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t'entrai Eorerence File

l_l^3i^S '

the Sllf stilling basin

A STRUCTURE TO DISSIPATE THE

DESTRUCTIVE ENERGY

IN HIGH-VELOCITY FLOW

FROM SPILLWAYS

Agriculture Handbook No. 156

Agricultural Research Service

In Cooperation with the

Minnesota Agricultural Experiment Station

and the Saint Anthony Falls Hydraulic Laboratory

UNITED STATES DEPARTMENT OF AGRICULTURE
PREFACE

This publication is a condensed report of the research that led to the

development of the St. Anthony Falls (SAF) stilling basin. It is prepared

especially for the use of those who have occasion to design this efficient and

economical outlet structure for dissipating the destructive energy in the

high-velocity flow at the exit end of chutes, dams, closed conduit spillways,

and similar structures.

The experimental work begun in January 1941 was completed in December 1943. The results of the tests were first reported in a processed

publication in December 1943 that was revised in May 1949 (SCS-TP-79).

A detailed report on the research has been published in the Transactions

of the American Society of Civil Engineers, volume 113, 1948, '^Development and Hydraulic Design, Saint Anthony Falls Stilling Basin.''

This cooperative V study in the solution of problems concerning the

hydraulics of soil and water conservation structures was made by the staff

of the Soil and Water Conservation Research Division, Agricultural Research Service, U. S. Department of Agriculture, in cooperation with the

Saint Anthony Falls Hydraulic Laboratory and the University of Minnesota Agricultural Experiment Station.

CONTENTS

Page

Preface 2

The Problem 3

Previous Work 3

The Test Program 3

Laboratory Facilities and Test Methods. _ 4

Hydraulic Jump 4

Test Results 5

Length of Basin_ 5

Chute Blocks 6

Floor Blocks 6

Force on Floor Blocks 6

EndSiU 7

Tailwater Depth 7

Page

Test Results—Continued

Sidewall Height 10

Wingwalls 10

Shape of Basin 10

Cutoff Wall 10

Effect of Entrained Air 11

Conclusions 11

Application of Results 11

Design Chart 11

Solution of a Typical Problem 12

Field Experience 12

Summary 14

Literature Cited 14

Washington, D. C. Issued April 1959

For sale by the Superintendent of Documents, U. S. Government Printing Office

Washington 25, D. C. - Price 10 cents
the SflF stilling basin

a structure to dissipate

the destructive energy in high-velocity

flow from spillways

By FRED W. BLAISDELL, hydraulic engineer, Soil and Water Conservation Research Division, Agricultural Research Service

THE PROBLEM

The research summarized in this pubhcation is

a direct result of the need for a stiUing basin to

dissipate the energy in the high-velocity discharge

from culverts, chutes, and other types of spillway.

^ Engineering literature abounds with descriptions of stilling basins located at dams throughout

the world. Each structure, however, had been

individually designed for a specific location. Additional studies were required to adapt a design

to other locations.

When the SAF stilling basin study was initiated

in 1941, at the request of the United States Soil

Conservation Service, little had been accomplished

toward the development of a universal design.

In general, the structures built by the Soil Conservation Service are of such size that few of

them can economically justify the individual

model studies that proved so profitable in the

development of stilling basins for large dams.

It was essential, therefore, that an eflScient and

economical stilling basin be developed and that

design rules be formulated so future stilling

basins could be designed without recourse to

further model studies.

PREVIOUS WORK

A study of the literature on stilling basins

carried out in 1941 revealed only two investigations leading to the development of generalized

stilling basin designs. To the writer's knowledge,

the only additional generalized studies that have

been published to July 1958 are those by Bradley

and Peterka {5-11)} In the simple stilling basin

studied by Stanley {18), the energy in the highvelocity flow is absorbed in a pool formed by a

sill or low dam. The Schoklitsch energy dissipator {17) is similar to the simple stilling basin

in that an end. sill is used to form a pool but the

^ Italic numbers in parentheses refer to Literature

Cited, p. 14.

jet enters the pool above its bottom. This type

is, therefore, somewhat more efficient than the

simple stilling basin. Although both the Stanley

and the Schoklitsch stilling basins are undoubtedly

satisfactory in dissipating energy, a smaller and

more economical stilling basin was needed,

THE TEST PROGRAM

Exploratory tests were made on the hydraulic

jump, the Schoklitsch, and other published designs of stilling basins. Analytical studies were

also made of several other stilling basin designs.

As a result of these preliminary studies, some

stilling basins were eliminated from further consideration because of their inferior performance

in dissipating energy while others were eliminated

because their size and cost for equivalent performance were greater than for the more efficient

stilling basin.

On the basis of the exploratory tests, the

rectangular stilling basin, developed by the United

States Bureau of Reclamation and described by

Warnock {19), was selected for further study.

This stilling basin had chute and floor blocks to

dissipate the energy and an end sill to deflect

the stream away from the bed. The length of

the stilling basin was 75 percent and the depth

Sb percent of the hydraulic jump length and

depth, respectively, but the indications were

that the size could be reduced still further.

Using this basic form of stilling basin, studies

were directed toward determining the minimum

dimensions for efficient energy dissipation and

the laws governing the design of the various

elements making up the basin.

The test program was divided into three parts:

(1) The culvert-outlet series in which the basin

proportions were determined for a narrow range

of the Froude number; (2) the flume-outlet series

of check tests, which covered a large range of

the Froude number; and (3) the turbine-room

series of large-scale check tests. The results of

these tests are discussed in this publication.
LABORATORY FACILITIES AND TEST

METHODS

All experiments on the SAF stilling basin were

made at the St. Anthony Falls Hydraulic Laboratory of the University of Minnesota, Minneapolis.

The laboratory is located on Hennepin Island at

St. Anthony Falls in the Mississippi Kiver. Up

to 300 c. f. s. can be diverted from the river above

the falls and returned to the river below the falls

after dropping about 50 feet through the laboratory. Water for the various experiments is obtained through pipes connected to a supply canal

running the full length of the laboratory.

The culvert and flume series of tests were conducted in a channel 24 inches deep, 18 inches

wide, and 8 feet long; the turbine-room series in

a channel 6 feet wide and 24 feet long. Since it

was impossible to observe from above the operation of the stilling basin under the jet and 'Vhite

water/' all tests were conducted on half-models;

that is, the models were split along their centerline

and one-half of the model was pressed against a

glass plate through which the action of the stilling

basin could be observed. Check tests showed that

identical results can be obtained from either full

or half models. A glass observation panel 8 feet

long was located on one side of the 18-inch channel

and a panel 2 feet high and 12 feet long on the

side of the 6-foot channel; the model centerlines

were located along the face of the panels.

Water for the culvert and flume series was

obtained through a 4-inch pipe and the discharge

controlled by a 3-inch gate valve. The rate of

flow was measured by a calibrated 1-foot type

IIS flume. Water for the turbine-room series

was obtained through an 18-inch pipeline tnat

was reduced to 12 inches before reaching the model.

The rate of flow was controlled by a 12-inch gate

valve and measured by the calibrated pressure

difference across the 18-inch by 12-inch reduction,

by a calibrated 1.5-foot type H flume, or by a

Pitot tube located at the stilling basin entrance.

For the culvert series of tests, the approach to

the models was a 3-inch square pipe. The depth

of flow at the entrance to the stilling basin was

determined by the discharge and the width of the

open channel transition used between the pipe

and the stilling basin. The depth at the stilling

basin entrance for the flume and turbine-room

series was set by means of adjustable gates located

just upstream from the models. For these series

it was possible to regulate both the depth and

velocity at the stilling basin entrance. The

approach channel width was 3 inches for the

flume series and 1 foot for the turbine-room series.

All models were made of wood—waterproof

plywood for the smaller models and pine for the

larger models.

The tailwater depth was controlled by stop logs

located in both channels at the downstream end

of the test section. Depths and sand-contour

elevations were measured with point gages located

on traveling carriages. Centerline profiles of the

water surface and eroded sand bed were sketched

on data sheets with the aid of a grid of uniformly

spaced strings placed against the glass observation

panels.

The stream bed downstream from the stilling

basin was formed in concrete sand. The effectiveness of each arrangem^ent of stilling basin in

removing the destructive energy in the water was

measured by the erosion of this sand bed. The

loose sand was scoured to its approximate ultimate depth in 30 minutes, and this length of run

was used for the culvert and flume series of

tests. Two-hour runs were found to be more

satisfactory for the large-scale turbine-room series.

Before beginning each experiment, the stream

bed was filled in with sand and a small stream of

water was used to fill the channel without eroding

the stream bed. At the beginning of the run

the valve was opened quickly to give the desired

discharge and at the end of the run the valve was

closed quickly. Data on the discharge, tailwater

level, and water-surface profile were obtained

during the run. Photographs were made during

many runs. After the run the sand bed was

drained and the erosion was recorded.

The procedure used in determining the best

proportions of the various elements making up the

stilling basin was to run a group of tests and make

changes on only one element between each test,

so tnat any differences observed in tue performance of tlie stilling basin could be attributed to

tJie change in the pertinent element. This single

element was varied in shape, size, or position

until the best proportions and location had been

ascertained. Other elements were then studied in

like manner until the best proportions of all parts

of the stilling basin had been tentatively determined. Because of the interdependency of the

various elements, it was necessary to repeat

certain steps to ascertain the effect of subsequent

changes on elements studied previously.

After ascertaining the most satisfactory stilling

basin proportions for a single rate of flow, the

dimensions were varied for other rates of flow to

determine the laws governing the proportions of

the stilling basin and its elements. All these tests

were part of the culvert-outlet series. Both the

flume-outlet and turbine-room series were check

tests. The only important revisions in the design

resulting from the tests with other rates of flow

were in the end sill height and the wingwall

shape and position. All changes indicated as a

result of the check tests were made and verified.

HYDRAULIC JUMP

All the dimensions of the SAF stilling basin

are related, either directly or indirectly, to the

hydraulic jump. The theoretical equation for the

hydraulic jump is
dl

4

where ¿2 is the depth after the jump, di the depth

preceding the jump, Vi the velocity preceding the

jump, and g the acceleration due to gravity (32.2

feet per second per second). The derivation of

this equation can be found in most books on

hydraulics; for example, the '^Handbook of

Hydrauhcs'' (15, pp. 8-23 to 28). Numerous

experiments by others have proved the validity

of this equation, which can be simplified to

dr d2=~ (-l+VSf+l) (2)^

where the Froude number F is given by the equation

F=IJ (1)

This dimensionless number (F), a constant

for similar flow conditions in the model and the

prototype, is also used in the determination of

the size of the stilling basin.

The length of the hydraulic jump is assumed to

be 5¿2j after Bakhmeteff and Matzke (1).^

TEST RESULTS

The SAF stilling basin design was developed

and verified as a result of 271 tests. The number

of tests in each series and the range of the variables are given in table 1, where Qis the discharge,

R=Vidilv is the Reynolds number, and v is

the kinematic viscosity. The tests made on

each element comprising the SAF stilling basin

will be discussed separately.

2 Numbers in parentheses opposite the equations refer

to the equations listed on the design chart, pp. 8 and 9.

^ Bradley and Peterka (5, 6) show that the hydraulic

jump length varies with the Froude number, reaching a

maximum length, of about Q.ld2. However, this difference,

in the length has no effect on the SAF stilling basin

because the hydraulic jump length does not enter directly

into the SAF design, and the tests on the SAF stilling

basin covered the practical range of Froude numbers.

Length of Basin

The full length of the rectangular stilling basin

described by Warnock (19) was not utilized in

dissipating the energy in the water. (The length

of this basin, LB, was 75 percent of the hydraulic

jump length, or, LB=0.75 X 5^2=3.75^2-) The

stilling basin was shortened in steps until a

minimum length equal to 0.70¿2 was reached.

Surprisingly, the depth of the scour hole was not

increased by this shortening until a length of

stilling basin less than I.25S2 was tested. The

channel erosion was markedly but not dangerously

increased when i^—1.00¿2. When the basin

length was 0.70^2? the scour at the end of the

stilling basin as well as in the downstream channel

was considered excessive and the energy dissipation in the stilling basin was poor. A stilling

basin length of 1.25¿2 was used in subsequent

tests in which the positions and sizes of the other

elements making up the basin were investigated.

The Froude number was about 30 for tests up

to this point.

Further study of tlie stilling basin length was

initiated after tentatively determining the best

sizes arid locations of the chute and floor blocks

and trie end sill. Triese tests covered a range of

trie Froude number from 3 to 150 and were part

of both trie culvert and flume-outlet series. As a

result of these tests, it was discovered that the

stilling basin was too short for Froude numbers

less than 30 and longer than necessary for larger

Froude numbers. The stilling basin length,

therefore, was varied for each of 12 values of F

until the best length was determined. The

performance of each length of basin was ^^rated"

and plotted, with ÍB/¿2 and F as coordinates, and

a curve drawn through the plotted points. Both

the experience obtained during the experiments

and the plotted data were used in locating this

curve. The equation of this curve,

¿B_4.5

d2 "F^-^s (4)

is suggested as giving a minimum safe length of

stilling basin; it is conservative, but not to the

point where the material in the outlet is wasted.

TABLE 1.—Tests of SAF stilling basin and range of test variables

Series Tests Q Fi d. C?2 F R X 10-3

Culvert outlet

Number

100

108

66

C.f.s.

0. 09 to 0. 4

. 04 to .8

. 40 to 21.

F. p. s.

4. 3 to 12

2. 8 to 22

9. 7 to 44

Ft.

0. 04 to 0. 17

. 05 to . 15

. 03 to 1. 27

Ft.

a 17 to 0. 8

. 13 to 1. 8

. 49 to 5. 5

3 to 57

5 to 200

7 to 288

12. 7 to 45

Flume outlet 14. 2 to 237

Turbine room _ 40. 6 to 2, 100

Total tests and

total range in

variabhîs.

274 . 04 to 21. 2. 8 to 44 . 03 to 1. 27 . 13 to 5. 5 3 to 288 12, 7 to 2, 100
Equation 4 was developed for a range of the

Froude number from 3 to 150, but it was later

used to design experimental stilling basins having

values of F as high as 300. The results of all

subsequent tests show that stilling basin lengths

determined from equation 4 are satisfactory.

Chute Blocks

The chute blocks, located at the entrance to the

stilling basin, serve to increase the effective depth of

the entering stream, break the stream up into a number of small jets, and help create the turbulence

required for effective energy dissipation.

The original height of the chute blocks was ¿i,

and the width and spacing, 0.75ái. A test on a

solid chute block, such as is used in the Schoklitsch

energy dissipator, showed that less energy was

dissipated in the stilling basin and that flow conditions in the channel downstream from tiie stilling

basin were not so good. A second test was made

in which the tops of the chute blocks were sloped

to direct the jets at the floor blocks. The result

of this change was to increase the depth of erosion

near the end of the stilling basin.

The chute blocks used for all subsequent tests

had a height of di and a width and spacing of

0.75¿i. These proportions proved to be entirely

satisfactory. It makes no difference in the performance of the stilling basin whether a chute

block or a space is next to the sidewall as long as the

blocks are symmetrical about the centerline of the

outlet.

Floor Blocks

Energy is removed from the water by impact

against the floor blocks and considerable turbulence is created by them.

The first tests on the floor blocks were made to

determine their best longitudinal position. These

tests show that it is equally as bad to have the

distance between the chute and floor blocks too

short as it is to have tJae distance between the floor

blocks and end sill too short. If the distance

between the chute and floor blocks is too short, the

blocks act like a solid chute block. If the distance

between the floor blocks and end sill is too short,

the blocks and sill act as a unit in deflecting the

jet upward.

Nearly identical results were obtained when the

floor blocks were located X^/S and is/2 from the

upstream end of the stilling basin. The results

for the Í5/3 spacing were slightly better, but the

difference probably is insignificant. The floor

blocks were located is/3 from the upstream end

of the basin for all subsequent tests. No reason

was discovered for changing their longitudinal

location as a result of these tests.

Floor blocks were tried with heights both

greater and less than di. This height of floor

block was either as good as or better than greater

and lesser heights. Accordingly, a floor block

height equal to di was used for subsequent tests.

The width and spacing of the floor blocks should

be the same as for the chute blocks. However,

for those stilling basins in which the sidewalls

diverge in plan, the width and spacing of the floor

blocks should be increased over the chute block

width and spacing to compensate for the greater

stilling basin width at the floor block location.

No floor block should be located closer to the

stilling basin sidewall than 3(¿i/8. Floor blocks

located closer cause a high boil that might overtop

the sidewall.

Insufficient water can pass between the floor

blocks if they occupy too much of the stilling

basin width; they then act more like a sill than

like individual blocks. The test results show that

satisfactory conditions exist when the floor blocks

occupy between 40 and 55 percent of the stilling

basin width. The aggregate width of all floor

blocks, therefore, should be held within these

limits, even if it is necessary to reduce the width

of the floor blocks to do so.

The floor blocks always should be placed downstream from the openings in the chute blocks to

break up the jets issuing from between the chute

blocks and passing along the stilling basin floor.

A single test made with the floor blocks in line

with the chute blocks was sufficient to show the

inferiority of this arrangement.

The floor blocks may be piers square in plan

with vertical faces, or their downstream faces may

slope as shown on the design chart.

Force on Floor Blocks

A knowledge of the forces exerted on the floor

blocks is necessary for their structural design.

No tests were made to determine these forces.

It is possible, however, to compute the maximum

probable forces, and the results of experiments by

others are available to modify these computed

values.

The impact force on the floor blocks required

to turn the flow 90"^ is given by the equation

F=AVi'w¡gj where F is the total force, A is the

area of the face of the blocks, and w is the unit

weight of water (62.5 pounds per cubic foot). Itis

convenient to write the impact force in terms of

(¿1 and F, since both of these values are required

in the design of the stilling basin. The force

per unit width of the floor block,/, is

f=wdi^F

This equation gives the maximum impact force

on the floor blocks per unit width of block. The

equation assumes that all the water approaching

the block is turned at right angles to its original

direction. Much of the water changes direction

only slightly, so the actual force must be considerably less than the computed maximum.

Other factors that influence the force on the floor

blocks are the shape, width, and spacing of the

blocks, the effect of the chute blocks, and the fact

that the mean velocity at the floor blocks is re-
duced by the chute blocks and the roller. Such

information as is available regarding the effect

of these factors will be presented.

The forces on stepped blocks and streamlined

blocks measured experimentally at the Massachusetts Institute of Technology have been reported by Harleman {llf). The stepped blocks

approximate the shape of the vertical-faced blocks

used in the SAF stilling basin. Harleman states:

'The maximum force exerted by the baffle piers

is of the order of 20 percent of the pressure force

due to the downstream depth.'' Since the downstream force is applied across the full width of

the stilling basin and the stepped blocks occupied

50 percent of the basin width, the maximum

measured force per unit width of blocks is 40

percent of the pressure force per unit width due to

the downstream depth. Using this latter figure,

it is found that the maximum force per unit width

of block varies from 27 percent of the theoretical

value for F=3 to 38 percent of the theoretical

force for F-=300.

Unpublished results of tests made at the St.

Anthony Falls Hydraulic Laboratory in connection with a model study of the Chippewa River

Reservoir Dam of the Northern States Power

Co. substantiate the MIT values. Piezometric

pressures were measured on the face of a baffle

pier located below a Tainter gate, and the pressures were integrated to determine the total force

on the baffle. Forces determined for three different rates of flow amounted to 43 percent, 24

percent, and 27 percent of the impact forces

computed as outlined above.

In view of these data and until better information is available, it is suggested that the force

on the floor blocks exerted by the approaching

stream be taken as 40 percent of the computed

impact force, ov

f=OA wdi^F=2b d^F

End Sill

The end sill, located at the downstream end of

the stilling basin, deflects the bottom currents

upward and away from the stream bed. In

addition, a ground roller is created under the

deflected stream, which brings bed material from

downstream and deposits it at the end of the

stilling basin.

The height of the end sill, c, for the culvertoutlet series was made ¿2/7. This end-sill height

proved to be satisfactory for the narrow range of

the Froude number for which it was derived, but

the equation was inadequate for a larger range

of the Froude number.

A thorough study of the end-sill height for

values of F from 5 to 200 was made as part of the

flume-outlet series of tests. The best height of

end sill for each set of otherwise constant conditions was selected, and the selected values were

found to be independent of the Froude number.

However, when ¿¡d^ was plotted against the Reynolds number ß, a well-defined curve wasobtained,

although there is no reason to believe that such a

relationship should exist. A study of tñe equation

for this curve showed that the height of the end

sill was unbelievably low for values of R within

the practical range. This naturally cast suspicion

on the form of the end-sill height equation and led

to the turbine-room tests, which were made at

higher Reynolds numbers.

The turbine-room tests confirmed the opinion

that the end-sill height was too low for the higher

values of R and indicated that c\d<¿ was independent of both F and R. A tentative equation (c=

0.07(¿2) was derived early in the test program.

This equation was checked by other tests until it

became apparent that this end-sill height would be

satisfactory. Subsequent tests were made to

verify this equation.

A review of the data obtained during the flumeoutlet series of tests shows that satisfactory erosion

conditions were obtained when c=0.07¿2. The

higher end sills given by the equation containing

R produced slightly better erosion patterns for

the lower values of ß, but the difference is so small

as not to warrant the use of separate equations.

The recommended equation for the height of the

end sill is

c=0.07¿2 (6)

Taîlwatcr Depth

Use of the blocks and end sill in the stilling basin

permits the depth of the tailwater above the stilling

basin floor level to be decreased over that for the

theoretical tailwater depth of the hydraulic jump.

Warnock {19) recommended a 15-percent reduction, so that the actual tailwater depth, ¿'2, would

be 0.85(¿2. Tests were made to check this figure.

If the tailwater depth is too low, the roller on

the hydraulic jump will be washed out of the stilling basin and the floor blocks and end sill will

simply deflect the stream and break it up. The

broken-up stream will land on the water surface

some distance downstream from the outlet and

erode the bed only slightly, with the depth of the

scour hole near the end of the stilling basin remaining unchanged. The structure will not be endangered tJaereby, but the energy dissipation in the

stilling basin is poor and the spray may prove

objectionable.

In determining the minimum permissible value

of (¿'27 the tailwater depth was decreased until the

roller was washed out of the stilling basin. The

relative tailwater depth at which this occurred

was plotted against F. Originally the relative

tailwater depth was assumed to be dWd<i, When a

paper {ß) describing development and hydraulic

design of the SAF stilling basin was published,

however, one of the discussers showed that plotting

the ratio d^d^ permitted the derivation of a relationship that is continuous over the range of

Froude numbers covered by the tests. As a

result of this discovery, dWdx was plotted against
A. SOLUTION OF EQUATIONS (l),(3) AND (4)

Procedure. Equation (I) df to Vf to F

Equation (3) df to F to d2

Equation (4) F to d2to Lg

4\ï

sil

B. SOLUTION OF EQUATION (2)

Procedure iFtodf to dg

dg in feet I

\

c in feet .07 OJ

iW^

2 3 4 5 is 8 to 20 30

Vri'iT|lM^avi' .'/V|1ihi|iiliii,'|.Vi|i'i'i''i'i'l'i'i'.'i''i'i''

0.2 0.3 0.4 06 0.8 I 2

C. SOLUTION OF EQUATIONS (5) AND (6)

Procedure : Equation (5) d2 to z

Equation (6)d2 to c

D. EXAMPLE

GiVEN: d, = 0.6 ft and v, = 40 ft. per sec.

SOLUTIONS OE EQUATIONS

(using curves and nomograptis)

(I) F = 63 (2) dg =7.4 ff (3) d¡= 6.1 ft.

(4) LB=6.3ft (5)z=2.48 ft. (6) 0.52 ft.

E.DESIGN EQUATIONS

(I) F.- -^gd,

(3)d'^=: l.4d,F'

(5) z= dg/3

(2) dg -

(4) Lc

d,

2

4.5dg

(6) c -= 0.07 dg

("H-^eFi-1)

FIGURE 1 ^ DESIGN CHART for SAF STILLING BASIN

Agricultural Research Service, U. S« Department of Agriculture, in cooperation with the Minnesota

Agricultural Exipefiment Station atttl the St* Anthony Falls Hydraulic Laboratory, University of Minnesota.

8
RECTANGULAR STILLING BASIN

HALF - PLAN

O» to 90*

45*Prtftrrtd

CENTERLINE SECTION

TRAPEZOIDAL STILLING BASIN

HALF- PLAN

F. PROPORTIONS OF THE SAF STILLING BASIN

6. DEFINITIONS OF SYMBOLS

above stilling basin floor, in feet

D' - side wall divergence, D' longitudinal to I transverse

F - the Froude number

g - acceleration due to gravity, in feet per second per second

Lß - length of stilling basin, in feet

d¿ - downstream depth computed by momentum equation ^/ " velocity at entrance to stilling basin, in feet per second

for the hydraulic Jump, in feet ' " ^^'9^* of stilling basin side walls above maximum

dg - water surface elevation in downstream channel tailwater level, in feet

Bi " width of stilling basin at upstream end, in feet

Bg " width of stilling basin at floor blocks, in feet

Bj - width of stilling basin at downstream end, in feet

c - height of end sill, in feet

df - depth of flow at entrance to stilling basin, in feet
F and an enveloping curve drawn above the relative depths at which the roller is washed out of

the stilling basin. The equation of this curve is

(3)

Sidewall Hcighf

The flow in the stilling basin is very turbulent,

and, as a result, the water surface is so rough that

some freeboard above tailwater level is necessary

if overtopping of the sidewalls is to be prevented.

In addition to the surface roughness, a standing

wave, or boil, is caused by the floor blocks and

end sill, which in itself requires freeboard above

the tailwater level. For Froude numbers less

than about 20, the crest of the boil is in the

stilling basin, whereas, for higher Froude numbers,

the boil crest occurs downstream from the end of

the basin and its full height need not be considered

in designing the sidewall height.

Average profiles of the water surface in the

stilling basin were obtained for all series, but the

maximum height of splash was obtained for only

the turbine-room series. It is from these latter

tests that the height of the sidewall is determined.

The maximum height of the splash Zraax in the

stilling basin was divided by ¿2. There is considerable scatter to the data, but Zmaxld2 is apparently independent of F. The range of 2m,axld2 is

from —0.02 to 0.31. A study of the data shows

that if the height of the stilling basin sidewall, 0,

above the maximum tailwater level is given by

the equation

z=d2l^, (5)

the freeboard will be sufficient to keep the splash

in the stilling basin. Because of the scatter in

the data, the freeboard provided by this equation

will, in some cases, be greater than is necessary to

protect fully the structure, but the safety factor

is not excessive for the average case.

Wingwalls

Wingwalls at the end of the stilling basin are

used as retaining walls to hold back the earth

fill. The ordinarily used wingwall is rectangular

in downstream elevation. Since the scour around

the end of this wall is severe, other wingwall shapes

were investigated.

The principal cause of the scour around the end

of the wingwall is an eddy along each side of the

downstream channel that is driven by the stream

leaving the stilling basin. It is imperative that

the concentration of the flow from this eddy be

kept off the stream bed. Two methods can be

used to prevent the eddy from attacking the

stream bed: (1) A submerged extension of the

wingwall, having a height equal to half the tailwater depth and a length equal to 0.6 of the sidewall height (the minimum length of rectangular

wingwall used in the experiments was 0.4 of the

sidewall height); or (2) a wingwall of triangular

shape in downstream elevation, the top having a

slope of 1:1. The triangular shape of wall is

recommended, because it is equally as satisfactory

in preventing scour as is the extended wingwall

and, in addition, requires less material.

Wingwalls have been customarily located perpendicular to the centerline of the outlet structure.

Tests have shown, however, that the wingwalls

may be extended parallel to the basin centerline

if field conditions make it necessary to do so,

although the boil height is considerably higher.

Nevertheless, the best overall conditions are

obtained if the triangular wingwalls are located

at an angle of about 45° to the outlet centerline.

Subsequent tests of other types of stilling basins

have confirmed the superior performance of the

wingwall having a 1:1 top slope located at an

angle of 45° to the outlet centerline (4, 12, IS).

Shope of Basin

The size of the stilling basin varies with the

initial flow depth if Vi does not change; any reduction in dx will reduce (¿2, the length of the basin,

the height of the sidewalls, and the depth of

excavation. In addition, a larger percentage of

the energy in the water entering the stilling basin

will be dissipated. A saving in overall cost of the

outlet will ordinarily be possible if a flaringsidewall transition is placed between the culvert

or chute and the stilling basin to accomplish this

reduction in di (3). In those cases where a

transition is used, the diverging transition sidewalls should be extended to form the stilling basin

walls. The resulting stilling basin is trapezoidal

in plan, as is shown on the design chart, page 8.

A few tests were made on a trapezoidal-shaped

stilling basin in the culvert-outlet series. The

stilling basin was designed for flow conditions at

its entrance. The width and spacing of the floor

blocks were multiplied by the ratio B2/B1 to compensate for the increase in the width of the stilling

basin at their location. All blocks had their axes

parallel to the centerline of the basin. Flow

conditions in the downstream channel were somewhat improved through the use of the trapezoidal

stilling basin. This is because the velocity of the

flow was lower at the exit from the basin, and the

widening of the stream to fill the downstream

channel reduced the size of the eddies along the

channel sides near the stilling basin.

Cutoff Wall

A cutoff wall is used at the end of the stilling

basin to prevent scour from undermining the

basin. Obviously, the depth of the cutoff wall

must be greater than the maximum depth of erosion at the end of the stilling basin.

Serious erosion near the end of the stilling basin

is prevented by the end sill, which deflects upward

the stream leaving the basin. A ground roller

under the deflected stream brings material upstream and further aids in preventing erosion.

10
In the laboratory, the scour sometimes reached an

elevation slightly below the floor of the stilling

basin, but the scour never reached a depth at the

end of the basin greater than the thickness of a

floor slab that might be used. Therefore, a cutoff wall of only nominal depth need be used at the

end of the stilling basin.

Effect of Entrained Air

Air is ordinarily entrained by the water flowing

in chutes laid on a steep slope. This results in a

greatly increased depth of flow of the mixture.

However, no air was naturally entrained by the

water during the model tests because of the low

velocities or the short length of channel. Because

entrained air may afi^ect the performance of the

stilling basin, a few tests were made in which from

10 to 117 percent of air was mixed with the water.

The stilling basins were designed as if the water

were free of air, and duplicate tests were run both

with and without air entrainment. Identical

results, within the limits of experimental precision, were obtained from the duplicate tests.

Although di is greater when air entrainment

occurs, ¿2 remains unchanged, since the air separates from the water, owing to the lower velocities

in the downstream channel. No increase in sidewall height is required as a result of air entrainment.

The results of these tests show that the effect of

air entrainment can be neglected in the design

of the SAF stilling basin. The resulting stnicture

will safely handle any flows in which air is entrained.

CONCLUSIONS

The following conclusions are reached as a

result of the tests made to develop and verify the

SAF stilling basin design :

1. The length of the stilling basin for Froude

numbers between 3 and 300 is

LB=4:M2IF' (4)

2. The height of the chute blocks and the floor

blocks is ¿i; their width and spacing are

approximately 3di/4; either a chute block

or a space may be located next to the sidewall if the blocks and spaces are symmetrical about the outlet centerline.

3. The floor block criteria are as follows;

a. The distance from the upstream end

of the stilling basin to the floor blocks

is LB/S,

b. No floor block should be placed closer

to the sidewall than 3i/i/8.

c. The floor blocks should be placed

downstream from the openings between the chute blocks.

d. The floor blocks should occupy between 40 percent and 55 percent of

the stilling basin width.

e. The widths and spacings of the floor

blocks for diverging stilling basins

should be increased in proportion to

the increase in stilling basin width

at the floor block location.

f. The floor blocks may be piers square

in plan with vertical faces, or their

downstream faces may slope as shown

on the design chart.

g. The force per foot width exerted on

the floor blocks by the approaching

stream may be taken as

f=25di'F

4. The height of end sill is

c=0.07d2 (6)

5. The depth of the tailwater above the stilling

basin floor is

d'2==lAF'-'% (3)

6. The height of the sidewall above the maximum tailwater depth to be expected during

the life of the structure is

z=d2l^ (5)

7. Wingwalls should be equal in height and

length to the stilling basin sidewalls. The

top of the wingwall should have a 1:1 slope.

Wingwalls flaring at 45° with the outlet

centerline are preferred to wingwalls that

are perpendicular or parallel to the centerline.

8. The stilling basin sidewalls may be parallel

(rectangular stilling basin) or diverge as an

extension of the transition sidewalls (trapezoidal stilling basin).

9. A cutoff wall of nominal depth should be

used at the end of the stilling basin.

10. The effect of entrained air should be neglected in the design of the stilling basin.

During the tests it was noticed that the performance of the SAF stilling basin was excellent

at discharges less than the design discharge. At

the design flow the SAF stilling basin provides an

economical method of dissipating energy and

preventing dangerous stream bed erosion.

APPLICATION OF RESULTS

Design Chart

The results of all the tests on the SAF stilling

basin are summarized on the design chart for the

SAF stilling basin (fig. 1).

The proportions of a SAF stilling basin can be

determined from the chart without the aid of

any instrument or any other design chart or table.

The use of the design charts is explained thereon,

11
a typical problem is solved, and the principal

dimensions determined.

The stilling basin dimensions obtained from the

design charts will result in a good design. Slight

variations in the dimensions, however, will have

little or no effect on the performance of the basin.

To simplify the construction, all odd dimensions

should be changed to even dimensions.

Solution of a Typical Problem

A rectangular SAF stilling basin is to be constructed at the end of a 3-foot wide chute. The

depth and velocity at the end of the chute are

0.6 foot and 40 f. p. s., respectively, the design

tailwater elevation is 377.0, and the maximum

tailwater elevation in the downstream channel

anticipated during the lif-e of the structure is

378.5 for the design discharge of 72 c. f. s.

Reading the principal dimensions from the

design charts it is found that: F=82.8, ¿2=7.43

feet, (Z'2=6.13 feet, iß=6.28 feet, 0=2.48 feet,

and c=0.520 foot. In order to simplify the construction, LB=Q feet 3 inches, and c=ñ or 7

inches can be used without affecting the operation

of the structure. The elevation of the top of the

sidewalk, which is determined from the maximum

tailwater elevation, is 378.5+2.48=380.98; use

381.00. The force on the floor blocks is 25x0.62x

82.8=745 pounds per foot of width.

The elevation of the basin floor is 377.0—6.13 =

370.87. The tailwater level and required taflwater depth also should be checked at discharges

less than the design value to insure proper stilling

action at all flows. Finally, consideration of the

possibility that the channel bed elevation—and,

as a result, the tailwater level—^may become lower

in time, suggests that the stilling basin floor be

set below the calculated elevation. The amount

will depend upon local conditions and the judgment of the designer. The wingwall will have a

length of about 9 feet, depending on the sidewall

height, and its top a slope of 1 : 1. A cutoff wall

under the stilling basin having a depth of 2 feet

or more should be used.

Several arrangements of the 6- or 7-inch high

chute and floor blocks are possible, the floor

Till- 1 1 6 feet 3 inches ^ « ... .

blocks bemg placed =2 leet 1 mch,

say 2 feet, downstream from the upper end of

the basin.

The chute and floor blocks and the spaces

between them can be made 0.6x%=0.45 foot=

5% inches, say 6 inches. This gives 36/6=6

spaces across the stilling basin. Now, locate chute

blocks 3 inches from either side of the chute and

one straddling the centerline. Two floor blocks

can now be located in the basin downstream from

spaces between the chute blocks. No floor blocks

should be located next to the basin walls. The

proportion of the basin width occupied by the

floor blocks is 2x6/36=0.33. This proportion for

floor blocks is lower than is recommended. This

difficulty can be overcome by making the block

width and spacing 8 inches. The proportion then

becomes 2x8/36=0.44. The total force on each

block is 745x8/12 =500 pounds.

Another arrangement of the blocks is to make

them 6 inches wide as before, but to place half a

chute block at each side of the chute and the

two other equally spaced blocks between them.

Three equally spaced floor blocks can then be

used in the basin, one straddling the centerline

and the others placed 6 inches on either side of

the center block. The block nearest to the sidewall

is therefore 3 inches from the sidewall. This is

greater than the allowable minimum of 0.6x%=

0.225 foot=2% inches. The proportion of the

basin width occupied by the floor blocks is 3x%6 =

0.50, a satisfactory figure. The total force on

each floor block is 745x%2===372 pounds.

Arrangement of the blocks is up to the designer.

Either arrangement given above would be satisfactory.

Field Experience

The first SAF stilling basin was built in western

Iowa in 1944. Since that time a considerable

number of SAF stilling basins have been built.

The exact number is unknown to the writer;

publications describing the design of the SAF

stilling basin are readily available for use by

anyone without restriction, and there is no way

to determine how many stilling basins have been

built according to the SAF design.

The writer has seen a number of SAF stilling

basins and has had reports on the performance

of other stilling basins. All reports received by

the writer and all SAF stilling basins observed by

him have shown satisfactory performance. The

following field structures are known to have

handled flows that approach the capacity for which

they were designed, so their performance will be

described.

The most thorough and complete test of the SAF

stilling basin was that performed by William O.

Ree (16) at the Stillwater (Okla.) Outdoor

Hydraulic Laboratory of the Agricultural Research Service. Mr. Ree concluded (p, 13) :

Tests of the St. Anthony Falls Stilling Basin during

a 2-year period at the Stillwater Outdoor Hydraulic

Laboratory showed that the stilling basin was very

effective and completely satisfactory. Very little

scour of the channel bed occurred. It should be

noted, however, that the bed material at the point

of discharge was a rather firm clay. A sandy material

might have shown a little different result.

Splash was not an important problem.

Figure 2 shows this stilling basin.

If someone is unduly concerned regarding

erosion in sandy material, figure 3 shows a SAF

stilling basin at the exit of a 48-inch diameter

closed conduit spillway located at an airfield in

northwestern Florida. The soil at the site of

this structure is a clayey sand. No scour of this

readily erodible bed material is evident.

12
In a monthly report, Glenn H. Baker, Soil

Conservation Service engineering specialist, cornmented on a visit to Spruce Knob Lake, in W. Va.,

made in 1953, as follows:

At this visit I had an opportunity to observe the

performance of the SAF type stilling basin in operation. During the inspection the gate was completely

removed from the opening to the 26-inch diameter

drain which caused the maximum planned discharge.

The basin performed according to expectations almost

exactly as indicated by the model test shown in

Ohio. There was a minimum of erosion in the

channel below the dam, and the other engineers were

impressed with the operation of this type of structure.

The model referred to was one developed for

demonstration purposes in which the pipe had a

diameter of 1% inches—one-seventeenth the size

of the Spruce Knob Lake pipe.

The third structure that will be mentioned is

a SAF stilling basin at the end of a chute. This

spillway is located in Crawford County, Iowa.

On June 22, 1947, the storm runoff rate exceeded

the design capacity of the spillway by 50 percent,

this figure being based on information made

available to the writer by Floyd Nimmo, construction engineer, through M. M. Gulp, Chief,

Design and Construction Branch, Engineering

Division, U. S. Soil Conservation Service. Figure

4 shows views of this structure taken before and

after the excessive storm of June 22, 1947. It is

readily apparent from these photographs that the

SAF stilling basin gave excellent protection to

the downstream channel despite the excessive

flow that passed through it.

FIGURE 2.—SAF stilling basin at Stillwater (Okla.)

Outdoor Hydraulic Laboratory: A, Drawing of basin;

B, with full-capacity flow.

FIGURE 3.—SAF stilling basin at exit of 48-inch closed conduit spillway in northwestern Florida.

13
FIGURE 4.—Box inlet chute spillway and SAF stilling

basin in Crawford County, Iowa: A, Before storm of

June 22, 1947; B, after storm of June 22, when storm

runoff rate exceeded design capacity by 50 percent.

E. I. Eowland, Arizona State Supervisor for the

Bureau of Land Management, U. S. Department

of the Interior, has furnished a number of interesting photographs of a SAF stilhng basin (figs. 5

and 6). In a letter to the writer, dated October

31, 1955, Mr. Rowland writes:

Enclosed are a few photographs of a drop structure

placed across the San Simon Wash in southeastern

Arizona. This is a replacement for an earlier design

structure which was not adequate and washed out in

1954. This structure, known as the San Simon drop

structure, has worked very successfully this year.

The peak flow water stood at 6%' depth in the impounded area above the drop structure. The spillway

lip is at elevation 88 feet (assumed) and the peak

water within the reservoir was at 94}i foot stage. It

was calculated that the maximum flow through the

structure at this elevation was approximately 2,200 cfs.

At this peak flow, the hydraulic jump in the box

outlet, as indicated by the flow line of water through

^ the lower structure was 13 feet above the floor of the

structure at this point. The heavy splash line as

indicated by the mud deposits on the side walls [fig. 6]

reached 16 feet in height above the floor. The walls

are 18 feet high at this point.

It is extremely gratifying to note that the drop

structure operated very effectively for volume flow

reduction and reduced channel cutting. You will note

in the picture [fig. 5,B], taken after all flow through

the spillway had stopped on September 26, that there

was no channel cutting, and practically no cutting

around the lower wing walls except that which was

caused by foreign drainage on the east wing, which

will be corrected.

Of most interest to us was the small sand fan which

developed immediately below the lip of the structure

and can be noted in the picture taken September 26

[fig. 5,JS].

SUMMARY

The stilling basin developed as a result of the

model studies at the St. Anthony Falls Hydraulic

Laboratory of the University of Minnesota has

become known as the "SAF stilling basin." It

has five distinct advantages:

1. The characteristics and proportions of the

stilling basin have been determined over a

wide range of conditions to be expected in the

field; the performance can be predicted

without making additional model studies.

2. The design procedure has been generalized.

3. The size of the stilling basin has been reduced

to the minimum that will assure protection

to the structure and prevent excessive erosion

in the downstream channel.

4. The SAF stilling basin is very economical to

construct.

5. Use of the SAF stilling basin under actual

field conditions has demonstrated its effectiveness and has verified the predictions

based on the laboratory tests.

A design chart, giving the proportions of the

SAF stilling basin and the design equations and

graphical solution of these equations, is presented

on the center fold, pages 8 and 9.

LITERATURE CITED

(1) BAKHMETEFP, B. A., and MATZKE, A. E.

1936. THE HYDRAULIC JUMP IN TERMS OF DYNAMIC

SIMILARITY. Amer. Soc. Civ. Engin. Trans.

101: 630-680, illus. (Paper No. 1935.)

(2) BLAISDELL, F. W.

1948. DEVELOPMENT AND HYDRAULIC DESIGN,

SAINT ANTHONY PALLS STILLING BASIN.

Amer. Soc. Civ. Engin. Trans. 113: 483-

561, illus. (Paper No. 2342.)

(3)

1949. FLOW THROUGH DIVERGING OPEN CHANNEL

TRANSITIONS AT SUPERCRITICAL VELOCITIES.

Soil Conserv. Serv. SCS-TP-76, 21 pp., iUus.

(4) and DONNELLY, C. A.

1951. HYDRAULIC DESIGN OP THE BOX INLET DROP

SPILLWAY. Minn. St. Anthony Falls Hydraul. Lab. Tech. Paper 8, Ser. B, 63 pp.,

illus. (Rep. by Soil Conserv. Serv. as SCSTP-106. 1951.)

(5) BRADLEY, J. N., and PETEBKA, A. J.

1955. RESEARCH STUDY ON STILLING BASINS,

ENERGY DISSIPATORS, AND ASSOCIATED APPURTENANCES. U. S. Bur. Reclam. Lab.

Rpt. Hyd-399, 125 pp., illus.

(6) and PETERKA, A. J.

1957. THE HYDRAULIC DESIGN OF STILLING BASINS:

HYDRAULIC JUMPS ON A HORIZONTAL APRON

(BASIN I). Amer. Soc. Civ. Engin. Proc,

Hvd. Div. Jour., 83 (HY 5): 1401-1 to

1401-24, iflus.

(7) and PETERKA, A. J.

1957. HYDRAULIC DESIGN OF STILLING BASINS:

HIGH DAMS, EARTH DAMS, AND LARGE CANAL

STRUCTURES (BASIN II). Amer. Soc. Civ.

Engin. Proc, Hyd. Div. Jour., 83 (HY 5) :

1402-1 to 1402-14, iUus.

14
/^--íífL

^^Hg'-:'

FiGUKE 5.—San Simon drop structure—Spillway crest elevation is 88 feet; dam crest elevation, 103; end sill elevation,

68; chute, 40 feet wide; and stilling basin sidewalls, 18 feet high: A, After completion of structure, July 10, 1955;

and B, after flow of 2,200 c. f. s., September 26, 1955.

(8) Bradley, J. N., and PETERKA, A. J.

1957. HYDRAULIC DESIGN OF STILLING BASINS:

SHORT STILLING BASIN FOR CANAL STRUCTURES, SMALL OUTLET WORKS, AND SMALL

SPILLWAYS (BASIN III). Amer. Soc. Civ.

Engin. Proc, Hyd. Div. Jour., 83 (HY 5) :

- 1403-1 to 1403-22, illus.

(9) and PETERKA, A. J.

1957. HYDRAULIC DESIGN OF STILLING BASINS:

STILLING BASIN AND WAVE SUPPRESSORS FOR

CANAL STRUCTURES, OUTLET WORKS, AND

DIVERSION DAMS (BASIN IV) . Amer. Soc.

Civ. Engin. Proc, Hyd. Div. Jour., 83

(HY 5): 1404-1 to 1404-20, illus.

(10) and PETERKA, A. J.

1957. HYDRAULIC DESIGN OF STILLING BASINS:

STILLING BASIN WITH SLOPING APRON (BASIN

v). Amer. Soc. Civ. Engin. Proc, Hyd.

Div. Jour., 83 (HY 5) : 1405-1 to 1405-32,

illus.

(11) and PETERKA, A. J.

1957. HYDRAULIC DESIGN OP STILLING BASINS:

SMALL BASINS FOR PIPE OR OPEN CHANNEL

OUTLETS NO TAIL WATER REQUIRED (BASIN

vi). Amer. Soc Civ. Engin. Proc, Hyd.

Div. Jour., 83 (HY 5) : 1406-1 to 1406-17,

illus.

(12) DONNELLY, C. A.

1947. DESIGN OF AN OUTLET FOR BOX INLET DROP

SPILLWAY. Soil Conserv. Serv. SCS-TP-63,

31 pp., illus.

(13) and BLAISDELL, F. W.

1954. STRAIGHT DROP SPILLWAY STILLING BASIN.

Minn. St. Anthony Falls Hydraul. Lab.

Tech. Paper 15, Ser. B, 35 pp., illus.

(14) HARLEMAN, D. R. F.

1955. EFFECT OF BAFFLE PIERS- ON STILLING BASIN

PERFORMANCE. Boston Soc. Clv. Engin.

Jour. 42 (2): 84-99, illus.

15
f«

\

i.'^.^.» '^

FIGURE 6.—Mud deposit on sidewalls of San Simon drop structure. The maximum flow line is 13 feet above the stilling

basin floor, and the maximum splash line is about 16 feet above the basin floor. Photographed August 10, 1955.

(15) KING, H. W.

1954. HANDBOOK OP HYDRAUUCS. ED. 4. 556

pp., illus. New York.

(16) RBE, W. O.

1951. RESULTS OF TESTS ON A CHUTE WITH A ST.

ANTHONY FALLS STILLING BASIN. Soil Conserv. Serv. SCS-TP-107, 13 pp., illus.

(17) ScHOKLiTSCH, A. (Translated by Samuel Schulitz.)

1937. HYDRAULIC STRUCTURES. 2 V., illus. American Society of Mechanical Engineers, New

York.

(18) STANLEY, C. M.

1934. STUDY OF STILLING-BASIN DESIGN. Amer.

Soc. Civ. Engin. Trans. 99: 490-523, illus.

(Paper No. 1867.)

(19) WARNOCK, J. E.

1940. SPILLWAYS AND ENERGY DISSIPATORS. Iowa

Univ. Studies in Engin. Bul. 20 (ProC

Hydraulics Conf.), pp. 142-159, illus.

16

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