m^^ 7574

HYDRAULIC DESIGN

of the

BOX-INLET DROP SPILLWAY

Willi âiilSiîtaâi iiiia^

Agriculture Handbook No. 301

Agricultural Eesearch,Service

U.S. DEPARTMENT OF AGRICULTURE

In Cooperation With the

Minnesota Agricultural Experiment Station

and the

St. Anthony Falls Hydraulic Laboratory

of the

University of Minnesota

NAL DIGITIZING PROJECT

MBP0000255
PREFACE

This publication is a manual for the design of box-inlet drop spillways.

Criteria, curves, and tables are presented for (1) determining the discharge

capacity of the box-inlet crest; (2) determining the discharge capacity of the

headwall opening; (3) the design of the outlet; and (4) determining the effect

of tailwater submergence on the spillway capacity. An example shows the

application to the design of a box-inlet drop spillway.

This design manual was first published as St. Anthony Falls Hydraulic

Laboratory Technical Paper 8, Ser. B, in January 1951. It was reprinted

without material change by the U.S. Department of Agriculture, Sou Conservation Service, as SCS-TP-106 in July 1951. The present manual supersedes

SCS-TP-106 and includes the trapezoidal weir and dike effect information

obtained by Neal E. Minshall from studies at the University of Wisconsin.
CONTENTS

Symbols. j^

Introduction '" I

Experimental background I-I"""ill..1111"Hill_" Í I i

Free-flow capacity ^ lllllllVll^lll""lll_lll 2

Control at box-inlet crest lllllllll.11 _l _llll_lll 3

Corrections II~IIIII__~_I~IIII~"I 3

Variation of discharge coefficient with head 11..Ill" 3

Variation of discharge coefficient with box-inlet shape 1.1111111.1 3

Variation of discharge coefficient with approach-channel width 1.1.1 3

Variation of discharge coefficient with dike position l_l 4

Elimination of dike effect "I_III_I" 4

Variation of discharge coefficient with approach-channel depth ...111 4

Precision of results ' 4

Summary (control at box-inlet crest) lllllllllll."111 6

Control at headwall opening lllllllllll 6

Discharge coefficient lllllllllllllll 7

Head correction lllllllllllll 7

Other factors lllll.lllll 8

Precision of results l.l.ll.l 9

Summary (control at headwall opening) llll.l 9

Outlet design lllllllll 11

Critical depth I..llllllllllllll 11

Straight section lllllllllll 12

Stilling basin 1111111111.1111111 12

Sidewall flare II-lllllllllllll 12

Basin length llllllll 12

Tailwater level 12

End sill llllllllllllllllll 13

Longitudinal sills lllllllllll 13

Sidewall height llllllllll 13

Wingwalls I.II-lllllllllllllll I 13

Summary (outlet design) lllllllllllllll ~_ 15

Submerged -flow capacity lllllllllllllll. 15

Factors influencing submergence effect l.llll 16

Discharge llllllll 16

Outlet-exit width ' 1.1111111111111111111 16

Other factors ~~~~ ~ IQ

Submergence curves llllllllllllllllll 16

Computation of submergence effect lllllll 16

Example of application III".llllll.lllllllll 35

Washington, D.C. Issued Aprü 1966

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

Washington, D.C, 20402 - Price 25 cents

III
SYMBOLS

A cross-sectional area of approach channel

B length of box inlet

c coefficient of discharge

Ct coefficient of discharge for a triangular weir

D depth of box inlet

¿2 height of tailwater above basin floor

dz height of tailwater above top of end sill

dc critical depth in straight section

dee critical depth at stilling-basin exit

F difference in elevation of box-inlet crest and top of end sill

/ height of end and longitudinal sills

g acceleration due to gravity

H specific head; depth of flow plus velocity head=/i+/i»

Ho apparent specific head at zero fiow; zero-flow head correction

Ht level of tailwater referred to crest of box inlet

AH increase over free-flow head caused by high tailwater level

h piezometric head

hp velocity head= V^/2g

L length of box-inlet crest=2B+W

Ls minimum length of straight section of outlet

LB minimum length of stilling-basin section of outlet

p spacing of center pair of longitudinal sills either side of outlet centerline

Q discharge

r spacing of outer pair of longitudinal sills

t minimum height of sidewall at basin exit above tailwater elevation

V mean velocity=Q/A

W width of box inlet

Wc width of approach channel

We width of stilling-basin exit

X distance from box-inlet crest to toe of dike

Y distance upstream from headwall to toe of dike

a included angle of triangular weir

6 angle wingwall makes with outlet centerline

Subscript 1 applies when control section is at box-inlet crest

Subscript 2 applies when control section is at headwall opening
HYDRAULIC DESIGN

OF THE BOX-INLET DROP SPILLWAY

By FRED W. BLAISDELL and CHARLES A. DONNELLY, hydraulic engineersj Soil and Water Conservation

Research Division^ Agricultural Research Service

INTRODUCTION

This handbook contains sufficient information

to permit the complete hydrauHc design of a

box-inlet drop spillway and explains briefly the

various factors that influence the design. Its four

major sections deal with the free-flow capacity,

the outlet design, the submerged-flow capacity,

and the utilization of the preceding information in

the design of box-inlet drop spillways.

The box-inlet drop spillway may be described

as a rectangular box open at the top and at the

downstream end. The spillway is shown in figiu*e

1. Storm runoff is directed to the box by dikes

and headwalls, enters over the upstream end and

two sides, and leaves through the open downstream

end. An outlet structure is attached to the downstream end of the box. The long crest of the box

inlet permits large flows to pass over it with

relatively low heads, yet the width of the spillway

need be no greater than that of the exit channel.

EXPERIMENTAL BACKGROUND

The design information presented here is based

on an extensive experimental program. The free

and submerged flow tests were conducted, with

interruptions, between 1946 and 1950. They

consist of 361 tests, each test differing in some

respect from the others and requiring approximately 35 observations made with differing flow

conditions. Thus, over 12,000 observations form

the background for the discharge design procedure.

Similarly, the outlet design is based on 386 tests

representing (1) the exploratory tests used to determine the general form of the outlet and (2) the

tests made to determine and verify the general

design rules for each element of the outlet. These

tests were made between 1944 and 1946. The

outlet wingwall design was modified slightly as a

result of special studies made in 1950. The dike

effect in this revision is based on a 1965 analysis

of data obtained in 1953 under the direction of

Neal E. Minshall at the University of Wisconsin.

A further addition is the information published by

Minshall ^ on the trapezoidal weir box inlet

shown in figure 2. Detailed descriptions of the

flow tests and the outlet tests may be found in the

reports by Donnelly ^ and by Blaisdell and

Donnelly.^ *

The test programs in general are adequate to

define accurately the values of the variables involved in the design of box-inlet drop spillways.

The tests were conducted and analyzed by laboratory personnel experienced in the conduct and

interpretation of hydraulic model tests. Every

feasible effort has been made to insure the reliability of the final results. The results are generally expressed in dimensionless form. This is

to aUow as much condensation as possible, yet to

permit the widest possible application to structures similar in geometrical form to the box-inlet

drop spillway and outlet discussed here.

1 MiNSHALL, N. E. Discussion of THE BOX INLET DROP

SPILLWAY AND ITS OUTLET. Amer. Soc. Civil Engin.

Trans. 121: 987-992. 1956.

2 DONNELLY, C. A. DESIGN OF AN OUTLET FOR BOX

INLET DROP SPILLWAY. U.S. Dept. Agr., Soil Conserv.

Serv. SCS-TP-63, 31 pp. 1947.

3 BLAISDELL, F. W., and DONNELLY, C. A. CAPACITY OF

BOX INLET DROP SPILLWAYS UNDER FREE AND SUBMERGED

FLOW CONDITIONS. Minn. Univ. St. Anthony Falls

Hydraul. Lab. Tech. Paper 7, Ser. B, 36 pp. 1951.

* BLAISDELL, F. W., and DONNELLY, C. A. THE BOX

INLET DROP SPILLWAY AND ITS OUTLET. Amer. SoC.

Civil Engin. Trans. 121: 955-994. 1956.
U.S. DEPARTMENT OF AGRICULTURE, AGRICULTURE HANDBOOK 301

PLAN

1 s u^me i[_g e_d ^

AH

SECTION AT CENTER LINE

FIGURE 1.—Box-inlet drop spillway.

FREE-FLOW CAPACITY

Free flow exists in the box-inlet drop spillway

whenever the downstream or tailwater level is so

low that it has no effect on the amount of water

that will pass the spillway. The problem then

is to determine what parts of the spillway affect

the flow and to evaluate these effects. Two

different sections are effective in controlling the

flow: the crest of the box inlet controls the flow

up to that point where the box inlet is flooded out;

the opening in the headwall controls at higher

flows. The flow at which the control changes

from one point to the other is dependent upon a

number of factors, the principal ones being the

box-inlet depth and its length.

Since the primary factors that influence the

free flow past box-inlet drop spillways are dif-
HYDRAULIC DESIGN OF THE BOX-INLET DROP SPILLWAY

Crown of dike

PLAN

SECTION AT CENTER LINE

FIGURE 2.—Trapezoidal weir box inlet.

ferent when the control is at the box-inlet crest

from what they are when the control is at the

headwall opening, the descriptions and the design

information for each control will be discussed in

separate sections. For convenience in use, the

design charts and tables are grouped together

following the descriptive material concerning

them.

Control at Box-Inlet Crest

Water enters the box inlet over the upstream

end and two sides when the section controlling

the flow, is the box-inlet crest. The common

rectangular weir formula

Q=c,L ^gH"^' (la)

is used to determine the head under these conditions. The equation is easier to use for some

problems if it is solved for the head

\c^L^¡2g}

(lb)

King's table 5-1 ^ gives the three-halves powers of

numbers and his table 7-18 gives the two-thirds

powers of numbers, which may prove helpful in

solving these equations. In equations la and lb,

Q is the discharge in cubic feet per second; Ci is

a dimensionless discharge coefficient; L is the

crest length, 2B-\-Wy in feet; B is the inside length

of the box inlet in feet; W is the width of the box

inlet in feet; g is the acceleration due to gravity

and is equal to 32.2 feet per second per second;

and H is the head over the spillway crest in feet.

The head H is here assumed to be the depth of

flow plus the velocity head. Most of these

symbols are illustrated in figure 1.

The discharge coefficient Ci in equations la and

lb has the value 0.4275 and Ci V2ör=3.43 when

BjW^l.Q, WclL>^,0, and£r/p>0.6. Here W^

is the approach-channel width in feet.

Corrections

A number of corrections must be applied to ci

in equations la and lb to take into account the

effects of various factors such as the variation of

Ci with head and the effects of box-inlet shape,

approach-channel width, and dike position.

These corrections are described in the following

paragraphs.

Variation oj Discharge Coefficient with Head,—

The coefficient of discharge in equations la and

lb varies with the head on the spillway when

£f/W^<0.6, whereas for Íí/T1^>0.6, the coefficient

is constant.

For design purposes the ratio HfW may be

computed, after which the discharge coefficient

Ci in equations la and lb can be read directly

from the curve shown in figure 3, using the lefthand Ordinate. An alternative way to determine

the discharge is to use 0.4275 for Ci, or 3.43 for

CiV2p^, and multiply by a correction read from

the curve of figure 3, using the right-hand ordinate.

This correction may also be obtained from table 1.

Figure 3 and table 1 are vahd when 0<iZ/T1^<1.5;

they should, be used with caution outside the

range covered by the tests.

Variation oj Discharge Coeffix^ient with BoxInlet Shape,—The shape of the box inlet in plan

has a considerable effect on the discharge coefficient. This variation is shown in figure 4.

Since the discharge coefficient Ci in equations

la and lb has been taken as correct when

BIW=l, it is necessary to apply a correction to

Ci if BjW is not equal to 1.

The ordinates of figure 4 indicate the correction

to be appUed to Ci for each shape of box inlet

between BW=0 and JS/W^=4—the range in

shapes covered by the tests. The correctionsmay

also be obtained from table 2. The discharge

coefficient is multiplied by the box-inlet shape

correction to correct for this effect.

Variation oj Discharge Coefficient with ApproachChannel Width.—The width of the upstream or

approach channel has a very great effect on the

discharge if the channel is too narrow. For

the longer boxes and longer crest lengths, the

approach-channel width can easily be so narrow

as to make part of the crest inefficient. Under

these conditions a change in the proportions of

5KING, H. W., and BRATER, E. F. HANDBOOK OF

HYDRAULICS. Ed. 5. pp. 5-32 to 5-45 and 7-62 to 7-67.

New York. 1963.
U.S. DEPARTMENT OF AGRICULTURE, AGRICULTURE HANDBOOK 301

the box inlet may prove economical or it may be

desirable to consider the use of a different type of

spillway.

The correction for approach-channel width

shown in figure 5 is a function of the ratio of

approach-channel width to crest length, WJL,

The correction can also be obtained from table 3.

When Wc/i>3, no correction is required. At

lesser relative channel widths the factor by which

the discharge coefficient Ci in equations la and lb

is multiplied becomes small. The tests covered

a range of relative approach-channel widths

WcjL from 0.4 to 10, and the corrections are

valid over this range.

Variation oj Discharge Coefficient with Dike

Position,—The proximity of the toe of the earth

dike to the box-inlet crest has an important effect

on the discharge coefficient because the dike toe

interferes with the free access of water to the boxinlet crest near the headwall. The toe of the dike

should be kept as far from the box inlet as is

feasible.

Little data were obtained regarding the effect of

dike position on the discharge coefficient. Such

data as were obtained were of quahtative rather

than quantitative value. For this reason, as mentioned in the section, "Experimental Background,''

the more extensive data obtained by Minshall

during his tests at the University of Wisconsin

were borrowed and reanalyzed to develop design

information on the dike effect. The effect of the

dike is shown in table 4.

The dike-effect data were developed from experiments on box-inlet drop spillways with relative

box lengths BjW of 0. 5, 1. 0, 1. 5, and 2.0; dike

slopes of 1 on 3; the toe of the dike ranging for

relative distances from the box-inlet crest at the

headwall XlWirom 0 to 0.6, and for no dike in the

channel that had a relative width WJL of 10; and

dike toes that extended upstream from the headwall to relative distances YjW oi 1.0, 1.7, 1.9, and

2.2. No effect of YjW on the dike effect could be

detected. The relative head HjW had an effect

on the dike correction factor, but no pattern could

be detected for the variation in the correction factor with relative head.

The dike-effect correction factors listed in table

4 were used to compute discharges to test the

agreement of the computed and experimentally

observed discharges. The ratio of the observed

discharge to the computed discharge ranged from

0.90 to 1.15 for most of the available data. Since

the dike correction factor includes all the residual

differences and unaccounted-for variations, this

agreement is felt to be satisfactory for design

purposes. However, the agreement is less satisfactory for values of HjW less than 0.2.

Elimination oi Dike Efect—The effect of the

dike on the discharge coefficient can be eliminated.

This is accomplished by sloping the crest of the

box inlet to fit the dike slope. The dike is then

extended to the sloping drop-inlet crest. This is

shown in figure 2. MinshalP has called this inlet

a trapezoidal weir box inlet.

An advantage of the trapezoidal weir box inlet

is that the dike can be constructed to a definite

concrete surface. Field experience has shown

that the toe of the dike is frequently built too

close to the rectangular weir box inlet. The result

is a decrease in the designed capacity of the box

inlet. The trapezoidal weir makes it more likely

that the dike will be installed as designed.

The capacity of the trapezoidal weir box inlet

is given by summing the rectangular and triangular

weir formulas

Q=c^L^IP''+c,j^iB.nl^9H'" (2)

where Ct is the dimensionless discharge coefficient

for a triangular weir and a is the included angle

of the weh*. King's table 5-2 ^ gives the five-halves

powers of numbers.

In_equation 2, the coefficient Ci is 0.4275 and

Ci ^j2g is 3.43 as for equations la and lb. The

same corrections, except for the dike position correction, must be applied. If the dike slope is 1 on

3, Minshall ^ assigns a value oí 9 to Ctjz tan ^ V2ôf,

which means that Ct=0.70, The indicated precision of this coefficient is approximately ±10

percent.

Variation oJ Discharge Coefficient With ApproachChannel Depth,—It is known from tests performed

by others ^^0 that the depth of the approach

channel has an effect on the discharge. Both

Huff and Kessler indicate a decrease in discharge

as the approach channel becomes shallower. All

the tests used as the basis for the design curves

presented in this report were made with the approach channel level with the box-inlet crest; i.e.,

the approach channel was silted full. Deeper

approaches will increase the discharge, and in this

respect the design curves are conservative.

Precision oí Results

Equations la and lb, when the discharge coefficient Ci is corrected for the effects of head,

box-inlet shape, and approach-channel width, and

when there is no dike effect, can be expected to

give the discharge to within ±7 percent under

ideal conditions. With dike effects, the precision

is about ±15 percent. This precision was ob6 See footnote 1, p. 987.

7 See footnote 5, pp. 6-42 to 6~46.

8 See footnote 1, p. 991.

9 KESSLER, L. H. EXPERIMENTAL INVESTIGATION OF THE

HYDRAULICS OF DROP INLETS AND SPILLWAYS FOR EROSION

CONTROL STRUCTURES. Wis. Univ. Engin. Expt. Sta. Ser.

80, 66 pp. 1934.

10 HUFF, A. N. THE HYDRAULIC DESIGN OF RECTANGULAR

SPILLWAYS. U.S. Dept. Agr., Soil Conserv. Serv., SCSTP-71, 67 pp. 1944.
HYDRAULIC DESIGN OF THE BOX-INLET DROP SPILLWAY

"/

0.44

0.4 3

w

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 I.I 1.2 1.3 1.4 1.5

Discharge coefficient and correction for head, with control at box-inlet crest.
6 U.S. DEPARTMENT OF AGRICULTURE, AGRICULTURE HANDBOOK 301

tained in the laboratory; under field conditions,

somewhat less precision must be anticipated.

Summary (Confrol af Box-Inlet Crest)

The preceding comments regarding the flow

over the box-inlet crest when the discharge is free

and the crest of the box inlet controls the discharge may be summarized as follows:

1. The general formula for a rectangular weir is

Q=0A275L^J2^IP^' (la)

or, in English units,

Q=3A3LH'^' (Ic)

When solved for H these equations read

n-{ ^ -T \0A275Ly/2g/

and

(lb)

Ks: =^Ji)

2/3

(Id)

The general formula for a trapezoidal weir

with a l-on-3 dike slope is

Q=0A27a^2gH'^'+0.70 ^ tan ^ V2^íí^/^ 15

or, in English units.

(2a)

(2b)

2. The discharge coefficients in equations 1 .and

2 must be multiplied by:

a. The correction for head given iù figure 3

or table 1 ;

b. The correction for box-inlet shape given

in figure 4 or table 2;

c. The correction for approach-channel width

given in figure 5 or table 3; and

d. The correction for dike proximity to the

box-inlet crest given in table 4. This

correction does not apply to equation 2.

3. The approach channel is silted level with the

crest of the box inlet.

4. The precision of the design curves and

tables is within ± 7 percent when there is no

dike effect and about ±15 percent when

dikes are used.

Control at Headwall Opening

The box inlet is fiooded out at the higher flows

and for the shallower boxes. Under these conditions, the opening in the headwall controls the

flow through the spillway. A method for determining whether the control is at the box-inlet

crest or at the headwall opening is presented in the

section on ''Example of Application.'' When the

control is at the headwall opening, the discharge

formula is

Q=cW^g{H-\-H,2y" (3a)

when solved for Q and

(3b)

when solved for H, In equations 3a and 3b, H is

measured from the box-inlet crest, whereas the

effective headwall opening is on the order of H+D,

D being the depth of the box inlet in feet. The

head correction ÍZ02 is therefore required.

9 i.io

a

S 1.05

.£

^ 1.00

J 0.95

e

S 0.90

H

^

-

-- j=j~*n=ss

0.5 1.0 1.5 2.0

J.

w

E.5 3.0 3.5 4.0

FIGURE 4.—Correction for box-inlet shape, with control at box-inlet crest Í ^>3j.
HYDRAULIC DESIGN OF THE BOX-INLET DROP SPILLWAY

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FIGURE 5.—Correction for approach-channel width, with control at box-inlet crest.

A number of factors affect the flow through the

headwall opening, and they determine the values

of the discharge coefficient c<¿ and the head correction i?o2 in equations 3a and 3b. These factors

are discussed in the following paragraphs.

Discharge Coefficient

The discharge coefficient c^ in equations 3a and

3b increases as the relative depth BfW of the box

inlet increases. The range of values of DfW

covered by the tests is from about 0 to 1.

The discharge coefficient c^ may be taken from

the curve of figure 6 or from table 5.

Head Correction

It is only natural to expect that the magnitude

of the head correction i3o2 in equations 3a and 3b

will approach the box-inlet depth for the relatively

longer and shallower box inlets and that it will

decrease toward zero for the relatively shorter and

deeper box inlets.
8 U.S. DEPARTMENT OF AGRICULTURE, AGRICULTURE HANDBOOK 301

TABLE 1.—Correction jor head {control at box-inlet crest)

[Multiply ci in Q =cil/y/2g W^ by correction]

H/W 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

00 0.76

.91

.95

.98

.99

LOO

0.80

.92

.95

.98

.99

LOO

0.82

.92

.96

.98

.99

LOO

0.84

.93

.96

.98

.99

LOO

0.86

.1 ___ Ó. 87

.93

.97

.99

LOO

LOO

0.88

.94

.97

.99

LOO

0.89

.94

.97

.99

LOO

0.90

.95

.97

.99

LOO

0.91

.95

.98

.99

LOO

.93

.2 .96

.3 .98

.4 _

1. 00

.5 LOO

.6 1 ---

1 Correction is 1.00 when iî/T7-exceeds 0.6.

TABLE 2.—Correction jor hoxrinlet shape {control at box-inlet crest)

[Multiply ci in Q=ClL^/2g IP^^ by correction]

B/W 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0 0.98

LOO

.96

.94

.93

LOI

.99

.96

.94

L03

.99

.95

.94

L03

.98

.95

.94

L04

.98

.95

.94

L04

.98

.95

.94

L03

.97

.95

.94

L02

.97

.95

.94

LOI

.96

.94

.93

L 01

1 . 96

2

. 94

3 . .

. 93

4

TABLE 3.—Correction for approach-channel width {control at boxrinlet crest)

[Multiply ci in Q=ciL^¡2g W^ by correction]

^ Correction is 1.00 when WJL exceeds 3.0.

TABLE 4.—Correction jor dike e^ect

{control at box-inlet crest)

[Multiply ci in Q =ciL^2g H^f^ by correction]

WJL 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0 . . 0.00

.84

.98

LOO

0.09

.87

.98

0. 18

.90

.99

0.27

.92

.99

0.35

.93

.99

0.44

.94

.99

0.53

.95

LOO

0.62

.96

LOO

0.71

.97

LOO

0.80

1 .97

2

1. 00

31 ._

X/W

B

W

0.0 0.1 0.2 0.3 0.4 0.5 0.6

0.5 0.90 0.96 LOO L02 L04 L05 L05

1.0 .80 .88 .93 .96 .98 1. 00 LOI

1.5 .76 .83 .88 .92 .94 .96 .97

2.0 .76 .83 .88 .92 .94. .96 .97

Tlie relative liead correction H02/D is a simple

function of B/D for box inlets having relative

depths D/W of 1/4, 1/2, and 1. The relative head

correction may be taken from the curve of figure 7

or from table 6 when D/W is between 1/4 and 1,

inclusive; however the curves of figure 7 and table

6 are not valid when D/W = 1/8. Although

figure 8 has been prepared to give the head correction for the shallower box inlets, it can be used

for any box inlet when D/W is between 1/8 and 1.

To utilize figure 8 it is necessary to compute,

before entering the figure, any two of the three

ratios B/D, B/W, or D/W.

Other Factors

A thorough study was made to discover those

factors which determine the magnitude of the

discharge coeflicient C2 and the head correction

ÍZ02 in equations 3a and 3b.

With regard to the discharge coefficient, C2 is

not affected by the box-inlet shape, the approachchannel width, or the dike position. The only

factor that affects the discharge coefficient is the

relative depth of the box inlet. This is discussed

above.
HYDRAULIC DESIGN OF THE BOX-INLET DROP SPILLWAY

o 0.50

.48

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.44

.4 2

0.40

.38

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Of V

—.«—.

— M

IMBKHH mmi O

O

u 0.0 0. 1 0 2 0.3 0.4 0.5

D

W

0.6 0.7 0.8 0.9 1.0

FIGURE 6.—Coefficient of discharge, with control at headwall opening.

u.u n "1 ' "" ""

"

+0.1

+ 02

+ 0.3

\

+ 0.4 V — T

+ 05 >

t

+ 0.6 ^

+ 0.7 ^ U— s

+ 0.8 _ :^

s.

+ 0.9 — — ÏS, ^ — — —1 —. ~^ » 1 -_ _«_ _. ___

4-1.0

— — — — —

—

— 1 — 1

0 I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17

D

FIGURE 7.—Relative head correction for D/W>}ij with control at headwall opening.

With regard to the head correction, i/02 is not

affected by the approach-channel width or the

dike position. The only factors that affect the

head correction are the relative length B/W and

the relative depth D/W of the box inlet.

Precision of Results

The discharge coefficient C2 in equations 3a and

3b is reliable to within about ±10 percent. The

head correction ÍZ02 is also believed to be reliable

to within about 10 percent of the indicated value

except for the steep portion of the curve of figure

7 where errors of ± 20 percent are possible. These

percentages apply up to relative heads H/W of

about 1.2.

The discharge coefficient and the head correction

apparently vary in such a manner that the errors

are at least partially compensating. The two

percentages mentioned are therefore not additive

but probably partly cancel each other.

Summary (Control at Headwall Opening)

The preceding comments regarding the flow

through box-inlet drop spillways when the dis-
10 U.S. DEPARTMENT OF AGRICULTURE, AGRICULTURE HANDBOOK 301

iD

J

L

11l\Vf

T\

IIV

ÖLSu

^* \\\\ * ^

o- \V[\" ~

UAJ

"vrrt

YJS V

"Turt

LJ_5U t

u\ >K ^

\\ \\ ,\V^^

iW N vN^

l\l\ \ ^ \ vk KvA \OyN

1\ vS \ vSS ¿2

LV^i^!-S^S3S 2' C5ËvV\,ïSV J^

^\ MVV^^V 0^J\s^^ V KOSS^¿^^

^)?^^!^^5^^^>^

^^^gggs^^ ^

m

fO

CVJ

tí

'tí

o

O)

œ|o

(í)

lí) á

fO

CM

O

Ó O

4-

CVJ

ó

4-

ro

O

+

O

tn

6

4-

M

CO

o

+

O O

9í

Ó

+

20,H
HYDRAULIC DESIGN OF THE BOX-INLET DROP SPILLWAY 11

TABLE 5.—Coefficient of discharge (control at headwall opening)

[C2 in Q =C2W^/2^(H+Ho2y^^

Coefficient of

D/W

discharge

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

C2 0.34

2.76

0.34

2.76

0.35

2.77

0.35

2.78

0.35

2.81

0.36

2.85

0.36

2.90

0.37

2.99

0.39

3. 10

0.40

3.22

0 43

C2V2^— 3 43

TABLE 6.—Head correction Ho2/DJor DIW> 0.25 (control at headwall opening)

BID 0.0 0.1 0.2 0.3 0.4 0.5 0.6 . 0.7 0.8 0.9

0 0.00

.49

.70

.82

.90

.92

.93

.93

.93

0.07

.52

.71

.83

.91

.92

.93

.93

.93

0.13

.54

.72

.84

.91

.92

.93

.93

.93

0.20

.56

.74

.85

.92

.92

.93

.93

.93

0.25

.59

.75

.86

.92

.93

.93

.93

.93

0.30

.61

.76

.87

.92

.93

.93

.93

.93

0.35

.63

.77

.87

.92

.93

.93

.93

.93

0.39

.65

.79

.88

.92

.93

.93

.93

.93

0.42

.67

.80

.89

.92

.93

.93

.93

.93

0 46

1 . 68

2 . 81

3 90

4 92

5 93

6 93

7 . 93

8.. _ 93

charge is controlled by the headwall opening may

be summarized as follows:

1. The general formulas are

and

q=c,W^g{H+Ho2Y"

Hi H/_Q_\

KCW^g)

2/3

"fioi

(3a)

(3b)

The discharge coefficient C2 may be obtained

from figure 6 or from table 5.

The head correction ÍZ02 may be obtained

from figure 8. If DjW is between }f and 1,

inclusive, iîo2 may be more readily determined from figure 7 or from table 6.

The precision of the design curves and tables

is probably within d-10 percent.

OUTLET DESIGN

The outlet is that part of the box inlet drop

spillway located downstream from the headwall.

Since the form of the outlet is determined largely

by the manner in which the flow leaves the box

inlet, it is pertinent to describe the outflow

briefly. The water passing over the sides of a

box inlet springs clear of the sidewalls and creates

a space between the nappes and the sidewalls.

These spaces are filled with water having a helical

motion about a horizontal axis. At the exit of

the box inlet the heHces from the opposite sides of

the spillway enter the outlet along the sidewalls

and create a considerable disturbance and uneven

distribution of flow across the outlet. It is this

poor velocity distribution and attempts to improve it that cause the major, problems in the

development of the outlet.

Since the critical depth is used when computing

the dimensions of the outlet, it will be discussed

first. Then the two major parts of the outlet—

the straight section and the stifling basin—are

discussed.

Critical Depth

The critical depth is the depth at which water

fiows when its energy content is a minimum.

As used here, the critical depth can be most

conveniently computed by the equation

dc=y- 9

(4a)

where dc is the critical depth in feet; Q is the

discharge in cubic feet per second; W is the

width of the spiUway and the straight section of

the outlet in feet; and g is the acceleration due to

gravity and is equal to 32.2 feet per second per

second. Because the exit of the stifling basin
12 U.S. DEPARTMENT OF AGRICULTURE, AGRICULTURE HANDBOOK 301

may be wider than the straight section, the critical depth at that point is

d. -4

(Qfw.y (4b)

where dee and We are the critical depth and width

at the exit of the stilling basin.

Table 7 has been prepared to facilitate the use

of equations 4a and 4b. There, the critical depth

dc or dee in feet is given for various discharges per

unit width Q/W or Q/We in cubic feet per second

per foot of width.

Straight Section

The straight section is used between the box

inlet and the stilling basin to assist in breaking up

the helical rollers described earlier, to improve the

flow distribution, to make better use of the available tailwater, and to improve the scour pattern.

The straight section has sidewalls located parallel

to the outlet centerline and in line with the sides

of the box inlet; that is, the straight-section width

W is equal to the box-inlet width W.

If the straight section is too short it will not

adequately perform its function of improving the

performance of the outlet. The minimum length

of the straight section is given by the equation

Ls=d, ( 0.2

\B¡W fl)

(5)

for values of JB/W'>0.25 where Ls is the minimum

length of the straight section in feet, and B and W

are the length and width of the box inlet in feet.

Ordinarily equation 5 will give a straight section

that is too short for practical use. When this

occurs the straight section may be lengthened to

suit the site with assurance that it will still function properly. There is no reason that the straight

section cannot be lengthened, covered, and used

as a highway culvert if desired.

It is not intended that the box-inlet drop spillway be used for a straight-drop spillway where

J5/tF=0 and the form of equation 5 requires uneconomically long straight sections for short box

inlets. Since the minimum value of BjW used in

developing equation 5 was 0.25, the equation

should not be used for box inlets shorter than

5/W=0.25.

Stilling Basin

The flared or stilling-basin section is used to

remove destructive energy from the flow and to

discharge water into the downstream channel in a

manner that will not damage the bed, the banks,

or the structure itself. The several features of the

stilling-basin design require a number of steps.

Sidewall Flare

It will frequently be desirable and economical to

flare the sidewalls of the stiUiag basin. Benefits

achieved thereby may iaclude less required tailwater depth, decrease in excavation for the entire

structure, and better flow conditions in the downstream channel.

The sidewalls may be parallel extensions of the

straight-section sidewalls or they may flare.

Rates of flare of each sidewall up to two longitudinal to one transverse are permissible. If the

sidewall flare is greater than two longitudinal to

one transverse, the flow does not spread out rapidly

enough to follow the sidewalls, the main stream

wül be concentrated at the center of the stilling

basin, and whirls wiQ develop between the stream

and the walls. Flares greater than 1 in 2 thus

become wasteful of construction materials and at

the same time produce poorer flow conditions in

the stilling basin and downstream channel. The

choice between the limits 1 in œ (no flare) and 1

in 2 depends on site conditions; the broad permissible limits aUow the adaptation of the outlet to

almost any field situation.

Basin Length

For economy in construction the fiared or

stilling-basin section should be made as short

as possible, but it must be long enough to dissipate

the energy in the flow. The basin must be proportionately longer for the short box inlets than for

the long box inlets because of the manner in which

the water leaves the box ialet. The equation for

the minimum length of stilling basin LB is

(6)

for values of B\W>^.2h, Greater stilling-basin

lengths may be used, butit will be more economical

to lengthen the straight section; lesser stillingbasin lengths should never be used.

Equation 6, like equation 5, should not be used

when B\W is less than 0.25.

Tailwater Level

The minimum tailwater depth ¿2 above the floor

of the stilling basin required for proper energy

dissipation is ordinarily a function of the critical

depth at the end of the stifling basin d^. However,

when the stuling-basin exit is too wide, still or

nearly stül water exists along the sidewalls of the

basin. That part of the outlet occupied by still

water is obviously not being used to dissipate

energy and can be eliminated. Still water occurs

along the sidewaUs when the stuling-basin exit is

wider than ll.ödce.

Two equations are necessary to determine the

required tailwater depth. When the stUling-basin

exit width We is less than 11.5dce, the depth of
HYDRAULIC DESIGN OF THE BOX-INLET DROP SPILLWAY 13

tailwater above the stilling-basin floor ¿2 is given

by the equation

d2=lMce (7a)

and when We is greater than 11.5^^^ the tailwater

depth is

d2=dce+0.052We (7b)

If it is desirable to measure the tailwater depth

from the top of the end sill dz rather than from

the floor of the stilling basin ¿2, equation 7a

should be changed to read

ds^=l.S3dce (8a)

and equation 7b should read

d,=0,SSdce+OMSWe (8b)

Satisfactory results can be obtained with wide

stilling-basin outlets and equations 7b or 8b, but

the wider basins make inefficient use of the outlet

and will be more expensive than a basin with a

narrower outlet width. Tailwater depths greater

than that given by equations 7a and 7b or 8a and 8b

may be used; lesser depths will result in greater

scour in the downstream channel.

End Sill

The end sill deflects upward the stream leaving

the stilling basin, prevents scour close to the exit

of the stilling basin, and creates a horizontal roller

under the deflected stream with the velocity at

the bed directed upstream, thus actually bringing

material upstream and depositing the larger material at the end of the stilling basin.

The height of the end sill is very important.

When the end sill is too high, the jet leaving the

basin jumps over the sill and lands some distance

out from the end of the basin, causing severe

erosion at that particular location. On the other

hand, when the end sill is too low, the water leaving the basin causes the same severe erosion but

it occurs very near the end of the basin. The

most satisfactory height of the end sill /is given

by the equation

/=á2/6 (9)

Longitudinal Sills

Longitudinal sills are used in the straight section

and stilling basin to assist in the distribution of

the flow across the stilling basin, to prevent high

velocities at the sides of the basin, and to reduce

the scour at the end of the basin and the erosion

of the stream banks. The sills may also be used

for structural purposes.

The following rules should be used to determine

the size and arrangement of the longitudinal sills:

1. When the stilling basin sidewalls are parallel,

the longitudinal sills may be omitted.

2. The center pair of longitudinal sills should

start at the exit of the box inlet and extend

through the straight section and stilling

basin to the end sill.

3. When We is less than 2.5W, only two sills

are needed. These sills should be located on

either side of the centerline at a distance p

of W/Q to TF/4.

4. When We exceeds 2.5W, an additional pair

of sills is required. These sills are located

parallel to the outlet centerline and midway

between the center sills and the sidewalls at

the exit of the stilling basin.

5. The height of the longitudinal sills is the

same as the height of the end sill.

Sidewall Height

The sidewalls must extend above the tailwater

level at the end of the stilling basin by an amount

sufficient to prevent overtopping and the resulting

erosion of the dam fill. Rough water in the stilling

basin requires a greater freeboard than is frequently used in open ditches. The minimum

height of the sidewalls above the water surface

at the end of the stilling basin t should be

t=d2/S (10)

or greater. All the rules presented here are based

on sidewalls extending above the tailwater level,

even where submergence must be considered.

Under submerged flow conditions much higher

sidewalls may be required; however, the freeboard

above the tailwater level may be safely reduced

somewhat because the water surface will be

smoother.

Wingwalls

The shape and the position of the wingwalls have

more effect on the scour of the bed and the dam

fill near the end of the stilling basin than has

been commonly supposed. Considerable study

was given to the shape and location of wingwall

that would best protect the dam fill.

A wingwall triangular in elevation is greatly

superior to a rectangular wingwall. Its top

should slope downward at an angle of 45° with

the horizontal. However, if conditions make it

desirable to use a flatter slope, the top may have

a slope as flat as 30° without changing the anticipated scour significantly.

In plan, the wingwalls should flare at an angle

e of 60° with the outlet centerline, although a

flare of 45° would probably make no significant

change in the anticipated scour. Wingwalls

located parallel to the centerline will cause no

deeper scour, but they will cause more extensive

bed scour between the wingwalls and are not

recommended.

793H-281 O—-66 2
14 U.S. DEPARTMENT OF AGRICULTURE, AGRICULTURE HANDBOOK 301

TABLE 7.—Critical depths injeetjor various discharges perjoot oj width

W

10-

11.

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-

40.

41-

42.

43-

44-

45.

46-

47-

48-

49-

50-

0.0

0.000

.314

.499

.654

.792

.919

1.038

1. 150

L257

1.360

1.459

L555

1.648

1.738

L826

1. 912

1.996

2.078

2. 159

2.238

2.316

2.393

2.468

2.542

2.615

2.687

2.759

2.829

2.898

2.967

3.035

3. 102

3. 168

3.234

3.299

3.363

3.427

3.490

3.553

3.615

3.676

3.737

3.798

3. 858

3.918

3.977

4.035

4.094

4. 152

4. 209

4.266

0. 1

0.068

.335

.515

.668

.805

.931

L049

1. 161

1.268

1.370

L469

L564

L657

L747

L835

L920

2.004

2.086

2. 167

2.346

2.324

2.400

2.475

2.549

2.623

2.695

2.766

2.836

2.905

2.974

3.042

3. 109

3. 175

3.240

3.305

3.370

3.433

3.496

3.559

3.621

3.683

3.743

3. 804

3.864

3.924

3.983

4.041

4.099

4. 157

4.215

0.2

0. 107

.355

.532

.683

.818

.943

1.061

1. 172

1.278

L380

L478

L573

1.666

L756

1.843

L929

2.012

2.094

2. 175

2.254

2.331

2.408

2.483

2.557

2.630

2.702

2.773

2.843

2.912

2.981

3.048

3. 115

3. 181

3.247

3.312

3.376

3.440

3.503

3.565

3.627

3.689

3.750

3.810

3.870

3. 929

3. 988

4.047

4. 105

4. 163

4.220

0.3

0. 141

.374

.548

.697

.831

.955

1.072

1. 183

L289

L390

L488

1.583

L675

L764

L852

L937

2.021

2. 103

2. 183

2.262

2. 339

2.415

2.490

2.564

2.637

2.709

2.780

2.850

2.919

2.987

3.055

3. 122

3. 188

3.253

3.318

3.383

3.446

3.509

3.571

3.633

3.695

3.756

3.816

3.876

3.935

3.994

4.053

4. Ill

4. 169

4.226

0.4

0. 171

.393

.563

.711

.844

.967

1.084

1. 194

L299

1.400

L498

1.592

L684

L773

L860

1.946

2.029

2. Ill

2. 191

2.269

2.347

2.423

2.498

2. 572

2.644

2.716

2.787

2.857

2.926

2.994

3.062

3. 129

3. 195

3.260

3.325

3.389

3.452

3.515

3.578

3.640

3.701

3.762

3. 822

3.882

3.941

4.000

4. 059

4. 117

4. 175

4.232

0.5

0. 198

.412

.579

.725

.857

.979

1.095

L204

L309

L410

L507

1.601

1.693

L782

1.869

L954

2.037

2. 119

2. 199

2. 277

2.354

2.430

2.505

2.579

2.652

2.723

2.794

2.864

2.933

3.001

3.068

3. 135

3.201

3.266

3.331

3.396

3.459

3.522

3.584

3.646

3.707

3.768

3.828

3.888

3.947

4. 006

4.065

4. 123

4. 180

4.238

0.6

0.224

.430

.594

.738

.869

.991

1. 106

L 215

1.319

1.420

L517

1.611

1.702

1.791

1.878

L962

2.045

2. 127

2.207

2.285

2.362

2.438

2.513

2.586

2.659

2.730

2.801

2.871

2.940

3.008

3.075

3. 142

3.208

3.273

3.338

3.402

3.465

3.528

3.590

3.652

3.713

3.774

3.834

3.894

3.953

4.012

4.070

4. 128

4. 186

4.243

0.7

0.248

.448

.609

.752

.882

1.003

L 117

L226

1.330

1.430

L526

1.620

L711

L800

1.886

1.971

2.054

2. 135

2.215

2.293

2.370

2.445

2.520

2.593

2.666

2.737

2.808

2.878

2.946

3.015

3.082

3. 148

3.214

3.279

3.344

3.408

3.471

3.534

3.596

3.658

3.719

3.780

3.840

3.900

3.959

4.018

4.076

4. 134

4. 192

4.249

0.8

0.271

.465

.624

.765

.894

L015

1. 128

1.236

1.340

L439

L536

1.629

L720

1.808

L895

L979

2.062

2. 143

2.222

2.301

2.377

2.453

2.527

2.601

2.673

2.744

2.815

2.885

2.953

3.021

3.089

3. 155

3.221

3.286

3.350

3.414

3.478

3.540

3.603

3.664

3.725

3.786

3.846

3.906

3.965

4.024

4.082

4. 140

4. 198

4.255
HYDRAULIC DESIGN OF THE BOX-INLET DROP SPILLWAY 15

Summary (Outlet Design)

The preceding rules for the design of the outlet

for a box-inlet drop spillway may be summarized

as follows:

1. The critical depth in the straight section is

d.=^-

(Q/wy

g

(4a)

2. The critical depth at the exit of the stilling

basin is

det

■■^- g

(4b)

3. The minimum length of the straight section

IS

'=^'(w+0 (5)

for values of B/W> 0.25, Greater lengths

of straight section may be used.

4. The sidewalk of the stüling basin may flare

from 1 in 00 (parallel extensions of the

straight section walls) to 1 in 2.

5. The minimum length of the stilling basin is

(6)

for values of B/W>0,25. Longer lengths

of stilling basin may be used but it will

require less material if the straight section

is lengthened to obtain the same overall

outlet length.

6a. When the stilling basin is less than ll.ödce

wide at its exit, the minimum tailwater

depth over the basin floor is

¿2=1.64 (7a)

If the tailwater depth is measured from

top of the end sill, its depth is

d3=1.33dc, (8a)

6b. When the stilling basin is more than ll.ddce

wide at its exit, the minimum tailwater

depth over the basin floor is

ck=dce+0M2We (7b)

If the tailwater depth is measured from the

top of the end sill, its depth is

d^=0.S3dce+0M3We (8b)

However, stilling basins as wide as 11.5^««

may make ineflicient use of the outlet.

6c. Greater tailwater depths may be used;

lesser depths will cause more scour in the

downstream channel.

7. The height of the end sill is

J=d2/ß (9)

a.

c.

Longitudinal sills will improve the flow

distribution in the outlet. They should be

located as follows:

When the stilling basin sidewalls are

parallel, the longitudinal sills may be

omitted.

The center pair of longitudinal sills

should start at the exit of the box inlet

and extend through the straight section

and stilling basin to the end sill.

When We is less than 2.5W, only two

sills are needed. These sills should be

located at a distance p of 1^/6 to W/4:

each side of the centenine.

d. When We exceeds 2.5W, two additional

sills are required. These sills should be

located parallel to the outlet centerline

and midway between the center sills

and the sidewalls at the exit of the stilling basin.

e. The height of the longitudinal sills is the

sanie as the height of the end sill.

The minimmn height of the sidewalls above

the water surface at the exit of the stilling basin should be

f=d2/3 (10)

or greater. The sidewalls should extend

above the tailwater surface under all conditions.

10a. The wingwalls should be triangular in

elevation and have a top slope of 45° with

the horizonal. Top slopes as flat as 30°

are permissible.

10b. The wingwalls should flare in plan at an

angle of 60° with the outlet centerline.

Flare angles of 45° are permissible. Wingwalls parallel to the outlet centerline are

not recommended.

SUBMERGED-FLOW CAPACITY

Submergence decreases the capacity of the boxinlet drop spillway whenever the tailwater level

is nearly up to or above the crest of the box inlet.

There are many locations where high tailwater

levels may affect the flow, particularly in drainage

work or where the "island dam" type of design is

used. Therefore, an evaluation of the submergence effect is necessary in order to make complete

the information required for the design of boxinlet drop spiUways.
16 U.S. DEPARTMENT OF AGRICULTURE, AGRICULTURE HANDBOOK 301

In this report the submergence effect is measured

by the increase in head /\H over the free-flow

head H for the same discharge. The submergence

is measured by the height of the tailwater Ht

above the crest of the box inlet. The ratios AH/H

and Ht/H are used when plotting and analyzing

the results.

The factors that affect the flow when the tailwater level is high are discussed in the following

paragraphs. Curves for evaluating the effect of

submergence on the flow through box-inlet drop

spillways are shown.

Factors Influtncing Submergence Effect

Several factors that affect the free-flow capacity

of the box-inlet drop spillway have no effect on

the submerged-flow capacity; on the other hand,

some of those factors that have no effect on the

free-flow capacity do have a significant effect on

the submerged-flow capacity. The two factors

having the greatest effect on the submerged-flow

capacity are the discharge and the width of the

stilling-basin exit. They, as weU as several factors

that have no effect on the submerged-flow capacity,

will be discussed.

Discharge

The fact that the submergence effect varies with

the discharge complicates the determination of

that effect. Under some conditions the variation

is not particularly great, but under other conditions the variation is very large. The submergence effect increases with the discharge up to a

certain point, but with further increases in the

discharge the submergence effect decreases.

These facts may be verified by reference to the

submergence curves shown in figures 9 to 44

(pp. 17 to 35). The discharge that produces the

greatest submergence effect apparently coincides

with that point on the free-flow rating curve

where the control section changes from the boxinlet crest to the headwall opening.

Outlet-Exit Width

The flare angle of the sidewalls has no direct

effect on the submergence, but the width of the

stilling basin at its exit We apparently determines

the magnitude of the submergence effect. The

wider the exit, within certain limits, the less will

be the effect of submergence. Apparently, there

is httle or no advantage in making the outlet wider

than 1.51^, since with wider outlets the decrease

in submergence effect is nil. The effect of outlet

width can be determined by comparing the submergence curves for different outlet widths when

the otiier variables have identical values.

Other Factors

The length of the straight section of the outlet

has no influence on the submergence. Also, since

the presence or absence of bed and banks in the

experimental test channel had no direct influence

on the submergence effect, it is assumed that variations in the locations of the bed and banks will be

unimportant under field conditions.

Submergence Curves

The submergence curves shown on pages 17 to 35

may be used to evaluate the effect of high tailwater levels on the capacity of box-inlet drop

spillways. All attempts to systematize further or

condense the data proved unfruitful, and as a result the curves are more voluminous than is desirable. Even so, it is realized that the curves

presented may not completely cover the range of

conditions experienced in the application of the

results.

Each of the 36 appended figures represents a

different combination of B/W, D/W, and We/W.

Reference to table 8 will give the figure number

for any of the various combinations of variables.

The several submergence curves in each figure are

for different discharges and represent values of the

ratio Q/TF^/2 gq^al to 0.6, 1.0, 1.5, 2.0, 3.0, 4.0, and

sometimes 5.0 and 6.0. (Table 5-2 in King's

"Handbook of Hydraulics'' " gives the five-halves

powers of numbers and may be used to facilitate

the computation of this ratio.) Some curves for

different values of QjW^'^ coincide; others fall so

close together that it was not possible to show

them separately in the figures, and these were combined into a single average curve. The differences

between the extreme and the mean curves are in

no case greater than half the distance to the nearest

curve of 0.05 AH/H, whichever is the lesser.

Computation of Submergence Effect

The computation for the effect of submergence

requires a prior knowledge of the dimensions B,

Dy W, and We of the box-inlet drop spillway, the

discharge Q, and the tailwater level referred to the

box-inlet crest if«. The computation procedure

to determine the increase in head caused by

submergence is as follows :

1. Compute the ratios B/W, D/W, and We/W

and select the proper figure from table 8.

11 See footnote 7.
HYDRAULIC DESIGN OF THE BOX-INLET DROP SPILLWAY 17

2. Compute the ratio QfW^'^ and select the

proper submergence curve.

3. Compute the head H for free-flow conditions.

4. Compute the ratio HtlH, enter the figure

with this value, and read the value of uJl¡TI

corresponding to the intersection of HtjH

and qfW'^K

5. Multiply AHjH by H to obtain the increase

in head AH caused by submergence.

6. Add Ai? to H to give the actual head above

the spillway under submerged-flow conditions.

Interpolation will be necessary if values other

than those given in figures 9 to 44, inclusive, are

desired. If the discharge is not known, the submergence effect can be determined only by the

process of successive approximations.

TABLE 8.—Figure numbers for submergence curves

B D

WJW

W W

1.0 1.25 1.5 2.0

Í 0.25 9 10 11 12

0.5 .5 13 14 15 16

I LO 17 18 19 20

r .25 21 22 23 24

LO .5 25 26 27 28

I LO 29 30 31 32

r .25 33 34 35 36

2.0 .5 37 38 39 40

[ LO 41 42 43 44

FIGURE 9.—Effect of submergence:

R D W

^=0.5; ^=0.26; ^'=1.0.
18 U.S. DEPARTMENT OF AGRICULTURE, AGRICULTURE HANDBOOK 301

FIGURE 10.—Effect of submergence:

1=0.5; 1=0.25; fî=1.25.

AH/H

FIGURE 11.—Effect of submergence:

#=0.5; 1=0.25; ^=1.5.
HYDRAULIC DESIGN OF THE BOX-INLET DROP SPILLWAY 19

FIGURE 12.—Effect of submergence:

^=0.5; ^=0.25; ^'=2.0.

AH/H

FIGURE 13.—Effect of submergence:

1=0.5; 1=0.5; ^=1.0.
20 U.S. DEPARTMENT OF AGRICULTURE, AGRICULTURE HANDBOOK 301

FIGURE 14.—Effect of submergence:

1=0.5; 1=0.5; ^=1.25.

FIGURE 15.—Effect of submergence:

^=0.5; ^=0.5, ^^1.5.
HYDRAtTLIC DESIGN OF THE BOX-INLET DROP SPILLWAY 21

JÍ

\ // /

.<.^n

/

II—.^^""^ Á 1 i T'

^ 32 /' !.__ 1 c

'^'^^^^^^ 30

—' / ~~ — 4

"" /

/ ~ ~ 46 A /

/

/

H B ^ >^ /

/

AH/H 2 6

-- / 4 2

/

-

2 4

/

:--—

on-i \-y / H-Î X 1 v? ]l^-^~' T

/

r^ 3 8

/ 36

D

1"' "

B 1 1 e A / 3 4

1 6

/

/ 3 2 Ht/H

^1* 14

/

^

-'X .

/

2 y

1 0

\ /

\A ^ 11

0 8

4 r n

26

(^ V

Ö«

w."^-

y^' V

0^ «^ 1 \^\

V ,

f ;°

AH/H

^yP <? "^K Î

' ?f-'T ?

^

_^ DB g» S2 Si \^ è

-> ^11 r

-0 4-0 2 00 02 04 06 08 tO 12 14 16

H,/H

FiGUKE 16.—Efifect of submergence:

Ï|P—^-O, p;^—^.O, ^—^U.

FIGURE 17.—Efifect of submergence:

^=0.5,^=1.0,^-1.0.
22 U.S. DEPARTMENT OF AGRICULTURE, AGRICULTURE HANDBOOK 301

FIGURE 18.—Effect of submergence:

1=0.5; 1=1.0; ^=1.25.

FIGURE 19.—Effect of submergence:

1=0.5; 1=1.0; ^=1.5.
HYDRAULIC DESIGN OF THE BOX-INLET DROP SPILLWAY 23

FIGURE 20.—Effect of submergence :

1=0.5; 1=1.0; 5^=2.0.

FIGURE 21.—Effect of submergence:

1=1.0; 1=0.25; ^=1.0.
24 U.S. DEPARTMENT OF AGRICULTURE, AGRICULTURE HANDBOOK 301

FIGURE 22.—Effect of submergence:

1=1.0; ^=0.25; ^=1.25.

FIGURE 23.—Effect of submergence:

1=1.0; ^=0.25; ^=1.5.
HYDRAULIC DESIGN OF THE BOX-INLET DROP SPILLWAY 25

AH- '*-.. "— K—ÏH - X \?» ^^'^m ^ \

'—"^

_^ \

r

FIGURE 24.—Effect of submergence:

R D W _=1.0;:^=0.25;:^=2.0.

FIGURE 25.—Effect of submergence:

j^= 1-0, ^=0.5,^=1.0.
26 U.S. DEPARTMENT OF AGRICULTURE, AGRICULTURE HANDBOOK 301

FIGURE 26.—Effect of submergence:

1=1.0; ^=0.5; ^=1.25.

AH/H

FIGURE 27.—Effect of submergence:

W~ ' W~ ' W ~^'^'
HYDRAULIC DESIGN OF THE BOX-INLET DROP SPILLWAY 27

FIGURE 28.—Effect of submergence:

AH/H

FIGURE 29.—Effect of submergence:

^=10--5=1 0-2^=10
28 U.S. DEPARTMENT OF AGRICULTURE, AGRICULTURE HANDBOOK 301

FIGURE 30.—Effect of submergence:

^=1-0; ^=1.0; ^=1.25.

AH/H

FIGURE 31.—Effect of submergence :

^ in. ^ in. ^^-^ ^ 1^=1.0; ^=1.0; ^-1.5.
HYDRAtTLIC DESIGN OF THE BOX-INLET DROP SPILLWAY 29

AH/H

FIGURE 32.—Effect of submergence:

^_10. ^-1 0-^-2 0

AH/H

7^3-281 O—06 3

FIGURE 33.—Effect of submergence:

1=2.0; 1=0.25; ^=1.0.
30 U.S. DEPARTMENT OF AGRICULTURE, AGRICULTURE HANDBOOK 301

AH/H

FIGURE 34.—Effect of submergence:

B D W ^=2.0; ^=0.25; ^=1.25.

AH/H

FIGURE 35.—Effect of submergence:

1=2.0; ^=0.25; ^=1.5.
HYDRAULIC DESIGN OP THE BOX-INLET DROP SPILLWAY 31

FIGURE 36.—Effect of submergence:

#=2.0; 1=0.25; ^=2.0.

AH-J ' „^ jTrrrt:^\—Î"

H -

\ Xî*

1 1^

—^

t" J

FIGURE 37.—Effect of submergence:

1^-2.0, ^-0.5; ^=1.0.
32 U.S. DEPARTMENT OF AGRICULTURE, AGRICULTURE HANDBOOK 301

FIGURE 38.—Effect of submergence:

1=2.0; 1=0.5; ^=1.25.

AH/H

r

rti

ïï-^-SPî:Ï^

-0 4-02 00 02 04 06 08 10 12 14 16

Ht/H

FIGURE 39.—Effect of submergence:

1=2.0; 1=0.5; f--= 1.5.
HYDRAULIC DESIGN OF THE BOX-INLET DROP SPILLWAY 33

AH/H

FiGUKE 40.—Effect of submergence:

1=2.0; 1=0.5; ^=2.0.

J 1 —-____^

AH-j "•v Si H - X

t ^

^—t^ uT

FIGURE 41.—Effect of submergence:

1=2.0; 1=1.0; ^=1.0.
34 U.S. DEPARTMENT OF AGRICULTURE, AGRICULTURE HANDBOOK 301

FIGURE 42.—Effect of submergence :

B D W ^=2.0; 1=1.0; ^=1.25.

FIGURE 43.—Effect of submergence:

l^-^ö, ^-1.0, ^=1.5.
HYDRAULIC DESIGN OF THE BOX-INLET DROP SPILLWAY 35

FIGURE 44.—Effect of submergence:

B D W

1=2.0; 1=1.0; ^=2.0.

EXAMPLE OF APPLICATION

The hydraulic design of a typical box-inlet drop

spillway is worked out here to illustrate how the

design information presented previously can be

applied. A number of factors other than those

mentioned must be considered by the designer,

and they may require that the proportions of the

spillway be altered from those proportions which

are determined solely from hydraulic considerations. These factors are outside the scope of

this publication and will not be discussed here.

The design discharge, the topography of the

site, and the exit channel conditions will be assumed, since their determination is not a part of

the spillway design proper.

It is assumed that the design discharge is 200

cubic feet per second. The approach channel

approximates a trapezoidal section having a 45-

foot bottom width and l-on-5 side slopes. The

controlled drop through the box-inlet drop spillway is 4 feet, the crest of the box inlet being at

elevation 100.0 feet and the exit channel at elevation 96.0 feet. The exit channel has a 10-foot

bottom width and 1 -on-3 side slopes, and a depth

of flow of 4.3 feet, making the tailwater elevations

100.3 feet with the design discharge. With this

preliminary information at hand it is possible to

proceed with the design of the spillway.

The equation

-(sll)" (Id)

will be used in the preliminary analysis to determine tentatively the magnitudes of H and L.

This is tantamount to assuming that the box-inlet

crest controls the head-discharge relationship.

Later it will be determined if this assumption is

valid and shown that it is not, in this case; but

the computation must be made to make the determination. Substituting 200 for Q and disregarding for the present the corrections to the

discharge coefficient, H is as follows for several

assumed values of L:

L (feet)

H (feet)

10

3.24

15

2.47

20

2.04

A head of 2.47 feet is satisfactory and the length

of the crest will temporarily be taken as 15 feet.
36 U.S. DEPARTMENT OF AGRICULTURE, AGRICULTURE HANDBOOK 301

The following combinations of B and W will give

the required crest length:

B (feet) 6 5 4 3

W (feet) 3 5 7 9

BIW 2. 00 1. 00 . 57 .33

The box 3 feet wide seems a little narrow so the

next wider box will be chosen as giving the best

box width. Tentatively, then, the box inlet will

be 5 feet long by 5 feet wide.

At this point it is well to compute the head and

to assume the control to be at the headwaU

opening, in order to determine if this head is

greater than the head obtained when the control

is assumed at the box-inlet crest. The greater

value will be the actual head. With W=b,0

feet, JB=5.0 feet, and Z)=4.0 feet, the ratio DIW=

4.0/5.0=0.80 and 5/Z?=5.0/4.0=1.25. If figure

6 is entered with Z?/W^=0.80, it is found that

C2 V2^=3.10; if figure 7 is entered with B/D=1.25,

it is found that iZo2/P=0.55, from which i?02=0.55

times 4.0=2.20 feet. The assumed discharge and

width and the values read from figm*es 6 and 7

are substituted in equation 3b,

fl'= (200/3.10X5.0)2/3-2.20= (12.9)2/3

-2.20=5.50-2.20=3.30 feet

Since this is greater than the 2.47 obtained with

the control at the box-inlet crest, the control

section is at the headwall opening. The tentative

head of 3.30 feet is satisfactory for the conditions

assumed at the site.

Up to this point no attempts have been made to

determine the head accurately. Now that the

principal dimensions have been tentatively established, it is possible to do this. Because the

preliminary computations have shown that the

control is at the headwall opening, the head is

given by the equation

\C2

Q Y

W^gJ Ho' (3b)

Since the discharge coefficient C2 depends on the

relative depth of the box inlet, this depth must

be determined. (The end-sill height was neglected

in the preliminary analysis.) In the example the

controlled drop is 4 feet. The height of the end

sill will be taken as 0.6 foot, this dimension being

based on an assumed outlet width of 10 feet, a

computed dc of 2.3 feet (equation 4b or table 7)

and a computed dz of 3.7 feet (equation 7). The

box-inlet depth D is then 4.6 feet and D/W=

4.6/5=0.92. Reference to figure 6 or table 5

gives C2 ^J2g equal to 3.26. In order to determine

the head correction flo2 it is necessary to determine

DjW and BjD. Because Z>/IF=0.92>0.25, i?02/Z>

can be obtained from figure 7 or from table 6.

Since B/D= 1.1, H02/D is found to be 0.52. The

head correction i/o2=0.52X4.6=2.39 feet. The

equation then becomes

-2.39=5.32—2.39=2.93 feet

This head is not the final head because it must be

corrected for the effect of submergence. Also,

this head is somewhat below the 3.30 feet computed initially, but in the absence of cost comparisons it will be assumed that the lower dike is

economical and the discharge computations will

not be repeated with a box inlet having different

dimensions.

If a storm is to be routed through the structure,

it will be desirable to plot a head-discharge curve.

The first step is to determine the corrections

when the control is at the box-inlet crest.

The first correction is that for head. Computations of H/W for a number of heads and the

corresponding values of the head correction taken

from figure 3 or from table 1 are given in table 9.

The second correction is that for box-inlet

shape. Since B/W=l, the correction for boxinlet shape is 1.00, as can be seen by referring to

figure 4 or to table 2. This correction is also

noted in table 9.

The third correction is that for approachchannel width. The experiments were conducted

with an approach channel having a horizontal

floor and vertical sidewalk. Since this is obviously not a typical field condition, some means

must be found to express the field-channel dimensions in terms of a channel having a rectangular

cross section. It will be arbitrarily assumed that

the depth of fiow and cross-sectional area of both

the field and the rectangular channels are identical.

The width of the field channel is therefore taken as

Wc=AIH. In the example,

W,=(45+5iî)H =45+5iî H

The width of the approach channel has been computed, together with Wc/L, and both values are

given in table 9. The approach-channel width

correction is also given in table 9, the correction

having been obtaiaed from either figure 5 or from

table 3.

The fourth and final correction is for the

proximity of the dike to the crest of the box

inlet. In order to make the headwall extension

as short as possible, the toe of the dike will be

located 3 feet from the box-inlet crest. The

relative distance of the dike toe from the crest

X/W is given in table 9, together with corrections

taken from table 4.
HYDRAULIC DESIGN ^F THE BOX-INLET DROP SPILLWAY 37

TABLE 9.—Rating curve computationsfor example

[Assumed dimensions: B=5.0 feet; W=5.0 feet; L=15.0 feet; Z)=4.6 feet; X=3.0 feet; dimensionless ratios: B/Tr=1.0;

D/TF=0.92;B/2)=1.1;X/Tr=0.6]

Items to be computed

Control at box-inlet crest: H/W .

TTci

WcIL

Discharge coefficient—correction for

Head (fig. 3 or table 1)

Shape (fig. 4 or table 2)

Channel (fig. 5 or table 3)

Dike (table 4)

Corrected discharge coefiicient ^

^ Qore.t»

Control at headwall opening, QheadwaJi *—

H

0.5

0. 1

47.5

3. 17

.87

1.00

LOO

1.01

3.01

16

80

LO

0.2

50.0

3.33

,93

LOO

LOO

LOI

3.22

48

102

1 Trc=45+5H.

2 Uncorrected discharge coeificient=0.4275 V2^=3.43.

The discharge coeflBlcient is corrected by successively multiplying it by the corrections. For

example, the computation when H=0,5 foot is

Corrected coeflBicient=0.87 X1.00

X1.00X1.01X3.43=3.01

The corrected coeflBcient is given in table 9 and

is used to compute the discharge, which is also

listed.

The computations just completed apply when

the control is at the box-inlet crest. Because the

point at which the control changes from the boxmlet crest to the headwall opening is not known,

it is necessary to repeat the computations for the

beadwall opening in order to determine that point

EIS well as to complete the rating curve. It has

been determined previously that C2 V%=3-26 and

Z?o2=2.39. If these values are substituted in equation 3a, the discharge, when the control is at the

headwall opening, is

Q=3.26X5.00(ff+2.39)3/2=l6.3(fir+2.39)3/2

The dischai^e as given by this equation has been

Domçuted for the same values of JE? used for determining the discharge when the control was

assumed to be at the box-inlet crest. They are

listed in table 9.

It is now possible to plot the head-discharge

curve. This is shown in figure 45. The section

that controls the discharge is that section which

ïives the least discharge at a given head. The

actual rating curve has been drawn as a solid

line, whereas the imaginary parts are dashed lines.

The two curves intersect just below the design

discharge; so, for the design discharge, the headwall opening controls the head-discharge rela1.5

0.3

52.5

3.50

.97

1.00

1.00

1.01

3.36

93

125

2.0

0.4

55.0

3.67

1.00

1.00

1.01

3.43

146

150

2.5

0.5

57.5

3.83

1.00

1.00

1.00

1.01

3.46

205

176

3.0

0.6

60.0

4.00

1.00

1.00

1.00

1.01

3.46

270

á04

3.5

0.7

62.5

4.17

1.00

1.00

1.00

1.01

3.46

340

233

4.0

0.8

65.0

4.33

1.00

1.00

1.00

1.01

3.46

415

263

' Oore8t=(corrected discharge coefficient) Li?^/«.

' Qheadwall = 16.3 (i/+2.39)8/2.

tion, as was determined previously, and the head,

also as determined previously, is 2.93 feet. Although the intersection of the two curves of

figure 45 is sharp, the head-discharge rdation is

actually curved at this location. Nevertheless,

the curves as drawn are undoubtedly sufficiently

accurate for all practical purposes.

The next step in the design of the structure

is to compute the dimensions of the outlet.

The critical depths of flow both in the straight

section and at the end sill are required and should

be computed first. Equations 4a and 4b are used

for this purpose. The width of the straight section is 5.0 feet, and the discharge per foot of

width QIW is 200/5=40. From table 7, the

critical depth dc=3.68 feet. The exit of the outlet is assumed to be 10.0 feet wide, or equal to the

width of the downstream ditch. There Q/We=

200/10=20 and dee=2.32 feet.

The minimum length of the straight section,

computed from equation 5, is

¿5=3.68(0.2/1+1)=4.42 feet

It may be necessary to lengthen the straight section in order to permit the dam fill to be put in

with the proper cross section, and this is permissible. After the submergence computations

have been made, it will be possible to determine

the final height of the dike, the dam section, and

the length of the straight section.

The maximum permissible flare of the stilling

basin sidewalls is 1 in 2. In order to increase the

width from 5.0 feet at the end of the straight

section to 10.0 feet at the exit of the stilling basin,

the basin must be at least

10.0-5.0X2=5 feet long
38 U.S. DEPARTMENT OF AGRICULTURE, AGRICULTURE HANDBOOK 301

0)

4>

I 2

^

y

w

-/

/^

h^«^

^^ <-'

- 2.9 3—- —

^

^^^-'^

^

•

_^

/

^^

•

/

•

•

4

100 200

Discharge — cfs

FIGURE 45.—Head-discharge curve for example.

300

The minimum length of the stilling basin

computed from equation 6 is

Since the latter length is the greater, it governs,

and LB will be made 7.5 feet.

The next step is to determine the required

miniTmim tailwater depth. The width of the

stilling basin at its exit, in terms of dee, is 10/2.32

=4.3. This is less than 11.5, so equations 7a and

8a are used to determine the taüwater depth.

The required minimum depth above the stiUiugbasin floor is

¿2=1.6X2.32=3.71 feet

If measured above the top of the end sill, this

depth is

¿8=1.33X2.32=3.09 feet

The depth íQ the downstream channel is 4.3 feet,

and the depth naturally obtained is therefore

adequate, if it is assumed the top of the end sill

is located at the channd grade or elevation 96.0.

If desired, the stilling-basin exit could be narrowed

somewhat so as to obtain a ¿3 closer to the depth ÍQ the downstream channel. The computation

might proceed as follows:

and

¿3=4.3 feet

¿,,=4.3/1.33=3.23 feet

From table 7, e/íí^e=33. Since 0=200 cubic feet

Çer second, Tt^e=200/33=6.06 feet, say 6.0 feet,

'his would then be the minimum outlet width

that could be used with the assumed tailwater

depth. Nevertheless, in this example a width of

10 feet will be used. In an actual design the

•width providing the most economical solution,

probably the 6.0-foot width, would be the logical

one to choose.

One other point should be made regarding the

elevations of the outlet floor and the end sill

relative to the available tailwater dei)th. If dj

and ¿3 had been greater than the available tailwater depth, the outlet would have had to be

lowered sufficiently below grade so that the elevation of the top of the end sill plus the required

tailwater depth ¿3 would have given an elevation

not higher than the tailwater depth naturally

available. However, if it had proved undesirable

to locate the end sill below grade elevation, an

alternative would have been to increase the outlet

width sufficiently to reduce the required ¿3 to the

depth naturally obtainable. The procedure for

making this latter adjustment has been outlined

above.

For the design of the details, the end-sill height,

computed from equation 9, wiU be/=3.71/6=0.62

foot, say 7.5 inches. (An end siU 8 inches high

could have been used, 7.5 inches being chosen

because it is the width of an 8-inch board.) This

final end-sill he^ht should be compared with the

he^ht assumed when the head-discharge curve

was computed with the control at the neadwall

opening. In this case the difference is 0.62—

0.60=0.02 foot and is so small that it can be safely

neglected. However, if this difference had been
HYDRAULIC DESIGN OF THE BOX-INLET DROP SPILLWAY 39

large, it would have been necessary to recompute

the head-discharge curve.

The number of longitudinal sills required

depends on the ratio WelW=10l5=2, Since this

ratio is less than 2.5, only two sills are required.

These may be located from 5/6=0.83 foot to

5/4=1.25 feet either side of the centerline. If the

sills are used to strengthen the floor slab, their

location within these limits will be determined by

structural considerations. Here, the centerlines

of the sills will be located 1.0 foot either side of the

centerline.

The minimum height of the sidewalk above the

tailwater level, computed from equation 10, is

¿=3.71/3=1.24 feet

The top of the sidewalk at the stilling basin exit

should be 4.3+ 1.24=5.54, say 5.5 feet, above the

top of the end sill.

The angle that the wingwalk make with the

outlet centerline will be assumed as 45°. The

tops of the wingwalk will be sloped to fit the dam

fill, and the walls will be terminated where their

tops disappear below the surface of the ground.

A better arrangement would be to extend the

wingwalls until their tops are at the level of the

end sill, but here the risk involved in shortening

them is not felt to be worth the extra cost of

extending them.

In the example, the tailwater depth for the

design discharge was purposely made deep enough

to cause submergence, to allow illustration of the

method of computing this effect. To determine

the proper submergence curve, it is necessary to

know the magnitude of the ratios B/W=l.Oj

DIW=0.92, and WJW=2.0. These ratios were

I computed earlier. Entering table 8, it is apparent

I that the submergence effect must be interpolated

between figure 28 where D/W=0.5 and figure 32

whereZ?/Tt^= 1.0. Because Q/T^^/2^200/55.9=3.6,

it will be necessary to interpolate between the

curves for QIW^^^=3 and 4 in figures 28 and 32.

The free-flow head is 2.93 feet and the tailwater

level is 0.3 foot above the crest of the spulway,

making the ratio 2î,/i?=0.3/2.93=0.10. The

submergence curves are entered with this flgure

and values of AH/H read off. The interpolations

are made in table 10.

TABLE 10,—Values oj AHIH jor B[W=LO,

WJW=2,0, and HtlH=OJOJor example

Q

D/W

0.5 0.92 0.1

3.0 0.01

.00

.00

0 02

3.6 0.02 02

4.0 02

The desired value of AH/H is 0.02, from which

Ai?=0.02X2.93=0.06 foot

and the head for submerged flow is 2.93+0.06=

2.99 feet. A head of 3.00 feet will be used in the

subsequent design.

These computations have determined the submergence effect at only one discharge. In order

to route a storm through the structure, it will

be necessary to compute and plot a tailwater

rating curve and then to determine the effect

of submergence at a number of flows so as to be

able to plot a rating curve for submerged flow

similar to the free-flow curve shown in figure 45.

In accordance with standard practice a freeboard of 6 inches is required to the top of the

headwall and a freeboard of 1 foot is required

to the top of the dike. The top of the headwaU will therefore be at elevation 103.5 feet

and the top of the dike at elevation 104.0 feet.

The design of the spillway is summarized in the

plan and section shown in figure 46. It will be

noticed there that it was necessary to increase the

length of the straight section from 4.42 feet to

5.0 feet in order to provide an adequate cross

section to the dike.

Although field problems will probably differ

considerably from the assumptions given for this

example, it is felt that most of the conditions that

might be obtained have been illustrated. The

best design, of course, depends on the skill with

which the designer applies the methods to his

particular problem. The attempt here has been

to provide the information that the designer

requires to compute the proportions of box-inlet

drop spillways.
40 U.S. DEPARTMENT OF AGRICULTURE, AGRICULTURE HAJSTDBOOK 301

-4- 7—r-^-i \ r—T-H n ^

Plan

5-6" -99-

Section on Center Line

FIGURE 46.—Proportions of box-inlet drop spillway for example.

U.S. GOVERNMENT PRINTING OFFICE : 1966 O—^793-281