.!-Y: would ,become quite low. · _Erqsic,n of the. riverbed.: was negligible fo:r;- all f'.].ows, however.

. . . . ~.: .

'l'h~ tests withc>l~t -teeth i11 th~ b:ucket ;indicated. t~t t4e pr~ funct-ion of the teeth is to stabilize the flow and reduce water surface fluctuations i,n the. channel downstre~. _The ~eats. also suggeat_ed .the fact that should the teeth in the Angostura bucket deteriora.te, oyer a . period of time in a prototype structure, the ill effects of the ·deterio­ration could be easily observed and evaluated. Discharges up to about half maximum would _be. sa~isfaetoey w:ith tbe teeth gone. _

Solid bucket. _The solid bucket design, shown in Figure 8, was . tested to compare the action with that of a slotted bucket. Figure 2

_ sh~s, th~ bucket performing ~der similar discharges and t•il water elevations •. _ For tbe solid bucket, a-11 of t_he flow is directed :to the water s~tace a short,distance downstream from the bucket, resulting in a very high boil. Part of the flow rolls back into the bucket while part continues on downstream. Since there are.no slots to provide flow · currents in a downstream.direction unde,:r;- theb9il, a.violent undercurrent flowing upstream, -or gl'OUDd roller, exists at all times. It is the .. ground roller that moves :gravel upstream and deposits it at. t_he bucket_ lip. Currents passing over the. lip then pick up the material and move. it downstream, ,res1µ.ting in a cont_inual circulation of bed material. The action itself is harmless except that the lip is- exposed_ t~. abrasive . action and with ~symmetrical operation of the spillway gates the . material -is o:rten swept into. the buc::_ket. O;nce the material is ~ the .Qucket,-, it is trapped and causes erosiqn of ~he concrete s~a.cei's -as __ it is moved about both. laterally and ~<>ngi,tudinally ins.i-de the bucket arc. Therefore, a solid bucket, without slots, has certain disadvantages where loose material may be carried into the bucket or where the high boil might be objectionable.

19

Some advantages, however, were found for use of a solid bucket. A lower tail water elevation is required to sweep the flow out of the bucket and the flow could not be made to dive from the bucket lip to scour the channel bed. However, in general, the slotted bucket performed better than the solid bucket.

Summary

The Angostura bucket performed better than an.y of the modified forms of the bucket except Tooth Modification II. However, the high teeth in Modification II were considered to be impractical for most prototype construction and the possibility of cavitation at high velocities is great. For small structures the relatively ~igh teeth might be practical in which case the use of Tooth Modification II should be considered.

The Angostura slotted bucket with or without modifications, in general, is considered to be superior in performance to the solid bucket, The Angostura slotted bucket also provides more stable flow and better energy dissipation than did the Angostura bucket with teeth removed; how­ever, with the teeth removed fairly good energy dissipation occurred without disturbing the channel bed. The Angostura slotted bucket without modification is, therefore, recommended for use on spillway structures where tail water depths are within the limits required for use of a bucket type energy dissipator.

Determination of Radius and-Tail.Water Limits

General

The investigation to determine the minimum bucket size and tail water limits for a range of structure sizes, discharges, and overfall height was accomplished with the testing of 6-, 9-, 12-, and 18-inch radius buckets, tested in that order.

For each bucket installation, a range of discharges was passed over the spillway. The head on the spillway was measured and recorded. The relation between head and discharge on the spillway is shown in Figure 9. For each discharge, the tail water depth was lowered slowly until the flow swept out of the bucket, as shown in Figure 10. Since the bucket study did not include flip-type buckets, the depth at sweepout was considered too low for proper performance of the bucket. The tail water sweepout depth, measured above the bucket invert, was recorded in Tables III to VI and plotted in· Figure 11. Figure 10 also shows the bucket operating with tail water depth just safely above the depth required for

FIGURE 9 .. _

,. 6 r---r--r--r----ir-----ir-----,----,----,----,----,-........ - ........ ------

1.5 i----t---t---t-------ir-------ir-----t----t---+---+---+--+--+---+----1

_.;.· ..

. t.4 1-.---+---+----4-----1-----1-------1---+---i---1----=-'4-,--4---+--+--~

./. 1.3 ... __ - __ -__ -__ +-__ -" _____ -_ -. __ +-_.--: .""'". __ -, 1-----1 __ !-,-..,.-.• -. ___ ------------+----"--+---+---'-"-. +----1-v--~ v-,. 2 l-----lf-----+---'-..-+---'-' ........... _+---'-.......... -'-'-.,.-+-,,.j.a..--+-"""--'-4----.1-----4-v------,r,I-_ '1-----1-----1

/ I. I i----t---t---t-------ir-------ir-----t----t---+---+v--+. .. .,;c.....-+--+---+---1

~

~ ~-0 ~/

~ ci 9 1-------1----1-----l..-----1---1-------4----+-,,·',c....._ _/.. +---·-· -1----4----1---1-------+----'----I

z _/v =x 0.81'--'--'-'--1----1---1-----11-----11--~-..__/--+_--+--+--+--+---+-'-----+----1

=~ 0.7 1------;_-+-. -_--_-+------il-----lVl--.... --'l~V,...--'-: __ __.---'--'--··;_-·;_· .... , _,·-~· _--4-,-_--'--+---+--+--4-------1

~ ,, ,,,,- ~o~sig~ head~o. 587

437

0.61----1---1-----11--_,,_,'-1---,,,,,.?---1----------+---+--+--+--+-----I

/_ 0.5 1-----11-----1,........:.· .::;.,·-~ ~?"-+--+-----1--'-------1---+--+----'-+---+--+---+----I--~ / ~

. ~

(l4 " •• / i .0.3 V "fi

·1 u,·

0. 2 ... ;-------+----'-i.. : ·-.21

0.1 ... ,---------1 ~ ... 00~~~~!-,,--.,....,....,,...~2-.....i.-~3~-__,__~4-......i.-~-5-........ __ 6.1..-· · _-.1..----17

' DISCHA.RGE 11q11 IN' SECOND FEET

·•.

·•;· - . PER FOOT OF WIDTH

DJS·CHARG,E: GALl:BR.AT•ON OF.­THE 5-FOOT MODEL SPILLWAY

...... ..,.

. ,.. : ·-

21

FIGURE 10

4 ,

··.:. ---- -·.·::. ~ --....... ~ __,.---:·.::·:·:. ~ ~ ~ ~~ ~ -. . ···:.~ / _... ~ ~ ~ ~' '- ' ~ ~ •... .~.,.,...-- -7 . . ... ·.. ~ ---.. ---'> --v __.,. ... · .... ·:. '-~....---. -=---- ~ ~ --~ ....__.,.. :.--::.--

. .. r,ro- - ...... - ~ --. . . ... .. . . ------------- "- .______........ __ .. · .... · ..... A. Tailwater below minimum. Flow sweeps out.

·-.. ~ .. -----::·:.. /7)~~ ~~---> =->- !Ill- • ·.·:=.·: .. (., ~-~ ~ ___.. Di,, --!I>- !>

·.':·::··:~--1/~- )~ ~..:::-- __ ,.. l> •••••.• •\..'-...A ~ <- ,) ~ --- ----------.. ·. ·.· . .-:. ····= .--a-------

1 • • • • • • • • • • • • • •

B. Tailwater below average but above minimum. Within normal operating range. ·

·.~ ---------------------.:. ------------ ,, _,,,..,. ___. --> ··:.~ ~ - "" <- "" / / __.... - l> -- ... ,._ .•••• ,. \. <;;: ) r c;. <~ 1/. ,,,,,,,.- ---. - .. ,._ • " • • ~~ ~ _,,,, _/I ~ :£la.. ... : _., - /, /,r-> ::----0.. .... · .. :·: .= .. ~ ~ -- ,,~~~-............... (>.) _,,.. -->- ---!> !I>-

• • •• ; • ~ ___,, )l .•.,:,- ........ -- l> · .. ·: .'•;: ...• ,:~ ~~::::i"c, -- -------

• •••••• •• 0

C. Tailwater above maximum. Flow diving from . apron scours channel

/2-;.::;::-- .... _ - --- - ----------: .... : . ~- "'"-: <-3- . --------- ... ----

___ ,.. . · .. : :·-~~~-: ~ ~ -- ~ =:-> •••·• ~_.,A' -- ~--------. ....... . ~-.,,,.,,, - - - -::;;::, .,.. ....... ~ . ~ ----\)loo .•....• ::--........7 -~ ~ '""" -;;> __ ..- ' ~ -- ~ . . • . .. . < C: r__,,I ------ ........ ____ -----------.-. • ·. • • ,' ,•,;.'•:•::: T ~/ .

D. Tailwater same as in C. Diving jet Is lifted by ground sc:­

roller. Scour hole backfills similar to B. Cycle repeats. --~

( Bed level 0.3-inch below apron lip at start of test)

6-INCH BUCKET - DISCHARGE. (q) = 1.75 C.F.S.

1 : H . 2 : T ( sweepout depth )

3 : q . 4; Tmin : v12

5:2g•X+H-Tmin

6 : V1

7: D1 : V1

8 : F •-,'iDi :!ll!Ul

9 : D1 • 2

lO;D1+!L 2g

• R 11 : v12

: D1+2g

. 12: T (diving depth) . 13 ; Tmax

: v12 14:2g=X+H-Tmax

15 : V1

16 : D1 : V1

17: F~ • T l • max

18 : ""'i)"9 : 1 V12

19 D1 + 2g

R

R = bucket radius (rt)

Table III

DATA AND CALCULATED VALUES FOR 6-IKCH RADIUS BUCKET

l

0.198: 0.274

0,767 0.765

0.31

0.967 0.965

4,231: 4.309

16.50 16,65

0.352

o.826

0.81

1~026

4,326

16.70

0.019

21.2

0.032 o.048

16.31 13,36

29.78 21.10

0.12

2.565

2,065

2.133

11.72

. -· 4.341: 4.374

0.12 0.11

2.576

2,076

2.1:98

11.89

2.435

1.935

2,417

12.47

Sweepout Conditions

o.480: o.481 0.581: 0.678 . o.413

0.943

1.03

1.023

1.30

l.ofll : 1.139 1.203

1.75

1.403

2.25 1.30

1.281 . 1.50

1.339 1.403 1.603 . 1.143 1.223

4.270 4.257

16.58 16,56

4.200: 4.187 4.178: 4.075 . 16.45 16.42 16.41 : 16.20

0.062

11.72

0.078: 0.079

10,42 10.31

18.40 15.57 16.21 . . 4.332 :_ · 4.335 4.279

0.12 0.12 0.12

Diving Flow.Conditions

2.464

1.964

. 2,439: 2.397

1.939 : 1.897

0.091: 0.107: 0.139

9.50 8.85 7,65

14.66 13,16 11.54

4.278 4.285 4.214

0.12 0.12 0.12

2.043

1.543

2.584: 2.983

2.200: 2.213

1.700: 1.713

2.881: 2.965

12.55 12.78 12.90 13.86 13,62 13.81

0.026 0.045 0,065 0.089 0.102 0.101 0.108: O.U!"8 0.163

12,67 9.84 8.62 7.40 7,06 7.20 7.42 6.70 6.02

77.92 45.72 29,76 21.62 19.06 18.82 14.26 13.23 10.51

2.159 2.243 2.486 2.538 2.643 2.685 2.983 3.009 3.128

0.23 0.22 0.20 0,20 0.19 0.19 0.17 0.17 0.16

H .. height of reservoir above the crest (rt) T = depth of tail water above the bucket invert (rt)

Tm1n .. minimum'tail water depth for good performance (rt)• sweepout depth+ 0.2 rt Tmax .. maximum tail water depth for good performance (rt)= diving depth - 0.5 rt

- q • discharge per foot of model crest length (cfs) . X .. height of crest above bucket invert• 5 feet

V1 ,. velocity of flow entering the bucket computed at tail water elevation (rt/sec) . Dl,. depth of flow entering the bucket computed at tail water elevation (rt) F "' Froude number of flow entering bucket computed at tail water elevation

Maximum capacity of bucket estimated to be 1,5 to 1,75 second-fee~ per foot of width.

23

sweepout •. · The t$.il water depth just. safely above ,the depth required tor the sweepout will, hencef'ortb,; in this report, be called the lover or minimum tail water limit.

·., . .

,, For each discharge the upper tail water limit. ,,as .also investi­gated,.,. Th~ tail l{ater was r~ised slowly until the flow dived f'rom the apron lip, as shown in Figures 3 .and ~Oc. , Wh~n .diving occurred a deep hole was scoured in the channel bed near the bucket. The tail water depth for diving, ~onsidered. to. be too hi,gh for proper performance of the buckf;t, .was, also recorded in Table III and plotted in Figure 11. .The tail.water ~pth that ;ts just ~,tely below ,the depth required for. diving wi:11,. h'9ncerorth, be called 1tbe uppe~;.or. maximum tail water limit.

Six-inch Radius Bucket

Lower t.ail w,iter '1:1.mit •. · At the ~eepout depth, the flow left the .bucket _in the form- of. a jet,_ Figure 10.. The movable bed was quiet and undis~urbed from the bucket.downstream to the po,int vt:i,ere the Jet landed. . The jet. scoured,. the cha_nnel bed only at the po_~t, of contact, and did not cause excessive wate.r. ·Surface. roughness downstr~~. A more unde.sirable flow pattern occurs, jµs,t before sweepout, however,. when an unstable. conq.ition d~:veloped in th~ bucket and in the. ch~l .causing excessive erosic;>n and: water surtac.e. rQughness~ I;t is this transi.tion region which makes it und~11irable to design .a .bucket for bot'tl submerged and flip action. ·

.,. At the loweJ:.: tail wate,r limit, i.e •. , just above ''sweepou.t, .the gravel. ui ·the movable. bed· began to· move.. The gravel was not -carried away front the. bucket, but instead was litted and dropped by nlJDlero'-\8 s-3-1. . eddies: that formed in the water between the main flow lee.,v~g .the bucket . and the movable bed. The action was not considered desirable nor particularly objectionable.

The lower tail water limit appeared to be from 0.05 to .0.15 of a foot above the sweepout depth. Only the sweepout depth was recQ~ded in the data shown in Table III since it vas a more definite point thQ the minimum low tail water limit •. A safe. lower limit :was established at the conclusion of all m.odel testing by adding 0.2 of a toot to the sweepout tail water depth.

Upper tail water 1imit. At the tail_ water depth required for diving to oco'IU", it was noted t.hat after 3 .or 4 minutes in the model the diving flow s'1ddenly ceased ~d the flow rose to the surface as shown in Figure 10.- ~he changeover occurred only _after the mdvable bed,became sufficiently,scoured to allow the grQund roller to form and lift the flow from the apron lip· to the water surf~e •. The ground roller then moved

25

the pea gravel deposit upstream into the scoured hole until the riverbed became nearly level with the apron lip. At the same time, the strength of the undercurrent was reduced until it was no longer capable of lifting the flow to the water surface and the flow dived again to start another cycle which was repeated over and over. Very little bed material was moved downstream out of reach of the ground roller even after several cycles. Five or s~x minutes were required for one cycle.

When the flow was diving, the water surface was very smooth; but., when the flow was directed toward the surface a boil formed and a rough downstream water surface was in evidence_. In the former case, part of the energy was dissipated on the channel bed, while in the latter case, energy was dissipated on the surface.

Near the upper tail water limit, diving occurred in spurts not sufficiently long to move bed material. As the depth approacbeditbat required tor sustained periods of diving, the momentary spurts occurred more often. In the test data recorded in Table III and-plotted in Figure ll, the upper limit was not recorded; instead, the tail water depth that caused sustained diving was recorded because it was a more definite point. At the conclusion of' all model testing., the upper tail water limit was established by subtracting 0.5 f'oot frQm the tail water depth at which sustained diving occurred. This margin of saf'ety was sutf'icient to prevent momentary diving in all cases.

The first tests showed that it was difficult to get consistent results for the tail water depth at which diving occurred. It was deter­mined that the upper tail water limit was dependent also upon the shape characteristics of the channel bed, especially its elevation downstream from the bucket. Since with a movable bed it was difficult to maintain the same channel bed characte~istics-between one test run and another, the gravel was removed from the model completely in anticipation that the upper tail water limit could be determined by merely observing the flow pattern.

The gravel was removed completely so that the floor of the model, which was 6 inches below the bucket invert., was ~he channel bed. With this arrangement there was no upper limit since the flow could not be made to dive from the end of the bucket for any tail water elevation, Figure 12.

It was then decided to try a solid wood floor at the elevation of the apron lip to re;,resent the channel bed. For this arrangement flow f'rom the bucket followed along the solid bed then rose to the surface downstream, as shown in Figure 12. For the higher tail water elevations the flow followed along the solid floor for a greater distance before

26

FIGURE 12

Tail water elevation is less than 7 inches . abov·e the sweepout depth.

~\/-:-·::>- -- -~t-. ?'~JtJy~i\ (~~w,;:::.-=-~\( P h~ . ,· Y~\\ ~ j /1/----:::__> ~~ ,i/ t - " /2;'~-_,.') ~-:,-~ / /1/ ' . '_/ /_ \.. ~ --'19'/ ____ >_._-> . ~ ~ "t:_~ p P. ~ ---v --;>- ,:, -

'---c:-~ixed bed~._--->~->~

A. FIXED BED 6 INCHES BELOW BUC-KET INVERT. DESIRAB·LE TAl!,..W_ATER DEPTH

. Tailwater eleva.tion is more than 7 inches -----. . · · · · ~ '\y .,:-0.: . above the sweepout d-epjh... .

~ · · rf'. ,jt~~~-J~~~7 ~ , , ~1////; ~ ~_::?" . --

. ~J$~/ ··.· .

431

Fixed bed-

B. FIXED BED 6 INCHES BELOW BUCKET INVE.RT. LESS DESIRABLE TAILWATER DEPTH

Toilw·ater elevation is·above sweepout depth.

. .

C. FIXED BED AT APRON LIP LEVEL Note:

Bucket radius is 6 inches. Discharge Is 1.75 second feet per unit foot of width.

FLOW CURRENTS FOR VARIOUS ARRANGEMENTS OF FIXED BEDS

27 I

turning upward. Since no other changes in flow pattem were apparent at high tail water elevations, again DO upper limit could be found.

Testing was continued using the pea gravel movable bed, molded level just below the apron lip. It was necessary to reshape the gravel bed before each test to obtain consistent upper limit results; even then it was difficult. Testing showed that it was important that the channel bed be slightly below the apron lip elevation. If the movable bed was at lip elevation, the diving flow pattern occurred at a much lower tail water elevation. Therefore, the bed was .maintained at approximately 0.05R, or'0.3 of an inch, below the apron lip of the bucket at the beginning o:f' each test.

Maximwn capacity. As the discharge was increased and the capacity of the bucket was approached, the difference between the upper and lower tail water limits became smaller. The maximum capacity of the bucket was judged by the general performance and by the range of useful tail water elevations between the upper and lower tail water limits, Figure 11. The maximum capacity of the 6-inch bucket was judged to be 3 to 3.5 second-feet or 1.5 to 1.75 second-feet per foot of bucket width. The performance of the bucket for 3.5 second-feet of flow with a normal tail water elevation is shown in Figure 10. The water surface is somewhat rough at this discharge.

Data were not obtained for other movable bed arrangements with the 6-inch bucket. In testing the larger radius buckets, however, it was decided to include a sloping bed arrangement in the investigation.

Nine-inch Radius Bucket

The 9-inch bucket was tested in the same manner as the 6-inch bucket. The bucket in operation, Just before diving and af'ter diving occurred, is shown in Figure 13. Judged by the difference between the upper and lower tail water limits and by the general performance, the maximum capacity of the 9-inch bucket was determined to be between 4 and 5 second-feet, or 2 to 2.5 second-feet per foot of' width. Discharges of 3, 4, 5, and 6 second-feet w~th a normal tail water depth of 1.85 feet are shown in Figure 14. For 6 second-feet the tail water range for satisfactory- performance was quite narrow since a depth of 1.65 feet was too low and 2.3 feet ~s too high.

Water surface roughness for the maximum discharge of the 9-inch bucket was greater than for· the maximum discharge of the 6-inch bucket. To aid in defining the surface conditions, measurements vere made for a range of flows with the tail water about halfway between the upper and lower limits, Figure 15.

28

A. Flow is about to dive from apron lip--maximum tailwater depth limit has been reached.

B. · Flow is diving from the apron lip--maximum tailwater depth limit 'has been exceeded.

Nine-:Inch Bucket--Discharge (q_) = 1. 5 c. f. s.

29

Figure 13

FIGURE 14

·.~

?: :'.\- ----------- ---------... ~ ------ --; /' ------: .. ·.· .. c-- <- <, .c1/ ----.. ------.... .·.:.·.:.~ ~.,} /"1/....---- ~---..--

•••. ~ / :r ~ "- ~ . .'· : : · .. : :_.. \. ~ / ~ ~c:r <: t ~ '-..':---...------.... . . . ......~,_,,.,~ ~- ~ ---

• I• ~ • ~ ------.. • • • • • ... ~-0-0--------• · .... · . ... :.:·-.... ·~ ·.

A. q = 1.5 c.f.s.

:.~ . : . '~ ------... ~ --- --:i,,, -----. . . . /4~ _., ------>-. . ~ _ .... - ----._.,.,,..., ----'>-·. :. : :: : : ~ r -:- "? 1/,,..,,..,,..,,.7~ ~ - .,, .... --~ ' , ~-, / ~ ~ ~ _,,.. • • • : : : . \. --~~'1'- ~ ~ ) ~ ~ ---- >-

. . : ·.·: :'",~ -:: t!. _c:.. <_./ ~ .._.i,. ~ _ _:._ • . • . • .·;:.· •:::· .. : • ~-o-;-------------• .. · ......... : : .

:~

B. q = 2.0 c.f.s.

. · .. ~ ~ -.:--~ - --........ ----. . . ,,,,- ..,____..-. . , ,, ---.. .·.·.:. _,---~? /~---:.. :ii.. ___ > --:,,.

·.::~~Jr'""? /,;r~_-'> --->- ,.. - .. . . :~ r, tf // ~->- ---.... "~\."- / ,,...,--__ ~ --- ~ "'"" -

• • • • • • '-''· ..:::::-, ~ - i>- - :,.. . . • ... ·.·:·\..~ ~.:>;) <: } ) j'~ ---'7"" ........ ~ C. Q" ~~--.......

,' I I • I I I I I I I I I a I~ 11 0 0 0'7.()D-- -------. - ------ ----

I I I• : I I I I I • I •I': : : •: •: =:

C. q_ = 2.5 c.f. s.

---~ --- --: :·. ~ /V.,.... - -~ ..______ ~ -I I I ~ \ ' -------- •-......____... . : : : •\.\ ...,--.. _,,.. 1/- _::----:--__ ---.,. .. ·.?: ~. ~~ ~ ' / 1/ < --:-> _,,,. -=---~> ....... ~'- ½~~ ) ~ ··: . .-::··=~~~-::..) t (). )_ ~ ---..... ··· .. , ..... •. ______ ,....,...--...... ________ _

• • • • • • : • : ••• • •• /1. •• ••• .: ;. : :. ·:

D. q = 3.0 c.f.s.

( Bed level 0.5.-inch below apron lip at start of test.)

9-lNCH BUCKET - TAlLWATER DEPTH= 1.85 FE ET

30

FIGURE 15

I-< -------- C ------·>I I I I I t<- - - - - - 0 - - - - --t I 1- -I I

k-E--1 1 - -:---------,.;

:~·:. I I 1' I

: ::·:~. - - . -----,; I I I . I I I · .,; . -". ·, ·. . . I I I I

. ,. I I I <l

:·: ·::-~::. : 'P ~ I · ·~ ;· ·. · . .. . I . 1 I I · ..... , ... ,.· .. , I . I I I •.· ... :·.t).·. I~ 1 I I .. ' : .. -..... ·: . . I . • 'ii .1_ .V . •'t;) · .. · .. . --- .... ---~----------- ____ ..1

-::.::.: ·:·· .. ~:. ·:· ".·: :- ---~- ·:: :: ·.: :-: .~~

9-INCH BUCKET

Q-cfs q;..cfs T-ft. A B C D E

3.0 1.50 1.85 25 19 415 25 5

3 .. 0 1.50 2,40 32 26 46 27 3.5() ,. 75 I. 85 26 19 45 25 5

,· 4.00 2.00 1,85 27 19 48 25 5 4,50 2.25 1,85 21· 19 48 28 6 5.00 2.50 1,85 28 18 150 32 6 5.50 2.75 1.85 29 17 51 31 6 6,00 3,00 1.85 30 16 52 32 6

12-1 NCH BUCKET

Q-cfs q-cfs T-ft. A B C D E

5.0 2,5 1.65 32 23 52 35 14 6.0 3,0 1.65 33 22 62 37 II

7.0 3.5 1.65 33 21 68 37 9

8.0 4,0 1 .• 65 35 19 70 37 6 12,0 6.0 36 7 90 40

NOTE: Dimensions A,B,C, D,and E are in inches

AVERAGE WATER SURFACE MEASUREMENTS

31

The tail water sweepout depth and the depth at which diving occurred are recorded in Table IV and plotted in Figure 11 :for a range of flows tested with bed elevation approximately o.05R, or 0.5 inch, below the apron lip. For .a given discharge the tail water sveepout depth was not as lov as tor the 6-inch bucket but the diving depth was higher.

The upper tail water limit was again difficult to determine since diving occurred over a range of tail water. However, a reasonably sate upper limit appeared to be approximately o. 5 of a foot below the average depth for diving to occur. The minilllWll safe limit appeared to be from 0.05 to 0.15 of a foot above the sweepout depth.

Upper and lover tail water limits were also determined with the channel bed sloping 16° upward from the apron lip to approximately 6. inches above the lip, since this type of installation will occur frequently in JD8nY' installations. Tests on this arrangement showed that sveepout occurred at the same depth but diving occurred with a much lover tail water depth. Diving occurred at about the same tail water depth as for the 6-inch bucket with the level bed just below the lip. The maxi.Jrlum capacity of the bucket did not change with bed arrangement. Thus, the performance with the sloping bed was nearly identical to the performance with the level bed except that the ,operating range between minimum and maximum tail water depth limits was greatly reduced because of the lover elevation at which diving occurred.

Twelve-inch Radius Bucket

The performance characteristics of the li•inch bucket were similar to those of the 6- and 9-inch buckets. Figure 16 shows the performance tor flows ranging from 5 to 8 second-feet with normal tail water depth of 2 .3 feet. Surface waves were greater than for the 6- and 9•1nch buckets; Figure 15 may be used to compare the surface characteristics for the 9- and 12-inch buckets. The maximum. capacity of the bucket ~ estimated to be from 6.5 to 7 second-feet, or 3.25 to 3.5 second-feet per foot ot width.

Tail water depths for sweepout and diving with the bed level approximately 0.05R, or o.6 of' an inch, below the apron lip are recorded in Table V and plotted in Figure 11. Again, as with the smaller buckets, it was difficult to get consistent data for the diving jet and to deter­mine the exact margin of safety required for establishing the upper and lover tail water depth limits. However, the safe margins appeared to be about the same as for the smaller buckets previously tested.

The tests were repeated with the bed sloping upward at 16° to about 6 inches above the lip; again, the results were comparable to those

32

~ DATA AND CALCULATED VALUES FIJI 9•IIICB RADIUS BUCKET

Run !lo. 1 2 3 Ii Bed was amoximate~ O.Q2!! below aEon 111! at bel!!!!!i!!I ot each run

i!i B : 2 : : 7 : : 2 : 10 : 11 : 12 13 lli 12 il, Bed Blol!!s UJ! f'rom aEon liJ!

11 : 18 12 : 20

Sveepout Collditions

1 H o.476 0.531 : 0.642 : 0.682 0.722 0.764 0.805 0.852: o.884 0.534 0.578 0.585 0.633 0.54 o.433 o.485 0.527 o.634 0.723 2 T ( sweepout depth) 1.02 1.11 1.19 1.33 1.41. 1.45 1.51 1.60 1.67 1.70

3 q 1.05 1.28 1.52 2.05 2.28 2.50 2;74 3.00 3.30 3.5:. 1.53 1.73 1.78 ·2.02 1.56 1.12 1.32 1.50 ·2.01 2.50 4 Tmin 1.22 1.31 1.39 1.53 1.61 1.65 1.71 1.80 1.87 1.90

: v12 · : 5:2g .. X·+B-Tmin 4.199 4,166 4.141 4.112 4.072 4.072 4.054 4.005 3.982: 3.984

6 V1 16.45 16.38 16.33 16.28 16;20 16.20 16.16 16.06 16.02 16.02

7: D1 0,064 0,078 :. 0.093 o.126 0.141 0.154 0.170 0.187 0.206 0.220 : V1

8 : F =l;jii 11.49 10.34 9.44 8.09 7.62 7.27 6.92 6.56 6.22 6.03 : Tm1n

19.12 16.77 14.93 12.15 11.44 10.69 10.oB 9.63 9.07 8.64 9 : 75i"" : V12 I

4.238; 10:D1 +2g 4.262 4.244 4.234 4.212 4.226 4.224 4.192 4 •. 188 4.204

R 11;~ 0.18 0.18 o.18 0.18 0,18 0.18 0.18 0.18 : o.18 : 0.18 : D1 + 7!i

: : : Diving Flow Collditions

CA) 12 : T ( diving depth) 3.40 3.03 3.01 2.46 2.38 2.44 2,44 2.32 2.46 2.37 2.68 2.39 2.37 2.42 3.07 1.96 1.86 2.23 2.69 2.43 CA)

13 Tmax 2.90 2.53 2.51 1.96 1.88 1.94 1.94 1.82 1.96 1.87 2.18 1.89 1.87 1.92 2.57 1.46 1.36 1.73 2.19 1.93 : v12 : 14: 2g=X+B.Tmax 1.519 l-946 2.682 2.802 2.782 2,824 2.985 2.892 2.014 2.354 2.688: 2.715 2.713 1.970: 2.970: 3.125 2.797 2.444 2.793 : . . . . 15 : V1 9.8<} 11:20 : 11.40 l-3.14 13.43 13.40 13.48 l-3.87 l-3.65 13.94 12,31 13.16 : l-3,22 l-3,21 11.26 : ~-84 ; 14.18 13.42 12.55 l3.4o :

: : ,16: D1 0.106 o.il.4: 0,133 0.156 0.170 0.187 0.203 0,216 0,242 0,252 o.126 O.l3l: 0.135 0.153 0.138: o.oBl: 0.093 0.112 0.160 0.187 V1 5.34 5.84 5-49 5.85 5.46 5.26 4.89 4,89 6,11 6:41 6,38 .4.15 8.59 8.19 7.oB 5.53 5.46

17 : F '"lijij_ 5,72 5.25 5,95 : Tmsx 2.733 22.l-3 18.82 12.56 11.07 10.39 9.54 8.51> 8,10 7.40 17.28 14.38 13,89 12;55 18.55 18.00 14.60 15.47 13.67 10.34

18: --D1 V12 : : 19:D1+2g_ 1.625 2.060 2.154 2.838: 2.972 2.969 2.077 3.201 3.266 2.480 : ~-819: 2.850 2.866 2.108 3.054 : 3.218 2.909 2.604 2.980

R 20; ~ o.46 0.36 0.35 0.26 0.25 0.25 0.25 0.23 0.24 0.23 0.30 0.27 0.26 0.26 0.35 6.25 0.23 0.26 0.29 0.25 :Dl+Tg

R. .. bucket radius (rt) B • height ot reservoir above the crest (rt) T = clepth of tail water above the bucket invert (rt)

Tm1n .. minimum tail water depth tor good performance (rt) ., sweepout depth + 0.2 rt Tmax a maximum tail water depth tor good performance {rt) = diving depth - 0,5 rt

q a discharge per toot ot model Cl'est length (eta) . X .. height ot crest above bucket invert .. 5 feet

v1 • velocity ot tlow entering the bucket computed at tail water elevation (rt/sec) D1 = depth ot tlow entering the bucket computed at tail water elevation (rt) F .. Froude number ot now entering bucket computed at tail water elevation

MaximlDR capacity ot bucket estimated to be 2.0.to 2.5 secolld-teet per toot ot width.

FIGURF. 16

\" .. -----:--~------· ~ _ _/--~ • • -------- - ,. =--....... :::.., .. ~-... ~.,. ::: .. ( (""' ") j ~ ~ '----). _:_ . • • . . \.., ~ ) tf :f / .-,--> ~ . .... \.,\.. ,,.,,...,.. _,. ~ ·:::.:.~~///rr (-r ( ;> ") ~~ . . · .. ·:.~'--- ~ 1/c . <- ,_/ "-.... - ...__ • • • • • • • ____,,.,; ,..-.;a:~~ <- <- <, ') ~

. • • • • • . -·... -0-00-- - ------ .,,,,..,,,, . . · .. -·:: •: .:. ::•: .·. ------..... : : . · .. ; -::.-.:: A. q = 2.5 c. f.s.

·.~ ---- ,_../~--=-::::--------.:.~------- i- / ~~:--:....~ .:_:·.1I ""' '~) J// ~ ~~-:__ --..... -~ "'·' ~ ~ - / ~ ( ( .) ) "-. "--: :-. -: : :~ ~ ~ c <<:_ ~- <--:___, ) ~ ~

• . • . . . • ••• l:Blill;t:IClO------- :.1.. ~ .·.· .·.·:·.·:-·-:· ::.·.·. -----~ ........ ____ _ . . . . . . . . . . .. · .... B. q = 3.0 c.f.~.

\. ----....__ ____ ·1..'\ /~ . .._ ---·:. ~--------=--- / .,,..---. ~ ... ~ ·.=.=.~. ~ C ) ) /1/!( rr _..-->--;_____ '--- -.. ··'''" I/~ ~ ............__ --:.. - -:a- . .. : ... : :\~'----~~ 1/c: ( ) ) ) (~., - ---~ . ·_· .. -.. ·~ ~ . ( ~'- "', ~-- ( ) ) ,..,,

• I •• I I I I•• 'lll1RR11~:,-..;______ ~ / • I I •• e I: I II·. II; I Ill •11 -------------~--

1 I • I • e • e e •• I 1 1 I e t I I : :•

C. q = '3.5 c.f.s. ·), . . . /,;-~ ==:::--:: •• \._ ---- ~.; :f _.,,,,-~ "-- .

·._=:~( () <; }" ::::-- ~ --.,., -: ·:;-"::.-.~--:1/"½ ,~. ()) (,) ~ ('",.) . .. . . . ·.~ . C 'C'- _.....;

• • • • • • • • • ·-- --c---- IIIIIIC.: ........... . . ... · .• · ..... ·.· . . . . ---------- . -=---- . . . . . . . . ..... ·... -.._, ____ _,_ . . . . . . . . . . . . . D. q_ = 4.0 c.f.s.

( Bed level 0.6-inch below apron lip at start of test.)

12-.INCH BUCKET - TAILWATER DEPTH= 2.~0 FEET

34

I : Y , •

~

DATA AND CALCULATED VALUES FOR 12-INCH RADIUS BUCKET

Run No Bed was a Bed slopes up :from apron lip • l 2 3 11 12 13:14:15:16

Sweepout Conditions

1 H 0,543 : · 0,592 : 0,637 0,679 0,729 : 0,765 0,811 0,850 ;, 0,887 :.: 0.961 1.02 1.221 9,565 0,651 0;723 ; . 0,839

2 T {sweepout depth) 1,27 1,33 1.40 1,45 1,52 1;56 1.68 1,72 : 1.78 l.89 1.96 2,23

3 q 1 •. 58 1.82 2.03 2.25 2.53 2;75 3.05 .B-~8 3.54 4.06 4,li8 · 6.08 1.67 2.00 2.50 3.21

4 Tmin 1,47 1,53 1,60 1,65 1,72 1,76 1,88 1.92 :· 1.98· : · 2,09 2,16 2,43 ~ ..

5 2g • X + H - Tmin 4,073 4,062 4,037 4,029 4,009 4,005 3,931 3,930 ':' 3,907 3,871 3,860 3,791

6 V1 16,20 16,U 16.12 16.11 16,07 16,06 U,92 U,91 u.M U,N U,TI U~3

7 D1 0,099 0,112 0.126 0.140 0,157 0,171: 0,192 0,206 0,223 0,257 0.284 0,389 V1

8 F =fiDj_ 9,10 8.51 8.01 7,60 7,14 6,84 6.41 6,18 5,93 5:49 5,22 4.42 Tmin · 9 -,;- 14.91 13.60 12.71 11.81 10.93 10.28 9.81 9.31 8.87 8.13 7,60 6,25 l~ .

10 D1 + 2g 4,172: 4,175 4,163 4,169: 4,166 4,176 4,123 4,136 4,133 4,128 4,144 4,180

R 11 ~ 0.24 0.24 0,24 0.24 0,24 0.24 0,24 : 0.24 : 0.24 : 0,24 0.24 0,24

D1+2g .

Diving Flow Conditions

12: T {diVing depth) 3,95 4,00 3,90 3,95 3,95 3,95 -- 2,91 2,87 3,22 3,17 3,00 3.25 3.00 2.45 2,35 CA> • C1I 13 : Tmax 3,45 3,50 3.40 3,45 3,45 3,45 -- 2.41 2.37 2,72 2,67 2.50 2.75 2,50 1.95 1,85

14 : ~" X + H - Tmax 1.093 1.092 : 1,237 : 1,229 : 1,279 1,315 -- 2.440 2,517 2.241 : 2.35 2,721 1,815 2,131 2.773 2,889

15 V1 8,39 8.39 8.92 : 8,90 9.07 9,20 -- 12,54 12,72 12.01 : 12,30 12,23 10.81 11.71 13.36 13,64

16 D1 0,188: 0.217 0.228: 0,253: 0,279: 0,299 -- 0.262 0,278: 0,338: 0,364: 0,460 0,154 0,171 0.187 0,235 V1

17: F •-liJii_ 3,42 3,17 3,29 3,11 3,02 2,96 -- 4,31 4,25 3,64 3,41 3,44 4,86 4.98 5,54 4,96 : Tmax l

18 : 7ii"' 18.35 16.12 14,91 14.63 12.36 11,53 -- 9.19 8.52 8.04 7.33 5.54 17,85 14,61 10.42 7,87 : V12

19: D1 + 2g 1,281: 1,309 1,465 1,482 1.558: 1,614 -- 2,702 2,795 2,579 2,714: 3,181 1,969 2,302 2,960 3,124

• R 20 : ~ 0.78 0.72 o.68 o,67 o,64 0.62 0.37 o,36 0.39 0.37 0.31 0.51 o.43 0,34 0.32

: D1 + "'Tg ------R,. bucket radius {:rt) H = height of reservoir above the crest {ft) T • depth of tail water above the bucket invert {:rt)

Tmin = minimum tail water depth for good performance (:rt). aweepout depth+ 0.2 :rt Tmax = maximum tail water depth for good performance (:rt)• diVing depth - 0,5 :rt

q = discharge per foot of model crest length {cfa) X = height of crest above bucket invert= 5 feet

V1"' velocity of flow entering the bucket computed at tail water elevation (:rt/sec) Di'" depth of flow entering the bucket computed at tail water elevation {:rt) F •.Froude n11111ber of flow entering bucket computed at tail water elevation

Maximum capacity of bucket estimated to be 3,25 to 3,50 second-feet per foot of width.

for the 9-inch bucket. The safe maximum limit appeared to be about the same as the upper limit for the 9-inch bucket with the bed molded level below lip elevation. These data are also given in Table V and plotted in Figure 11. The maximum capacity of the 12-inch bucket was considered to be the same with the upward slopi~g bed as with the level bed.

Eighteen-inch Radius Bucket

The 5-foot-high model spillway with the 18-inch bucket repre­sented a relatively low structure such as a diversion dam spillway.

The performance of the 18-inch bucket is shown in Figure · 17 for discharges ranging from 6 to 11 second-feet with normal·tail water depths. The capacity of the bucket was estimated to be 5 to 5.5 second-feet per foot of width.

With the movable bed molded level, approximately 0.05R or 0.9 of an inch below the apron lip, tests for sweepout were made and the data obtained are recorded in Table VI and plotted in Figure 22. Depths for sweepout and diving were even more difficult to determine precisely than for the smaller buckets. In fact, the sustained diving condition could not be reached by rai~ing the tail water as high as possible in the model for any discharge. However, the tendency to dive was present and momentary diving occurred, but. in no case was it sustained.

The minimum tail water depth at which the bucket operated satisfactorily was found to be 0.l foot above the sweepout depth, however, 0.2 foot was used, as for the other buckets, to provide a factor of safety.

The maximum tail water limit or the maximum bucket capacity were not determined using the sloping bed because of difficulties in maintaining the bed shape while starting a test run. Performance with the sloping bed was, therefore, assumed to be consistent with the test results on the 9- and 12-inch radius buckets.

Larger and Smaller Buckets

Larger buckets were not tested with this 5-foot spillway because of the increasing difficulties in measuring bucket capacity and tail water depth ·limits for near capacity flows and because a larger bucket operating at near maximum tail water depth limit would either submerg~ the crest or, closely, approach that condition. It was not intended at this time to investigate a bucket with a submerged crest.

Smaller buckets were not tested because very few, if any, prototype structures would use a bucket radius smaller than one-tenth

FIGURE 17

-~ .. •·. . /;...-.... -------··

0 i~}\\UJ)1/:s~:?(~ -: '<: :\ ~ _...~ ~c"' ~--~--~-'::::_

43'7

• I • t ,............_--.._____..,. I •,

••••• •• ••••• • ·.::-: • . 0' I I • e • •' e I I I I I I I I I • I 0

I I I e I • I I I : II I II I ; ·: : : I I I - •

A. q_ = 3 c.f.s. ,· Tail water depth = 2.30 feet.

\. -----. \. \. ~,;, - -""' ......__ _ -: ·. ~------------;----~/ .,..--:->_--....._ ---:,. .·.·-.-~\\' < r, J -<~~. // /,~ ?: ) ~ ~;:: .... ~ /~½ ~ :r ,r ( ~ )) ,"-. • • .. • -.- rr -/ / ,/ ~ ( "" <- ~ ~

• : • • • • ••• :lo, ------~ ..,- ( -o:::0-o-- - --- --, .• ••.••. • -~>- ••• •• 0

. : . ·. ·>.:-:.: :·.::_.:_::·.<.=.:.:·.:·:\::: B. q_ = 3.5 c.f.s., Tailwater depth = 2.30 feet.

'.(\ ' _/'-:;:::;--~----·... \ ' ' ' ~i ~ --- ---. ·.: _:~"(------;.-.:j (. //~_:_-:----- >'

• • • ··, :\"' ., ( ( ) ~ / / /~ ~T ~ /4' --->-:, ·. ·:. ·>: ~ \-::-,. ~/1//c., ( ~- ) ~-=--~~

I I I I ,- - ~ /~~~--,0-000-- -••• : • • • • •• ~ ~.,... •••• • ••• 0 0

· .. ::-: : ...... _.:: .. ::._:.:.=.t·/:.·~.:·\\ C. q_ = 4 c.f.s. ,. Tailwater depth = 2.30 feet .

. \ ~------------:. ~ \ ~- -<) ~ ---------... : .~\ ~,---~~=----~ ~ :·-:.\"«ir- , ;, ;. __,--"' ------> i> ~

• • • • • • ~ /' /~.,,..-~7 ---------::. -::.·:=_.~ ... ~1/./., ,.,. (.,. ,>' ~ .. ' ... •. ,,, . .c ~ ,..)"" .. I •• •• ~ -~'!2C)oo- '-... .,/ V) ,r

• • • • • • • : • • • • • • •. o o-c,-0~ "' ( "'-) •••••••• • ·.·.·.··.:·.··. :·.·.: •• 0 .__ ____ ,__,_

. . . . . . . . : : : . : .... : : . : . : : : : ... · ·: ·. D. ·q_ = 5.5 c.f.s., Tail water depth = 2.45 feet

( Bed level 0.9-inch bel.ow apron lip at start of test.)

18-INCH BUCKET PERFORMANCE

37

Table VI

DATA AND CALCULATED VALUES FOR 18-INCH RADIUS BUCKET

Run No. ,Bed was a 1

: . . .. Sweepout Conditions

: 1 H 0,631 0.734 o.804 0.898: 0.926 1.001 1:083 ·: 1~150

: 2 T {sweepout depth) 1.45 1.78 :

: .

3 q 2.00 2.56 2.99 3,61 3.80 4.35 4.98 . 5.48 . 4 Tmin : 1.65 1.85 1.98 2.07 2.15 2.23 2.32 2.45

v12 3.981 3.884 3.824 3.828 3.776 3,763. 5 28 = X + H - Tmin 3.771 3.700

: 6 V1 16.02 15.86 15.70 15.70 15.27 15.68 15.67 15.44

1 D1 0.125 0.161 0.190 0.230 0.249 0.277 0.318 0.355

8 V1

F =.-/gD1 7.98 6.94 6.33 6.76 5.39 5.24 4.88 4.56

9 Tmin 13.22 11.46 10.39 9.00 8.64 8.03 7.30 6.70 I>! .. ~ v12 .

10 D1+- 4.106 4.045 4.014 4.058 4.025 4.043 4.081: 4.055 2g . . R

11 v12 0.37 0.37 0.37 0.37 0.37 0.37 0.37 . 0.37 . D1+""2g ..

Diving Flow Conditions . ·•. . 12 T {diving depth)

: . .. 13 Tmax .. ..

v12 14 2g = X + H-: Tmax . -: . 15 V1

.. . ·=

16 D1 V1 NO DATA TAKEN

17 F =_./gD1

18 Tmax 75i'"' 2

19 V1

D1+-2g

R 20 v12

D1+ 2 .. -R = bucket radius {ft) H = height or reservoir above the crest {rt) Ta depth ot tail water above the bucket invert {rt)

Tmin = minimum tail water depth tor good per~ormance (rt)= sweepout depth+ 0,2 rt Tmax = maximum tail water depth for good performance {rt) = diving depth - 0. 5 ft ·

q = discharge per toot ot model crest length ( cts) . · X = height of crest above bucket invert= 5 feet ·

V1 .. velocity of flow ent.ering the bucket computed at tail water elevation (rt/se.c) D1 = depth of flow entering the bucket ~omputed at tail water elevation (rt) · F = Froude number. of flow entering bucket computed at tail water elevation

MaxiDlum capacity of buc_ket estimated to be 5.0 to 5.5 second-feet per foot of width.

38

the height of the spillway. Small radii bends are usually avoided on high structures where velocities are also high. Therefore, the available data were analyzed, and with some extrapolation, found to be sufficient.

Data Analysis

. Safety factor. At the conclusion of the testing the data for the four buckets were surveyed and the margin of safety between sweepout depth and minimum tail water depth, and between maximum tail water depth and the depth required for diving were definitely established. An ample margin of safety for the lower limit was0.2·foot and :for the upper limit 0. 5 foot. These values were suf'fic ient :for both the level and sloping movable beds previously described. The selected margins of safety are included in items T~in and Tmax of' Tables III, IV, v, and VI. ··

Evaluation of variables. To generalize the data in sµch a way that it can re$dily be used to determine the minimum allowable bucket radius "R," the safe minimum tail·water depth •irmin 11 "1ld the safe maxi­mum tail water depth "Tmax".for·any prototype overflow spillway whose crest is not submerged by the tail water, it is necessary: to consider the variables, shown in Figure 18, that affect the unknown requirements. The maximum capacity of a given radius bucket is increased slightly when the tail water depth is at an intermediate value between the minimum or maximum tail water depths;, but since bµckets are usually expected to operate over a range of tail water depths the bucket capacity 1s not a f'unction of tail water depth.

The elevation of the movable bed with respect to the apron lip and the slope of the spillway face do not, within ordinary limits, affect the sweepout depth or the size of bucket. Frictional resistance on the spillway face affects the minimum depth limit, the maximum depth limit, and the minimum allowable bucket ,radius since head losses caused by skin friction reduce the effective heightot fall •. However, frictional resistance is, primarily, a function ot head or discharge and the height of spillway above tail water elevation; therefore, friction effects need not be considered as a separate variable. The effect ot friction losses is discussed further in a following portion of this report.

Data obtained during the tests includes the sweepout and diving depths for a given height of model spillway above tail water elevation "h." The given slope of spillway is "So" Figure 11 shows that the sweepout depth is a function of' the radius of bucket "R" and the head on the crest "H." "H" may also be expressed in terms o'f" discharge "q" per foot of spillway width; however, "q" and "R" are related by the discharge coefficient "c" in the discharge equation

39

FIGURF: 18

-=-= ________________ Reservoir _EJevation_ _____ ___ __ _____f _ - . I

431

H • I __________ Crest Elevation __________________ ~

v, .Froude Number F = J 0 ,--Vi / Q I ,

~ -J."'., .------------

I I I

;h T I _ _ max. I -

· T.W. levation

I ;-;-. 1 --::- mm. l __ "f:g T -_,Apron Lip 1

I I

' Channel BediElevation-,

Bucket Invert-'

DEFINITION OF SYMBOLS

40

Therefore,

Tmin = f(h, S, R, Hand q)

Figure ll also shows the .tail water depth at which diving flow · occurred'to depend upon the elevation of the channel bed with respect to the apron lip, the bucket radius, and the head on the crest. Therefore

Tmax • f(h, s, R, B, q and elevation of channel bed in relation to elevation of bucket apron lip)

The minimum allowable bucket radius tor a given height of model. spillway above tail water elevation, with given slope of spillway, is a function only of the head on the crest, Figure ll. Therefore, the minimum allo~ble bucket radius Rmin may be expressed:.

Rmin • f(h, s, Band q)

The velocity entering the bucket "Vi" and depth "D1" are functions of bead, discharge, height of' spillway above tail water elevation, and spillway slope.

V1 and D1 = f(b, s, Hand q)

The Froude number, a dimensionless parameter, is a function of velocity and depth of flow and may be expressed

Substituting F for h, s, Hand q

Tmin • f'(R, F)

Tmax = f'(R, F, and elevation of' channel bed with respect to apron lip)

Rmin • f(F)

Bumerical values f'or the Froude number were computed from the available test data in the tables for points at the intersection of the spillway f'ace and the tail water surface. At these points all necessary

41

information for computing velocity and depth of flow can be determined from the available test data which includes reservoir elevation, discharge, and tail water elevation. Since the Froude number expresses a ratio of velocity to depth and is dimensionless, a numerical value represents a prototype aa well as a model flow condition.

To express Tmin, Tmax, and Ras dimensionless numbers so that they may also represent prototype flow conditions, Tmin and Tmax were divided by Di,; R was divided by D1 + V12/2g, the depth of flow plus the velocity bead at tail water elevation on the spillway face. These dimensionless ratios and the Frou.de number, computed from test data, are shown in Tables III, IV, v, and VI. In computing the tabular values, frictional resistance in the 5-foot model was considered to be negligible. In Figure 19 the dimensionless ratio for the bucket radius is plotted against the Froude number, using only the test points bracketing the estimated maximum bucket capacity. Values were computed for both the sweepout and diving tail water elevations since the Froude number and

R

Di + V12 both vary with tail water elevation. For example, the maximwn 2g

capacity of the 6-inch bucket is q • 1.5 to 1.75 in columns 7 and 8 of Table III; data from lines 8 and 11 and lines 17 and 20 were plotted in Figure 19. The two points thus obtained for each discharge were connected by a dashed line to indicate the trend for constant discharge. Eight · dashed lines were thereby obtained for the four buckets. A single envelope curve was then drawn, shown as the solid line to the right of the preliminary lines, to represent the minimum radius bucket. The solid line therefore includes a :factor ot safety. It a larger factor ot safety is desired, the solid curve may be moved to the right as far as is considered necessary.

Since both the upper and lower depth limits are functions of . Tmin Tmax

the bucket radius and the Froude numbei; Di and Di for each test point in Tables III through VI were plotted versus the Froude number in Figure

R

201 and each curve was labeled with the computed values of D + V12• 1 2g

Since the upper tail water depth limit varied with shape and elevation of the movable bed, two sets of upper tail water depth dimensionless ratios were plotted, one tor each of the tvo bed elevations tested. The curves drawn through these points in Figure 20 may be used to determine minimum and maximum tail water depth limits tor any given Froude number and bucket radius.

431

12

I

10 I I

9 l \

~ --- - --Q= 1.5 cfs. 8

,

' ,

I L ;: " 7 c~ ' ., I\

~-' -le > (;'> 6

.. q•l.75 cfs? - II

: q= 2.0 cfs/. ' .. "' II

5

..... Q=2.5 cfs.~ ' -, - 1, .,,

: q =3.25 cfs:- .,, . ., . .. q =5.0 cfs.: : q=.3.5 cfs.- ·~ -q=5.5cfs. --1- ,- \ ,. .

4

3

2

0 0

II.. .... ... ...

0.1 0.2 0.3 0.4 0.5 0.6 0.7 R.

MINIMUM ALLOWABLE o,+v.212g .

EXPLANATION o For bucket radius (R) = 6 inches a For bucket radius (R) =· 9 inches 11. For bucket radius (R) = 12 inches ~ · For bucket radius (R) = 18 'inches Bed level approximately 0.05R below

lip of apron.

FIGURE 19

MINIMUM A·LLOWABLE BUCKET RADIUS

43

FIGURE 2Q

16

0

15

14

13

12

II

10

9

51~8 II

LL 7

6

5

4

3

2

l...----"' -,, ... ..,,o-

~~ Use these curves to determine maximum tailwater depth

lo --limit: (Tmox./D1) obtained from data shown in • ·

' t;) ,Ar \

Figure II and computed in Tables m to:m.--------, V I

Use these curves to determine minimum tailwater depth /

Use these values when bed level is approx. I I

limit: (Tmin./D1) obtained from the data shown 0.05R below apron lip. ---------, I

/~ ,.- Use these values when bed slopes up )

I

in Figure II and computed in Tables m to JZI--, ~i.-I I

I : from apron lip. I I

I: ~ 0 '" I I I + I I v· I I

I, ';..-- ................... I I,' .I. R •0.20 J. o,+vf/29 __ 0 20-

~ V i.,.- R _,.,0.30 I I l'-vO· ------- ·1 I I ., ........ . o,+v,z12g o·.3o - - -- I _: 0.22-· '-- I

l1 ,-~ V.,...,.o. I ~--0.25 -q,; i--------- I

I I I

I~ '7 i----L..-- - I I

- - R :0.2~ .---- ---- --0.20 0.30 v A

~ ~ .l>' D1+v1

2/2g · i---- - - ,0,4U - - - 0,30 I I

~--0.17 i.----- -- -0.40-i------- I I I

.A1 i------ - - I _i,:.:..:.- - - - ,- I I - I I

~ ~ .,,,.-Y, ~ ~ -- i--- .... --- - 1 0.40

L --~ ~ -- ---- c--i-------- 0.50 -------- 0.4-0- '- I I ,.-0.36 · 0.50-

,___ ---- ,. - - - --- . I

~ :::?"'-- - ~--o.:;:-- - ,,_ __ 0.30 - -- 0.50 11' -~

i...-- - --- -0.46 J\,60 ----- 0.50- ---:--.- I

po.ill---c...--_ -0.43 _ ---- r-!- - 0.60" --------- .i I -------- JI - -1---- -~ - -----,___ 0.60 ,_

~ ~ ;;;,--:

-- l -- X _ x-~- o.51 --- -i-.-rn - 0(0 I -= - -- ------ r'.-O.l - -- - I

.... ;-"o'.lf>• _,.. - -- - l

~::' ~~ - - =-- Maximum tailwater depth llmit {Tmgx./D1 ) -::::::::-- :::::-- - -.A' I~ A including an extra factor of safety. ___ .,

- R

6-~ ~ ·-- -o,+v,z/2g o.68

----00 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 4-0 41 42 4-3 4-4 45 4-6

T min./D1 and T max./D1

DATA BUCKET R RADIUS BED ARRANGEMENT DESCRIPTION OF DATA POINT

SYMBOL (R) INCHES D1+V11/2g

0 6 0.11 For any position of the bed Min. tailwoter depth limit D 9 0.18 For any position of the bed Min. toilwoter depth limit /l 12 0.24 For any position of the bed Min. tailwoter depth limit

0 18 0.37 For any position of the-oed Min. toilwoter depth limit ~ 6 o.16to 0.22 For bed level approx. o.o5R below apron lip Max. tollwater depth limit.

• 9 o.23to o.46 For bed level approx. o.05R below apron lip Mox. toilwoter d,epth limit a 12 0.31t0 0.68 For bed level approx. o.05R below apron lip Max. tailwoter depth limit

• 9 0.25 For bed sloping up from opron lip Max. tailwoter depth limit X 12 0.43t0 0.51 For bed sloping up from apron lip Max. toilwater depth limit

DIMENSIONLESS PLOT OF MAXIMUM AND MINIMUM TAILWATER DEPTH LIMITS

4~7

44

Note that the upper four curves in Figure 20 are for the minimum tail water condition and apply to any bed arrangement. The ten lower curves extending far to the right apply to the maximum tail water limita­tion and have two sets of labels, one for the sloping bed and one for the

R 2 .

level bed. Two curves are shown for each value of Dl + Vl; the upper 2g

or solid line curve has an extra factor of safety included while the lower or dashed line curve is according to the data in Tables II through IV.

Although the curves of Figure 20 may be used as shown, a simpler and easier to use version ot the same data is given in Figures 21 and 22.

Tmin Figure 21 contains a family of curves to determine ,r- values in terms

. 1 R

of the Froude number and D + V12• Figure 22 contains similar curves to 1 2g T .

determine ~ and includes the extra factor of safety discussed for

Figure 22. The two abscissa scales in Figure 22 differentiate between the standard sloping bed and the standard level bed used in the tests. Figures 21 and 22 were obtained by cross-plotting the curves of Figure 20.

The tail water sweepout depth "T" in Tables III through VI was Ts

also expressed as a dimensionless ratio Di and plotted versus the Froude

number in Figure 23, and a curve for each bucket size was drawn. These curves were then cross-plotted in Figure 24 to provide a simple means for determining the sweepout depth for any installation. The difference between sweepout depth and the depth actually encountered indicates the margin of safety.

Practical Applications

To illustrate the use of the methods and charts given in this report, a step by step procedure for designing a slotted bucket is presented. The data for Grand Coulee Dam spillway will be used as an example. The calculations are summarized in Table VII.

For maximum reservoir elevation 1290 at Grand Coulee Dam the spillway discharge is 935,000 second-feet. Since the spillway crest is at elevation 126o the head is 30 feet. The length of the crest is 1,485 feet making the discharge per foot of bucket width 630 second-feet. The tail water in the river is expected to be at elevation 1009 for the

45

FIGURE 21

10

9

8

7

6

4

3

2

437

'-

' , .. ......

.. ......

........... ~

..... ........

i-----

·--

0.1

' I"..._

' ... ,

... , ......... ........ ........ ""16 , ... .... ...... ,..... .....

...... 15 ..._ ~ -.... "- r-,.. ...... --......... ~14_ -....... i...... ---...... ...... ~I"'--, --13 ........ _ --~ ..... -- -..... 12 ..... ---~ ..... - ----,_

i-- II ---- --- ~--- ,_ r---10 ----· ----- -r-i-- 9 -r---- - a~

7

6

5

4

3

Tmin./D,. f.

NOTE For values of "F" greater than 10 use Figure 20.

0.2 0.3

R 0:4

- ----- --- -r--- ---i---

i-- ---r----

-

0.5

MINIMUM TAILWATER LIMIT

46

0.6

437

. FIGURE 22

10-------.-........ ---...-. ......... .,..,..........,....,....,..,...,...,., ........ --r--r-~.,.....-,.......,.--,---,-""T"'""~,.......,.......,......,..--r--r-,.....r-T--, \I\ \ \ '\ \I\' \l\'l\

3

2

\ ~ ' \ \ \ \ ' \ '' I\ ~

~r-..... ', .... ~r--..._r-,, ... ~ ...... --....;:,,

.... ...... ...... ....... ~ ~

l----+---l--+---l----i--~1--+--+--+--+-+--+----1---l-_--+-_---l_ 5 """"'1:-+-~1-' ...... ~ .... +'~r--..:-l ... ""' .... -.l:: ...... ~ .... ,d-=" .... ""t, ..... -=:!--+-+-+-t--1 .... ..... """

...... .... ..... ...... ...... ...... ...... ....... ......

4-- I"'"-,._ ~ ...... ~ ......

Tmax./D1-{ -- ...... ...... ....... r-- ""r-...

·~ .......... ~ --NOTES -

Tmax/D1 includes the extra factor of safety shown in 1--+--+--+--+-+--t Figure 20.

For values of "F" greater than 10 use Figure 20. i--+--+--+--+-+--tFor channel bed elevation o.05R below apron lip or lower

use coordinates for bed approx. 0.05R below lip. 1--+--+--+---1--+--1 For channel bed eJevation higher than 0.05R below apron

1---1---+--+--+--+--1 lip use coordinates for bed sloping up from apron. 1---1---+--+--+--+--1

00

0.1

0.1

0.2

0.2 BED 0.3

0.3 0.4 0.5 APPROXIMATELY 0.05R BELOW LIP.

0.4 0.5 0.6

0.6

0.7

0.7

0.8 BED SLOPES UP FROM APRON

R

MAXIMUM TAILWATER LIMIT

47

FIGURE 23

437

18

17

16

15

14

13

12.

II

~ 10

- 0 > 01 9

II

8

7

6

5

4

3

2

0 0

....... /.,,,

R /,

' o, + v,2/2g= 0.11

/ Bucket radius R = 6 inches-~,

V / ~

0 / V V 0.17

/ V <I ~ ... - R = 9 inches

,v )' ..,v / /0.23

:

OJ p / , / ~- R =·12 inches J ,/

/ f/ / J rf,J "o.35 r;-

'/. '{ V R = 18 inches /). '/Si V

....I 7'? / ,0 r/

A '£ >. r/ ~

J 1/

w lb

J.' '/

/I

2 4 6 8 10 12 14 16 18 2.0 22 24 26

T8 /D 1

Note : Bed arrangement not critical for sweepout condition

TAILWATER DEPTH AT SWEEPOUT

GPO 85Z879

48

437

II

LL

10

9

8

7

6

4

3

2

1---

0 0

'- ...... .... ' " ['. ~ ......... .......... .......... . ......... I.......,~

I'-- I'-- , .... I'-'"IS

"'r-,..._ ""r-,..._ "' ... ... ........ f',,. ... 1"14 ,.....

""r-.... I""',.~ r---.. . r--.. I""':-... ..... ~ r---.. '13 I'-.._

~~ f',,...._ ~ ~ I"'

.......... 1""12 ..... I"-,, ..

I"'-,. I"'-,. - ...... r-- ....... r--

t,.. II -r-,... ... -r-,... ...... _ .... ......

.... ...... ...... -r--_ I"'-, ..... -,o_ r--- .....

.......... r--- --· r-- r--- r-,... -9_ --

-i- ...... -r- r-,..._ I r- i--,_ - r- i-,.

r-r- .. 8 . --I"'---i-- r-

r-i---- 7 ---~

r-i-- --~s--

-- i-I"--- 5

.. -- - 4 l

.. _ - I - Tsf.= 3

D1

Note: For va I ues of "F"greater than 10 use , 1 , , 1 1 1 1 I I 1 1 1 1

Fi11ure 2.3 I I I

O. I 0.2 0.3 R

0 1 + v12

2g

0.4

TAILWATER SWEEPOUT

49

I I I I

0.5

DEPTH

FIGURE 24

- .._

0.6

Table VII

EXAMPLES OF BUCKET DESIGIII PROCEDURES ,,

: : : . : . 'Grand Missouri Angostura : Angostura: Angostura: Angostura : .,Col!,l.ee : Trenton : Diversion

-: Dam .'Dam Dam Dam . Dam :- Dam Dam :

1 : Q 247,000 180,ooo 100,000 40,ooo 935,QOO: 133,000: 90,000 .. 2: Reservoir ele"V&tion 3198.1 3191.0 3181.5 3170.4 1290 : 2785 2043.4

I 3: Crest elevation 3157.2 3157.2 3157.2 3157.2 ·1260 2743 2032

4 : H 40.9 33.8 24.3. 13.2, 30 42 17.4 . 5 L 274 274 274 274 1485 266 644

: 6 q 901 657 365 146 :. 630 500 140

7 Tail water elevation 3ll4 3106 3095 3084 10!)9 2700.6 2018.3

8: v12 2g (theoretical) .. (2) - (7); 84.1 85.0 86.5· 86.4 281 84.4 25.1

9 V1 (theoretical) 73.6 74 75 75 130.5. : 73.7 40.2

: V1 lactuali 10 0.98 0.98 0.97 0.93 0.91-: 0.90 0.98 ; V1theore ical) 11: V1 (actual) 72.2 72.5 72.8 69.8 : il8.8 66.0 39.li-

: V 2 : 12 : ~ (actual) 80.9 81.6 82.3 75.6 219.2 67.6 24.1

: g

13 Di 12.48 . 9.06 5.01 2.09 5.30: 7.58: 3.55

lli-:-(15i_ 3.53 3.00 2,24 1.45 2.30: 2.75 1.88 : V1

15 : F ';JiDi 3,61 4.26 5.73 - 8.li-9 9.u : 4.23 3.70

16 • D1 + V12, 93,38 90;66 87~31 77.69 224.50: 75.18: 27.65 "Tg

17: R 0.50 o.43 0.30 0.15 0.13: 0,43 o.48 v12 (minimum)

D1 + 2g

18: R (minimum) 47 39 26 12 29 33 13

19 : R (actual.1¥ used) 40 40 4Q 40

20 : R (recommended) 30 35 12.5

21: R o.43 o.44 .. o.46 0.51 0.13 o.li-7 o.45 vi2 (actual)

D1 + 2g

22 : Tmin :Ti" 5.li- 6,6 9.3 16.4 13.8 6.6 5.5

23 :·_Tmin 67 60 46 34 73 50 20 : Tmax

5.6 17.6 60,0 18.8 8,8 24: ~ 7.9 13.0 •. 1

25 ; Tmax 70 72 88 125 :• 100,7 99 31 .:. Ta -:

26: i> 5.0 6,0 8.o 14.4 u.8 5,7 5.0 : 1

27: Ts 62 54 40 30 63 44 :- 18

Q • total discharge (eta) Line 10 frau Figure 25 L ··bucket width (ft) Line 17 from Figure 19 q .. discharge per toot of bucket width (eta) Line 22 from Figure 21 B .. height of reservoir above crest (ft) Line 24 from Figure 22

Vi'" velocity of flow entering the bucket computed at tail water elevation (ft/sec) Line 26 from Figure 24 D1 • depth of flow entering the. bucket computed at tail water elevation (ft) F = Froude number of flow entering bucket computed, at tail water elevation R = bucket radius (ft)·

Tm1n"' minimum tail water depth limit (ft) Tmax .. maximum _tail water depth limit (ft)

Ta • tail water aweepout depth (ft)

50

maximunl flow. The velocity head of the flow entering ~he basin at tail water elevation on the spillwa7 face is the difference between tail water. elevation and reservoir elevation or 281 feet. Then, theoreti­cally, the velocit1, "Vt," entering the tail water is 130.5 feet per second; V1 • ,/ 2g(h + H • - . -

The _actual velocity- a.ad velocity head are less than theoretical at this point, however, due to frictional resist&Dce on the spiliway face. Using Figure 25, the actual velocity- is found to be 91 percent of theoretical. Pigure 25 was prepared to reduce the computation work on the preliminary design of overfall spillways and is believed to be reasonabiy acc_urate. However, only a limited amount ot prototype data was available to develop the chart so that the-data obtained from the chart should be used with· caution. Entering Figure 25 with the·- height of tall of 281 feet as the ordinate, and intersecting the curve tor 30 feet.of head on the crest, the abscissa is found to be 0.91. Therefore, the actual velocity in this example is 91 percent of 130.5 or 118.8 feet ~r second and the corresponding velocity head is 219.2 feet. The correspo~ng depth of flow D1 on the spillway- face is ...!lv or 5.3 feet.

V l Having determined D1 and V1, the Froude number, F • -,J ~, is computed to be 9.u.

Entering figure 19 with Froude number 9.11, the dimensionless ratio of the minimum usable bucket radius is found to be 0.13 from the solid line env,lope c~e. The mini:mull allowable bucket radius is then computed to be 29 feet. In round numbers a 30-toot bucket radius would. probably be used. For the 30-toot radius· the bucket radius dimensionless ratio wo'llld remain 0.13. Entering figure 21 with the bucket radius

I • T dimensionless ratio and the Froude number, ~ is found to be 13.8. The

minimum tail water depth limit is then 73 feet, measured from the bucket -invert to the tail water surface elevation. Entering Figure 22 with the -

T· dimensionless ratio ot the bucket radius anti the Froude number, ~ tor .

. l bed elevation below the apron lip is found to be 18.8. The maximum tail . water depth limit is then 100 feet.

The riverbed at Grand Coulee Dam is at elevation 900, approxi­mately. It the bucket invert is placed at riverbed elevation the tail water depth would be 109 feet which ·exceeds the upper limit of 100 feet. Therefore, the bucket should be set above the riverbed so that the tail water depth from the bucket invert will be between 73 and 100 feet.

The bucket would then perform as shown in Figures 12A or B. Performance similar to Figure 12A would 'be.preferred but the performance

51

Fl GURE 25

437

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52

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PROTOTYPE TESTS x ·Shasta Dom o· Grand Coulee Dom

HYDRAULIC JUMP STUDIES

CURVES FOR DETERMINATION OF

VELOCITY ENTERING STILLING

BASIN FOR STEEP SLOPES

0.8:1 TO 0.6:1

shown in Figure 128 would be acceptable. Performance similar to that in Figure 12A will occur if the buc~t invert is placed so that the tail water depth is close tQ the lower limit. A tail water depth of between 75 and 80 feet would probably be most satisfactory.

To determine the sweepout depth enter Figure 24 with the Froude number and the bucket radius dimensionless ratio; the sweepout depth dimensionless ratio is 11.8. The sweepout depth then is approxi­•tely' 63 feet. Thus., the minimum tail water depth limit of 73 feet provides approxiately 10 feet of margin against flow sweeping out of the bucket at the maximum discharge. Therefore., the bucket invert should be set-to provide about 75 feet of tail water depth •

.Another solution tor.the Grand Coulee example presented here would be to use a larger radius-bucket it for some reason the bucket could not be elevated. A larger usable range of tail water will also be obtained-. J'or example, instead· of using the minimum 30-foot radius bucket., try a 50-foot radius bucket. · The bucket radius dimensionless ratio then would have a value of 0.23, and from. Figure 21 the minimum tail water depth limit dimensionless·ratio is 15, and from Figure 22 the nvn:imwn tail water depth limit dimensionless ratio is 33. The lower tail water depth limit is therefore 80 feet and the upper.limit 175 feet.

If the invert of the bucket is placed at riverbed elevation 900, the tail water depth would be 109 feet which is well within the two limits. However., if the. bucket invert was placed below riverbed and the. bed was sloped upward from. the apron, the dimensionless ratio of the maximum tail water depth limit would be approxiately 19 as found in Figure 22. The upper depth limit therefore would be only 100 feet. The. tail water depth would be greater than 109, therefore., riverbed scouring would probably occur as a result of diving flow.

Before adopting either of the buckets discussed, intermediate discharges should also be investigated, taking into account the fact . that the bucket might be required to operate at maximum discharge with tail water corresponding to the discharge just before it was increased to maximum., and perhaps without the additional tail water depth created by powerplant discharge. After the bucket radius baa been determined, the bucket design may be completed from the aata in Figure 1.

The investigation ot partial discharges is shown in Table VII tor the Angostura Dam spillwa)" where the bucket actually determined from model tests is shown, using the methods and curves in this report, to be undersized for the maximum discharge, correct for three-fourths :maximum, an4 oversized for smaller discbarg~s.

53

The fact that the methods of this report show the need tor a larger bucket than was built tor Angostura indicates that a factor of.­safety is included. in the charts in .this. report. This is a .desirable feature when bydraulic-model studies are not contemplated. On the-other hand, hydraulic model studies make it possible to explore regions ot uncertainty in any particular case and help to provide the minimum bucket size c.onsistent with acceptable performance.

Other examples in Table VII include an analysis using the data tor Trenton Dam spillway. This spillway utilizes a long flat chute upstream trom the energy dissipator. Friction losses are considerably higher than would occur on the steep spillways tor which Figure 24 was drawn and other. means must be used to obtain V1. and D1 tor the bucket design. In the example in Table VII, actual velocity measurements taken from a model wer, used. It frictional resistance is neglected in the velocity computations, the minimum tail water limit would be higher, . providing a.grea.ter factor of safety.against sweepout, but the maximum tail water limit would also be higher which reduces the factor of safety against now diving.

. . Tail water requirements tor bucket versus hydraulic JUlll1?• In general, a bucket-type dissipator require• a greater depth ot tail water than a stilling ba11in utilizing the hydraulic Jump. This is illustrated in Table VIII where pertinent data from Table VII 1a summarized to compare the millimu!D tail water depth necessary tor a minimum radius bucket with the CQJII.PUt4'4 · co~jugate tail water depth tor a. hydraulic Jump. Line 6 . shows Tm1n tor the buckets worked out in the section "Practical Applica­tions." Line 7 shows the conjugate tail·water depth required tor a hydraulic Jump tor the same Froude number and D1 determined·trom the

eci~tion ~ = 1/2 (,J 1 + 812 - 1).

Table VIII

COMPARISON OF TAIL WATER DEPrHS REQUIRED FOR BUCD:r AND HYDRAULIC JUMP . . . • : . • : . . . . .. . .

. . . . . . . . . . . . . . • • • • • f. • f. • • • • • • 'Ill' • W' •

·I-~-~ ·S -ra ·ra. ;~g;~g;~g;~g;8,;8g; : a,i!5: 8,A: JA: 8,A: 'di!5: 'di!5: •:r= ·r=. •s:t .9 •i .

4C :< : :< :J.i =~~ : . . . . . ....., . '-"' . : . . . . : . . . . . .

g ~ .... ! A : ~ s:t s:1 : 2 ~ 0 a, a, ~ : .... Jot ... • ::£ ~ k • .;::i E-t : Q . •

l :Q in,tbousands:247 :180 :100 : 40 :935 :935 :133 :9()

: cts . . . • . . . • . • . • . . • • 2 :Vi tt/sec • 72 • 72 : 73 .. 70, :119 :119 : 66 :39 . . .

J~ ' ; ',' . . "a,•·:.· .. . 'a! ! ••. ·• . oj .. :: . ·:ctJ : .: : .. , .. -'4.>· .; . : ·; ~:,. ffl .. : s . . . . . .

~ M ~ - ,: M or! . :• .... : . ::s . . '3 •· .. , A .. E . ::s ..• , . . ·-·. . . .

~ :it ~ . +> ·a ~ _,+J·a·· J~.-ffl 0. . .o • . ·U·fa t) ffl. ~ . .

0 ~ -- ti). ·•' . (IJ •. . . . .~A:· iA·: -aA.: ti A .0 tll . :-- io-A . it, A : +> tll 2! . . . . ,:::: ·: ; ~ ..• .. ~ • ... -~ = m- cc a =

,:::: ..• ..... ~--. ; ,· . •<( ... '. ' .. , .•.. . 0) . ::e: .. . . . .

,;.' .. ,• -~;: '.: . • ··G· ·• M M : 'n . . ... ··- -~ .;, .. 0 E-t A· . •· . . · .. •: ~- . ,. ~ .. ... •·· . •· . .•. . . , . .. ·• . . . ..

3 :D1 tt 12.5: 9.1: 5.0: 2.1: 5.3: 5.3: 7.6: 3.6 . . . ~- . . . .. '..,. . . . :: -: . . • .. . .. ; ;~ . ·"' . . .

4 -:F . ,3.6: ·4.3:; :5.7,:,,v8. 5: ·• g.1: 9.1: 4.2: 3.7 .. . '.·., ··:;.: . .. . . . ... . . 5 :Tmax ft 70 72 88 :125 :101 :175 99 : 31 . . :

;Tmin .

6 ft 67' . 60 46 34 73 80 50 :20 . . . . . . . 7 :Tconj ft . 57 52 38 . 24 65 65 42 :17 . . . . . . 8 :Bucket radius . 47 39 26 . 12 30 . 50 35 :12.5 . . .

The values in Line 6 are for the minimum allowable bucket radius. !.f. a large?' than __ min.1.m~ bucket radiuELis used.,__ t_he required minimum t·an wate.r_dep_th-"b..e.cQm.es greayr., as shown in Line 8 for the two Grand Coulee bucket radii.

Summary of Bucket Design Procedures

The Angostura-type slotted bucket, Figure lB, is well adapted for general use as an energy dissipater at the base of an overfall spill­way. It is considered to be superior to the solid bucket in all respects. Wherever practical the higher teeth recommended in design Modification II, Figure 8, should be used. Also, wherever possible the elevation of the bucket invert should be placed above the channel bed so that the tail water depth above the bucket is close to the lower tail water limit, as in Figure 12A, for best performance.

Buckets are particularly suited to installations where an excess of tail water exists which would drown the hydraulic jump, or where deep excavation presents no problem.

The curves of Figures 19 through 24 should be used to obtain the essential dimensions for the Angostura-type slotted bucket. ·From the curves the minimum bucket radius; the required tail water depth, and the maximum permissible tail water depth can be determined, as illustrated in "Practical Applications" and summarized in Table VII. In addition, the

55,

tail water sweepout depth, which is an indication of the factor of safety of the b_ucket and it.s .vert:lcai ple.cement,. can be ·used t.o ~heck the place­ment specifications. Figure 1 should be used to obtain the bucket dimensions. afte.r the radius has .. been· establ:f.sbed. Caution should be used in de·signing buckets for large structures such as 200-foot high spillways with discharges· of 500 or more second-feet per foot of width, and low structu:i'es where tail .water may submerge the spill~y crest, without model verif'icat::lon·~ . Model testing is desirable in all cases, however. . .

The design curves presented may also be used for determining the radius and. ta11· water depth requ;l.reiaents f'or a solid bucket if' ~or·, some reason it was desirable to use .one.

. OPO 844490