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Masters Theses Student Theses and Dissertations

1965

Discharge characteristics of side weirs Discharge characteristics of side weirs

Edgar Snowden

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DISCK4RGE CHARACTERIS::rrcs OJ.11 SIDE ";,JEIRS

EDGA:2 SNO\')])EN IV

submitted to the Faculty of the

T.J?-:~_:\TERSITY ,JF MISSOT.JRI AT ROLLA

DEGR~E OF

NAS'.:2ER OF SCIEl'JCE IN CIVIL E>:GL\JEERINCx

Rolla~ JYlissour·:L

1965

APFRO"VED BY

u~ (advisor-) --~"~'":j _J_,, _Q~~

f2L£~ ~_Jti_~

ii

ABSTRACT ,

The purpose of this study is to investigate the division

of flow of Hater in a flume of rectangular cross -section l'lhen

the flume is prc,•ided with a side weir. An equation has be~:~n

derived so that the quantity of water flowing over the side

weir compared to the quantity of water flowing in the main

c:-.. annel can oe predicted. This ratio is acceptable only

"

within the ranges of heads) velocities, and weir lengths im-

posed by the geometry of the system tested.

i:..i

A CKNOvlLEDGEMENT

The a~.~--~::-lor wishes to express his deepest appreciation to

Professor V.A.C. Gevecker for his consideration, encourage­

ment, interest, and helpful criticisms throughout the research

and writing phases of this study. His guidance has made this

thesis possible.

iv

TABLE OF CONTENTS

Page

ABSTRACT .......... . ii

ACKNOWLEDGEMENT ........ . iii

LIST OF ILLUSTRATIONS ... v

CHAPTER I

Introduction .. ...................................... l

CHAPTER II

Review of Literature ......... . ..... ' .. ,. ....... . 3

CHAPTER III

General Discussion of the Problem................. 11

CHAPTER IV

Test Apparatus . . . . . . . . . . ' ............ . CHAPTER V

Test Procedure.

CHAPTER VI

Test Results .... . . . . . .• . •

CHAPTER VII

Conclusions.

CHAPTER VIII

Recommendations ..... . ...................... " .... APPENDIX ..... · ..... . . . . . . . . . .......... , .. BIBLIOGRAPHY. . .............. . VITA ........................................ .

20

39

L..., •..!..

7?

78

Figure

l

2

3

4

5

6

7

8

9

10

LIST OF ILLUSTRATIONS

Test Apparatus ................................. .

\<Jare Suppressor ................................ .

Head-Measuring Gace ............................ .

Calibration Curve - 12 -inch Su.p:oressed \IJeir ..... -

Discharge -Head Curves f'or S i.dc \·J2ir-s ........... .

Flow-Length- Head Ratio Curves for Side Weirs ..

Depth-Energy-Discharge Curves .................. .

Comparison of Flows- Oblique View ............. .

Comparison of Flows- Side View ................ .

Comparison of Flows - End View· ................. .

v

Page

15

18

19

22

25

28

35

37

38

vi

Gertrude Stein lay dying. About her gathered her rriends~

the great authors and artists or her· day·. 11 ~\l:.at_. 11 she asked,

nwhat is the answer?'' After a spell of r.onc'.erous silence,

she sparkled. 11 Well ~ gentlemen~ ir no o·,1e knows the answer~

what then is the question? 11 And died.

CHAPTER I

INTRODUCTION

1

A study o:f the characteristics of :flow over side weirs

was suggested by a report on the research conference o~ the

Irrigation and =~ainage Division of the American Society of

Civil Engineers held at Logan: Utah, during March, 1964.

This is not a new subject. It is a problem dealing primarily

vli th division of flow about which little is known.

Side weirs have many applications. The research con-

ference was specifically interested in the relief of excess

flows in irrigation channels by means of side weirs when the

channels are subjected to inflow from adjacent watersheds.

Problems solved by side weirs have ranged :from the regu-

lation of :flow in diversion :flumes in Tasman~a, to· the sup-

pression o:f waves in canals in Italy, to tt-.;.:-· ;-rotection of

Hoover Dam against ovc-:etop.~:J:..ng. At t:i:1e pre.:>S.t<~:- ti:ne, the

U.S. Department c:·· ,:.gf."'j_-:;n.lture and the U. 3. ::.;,;;;::x.::<~rl'l.ent oi~

the Interior a:.~ ... c :ln\>):C.s~,·i:;ed in the feasibilj. ti •:::'' discharg-

ing excess f'lo~,r in ir·rigation channels ir.to J:";r: .... c ·; rsvines

in order to prevent the flooding of developed :2.

The research :for this paper comprised ;:; ,, -;~udy ·')f the

phenomena associated with the division of flow of water in

an open channel. The flow was divided into ti'I!C parts, that

which continued ~n the op~~ channel and that which flowed

ov~r --~ s.1d~;,. weil:',it,;,(.:tz'h~~,.:~*D~'~:t+sa't;:1on _.·a,tudied the effects ot: ~·<· .. ,) . . ,: .. :~«~,·:"'' , ... ' ·., ' , . . ·'~~:;·, ~:,~. ':·· ..

', . .<, i"(,<> ; ¢;•'.f ~. ·_,.,

2

geometry on the quantity of flow over the side weir .

•

wri~incs and experiments

·; . ... _ .. clc...-:..:-::.) .L~r·

also clouded by their varied and unwaverin~ conc:us~ons. On

one point some asree: t~e installation and location cf ~

weir give it various characteristics which require t~~t an

the Fruehling formula for flow over a sid2 weir

where

Q ·i -'""1 !.. ~ _-: '-·· .._.·

H

enC c: t~e sill.

They notice~, contrary to t~eir observatis~~.

stated that the failure of "co

~orm as desired was due to their low efficiency and that the

len;:>;ths given to tllese v.J:::::.

velocity of flow.

sur~ace had flattened out a~ ~his increase~ aep~n.

die~ r.ot occur. In explanation, tt1cy could on~y s~~~c~~

Co le::nan and S:;<:

_ .~sr ~edified to include the . ; "" ' - .. ~

the weir length req~~~ea ~o

ma~n flow to a given level~

~he ncad on tha upstream end of the weir,

the head. on the downstream end of the weir, and V is the

average ·/clocity in the main channel. By assigning values of'

··' )

!;j = 10 1 J v -- l1 1 <~2 - "-T J and.

they illustrated the inefZicie~cy of the systc~:

velocity of three feet per secondJ a weir lsngt~ oZ 86 fe~~

was required to reduce the head 3.94 feet; a velocity of

i"'i VG fer.:;t per second required a length of 114 foe"~.

equation is more striking when efficiencies are disresarded

and the original tnov.ght pursued. At what len6tl'"l of sid~o:

•qeir j_s the flow reduced to sj_ll level? :B'or t:r~e dov;nstrearn

head (yl) to be zeroJ the length of side wei~ ~~st ~e

infinite!

posed the formula

where H is the head on the downstreax end of ~~c side weir.

cr.ar ... nel.

t , l . - " . l 928 4 His repor was puc lsnea ~n -. .

of momentum and conservation of' ene::r."gy to tr1e :flow of l'lat<-'~r

over the sides of trapezoidal channel3.

ment with I-Unds 1 theory by allm>V~i..::.1.g i1i:::- c:. ·-:: ;_;i:c-1al trapezoidc..l

channel to .s.pp:c_:_;d.ch one of rectanguj_ar c:o:,:->s -=~ection. Hence,

6

the water while it is p~s~lng over ~h~ weir.

C(.;;.ssion to r:is ovm

fied Bernouilli equation,

Q Ch'H"\; 2g

v-Jhere

c 0.6

H = head on a-t upstream end. of.·

weir

decrease in velocity.

Tyler~ Carollo_,

tc

-formulas pr·e s eo_~~ t ly in use. ::::J

the c.::::.e of the Coleman-SmJ.tL rormula.

and Smi t:r~ froni further consideration~ suggesting that the

7

similitude in ad~~ting the results of their expcri~e~~~ ~o

p::c·actical use. n6

Tyler and associates lJlo-'cte:d ti1\Jil~ o~~:1: da.. t::~ aca::_~~3 t

did not agree. A larger. v~r:~~lc cocf~icient was i~dicatcd.

For a weir length of one and one-half feet, t~GY ~ou~d t~c

be expressed as a f'unctj_:::w ._,.,_

:investigated t1-:e establ·i~~-.::·.:-:.:::. , _ _._L

.f'or;;,ula for weirs with eno. con·crac 'v:Lons Lo predict t£-1e per-

formance of side we:'"-rs ~

wr1ere

b = 0.1

L = actual length of weir crest

N numce:c of end contractions

bette~ suited for siae weirs, althou~~ in extreme c~scs

Ernest .··. Schoder and Kenneth B. 'l'Ur::-J<;;:· :::.c.:.::<:tioncd t.:·:.s

c as~Lc weir formulas, and after twenty-fi ·.r~:: '".;,nc~::c-ed. t;ests

found the: .. the immediate problem was not or.e oi· side weirs

rather of weirs in t:,eneral. cor: i't;.. s i ::;; ll ,,. :C~1

.Ce::oence to the m. a·,--,ly ,_-,....,...!..-' :-d- -~ rl,'·:.·"·. 0-, r.;,;-v-,r:>r· {· "1Y>Y" <·',--.·ow-·- ; C• C' • 7 .1. .. 1 J..J v.r_ ,._,. ._._._.._ ~ c .. !....·--.!.>~'-- ~ vu ...... ~I -L \._)...._ .. :,LA.....L.:...::..~...).

B head on weir rneasured at t1-:e beginn:J..ns:; oi' tLe o.::.."'s.\·I-

down curve

Va the mean velocity of approach above the weir crest

measured in the cross-sec~icn as H

measured in the same cross-section u~ H.

To this paper, R. L. P(-},l~s~:.a~l..l ~ceplit:.:d t:-~a t l1i s exr)e:ci-

once with water led hirn to doubt 11 :::...::-- there :'t.s any suc!'~ thints

as precise weir n8 meat:.urenc;;t::~. Clemens Herschel~

8

President of the A • S . C • E . , added two quotes to the disc:us:::ion

of the paper:

and

Dani2l 3ernouilli of~en said to rr:e ~o 2~c~e~ a 11 cor:~·:·:·~~ -~-- ~; 2.:- ~-J c:d. r-. o r·:rLLll ~ls : i1e l~e ~- i e '1~n 8 tl1.s.. .. c ~~::e ·.::- ~ ga~n.i­za ti . ..JD ;::; ~~- Natu:::-e is tc;,o s :Lmple to lea.d to tl:ceiT:; and should sne :ind such, ~he explanation is tha~ one 1 s computax:J..Dns were based upon f'alse hypotheses. :19

11 Tt~,::;se things are beyond all use~ ar1d I G.o fC:'C..J:' 'Gi"r~ .. :. nlO

T·::::::: .. .:.s R. Camp f'ollowed Hinds 1 energy-momentum r.1ethod.,

establishing Hind~ 1 equatjon in differential for~.

c~annels to obtain the surface profile of the water in the

"' -; d.- " C '~ r n"'" e -.l ll ......., __._ ...:... l.t. C).. ..... .1. •

Edwa::c·d I-I. Taylor used an altogether nevJ approaci~. He

prov_ -~ a graphical solution to the division of water a~

.~unc ~..;ions. He reasoned that the momentum equations are

complicated in cases of flow division by the inclusicn o:

three depths~ and that to assume a relation among t~em was

to assume a solution to the problem. Ee remained ~i~~ i~

h~2 belief that a rational analysis of division o~ flow

pi·oblerns is r1ot --, r

practicc.l _ _~_e::

Harold Tults studied water surface p~ofiles associated

with side weirs and found

ity distribution in the cross-section, snd ~~ the locatio~ o:

"che spilJ.··ay in the canal. nJ 3 For a s:c. ~- r -.~. s id2 '::c ::..:c·

located in the middle of a long canal~ ~e

by the maximum permissj_ble conveyan> ::3.e~".,

head in the upstream fl.::Y;-: is :Ligher than C.owr:2. the

,,-- ,. -.-.,-"Y by "',"-. ..-.J.· c +-_-l_on 1114 the e:,.cces~·. , ~ -~~--·--_ .... _ c~ \ -- ~ ~..~_ ~ ·

. l r­

J:'C::CE:Dt tex~.-? Two of these pro-

files ,~~- exist only when critical or supercrjti~al flow

2.0

exi;c;ts .. HJ:"lich restricts tl'h,; s::...lrf'ace shape in the :-::.o:r-·c us:.;.::Ll

cases of flow to one of only three possibilities.

~~e effects of the location or inlets and ou~lots o~ a

system was throughly studied by the Bureau of Reclamation in

a model study 6f the Boulder Creek supply C <">"(1<=l..l~ 16 \,...(,.-_c.;.. •

had been designed to include two drainage inle~s and two over-

flow sections. It was found that the cap&city and location

of the overflow sections were not entirely satisfac~ory.

Specifically.. ti1e study indica ted "that a snort sid·3 v-:c: ir· was

more efficient than a long one_, a side weir was more efficient

when located upstream rather than dovmst:c·eam from an :.:._nlet_,

and that the flow depth imrnediately upstr·eam cf thG •:;eir· v:as

alvmys less than that depth irnrnediately dcwnstreaii1.

This lengthy review of literature is by no means a com-

I . d plete resume of all the works en side weirs published urins

this century. It is a su.m:rnary of severaJ. of the r::ore impor-

tant papers availeJ:.'le t;o t:ne a.u.thc:r·.

CHAPTER III

GENERAL DISCUSSION OF 'I':HE PROBLEM

-. i ..I....L.

Little is known about the behavior of floH of vJatc::r ove:::·

weirs and less is known about the division of flow.

the necessity of research in the field of side weirs ~s in-

dico.. ted~ the research mic;ht be directed tcn·Iard any or:2 of

many problems.

ri&lize and each study demands further investigation. A

fundamental and hopefully useful characteristic~ whicn warran~s

study~ is that of the ratio of flows. In conductins this

ing the study to just that.

relat~ the quantity of flow over a side weir to t~e ~uanci~y

remaining in the main channel of a rectangular flume.

numerous equations are available to determine these rel~tive

flows~ mode 1 studies have ctQ;ain and agD.in proved the tl-:.eo::::-·e-

tical predictions to be of dubious value. Is there ~hen any

relationship ~o be found?

What are t!-.c L·dc::;pe~cdcnt variables? ·.:·r::.e lengt::·1 of the

weir) the es o: discharge~ and the ~--' l. '

easily ~· ~~ureo q0antities.

used ~ ~ measure of the flow over the si~c ?he c.;.p-

s trea:-:·. ::..:Kl downstream angles of discharge ('::-: cons icwred

impor".. .. t because they are dictated by the -._,:::-:loe:::..ty of' t:.:1e

flow in the ma~n channel and the head on t~e ~2~r.

l •:)

Division o~ flow should vary with the heads ~nvolved.

Where should the heads be measured? Since previous studies

included the immediate upstream and downs~ream heads, a

r·elation with only one head i"las sought. A knovm head, imwed-

iately downstream, does not mean that an equal and constant

head exists for the rerna~nder of the channel, beca~.;.se the

level of the i-Jater continues to rise do·,mstream from the side:

weir. The head considered ~-:ere, then, is t~>-::e head consid,::r-

ably upstream o~ the side I:Wir. Tl.:Lr.:> hea'-.1. was allov-.red to

vary and the ef~ects on t··le di vis}.on of fl.ovv- were measur·ed

in this study. To reduce "cl1e D."i..l.i-:lber of variables, a constant

height o~ weir crest and n constant bottom slope of zero

were used.

The problem was restricted further by the decision to

place the side weir midway in the length of the flume, makin££

this study one pertaining more to irrigation channels than

to dam spillways. Such a decision influenced the surface

profile that was obtained.

Quantity, head, velocity, weir length, and angles of

discharge were the variables, and the constants were the

geometry and ro:..~ghr.ess of the flume, the pos 1 tion and con-

struction of i::i.-:.e ·:;;.::::lr, c.r.c. the physical pror ... c~:eties o:f:' 1:vater.

'• Tt.is test .... :. :·.:odel study without a 1-c::..cv.;r. 9rototype.

Although data o·c·cu.::..:.:l.::d using the smaller wei r·s v~er:: used to

predict the characteristics of the longer we~rs, i~ was un­

fortunate that the results of this laboratory test could not

13

be compared with those of ah existing canal. Geometry of the

cons true ted :flume limit the application of t.he re'sul ts to

flumes of similar ph~sical dimensions and not to flumes in

general.

CHAPTER IV

TEST APPAHATUS

11..:-

The tests conducted in this investigation were performed

in a square wooden flume (Figure 1) designed and cor~structed

by the author. Because laboratory space was critical> this

wooden flume was constructed inside a much larger plexiglas

flume which immediately established the limits of the dj_;·nen­

sions of the wooden flume. The plexiglas flume measured 36

feet in length~ and 2 feet in both height and width. The

plexiglas flume was set to a zero per cent slope with a

Dumpy level. A maximum delivery of water only half filled

this horizontal plexiglas flume. The maintenance of steady

flow was difficult.

To simplify measuremc::nts and computations~ the dimensions

of the main channeJ. of' t:·.·_, wooden f'lume were chosen to be one

foot in width a~~ one ~oot in height. T~c :ength of the main

channel of th"::. .~;;c.\;~er flume was chosen tc -~:c_:.~:,~~ ·::;:r:c- 36 foot

length of p:;.~__ . <~ _:;; flt:..n:;e. Placement of t.r~c, ~-,..':..de ·::.,: ~: 2 m:2.dway

in chanr.e:i. a.~·- .-.:Y.\1 C~d. 18 feet for stilli~J.g before the ·A'·=J.ter

reached _ ___ ,10~ '-lei::- and another 18 feet for fur·:_;>_·J:t> still-

. ing be:f"c:.: ; ' ... ~ •.. ~e~ ~eached the end weir .

:L'Lc: wate:..·· ::~c~SSlng over the side weir vva3 car2::...ed in a

secondary flume parallel to the main channel. The dimensions

of this secondary flume were 8-1/4 in-:::hes wide and 12 inches

high. •

:.6

The flume was constructed of exterior-grade plywood

treated for water resistance with PENTA~ a sealing compound.

This procedure rendered t:'ne plywood useful throughout the

testing phase or the investigation. The side panels were

1/4-inch thick~ which proved to be unsatisfactory since they

were still subject to bowing even after horizontal and verti­

cal braces had been placed every two feet. The bottom \v-as a

satisfactory :i./2-inch thick. All joints were made watertight

with a water-resistant~ powdered glue and with coatings of a

polyester varnish. There were no leakage problems.

The suppressed weir at the end of the main chanr:Gl was

1/~6-inch galvanized sheet metal~ which had been file~ to a

sharp edge. The weir was placed with its edge 2 inc~es above

the channel floor.

The rectangular side v,eirs were cut ·':rc:r. 26-gc...ge ga..J..­

vanized sheet metal to lengths of l-1/2~ 3, 6: 9o :2. 24; '36,

and 42 inches. Each side weir was placed with its edge 4

inches above the main channel floor.

To facil~tate placing and removing the side weirE, 2.

rur1ner, providing . a watertight seat, was fitted into the f>ide

and bottom of the channel. The runner caused a smali amount

of distortion in the flGw of water, but the amount waa less

'chan vii:1at rr;ight have been experienced had v1ood screws been

used to fasten each weir to the side of the flume ..

Various thicknesses o~ honeycomb baffling were used at

17

tr"'e up~3tream end of the main channel :::.n order to reduce tur­

bulence. A ch~et one inch thick was found to be ·the most

effective. \IJ"ave formations were reduced by floating a mat

of wooden slats on the surface of the water for the first

10 f-2-et of channel length (Figure 2).

Heads were measured with calibrated dials and rods

placed 6 feet upstream from each weir (Figure 3). Heads

could be measured to a thousandth of a foot.

The water supply was obtained from a 5 inch pipe con­

nected directly to a 12 inch feeder line. A gate valve in

the line was used to control the rate of flow. The water

passing over the side weir emptied in"Co a weighing tank

which was mounted on a sca1e -~vi th a capacity of one thousand

pounds.

Time was measured with a stopwatch reading to ·:·.,;e near­

est tenth of a second.

Figure 2

Wave Suppressor

J.8

19

Figure 3

- .Head - Measuring Gage

20

CHAP'I'ER V

TEST PROCEDURE

The scales :for weighing the water flowing ove:::-> the weirs

were calibrated by the use of standard weights. The weighing

tank on the seaL:::> had a capacity of' five hundred pounds of

water. In the range from zero to five hundred pounds the

scales indicated no appreciable diff'erence from the standa~d . weights. No adjustments or corrections were theref'orc ncces-

sary.

The stopwatch used for the experiment was assumed to be

accurate~ but since the same watch was used in all t~a test

any inaccuracy would affect each test similarly but not sig-

nif'icantly.

sarr;e readings - \_. ... -the channel

:floor and the ·~(_)_) or· an iron bl·.:>Ck placed c_,r: ·:.!·l.: :'L,.J..nnc:l

:floor.

The suppressed weir located at the end of tne ~na~n

channel was calibrated by 48 test runs during whic~ the side

weir was barricaded. Heads r,vere measured six :feet upstream

of the suppressed weir. The scales were placed beneat~ the

discharge :from the suppressed weir and the scale ar·m was

weighted lightly. When the weigl:.t of' water in the weighing

tank was suffic~ent to raise the scale arm~ the stopwatch

was activated. A heavier known weight was placed on the arm~

21

and when the weight o~ the water raised the scale arm again

the time was recorded. The quantity o~ flow in cubic feet

per second v;as computed to three signi~icant ~igures" since

head and time each contained three significant figures.

Qu.antity (Q) was plotted against head (H) on logarithmic

paper (Figure 4). To obtain the equation of the line best

~1 tting these points, the method o~ least squares vms applied

using both the desk calculator and the digit'al computer. The

quantity-head relationship given by both methods a~reed:

This is in reasonable agreement with the familiar Francis

~ormula:

Both equations give quantity per foot of crest. The di~~er­

ence between the two equat:Lo:~s was cnO'tlg:~. t,.: :"eject tne use

o~ Horton 1 s tables based on the Francis ~o~:-.:1:.J.a_, and instead

a_ graph was drawn accord:.ng to the experimer,t;;1.: eq_uation.

Quantities could be read from this graph to three 3~~nificant

~igures. The pe:d'o:rmance of t:;his suppressed we:i..r :::_::;_}_owed

the reading of q~antity of flow from measured heads ~ithout

having to m8.<:, i."<::::'...·ghings o~ main channel flow.

The barrier across the side channel was removed. The

side weirs were tested in order of increasing lengths. Heads,

measured six feet upstream ~rom both the side and suppressed

end weirs, were allowed to vary. The water ~rom the side

weir was caught and weighed in a manner similar to that used

22

i .. i.

0 z 0 0 w (j)

0:: w Q_ t_i

1-w w LL

0 m :::> u z

a w (:J 0::: .q I () (f)

0

,02 .03 .04 .05 .06 .08 0.1

HEAD ( H) IN FEET

DISCHARGE ( Q) VERSUS HEAD ( H >

CALIBRATION CURVE FOR 12-INCH SUPPRESSED WEIR

FIGURE 4

23

in calibrating the suppressed weir. Measurements were taken

of the upst:..""'eam and dov.r.n::.;-'c.ream o.nglec of discharge of water

over the side weir. Side weir discharge was measured for at

least twelve different heads for each size of weir. Suffic-

ient check runs were made to insure accuracy of measured

quantities. Five minutes were allowed to elapse between the

opening or closing of a valve and the measurement of a head.

There was a definite trend to the data collected~ but

when this trend deviated at longer weir lengths the following

check on the data was made. The barrier was placed across

the side weir and the flume was allowed to flow nearly full.

After thirty minutes the flow was measured and was proved to

be constant. The side weirs were then successively placed

in this channel of constant flow. The heaJs on both weirs

were measured. The flow from the side wei:.· v:s.:.:.. l:Jeighed and

added to the flow over the suppressed weir. Ti':e s:J.:o:r. of the

flows equalled the total constant flo'.'/, After- ea.:::! side WE:."ir

checked, the barricade was again inserte~~ and ~h~ quantity

of flow in the main channel was reduced. .--·· . ' '.;:.c-12 exper:unc:;nt con-

tinued similarly after another thirty mirwte wait for co~stant

flow to be assured.

The digital computer was used to calculate the quantity­

head relationship for each side weir by the method of least

squares.

CHAPTER VI

TEST RESULTS

24

The :first test was per:formed to correlate· the discharge

o:f and the head on the suppressed weir at the end of the main

channel. The relationship was :found in equation form

Q = 3.78Hl.5l

per foot of weir crest. The difference between this equation

and the Francis formula was not significant. A comparison of

exponents indicated acceptable test procedures. The var· ·::.nee

in coefficients allowing discharges ten per cent in excess

of the Francis formula was attributed to the inherer:c prover­

tiee. of' the constructed flume and vleir and to the relatively

small heads to ~hich the equipment was restricted.

Each side weir was analyzed "':;C> dete::·;·;_: .. --.. 2 if' an elementary·

equation for discharge could be found. W~~~ ;:otted on log­

arithmic paper~ the data showed that fo1 . ., <;. g:i.v-.;.~n side weir an

equation of the form

Q == cnN does exist. To determine the equations for the lines best

fitting these sets of points~ the method of least squares was

used. 'l.'he results are shown in Figure 5. On this gra:ph~ the

points represent the obser\red data~ and the lines are drawn

according to the calculated equations.

If the equation for the 12-inch weir· had been known, the

0 z 0 0 w (f)

0:::: w Q_

1-w LJ..l LL..

0

a: ::=> 0

z

w (!)

0:::: <( I 0 J)

0

0 0

.01

DISCHARGE

WEIRS OF

25

(';'? • .J <- .0.::> .04 ,05,06 .08 c.: 0_2 0.3 ,...., -~

v;-r o.::-: o.s

HEAD ( 1-n IN FEET

( Q) VERSUS HEAD (H) FOR SIDE

VARYING LENGTHS ( L)

FIGURE 5

equation ror the smaller weirs could have been predicted by

reducing the coerficient in proportion to the change in we~r

length. The equation for a weir longer than twelve inches

could not have been predicted within reason. It is inter-

esting to note that the.predictable weirs were subjected to

greater ranges or head, velocity, and r1ow. It app~ars that

the practice of using a suppressed weir formula to predict

diacharge over a side weir is justifiable within a range or

r-elat1vely small main stream -Jelocities, heads or.. side weirs,

and weir lengths.

Attempts were made to inspect visually the flow of water.

It was found that streamline flow did not exi3t, confirming

the work of Coleman and Smith. The two methods used to

visualize flow "~Jere c:rude. T:h.e dye injection method indicated

that a strcanl~:.;.::; ·;;as ::'..iable to c.hange its direction at any

moment regard:sss or time or head. Turbulence prevented the

dye rrom defining any prolonged strea:;-:~.~-::J.e. An air bubble

method only -~'c.: .• ~,~::::d greater disturbance::_;_, ·~he: f'low. The

bubbles wer-0.~ c:J.~· •. f·_,~icul t to detect when mad·e st.n3..ll enough to

keep the a:no~Jr:t of disturbance at a minirr.um. r.r·~e bubbles

also r·ost.=.: -:o the surface too quickly to g:l. ve an a de qua te

indication c. streamline motion.

Fro~de numbers were computed and were less ~han oneJ

indicating that the·velocity.~as always subcritical. Reynol~s

numbers indicated turbulent flow throughout the entire exper:: -·

ment.

_,_ .....

27

The rat~o of the d~scharge of flow over the side weir to

the discharge over the su:::;~:,ressed \·:eir, Q2/Q1 , was exaE1ined

next. Th~s ratio, a dimensionless quantity, was plotted

against the ratio of length of side weir to the head on the

side weir, L/H, another dimensionless quantity. The head

was measured six feet upstream from the upstream end of the

weir. The ratios when plotted formed a·family of slightly

curved lines. Although the lower end of each curve approached

a straight line, the upper portion was definitely curved.

These upper portions were in the region of the largest heads

and highest discharges. It was found that plotting L/H versus

Q2 /QT , where QT equals the total flow, gave a straig~t lir.e

relationship on logarithmic paper, with some scatter.

11he computer was again called upon tc gj.ve the equation

oZ the line best fitting these points. ~ne lines and the

equations are shown in Figure 6. By a lcr::s ~_, tr:::-'::;ch of the

imagination it appeared there might be ~;.. re-~3.t:i.o2:snip betwe&:n

the coefficients and the weir lengthr To fin~ su~~ a relation­

sh~p would g~ve a general eq~ation for the ratio o~ discharGe.

Dimens~onal analys~s allowed such a study.

There are many pert~nent values that may be used in Qe­

veloping prediction equations for open channels with constant

bottom slope and cross-section. Because roughness was the

same in all cases and because the variation in temperature

was small throughout the. experiment, :t."'o·:l.ghness and the propeF­

ties of water were disregarded in this e.r:alysis. The

' -N

0 - -1-0:: 0 -w -~

~ w 0 0 _J -

(f) lL

0: _J w <! > I-0 0

r-3 0 _J I.L

~r-·· i -_ .; , -:I'-: :--.--~--~· ·-=-'""' .... _,_ ..... _;r.r.~-, ·-~·7"""--l~~G~~---~~=-~~-i"-~ ---t·~~~-~r~-~-;~-~-

(]···- -- . -.•. i_-- - •_~_:.:~:-~!..:-[·. ~---:------:-- --_-·_--,_-_ :·- ___ ; \ i·r L~_36~'Q2/QT=6.50(L/Hr·B6 ~1 _ _:___ : 1 1 I :C i l J : . l : J •1 1 : . . : : i c r -1 i IT: Tr ~ : . : : I L~ 24:' Q2/i.H;3,38( L/H) -. 9D : ! Li= 42"

·-1- --~---~ \ .• j.l II ' ' . ' t N I __ ! ' I •

1 -~~-~ !~~J:·:t---: . ~: 12,. Q2/ QT: 0. B~L/H)-:·.7 7 _· _: ________ : ____ ~-:-. __ .L.:·J. -_f.'·_·,_.-

c C(''

0 . t .l ;;,.'I 5' II tel ';;.1- • ' ,-

r 1!,-c ~~­

c r• (~

··!·' l

! . . 1"'

r ,. i . I i

\ :~ ;-:i~ i,i: ~- -- !-- _1 -,- '--: : _·· ' __ : : ••• : _: ... '!-'.~

\ _l __ 'L~9, Q~/QT,=0.49{LiH.x· B? 1; · · ! • i - ·, c·:·:: ' . I : ' . ' I ...

II ' i ' I l= 6_, Q2/:QT= 0.24{L/Id)~.,82: -I. ! I ·:·-+------!:--:. -+ '- :.:.:·~~-- f'- ; .•. :·

,- -1·- -1 ~l -1-1 I l I • ' -'

i : . i 'j I l-: 1 I+ -

Q12/ cir=io~;o~s(1Li;H)-·' 82 :r-_·-·~:·--r·1---K-: ~--·----- -

! • '

--~.

. '-~

~I ... ' i : '· . L i i I i ' f

i· . \

.. ·'·· l : ~~~ -)11 I·:~--·~·,, I . . i I. ' I I ' ·, . I. I .I. . ! ! .

-i I :. : . ' I • • -- •• • .. - ·:. --1 ·]- ' .• -· I - - : j I'. : . ,-- ; .: I ' i ' j ' : I ' 'I l j • I I . I ' . ·. '. I j • ' ' I ' • ' • I . . I . ' . ,· l . I__ I

1 l 1 , I \ , I I I ! 1 -t j

-l- r 1. ·I, -:·I . ; . • - • : ! I I I j · ' , 1 • • t 1 • j 1 --1 · I 1 1 ! ; ' •'t· 'j I I I I ' I I I I I ' : ~-· I 1 '' '-; ' ' I l • j I . • I • • I • I [ ' . ' ' . I I I • I ·l ' I I · ·r-r· · I .. , . , ' . -~ t - ' o ,. '·-t· .). . I •- f'. ·1---·- -~· T'. .. .. r· " ' • J

I ' I I . . ' ' I • I . j I I I . I I I -r ·;-~·--. -, ,... . : . _. ·- -- --~· .--1- t I __ .. --- - ,- ·---~-- ---- ,. - . - l·r :-: Jy :-: : ,_:I! I.--., :r·-··. J. -'~- -~ :+--t-·-- -~--:_ .... ...: . .r. ·r·:--~-~---j~---~-_1_-~--~~-. ; '" I . ' . ·I I I I ! I I . I I I I I I ' .. , _, I .. j I I '

.. ----_ --·.--' _, __ -~-rl_ .... .:. ' ... --j---- . - .. ·--.- ,·,- 4- _, ___ 1_ I- ------1--- ___ ../ .... '- -~--- • --! -,- -- l -L-t -·. -1- ----,·- --· , - ·~-· ·--- - ; ----1- .. -~-...: I I . :I. I . r • r I I I I ' ' I I I I I I '

·_ . . . I t • I , .... -. . I I. . I I ' .. ' . ,,. I I . . I . I ' I I . : . I .. ; I I I I I I I I I I ......... ' I ' I .,.....,.~_..~,_..., ... ,-.~"-"'-----~ ... , __;z;:,,_-_ .. ,co,-..-.... '"' .• ·•--·~· ...:i-.. -.....-alit' . ....-· -~.~·•.o-a.a....,:t.'W.:...,.__~-.. ·~~...._~~--.':':QIJI.,. '~~~ra ->--~~~>Cit&! '""- *"-~•t'L>wo ....... -~~~~

c; 0,1 0.{ r~;::_ ):i 0;-::; O_l' 1.0 2 0 :-~.0 :j_') 6.0 b!J IU 20 30 .:JO 60 c~',) 100

LENGTH

Q21Cl-r

OF SIDE WEIR

VERSUS L/H

FIGURE 6

( L) I

FOR

HEAD (H)

Sl DE Vv E IRS

..

f\) CX>

29

quantities that would contribute were considered to be:

Q2 flow over side weir

QT total :flow

V ve locj_ ty of' wa tE~r 1..n C'lu:!·;c .-~_1-:'t.·:·r pas sing ;:.; ide weir

L length o~ weir

vl f'lume width

H head on si.de weir measured some distance upstrean,

of' weir.

Six quanti ties· involving three basic d:'Lrr.ensior.:s requJ r(; t.Lpee

pi terms by the Buckinghan Pi Theorem. One possible selec-

tion of' pi terms is

Because these pi terms plot as pa~allel lines~ it is evident

they combine by multiplication. Hence

where

TI 3 - L/W

Glenn Murphy expl~esses nl in his Si:nili tude :::..n Enginee::c-i:r-'<::;17

as f'ollows

TI 1 F(n:2,n: \

- 3'

an equation which required a brief' explanation. It says.

that an empirical equation :for a dimensionls3s quantity can

be :found in terms or a function of two other dimensionless

30

functions, by plotting tl1.e original quantity against one o.f

the other runct1ons keeping the remaining quantity a constant.

The bar across a term ind1cates the quantity being held con-

stant. Then the original function is plotted against the

term that was previously held constant while the variable in

the first plot is now held constant. The equations for t}-:ese

two lines are multiplied together. The multiple is divided

by the value of the original quantity at the point where the

tv-ro other quanti ties v-rere held constant, and the quotient

gives the empirical equation for the _original dimensionless

quantity.

In Figure 6 there ar·e seven eq_u2.t::to:~1s f"or Q2 /QT versus

L/H with L/W be1ng held constant, seven forms of F (rc 2 , n 3 ).

Because the L/H ratio W&3 ·..:~.ncontrolled by -sre ey_t!ipment used

to conduct the tes·L;::..) the data had to be sear·e;_-,e\'l to find val-·

ues or constant L/H r.s.tios. There v..-ere -r:ew ::::·..:~~1-: va.~.ues, but

a value of 6.5 ror L/H was found in the ca;:,e --·;· -.=-· ~c ·-. ,,, o.--· 9 ..... ·- . ~"-· ~ ' and

12 inch weirs. At this constant L/H, a plot v:as mc..:ci.::: of

Q2 /QT versus L/W. The equation of this line is

F (:;:;:-- TI ) ·-· Q ., 77TI l • 7 '"2' 3 - ,..L 3 . ( l)

Multiplying this value first by the equation f'or the nine­

inch weir and dividing by the value of' Q2/Gl}", at L/W = 9 11 /12''=

0.75, and L/H = 6.5, gives the equation

~ _ 78k~.82n 1.7 '"1 - . J c 3 .

For the six-inch weir the equation is

3l

TI 1 = . 77511 2 - • 77n ~1. 7 .J .

Although equat1on (1) was based upon a line passing through

only four points, the resulting equations justify a generali-

zation of the form

- rrQ.,. . .... 8 'i'' l. 7 7t 1 - . u" ~:? .. , 3 .

Substituting for these values, the following is obtained:

Simplifying,

which 1n the case of a one-foot wide channel becomes

(2)

'3~ \. I

These emp1r1cally derived equations cannot be orrered

for general use because the effect of the channel w1dth could

not be measured due to the geometry of the system. vrnen com-

pared to the measured ratios of flow, the calculated results

g1ve totally unacceptable percentages of e~~or i~ isolated

cases throughout all the tests. For the ~·n~1lest and largest

weirs, the calcu~ated results ave~aged ~in~ per cent in ex-

cess of and les~ than the measured results ~espectively.

the weir lenc~ths ranging .from three inches to two f'eet the

average error was seven per cent. Though such errors are not

t · , · · · · sl· ern the fact that the error is accep ao~e ln englneerlng ae a ,

no ~reater shows a tendency for the water to divide in accord-

ance with the geometry of' the system and its velocity. The

greatest errors occurred at the lowest heads, where surface

tension apparently has an ~f:fect.

32

A plot or the ratios o~ ~low to the Froude numbers also

gave a ramily or curves which were approximately straight,

parallel lines. This confirms the before-mentioned state­

ment that the division o~ ~low depends on the geomet.ry and the

·velocity. A similar plot using Reynolds number gave a ~amily

ofparallel lines. In the Reynolds number relationship the

properties of water began to show their e~fect.

If the division of ~low is dependent on velocities and

head, the upstream angle of discharge shoulq·likewise be so

dependent. Graphing angles versus flow ratios, angles versus

heads, and angles versus velocities proved to be inconclusive.

A scattering of points was the only result of.such plottings.

The data and the plots showed that for each weir there was a

maximum angle of discharge. The maximum angle of discharge

was smaller for a longer weir. The data indicated also that

the velocity increased with head. These observations can

explain the existence of the maximum angle. At low heads,

the angle increases with head. As the head increases, the

angle continues to increase while the increasing velocity

tends to drive the exiting water back toward the flume. At

large heads, the angle decreases with increasing velopity

and is ~ndependent of head.

As the weir length is increased, the upstream water

level is drawn down and the resulting heads are lower. Since

it is the head that acts to increase the angle, the lower

heads mean lower maximum angles · o'f discharge.- Also,· the data

33

indicate that ~or a given head~ the velocity in the channel

containing a longer weir is greater than the velocity in the

channol containing the shorter weir. The angles indicate an

increased ratio or rlow with increasing head and a decreased

ratio o~ ~low with increasing velo.ci ties. Although no con­

clusions can be drawn rrom the angles'themselves~ their be­

havior adds ~urther justification ror raising the head

(always less than one root in these tests) by a decimal ex­

ponent in the derived equation.

An attempt was made to:de:termine what length of weir

would be required to reduce the down stream head on the side

weir to zero. According to Coleman and Smith~· the length is

in~inite. The test was conducted on the longer weirs and

the heads were continually reduced so that a nappe was main­

tained at the upstream end of the weir. The down stream

head was always considerably higher than the upstream head.

Even with the longest side weir in place~ the downstream head

remained greater than the upstream head. Only when the nappe

was allowed to disappear did the downstream head begin to

decline. FinallY~ when no water passed over the downstream

crest or the weir, the head was so small upstream that the

water just skimmed over the upstream edge of the weir and

down the outside o~ the weir. Within the geometric limita­

tions of this experiment, it could not be determined at what

length o~ weir, ir any, the downstream head could be made

zerp while the upstream portion continues to act as a weir.

A constant harassment during the testing was the com­

parison of the two measured heads. As far downstream as

34

twelve feet, the head was often higher than the head measur­

ed upstream from the side weir. This had been noted by

other experimenters, but the difference in heads and ·the

lengths between gages were not recorded. Witp the upstream

gage 12 feet from the flume entrance and the downstream gage

30 feet from the entrance, the difference in heads was a

great as .05 feet. There were noticeable rises in the water

surface, particularly by a standing wave beginning at the

downstream end of the weir and' extending into the main channel

at an angle of 45 degrees; but none of these ~ises could be .

con~3idered a hydraulic jump in the spectacu.lar sense of that

term.

Tults states, "Fundamentally, the flow along the crest

of a lateral spillway may be treated as a flow division where

the divided water lost over the crest of the spillway, does

h . d 1118 A 1 . . t +-not affect the energy ea . pp y~ng a plc ure Lrom

Vennard19 (Figure 7), it is seen that since the flow is

always subcritical, a hydraulic jump, a jump from super­

critical to subcritical velocity, does not occur. This

figure (Fig~re 7b) shows a rise in the water surface for a

decrease in quantity of flow at a constant energy. Hence,

the illogical variations in head can be explained by the

characteristics of flow.

CONSTANT DISCHARGE

ENERGY )

CONSTANT ENERGY

I SUBCRITICAL

:c 1-­a... w 0

01 SCHARG E

B

DEPTH- ENERGY- Dl $CHARGE CURVES

Fl G U RE 7

35

)

36

3 Inch Weir

36 Inch Weir

37

3 Inch Weir

Figure 9

Comparison or Flows -- Side View

3 Inch We~r

36 Inch We~r

Figure 10

38

End View

C:-IAPTER VII

CONCLUSIONS

39

The results o~ this study produced in~ormation appli­

ca-:)le to the use o~ side channel weirs in irrig.ation and

drainage projects. Several conclusions are drawn as a

dir·ect result- o~ the 1\'0rk perf'ormed in this study within

the small range of' heads and velocities encountered. They

are as f'ollows:

l. The f'low of' water over a side weir can be computed

by an equation of' the f'orm

Q. = CHN.

2. The ratio of the f'low over the side weir to the

total flow can be expressed in terms of' length~ head~ and

chaYJ.nel width.

For the system teG~ed

n -·- 0.9

m = 0.8

p = 1.7

3. The ratio of' t·. ' f'lows can be expressed in terms

of' Froude numbers and Reynolds numbers.

4. The downstream head may be larger than the upstream

head~ and .this higher head might continue .f'or some distance

downstream.

40

-·. A side weir three and one-halr channel widths in

lc::-;'"'··:~h cannot reduce the downstream head to zero and still

--~~ion as a wei~ with a nappe.

4l

CHAPTER VIII

RECOMME:N"""DATIONS

A study is never concluded. Wl'"len time demands that a

s~op be made~ more ques~ions have arisen than have been an-

sv.Jercd. The cons true tion of the apparatus asks~ 11 Is there a

cc"..:.tcr way? ll The data ask,. l!Is there such a thing as a

~:::rccise weir ;;.2asurement?" The results beg, 11 Why? 11 The

~:,·o:::::-'d~.> of' t'n.e critic still sparkle_, TlWhat is the question? 11

It ls hereby recommended that:

l. Side weir investi.gations be made varying the channel

~~d~h and the heights of the weirs concerned in order to in-

crca22 the head on the side weir.

A study be made on a side weir in a flume with steep

bottom slope so that the velocities of flow might reach the

[::>upe:..'"'criti.cal ;:;tage.

3. A study be made where the length of the side weir is

increased to a great extent in order to determine the effect

o~ lenGth on the downstream head.

4. A study be made to determine the surface profile of

the water as it approaches, passes, and continues past the

~>ide weir.

5. A study be made to determine the discharge characte~

j_~_.-t~ics of side weirs whose crests are not parallel with the'

c:hannel botto~n.

6. A study be made with an end weir of adjustable

~e~3~t to allow a constant head to be kept on the side weir

~or different rates of flow in the main channel.

43

APPENDIX·····

DATA FOR CORRELATION OF THE END

SUPPRESSED 12-INCH WEIR

44

45

, .. .. _:__=:::BRATION OF SuPPRESSED END vJEIR

.. ·. ~:_ .--) l ~~ 0 1..,. Ti::::e ~' ~) . ~~eight. Q Hc::s.d ·. -- .-·~ --~ (~· :." "v'Ja te r r .., .- n \ ( \ (1bs./cu . .ft.) ( cf' s) \ J_ '.J>"j ) (SeC) ( ~""~ ) - v.

------ "" -------·--------200 25.6 62.30 0.101 0.125

2CO .... 9.8 62.30 0.123 0.163

300 20.0 62.30 0.161 0.241

300 17.1 62.30 0.177 0.281

300 l r- ~ .-.O.J 62.30 0.185 0.293

-::; r,r, ·v'..: l4 0 -'- •__./ 62.30 0.195 0.324

300 ::._2.2 62.30 0.220 0.395

3CQ 24.6 62.29 0.143 0.196

300 20.4 62.29 0.157 0.236

300 19.9 62.29 0.161 0.242

300 18.6 62.29 0.169 0.259

300 "'7 9 j_ I • 62.29 0.176 0.269

JtJQ 17.3 62.29 0.178 0.279

300 16.7 62.29 0.182 0.282

300 1[..~ Li --" . ' 62.29 0.189 0.313

300 15.1 62.29 0.198 0.319

?.C·O 11.5 62.29 0.229 0.417

300 ~-'-·6 62.29 0.230 0.414

300 11.7 62.29 0.238 0.410

30C - '1 9 .l..L. 62.29 0.232 0.405

300 11.! .. 7 62.29 0.200 0.328

300 16.0 62.29 0.190 0.302

300 19.8 62.29 0.168 0.243

46

C.t -~ --~~-F~J~ ~IOl\f OF SUPPRESSED E:N""D \'ll'EIR ( col-:tinucd)

I· . . of ,_-_; :l. n:: e Sp . 1~.Jc ight \) ~ :0 Q :read ' . . ~:~· ;._:-..._ -l:.- ___ ; J:~ VJater i -i ·, ' ) \- '-~-· ~ ( ,_. 2C) ( 1 b"' /c,l f'·'-) ....... u. \.-V (cfs) r .c._,_ ) ', -'- v •

---.-.---.·-·--·----3CO 20.3 62.29 0.160 0.237 r,,,......r, LVU 18.6 62.29 0.130 0.179

200 19.1 62.29 0.127 0.168

200 2::...2 62.29 0.117 0.151

200 26.5 62.29 0.102 0.121

200 26.3 62.29 0.102 0.122

2GO 18.7 62.29 0.132 0.171

,·:.Jr11'"' .::_\___,V 16.3 62.29 0.139 0.-91

;~oo 16.2 62.29 0.144 0.198

2CO 13.9 62.29 0.160 0.231

2VG 13.2 62.29 0.167 0 2L-:: . ' ...)

r-..., _,....,_ r\ .-.:..uv J..2.2 62.29 0.169 0.263

200 12.0 62.29 0 '7ll • .L ' 0.266

200 11.4 62.29 0.178 0.281

200 11.1 62.29 0.182 0.289

200 i0.6 62.29 0.187 0.303

300 1~ r .:J.G 62.29 0.190 0.308

300 14.1 62.29 0. 206 0.340

300 12.7 62.29 0 ?ill • L_ ....... • 0.379

300 11.8 62.29 0.228 0 . ..-08

300 11.6 62.29 0.229 0 1:.., r .4-J...?

300 10.6 62.29 0.242 0 1J.;:::::2 . ' _,

300 9.5 62.29 0.281 0.559

300 7.6 62.29 0.294 0.633

"S!-\.TA :s'GR 1~-INCH WEIR TEST

~ ...

(\ ~ :.:_: . )

·~~ ,_ u. ~ .. i -'c i t~ y .'3 i Ci. o l;J e i r

viEIR TEST

Suppressed

(ft. )

Quantity Suppressed Weir

C::l..,

( c f~)

Velocity

(ft/sec)

~-8

S::otal FlovJ

Q.--;-, (ci"'s)

-·-··-··-·- -~-- --~~---· ----------·----~-----------------

r~ . , .-'" -.._,,.',.__)~

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

j_ s

. -·· ~

. ... ; --"' '· )

,.-....r-/f"\ • '-..- I ' . ...J

.070

.0057

.0071

. OlO~-

.0117

0155

.0

0268

.0528

.0023

0 ,.,...- /') r-)

• Qc...:::_

. oL:.o6

.0153

0 ()·~-­

• vO_j

.0290

. 01'"( '-,·

.0057

.258

.260

. 2'T8

.286

.308

.382

.461

.495

~a' .:J 0

.213

. 9~-5

.520

• )_~68

1.1?~1 • ' .__ I

.368

.. 305

-=· s· "' ·...) 0

.322

.250

.480

4 ()~

. 0)

.550

.570

• 6LJ-O

.670

7·:-o • I 0

.900

1.18

1.30

1.33

.365

l • 52

1. l~O

1.22

1.05

.850

625

.500

.891

.672

.464

1.13

1 llL • _L '

1.23

1.26

' 32.J. _L • '

1.39

1. L~8

"' 6LL ..l.. • '

1.88

1.97

1.98

.96

2.14

1.92

1.77

1.59

1.32

1.16

1.61

1.3'7

1.11

.486

l.i02 . . ,;/ 5 c·"'· . ov

.582

.655

.686

.781

.929

1.225

1.353

1.393

.367

1. 594

1.462

1.270

1.091

.878

.640

.506

.920

.690

.470

Head on Side Weir

H _(I_~_j __ ._, .. ,, .. ·

.077

.083

.102

.110

.130

.lL~ 3

.173

.?10

• 211-1-+

. 3.10 ,,

)jl)

0~,.,

• _)1.

. ~3J~)

. :j~~-)

Q2/QT L/H Froude Froude Reynolds Angle of Discharge Deviation of Nu:·:;ber V2 /gL

I·Tumber' V2 /gH

N11mber pvr/u

Q2 /Q.T Upstream Do\'TnS tream fro-;n computed

values x 1000 (degrees)(degrees) (%)

-""-=-----...------·.- ,..;.~,.,,_..~·~_...._ .... J/11.,#.,.,_.,~ •. -._.M~ ,,_.,..'1..,'!'~.·-~·~-........ ~---·..,.,""'~""- .• ,... •. ,.__ ... _"'-4-00..:<.1'...-..--7, ·:-r < ~ ··---~·"'· .·-~~-...... ,u-........ """"'-..,_.., '>,&/V'"I:• , • .,:I~UI"'""'·•-_,.-.._..,,,.,.. ..,....,.,._,,.,-~"''ll!•,.,.r ..• ·•· :•.~·-..,,._, .• ·.:·~-~-... ~-~' -~.-..~~_,._..,.,.,.,.,,.

.011'7

• 01)+l.i-

.0186

,0201

.0222

.0226

.0262

0 ~) 10 . .)-·

(' . ..,,·s • \j •'\r)(

•-'

OJ· oo . . ./

! )•1 ~~- ~··r ' \..,/· .. -

rn(' t \- .I',.._)_)

~~-~ ; ~ (~ ~~

'I, "'', t 1,,:;.,· ... J

1.623

1.506

1.225

1.136

.962

. 8'7L~

,'(23

.595

.512

. ~~o·:.; • ' J

;·2

i.L,O]?

. :bl.

')'J. . ...-

. 31'7

. 322

.375

.394

1111~'" • L-fLtO

LL3o . '

:;lLIJ • _.I I. (

r/·8 .00

n.-78 .o '-'

(l(h • ..)•)i

(--..,.r-•11 • ;: { ,~_r

. 2~~9

!. . '1. ':J

~ I j 'I. ·- t ... _ _,)

.093

.094

.105

.109

1- ·r • J.' I

.124

1 -·~ . 5J

.152

l .... (r:: ·~ :J

'1 'i·) . ___ (.),_

.18·

. ()"() l(i()

• l. .:.· _)

·-~

24.8

25.2

27.8

28.7

31.2

'-!-2.8

45.9

lW.6

1.n.1

' ') 0 ... '- • .J

r- •') r :::> _) • \)

1 o n -~ .. ./ t ._)

! : c I Ji . ../ __ ,. , r

' ~, . ' ·"" j J

lj.Q

48

52

55

60

60 r• .--· ,,, /

56

:3'7

52

5-~~

", 1 _..,~--

')

,- .. \_... :,_)

~-8

55

47

l.f6

43

rr2

39

36

24

10

10

~-))

.. •')

~:} ~-)

''2'/ .. 1:

-J-2L~. 5%

+12.5%

+ 3.6%

+ 2.0%

-t. C.. lof.. • J, ;o

-'-·l 0 7ot'O I -·· ' I

+11. 2Jb

J.l '1 0°1 1 ..... , ;o

' 5 ?.·r./ T • . ;o

-'· ·\ 7 rvl ' -- ! r \_,•,.J

1·1 '! • '1:-/;

, -~ .-, ~r·c/ "i '.:. .) • ;J

' -~ l -, --< . ..-/,"'

') ( J ., ' _,.,

49

continued

Head on Side \·Jeir

0.2/QT L/H Ii'roude 'T , 1, ·u·r·'l''<"' -.... - li u-' J..

V2 /gL

Froude Number V2 /gH

Reynolds Number pvr/u

X 1000

Angle of Discharge

Upstream Downstream

(degrees)(degrees)

Dev:tat:ton of Q2/QT

from ccrnpu ted values

( 7&) H (ft.)

-~--·~·""""""""'"""""""'......._..,..,._,~,.._. • ..,..._._ ... ._~.,_~;. --"'·--·--~-""~--->: .. ; ·,·-.~o,.r..:~_; .·..&.o~~,...._..-.,~-:.'ro.;.,·•~-·-•-~--....-.-rt-..:'11. . ...-..-.;;-. .....,...-.-~---·;·"'"""'..,. . .:~..--.... -....._ ...... J..~'•-''"''· ... _..,.-,..,,,.;:.,..-..·..,..""""'··-.·•...,......--.. --,.,.,.r"-."'""• ·..--· ... -.=--~·-. ,. __ ... ,..... .... ........., ............ ,~ .. ....,..,.," --

.279 .0393 • [~L~8 .915 .180 50.7 58 32 + 9.0%

.241 .0372 .519 .778 . J.6l~ 45.5 60 35 + 3.1%

.185 .0317 .676 .628 .11.~7 J.l~ .1 56 33 - 1.6%

.·131 .0239 o:=.4 .. ;_~ 33 .115 30.8 54 35 - l. 75'~ o/J

.O'TO . 0121.~ 1.786 . 331-l- .097 r.r " l.l1 41.~ +13.3% C::J,C..

,200 .0315 .625 .6J!.Jj. . J.L~6 .~a [ 60 l.J.O -~- LL 8% _)_;;.0 & I • I

.145 . \)252 .862 Llf6 .119 hl.9 55 )f f~ -! J gcrl .. - - -- • jJ

.070 .0121 ] '{oc .]06 ',- J?. 23.7 J.~o 60 !- J 5 lL% -' U()

I - • I I

50

5l

DATA FOR 3-INCH WEIR TEST

...... -, ·-~ -~ .t

-" \._.·,_;

.-'·: I ~-j. _:_··o

,-·-. -"",1) c_ _:;;,.:...

--, ~:· ::) .1. \....J ·~J

-- ·--_.,_ ... _; ._.1

--: -.' ) ___ _, .. _

l •'/ . -'- ' '·-

,..., ·-· .-• V~)L..)

. --~- 0 ~3

057

Q ~J. :-:i(~ t ~L ~ :.l S ::_ c~~(_; ~~I c i r

0933

O'"l )_• • :; -~~ r

0325

( ... ) -. rr ~ . '-'- ./

.0120

. 0835

0 -;;;,)_; 8 . ..) '

0200

.0102

.0930

.0531

.0231

.0323

nl '. '") L:. • \..../ ' ,C.,. I

0(~17 • ..._.-- l

.0322

C-'"'­.U'..)

3-INC~-I SID:t: h'EtiR TEST

Hes.d on Su.p­pr-essed v!ei L'

Quantity Suppressed l~! c-:i l~

Q.l

Velocity Total Flovl

( c f" <,-,_~ \1 ( ·r'"' _._ I c -==> .... \ - i.J; '-''--\J I

-------·----~~----~-------------------

.1.~65

.416

.360

3 -, l1 • ..L-r

0'"'5 • .::.d

.252

;: ;,6 • .t,....!..l _ _._

. iJ.Ol

. 3l.i-4

.320

.296

.255

.441

.2-1-18

.375

.305

.320

. 386-

. 380

. 321

.247

1.20

.980

.650

.570

.480

i l ~-= ..L • _, __ ___

.950

.750

.670

.660

.l~-70

1.10

1.00

.850

.603

.660

.720

.900

.868

rr-8 .0::::>

• l.J-60

1.89

1.68

~ 5? .L. ~

1.35

1.26

1.14

1.88

1.67

l )17 ..... -;-

1.37

1.29

1.11

... 8-..L. '.l

l. 71

1.57 .., .....,3 ..L._J

1.35

1.42

- 6....., .L. :;,

1.61

1.38

1.11

1.293

i or:::4 -· _.1

.851

.683

.588

.492

1.01LJ.

.78:5

. 705

620

J, gr-• '-I- v

1.193

1. 07lt

.903

.658 ,--,...2

.0':::}

.762

~---2 .;:;o

.920

.690

.470

. 0721

.0704

0603

• OLi-7 5

.0297

~'"'? '· --• v_LJ-:;.

.0630

.0578

0 ;,9..-, . ..... :;,

.0322

0212

.0779

.0690

0587

.0426

.0556

.0641

0 ~·--s . :JO

OL6,­• : 0 .

.0223

Head on Side Heir

H (rt)

.266

.232

.188

.133

.093

.058

2llr • - ' :J

.232

.171

l'"'r.: ' jlJ

. 092

. o~G ; ... ,- 1! .<\} r

·)•)'"") . ,·_ ~-)

i (~ :~ / __ )

I /l'J" 1~1-, . ; r1 ~ _] 1 J.'j_C)!_._t,l_e

,. 0 • ::;'-!

1.078

1.330

1.880

~?. 688

il ) l 0 .. , . .) ··-

1.020

l C713 J. • ) I (

J ,1' :2 "1 ·' ()

. • _j()

') ... , ' .

•-. I J (

' 1 .... - •

:'. ~ I : :. (_) / !-

, ~)-\:.· (

' ' -~ : ~ {_)

·. (;. -~ t I __ ~-_....:

1'-f~)_~rt~::: r ·'"2 /:.'T \j 1 o··.J

• Ljlj)~

.350

.287

~?h . ·- ._____ ~-'

l 07 • -1.-_../

.161

!, ·-o • 'i j..)

J'' r '··O . '-

')<g • c.t_.;(

f)"""'·~-..

. (_ jj

. ~~ (=~!s

'-'-J)

' ' I '"'

P:coude iTu.rn be :c V2 /gH

.175

.150

l ·)r • .)0

1- ··r , j_

.109

Oc.r . _)()

• lr(9

.1 1""2 '_) ..

.131

. J;~o

. i 1 j_

I " [~

/ _ _,·

FeynoJ.ds T\r U. L~ l; (~ rJ pvr·/u

X 1000

26.9

42.9

3'7. LJ.

31.5

28.2

2h .~-~

lJ8. 5

1.~2. 6

., r· c

.):J.U

·)'3 ( ) • 0

..-,(""1 n / __ -:1.). 1,)

'·::; '( I - • _.1

I,' • .. I

' I •

) f )

.~-,,c··lr=> o·'·, Dic·c}<"'r'·'' l)·"'Vl''•ltio· o·"' "'_, . C) L -~ r ... o .o. _ ~~ e _ '~ . . c _ n .L

G2/Qrr Ups trca.m Do1·ms treo.m fJ:om cornptJ. ted

values ... ·-·-~·-~ .. -.... ..," __ . ..,.

57 LJ-2

52 37

LJ-6 ~-0

50 ho

l'" rC: 42

36 55

5'( Lj.L~

51 !.J.]

51 li-5

!' l :J '- ~~ ) !-

)I fl } . i'T

Tl ·-~ ') J·

; :.r'! ;_ :~ ; . _/ ' /

.' '.: "i

( !Jb) .. ~~ ._, .• ,~p~='"'"'""'-~ ;><\}_, __ _ _..,. .... ~,_..,._ -- = .~___.. .. .._._._-,.. .. ~"'"''.,..,..

+ 7.0%

+ 1.0%

-· 5. 8%

6. 370

+11. 670

7.0%

, r:- od T 0 • 7/0

+ 9. LtJb

- r~ ad ...-·'JfO

n r;r:f () I ~);J

J

1 --~ ' ()/~ ; -I. . "

'\ _j I

() • ' 'i

53

continued

Head on L/H Froude Froude Reynolds Angle of Discharge Deviation of

Side Weir Numter Number Number Upstream Dov.rnstresm Q2/Qrr

H V2 /gL v2 /gH pvr/u from computed (ft) . values

--·-·--.. ,~~-·---· . ~~--~,~=-·--··-~~~-. .J:..Q.OO~-----~~-~------· ~------------.. --.-·J%2__ ___ . ___ .... ----~-·

.120 2.083 .219 .116 30.2 50 45 - 3.2%

.115 2.174 ,200 .108 29.1 50 ~2 .. 1.5%

.131 1.908 .226 .116 31.5 53 1~-5 - )~. 7%

.153 1.634 .250 .124 33.8 5'7 1.~8 -11.8%

.203 1.232 .330 .149 1+0.6 60 50 Of_ - . 2 .l7o

.182 1. 37l~ .322 .1L~7 . 39.2 60 48 + 1.7%

.132 1.894 .236 .121 31.8 !.~5 50 - 1.5%

.057 l~. 386 .153 .092 22.5 30 60 + o. s;~

\ 'l.

54

55

I

DATA FOR 6-INCH WEIR TEST

56

6 -INC-I SIDE HEIR TEST

I:i( _ Qua~-~ci ty Head Quantity Velocity Total Q2/Q.~ . ...., . ..

Wei:.:-- Sup- Su:opressed ,_, .... L ~la.e on Flow s~~:..c: pressed We:_;_:c ~_-_:\_: ~L :--.. ~~reir

-~- i. 12 Q.': Qrr : :• _,_ ) I r ·.c. ) (ft) c c :rs) (:rt/sec) (crs) \ -- '-' \ v ___ .. ..;

-- .... ~~----~--"'""-·---....... ,... .... ~.-~--,.,---r

.u_:;,o .0193 .278 .550 1.24 .569 .0339

. o.:_;-1 .0151 .279 .550 1.26 .565 .0267

Q7C • i :l . 03Ll-9 . 305 . 630 1.32 .665 .0524

.097 .0458 .309 .640 1.34 .686 .0667

•.. ·- J .0569 .312 .. 650 1.36 .707 .0804

.l35 .0692 .336 .720 1.43 .789 .0876

.2.53 Q708 ?l.llJ. .760 1.49 • 81..~0 .0950 • l ../ . ..) ' .

.l'[d . ogol_J. . 375 .860 1.59 .950 .0951

. ~·-93 .0995 .388 .900 1.62 .999 .0995

0l r:.~ .1278 .424 1.05 1.78 1.178 .1085 . ~- -"-...-'

. J .. 8~5 .1010 . 386 .900 1.63 1.001 .1008

. 15E, 0'78"'1 • I - .349 .780 1.51 .858 .0910

.ll2 0400. • ::J '--' . :::_;:'.8 .640 1.34 .689 .0721

.cso • (;~_L.! 3 .263 .500 1.16 .514 .0278

.060 . c~ ,~.:.S .271 .530 1.21 -551 .0372

.075 .0299 9:' •- Li• .590 1.28 .619 .0482

. 092 o-.:-- . • .J'·- ·, -=<0 C'; . ...... '-' .640 1.35 .678 .0566

.180 .0960 .361 .820 1.53 .920 .1043

.130 . o6oL~ .311 .630 1.32 .690 .0875

or;l .0172 .246 .450 1.09 .470 .0365 . ..---

He:::..d on Side '.·Je1r·

H (ft)

L/H ll~ .L --~) '). c! .. e :\I')·-:~::·,=: l~

v2 /;;L

Froude ~·T unJ; (:; :c V2 I t)-i

-.< . '-, ,- -,, !) 1 '1 .~ -~--v .... -- --~-o , T ' i'': , __ :_ c·~ c c~ r~ vo;r/u

X 1000 --~----- .. -- ... ---..--~ ...... .,..-.--·-------~-~ ... --... ~ ... -- _,_ .... _, ......... -..,:,_, .. ~-·----- _._ ..... ___ ........ ~A>-•.t...,-··- .... -· .,.... •. :~· -- - --·-· .... '""""

.056

.041

.079

• Q9r{

.123

.13~

.153

.1'78

'l '93 ... . 21/)

I 1~ ;

l . ,)

1 -- ) •... .L c._

!"))0

(·;': ()

() ,-,09 u.';;c

qr-].2,1__.)

6.330

).15:5

1! .• 065

-:{ '((-.}I .J. j -j-

.--, r '"8 _).20

;::l,809

2.591

·) -~~ "(: --· • ,J :: .)

") r:o·~ 1",. I! ,_}

j,:L()

;! _,--}, . -- ...

1 {' '1 ___ ·)(:()

,, . :r)j

(\C)·-:-• J:;J

.099

.108

.111

115

. 12'7

1 •')8 • -- _j(

] r--·y . . )

.163 .i • , I J._/l

'1 ~:-•. Ll__.,)

• :1.-:~2

.1L1

j -~-~ ~-~ '"' ' ~

_:~j 1_

o lOr(

.113

. J.1lt

.117

.120

.126

l -~r:; • --- ... /'J

.145

.14'{

.166

1 11 0 I,_.'·!'" ....I

l ·~r( --·. ~)

I i_ :_·

.-:l:, ( • ·~ ./ I

"1

27.0

26.8

29.5

]0.6

31.9

33.9

35.9

39.3

1!0.5

• 11 r- ? ,-:_)' .)

1:o.s .-,( (

_}] I t)

" ~ :·_I ~:t I ~

.~--.~~~.C)

1\i1L;lc · (• f).i.bCf1Ci.l~;:;i2

fJr'·-•tC·JC . .--,1-'J r~~-)-,",~c·l·r·, ,.,-.,1 ·. )...)1:. .1.. ~-u.. 1 _....)._ dJ.-•,:) .~ ....... c.11

3}~

23

36

lj.2

L~8

1~8

~~ 8

51

h.ls j

r- , ..

:u

)5

jO

I. f ,, . r

;·~ _: ~

.. ··-~ .... -.-.- _...,,_, __ r..r·,..,u ...,,....,. ,._,_

60

6r(

53

}_~9

L~ 7

L~o

L~·r

'I

50

l!8

Ji ( ·-rO

'.·g ~ ~ ...

1:' 'i I

. -.-r ( ')

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

D'.; Ii_e. i::i.o1l of

0,2/QT r'L'Cm conpu.ted

vo.lucs ( cl)

·.· , .. __ j:~ ... - ~ .. -~ ... ··- ..

+18. 99b

1 ') '7 oaf .-... 1o

+ 5.1%

-· 3 }lot • Tj0

-· 2 qot • ;.;o

- L~. 37b

2 ]d - . . ;a

.!. 9 5;;1 l • ;0

l '] () ']t-.-f -.-.. • _)/J

I "Ll jd .. - - . ·/')

-~- R }! c01. t \j • T;

+ ') s>:;)t "' '·--,

l -, -1 .• --, J

1 . f .... :~' ~: .- ..

. ·- i;J

}I·

57

Herld on r1 • 1 01.c e Vcir

H (ft)

.075

.092

.180

.130

.051

T '· .uj 1{ F:c·Jude 1J t..t r;: ;J~_:: r V2 /c·L

I ......_.-

,, :.ca.::•-Y~_..,.._.;d:"_,:.•·· ~--.•... ,_ '- ....

6.666 .102

•:. !I ':lL\ _.) • 1., • .) • , , 3

• _1__1.

2.TT7 -1 1! l-. -- -,-)

'1 OJt C .) • <)'-.-1) .108

o :;oJ..t. ..I • ' • . err J.~

li'r(Ju.c1c .i'Jun:ber V2 /gH

.110

.119

.138

.113

'IP9 'V,J

-~~n··:1o.lcl·' .l -"--J _ . .,_v

l\}11n1br;r ovr/u ~ ' '

X 1000

i\;Htl C; of' Di SC 11')'o(,'O D·::;via{·j ,..-.,"1 of i l. -~ .. , {..:J- \...... ~ ~ -·-) 1 :..~.1 l_; \_, . ~..... ~ v .. 'v 1 .

Q,) /nrn JL~-~J •

Up~:> t:ceam Dovms tr:0am f:_r_•om cornpu ted values

(7&) , .. ~, ~,...._,, ">oS•,_.. '·"-'o"'J'«, J.~"><j. ........ , •• _-~ -·•'•>•'··-'"""'Jti·-·"'~• .,, .•• _. .... , ... L ..

~- ___ ,_ . .,.,. · .... ·'"•' • . •. , ··t.-~ • ~--'

28.5 1}0 57 + 8.'-l-%

30.6 ~-2 42 + 8.7%

36.7 l!-5 50 1 ro' + . O;b

30.0 50 LJ.5 -- 6 1% • -1

13.1 35 50 + 6.2%

58

59

DATA FOR 9-INCH WEIR TEST

60

9-INCH SIDE WEIR TEST

Head Quantity_ Head Quant:Lty Velocity Total Q2/QT on Side Weir on Sup- Suppressed Flow

Side pressed Weir W<~ir Weir

H Q2 Ql QT (f't) ( CfYs) (ft) ( cf;s) (ft/sec) ( c:r·s)

.053 .0283 .268 .500 1.15 ~ ~: t .528 .0535

.067 • 0~ ~~ .287 .580 1.28 .620 .. 0646

.079 .0508 .292 .595 1.29 .641 .0792

.096 .0673 .308 .630 1.33 .697 .0965

.110 .0795 .312 .640 1.31 .720 .1104

.054 .0322 .257 .480 1.13 .512 .0628

.086 .0572 .288 .570 1.25 .627 .0911

.102 .0734 .304 .620 1. 31 .693 .1058

.123 .0927 -3~5 .690 1.41 .783 .1184

.141 .115·' .344 .760 1.48 .875 .1314

.163 .130·. . 360 .800 1.52 .930 .1397

.183 .164 .404 .960 1.68 1.125 .1462

.227 .217' .. 423 1.05 1.78 1.267 .:).:712

. 199 .187·· .. .404 .960 1.68 1.147 .1630

.175 . .. 157;· .387 .. 860 1.55 1.017 .1543

.150 .-121·. . 349 .760 1.51 .881 .1373

.162 .136' .360 .780 1.54 .920 .1478

.118 . 0870 .304 .610 1.34 .690 .1260

.052 .0258 .242 .440 1.08 .470 .0548

Hcci.d on L/H Froudcc Frou.d~~ T.l --- r }ric· nn~lP 0~ Di~cb~rnn De:\ ~at:Lon of' ,~_cyD.J. '--·'::> .-.L- ::) __ ..._. l .... ~_... .. 1..,.~. l/._...

Slde \~eir Number Nu.m1.· :e :Jrn-oer Q2/Q~r H V2 /gL v2;o·:· I

(ft) o.tl. pvr;u Upstream Downstream from computed

Vel lues X 1.000 (c::\

_.._.....__ ... __ .,,_a-~·-=--~-~,--....._, •- -~.r~r-..,·-· ",,--_.,.,._., '- _ ~-- . ..r.~..,.,-~"7--.-,-......, ••• - .. _ ..... --~--~-·---~------ -~-----·-·-----~ .. ----------·-'"-- -.I--·-·-·"--·---

.053 1LL 151 .055 .oglt 10 7 ~-)5 55 .L 5.1% . l. I

.067 11.194 .068 .112 27.9' 32 58 - 2.0%

.079 9. 49l{. .069 .124 28.6 37 49 - 0.9% I

.096 . 7.813 .073 .116 30.1 42 53 6.0% -

.110 6.818 .071 .109 30.1 43 50; - 8.8%

.054 13.889 .053 .093 19.3 26 58 - 10.5%

.086 8.721 .065 .107 25.4 36 43 - 9.7%

.102 7 I 353 .071 .113 29.8 42 46 - 11.4%

,123 6.098 .082 .125 32.3 4L~ 45 - 5.3%

.. 141 5.319 .091 .133 35.1 46 46 - 6.0%

.163 LL60l .096 .136 36.8 Lt7 44 - 0.5%

.183 lt. 098 .1rr .153 41.3 47 40 + 3. 9/b

.227 3. 301+ .131 .167 1+5. 5 44 45 + 5.9%

.199 3.769 .117 .153 L~l. 9 45 48 + 0. 35~

1!.286 37.8 43 45 6. 77b 0'

.175 .099 .135 - 1-'

63

D . .:.·..:·..-\ FOR 12-INCH WEIR TEST

64

12-INCH SIDE "WEIR TEST

l:..:c:.~d Quantity Head Quantity Velocity Total Q2/QT or. Side Weir on Sup- Suppressed Flow

S .. -... d.e pressed Weir ~ ... : _; ir vJeir

H Q2 ,·. Q] . Q,.,. ( .-. .._ \ (c:rs) (f't) (cts) (f't/sec) ( cfs) \ l.. 'v I

. os.L~ .0417 .247 .45G 1.0$ .492 .0848

.060 . 0519 .257 .480 . 1.13 .532 .0975 .·.

0~,~~~ • j •• .0628 .268 .510. 1.17 .573 .1096

.088 .0897 .290 .580 1.27 .670 .1339

- .llLJ- .307 .640 1.35 .754 .1511 ,..LUO

.126 .136 -335 .720 1.43 .856 .1588

'31:::: • J... . -' 1c:::;c • ~7 .346 .760 1.48 .919 .1730

.1:53 .181 .371 .850 1 .. 58 1.031 .1765

.:::...30 .141· .332 .720 1.41 .861 .1637

. ogL:. . 099· .302 .620 1.32 .719 .1376

l 1.L., .169 .352. .780 1.50 .920 .1836 ·-·.l.. .100 .106 .301 .620 1.33 .690 .1536

Road on ........ . - ..... 1/H Proude ::)ide Weir Number

H V2 /gL (ft)

................ ,._......_,..~""~....-

.054 18.519 .036

.060 16.667 .039

.078 12.821 . 04 3

.088 11.364 .050

.108 9.259 . 057

.126 7.937 .064

.. 135 7. L~07 .068

.153 6 5 ~,c, • J .) .078

.130 7.692 .062

.094 10.638 .054 .

.141 7.092 .069

.100 10.000 .055

Froude Number V2 /gH

---.-..-.087

.093

.098

.109

.120 .

.126

.133

.144

.121

.115

.134

.117

Reyno :1 d;:~ Angle of Discharge J}::vJ_a~=ion of' N'J.mber Q2/',ll pvr/u Upstream Downstr2am from ·c 11l1pU. tcc1

values X 1000 (?s)

-~----''""-""'-'-'~--~ ~.:~ ---~--""""'- ·.·-.--,c .. .,"'C'--..,..,.--.....,_----~-

23.1 23 60 -- 12.1%

24.5 30 48 - 6.1%

25.8 32 4L~ - 8 .d__ '. '/0

28 .4 35 43 - 19.0%

30.8 41 45 - 1L~. 5%

34.3 40 40 - 6.6%

34.8 43 40 - 9.8%

37.8 42 43 - 1.4%

32.9 37 47 - r(. Oojo

29.5 . 37 L~7 -.17.6%

34.9 43 45 - 12.3%

29.7 40 45 - 21+.4%

0> V1.

DATA FOR 24-INCH WEIR TEST

- .

67

24-INCH SIDE "WEIR TEST

Head Quantity Head Quantity Velocity Total Q2/QT OD. Side Weir on Sup- Suppressed Flow

Side pressed Weir VJe:l.r Weir

H Q2 Ql QT (rt) ( cf''s) (f't) ( cf''s) (:rt/sec) (cf's)

.045 .0536 .233 .420 1.05 .473 .1131

.056 .0767 .247 .455 1.10 .531 .1442

.063 .0918 .257 .480 1.13 .571 .1605

.072 .110 .269 .510 1.17 .621 .1787

.081 .128 .281 .560 1..25 .688 .1860

.089 .165 .296 .600 1.30 .765 .2156

.100 .198 .312 .650 1.36 .848 .2334

.112 .235 . 337 .720 1.43 .955 .2460

.126 .270 . 358 .780 1.48 1.050 .2571

.104 .211 . 318 .660 1. 36 .871 .2422

.084 .150 .288 .570 1.25 .720 .2083

.043 .0477 . 230- . 410 1.03 . 457' . .1077

.120 .256 .331 ;660 1.40 .920 .2782

.089 .160 .294 .530 1.30 .690 .2318

.044 .0511 .236 .420 1.08 .470 .1087

DATA FOR 36-INCH WEIR TEST

70

36-INCH SIDE 'ltv"'EIR TEST

I~c0 .. \..~ Quantity Head Quantity Velocity T.otal Q2/QT on Side Weir on Sup- Suppressed Flow Side pressed Weir Weir Weir

H Q . . Ql "i

QT , ~ct) . ( cf'~) (f't) (crs) (ft/seo) (cfs)

.086 .274 .319 .67 1.38 .920 .2978

.076 .197 .277 .50 1.24 .690 .2855

.034 .0594 .231 .42 1.05 .470 .1263

.113 .340 .352 .77 1.48 1.070 .3177

.098 .313 .339 .73 1.44 1.013 . 3089

\ . 087 .264 .316 .66 1.36 .894 .2953

.070 .209 -.286 .57 1.25 .749 .2790

.057 .142 .262 .50 1.16 .602 .2358

.045 .101 .249 .46 1.11 .531 .1902

.028 03°7 • ;;I I .241 .37 . 97 . 384': .1031

.056 .149 .267 .51 1.17 .659 .2261

. 073 .226 .293 .58 1.26 .806 .2803

.100 .344 . 330 .70 1.41 1.044 .3295

.llO .404 .345 .75 1.46 1.154 .3500 '

HE"a:d c:-l lj r~ ~-... _-_,. ·": ... ;_ -, I;.:··.,_~}-. -·~-. r ,-.. -.-, -~ l .--:., !\ ~~l. -~~!- <· ci ~· f):~ :- e ~ -~- .. j )~ \ ~~- ~'- ·t· ~~(I }'1 (,If' ...J. -· .. • ~ • - • ' •

S J. cJ. :~ 1~} ~--~ ~:- ~~ -. l:. ': : '.--. -~. ~ ; :. ·,' ; I·" j_' J: :, H v;) / . ·2; " U fJ ;:; -~-; ~ ~- Z:~i :-: J}~J L~l-1 ,:::_ t }.-· ~-- El ~ ;; V L-!- ncv- ~· ,) t (:: c1 (ft)

vc:Llu:.;;=:; X 1000 ( ('

-.....-....-.. ,--= ;"0,..· -~.--. -'"""-=-··-. 7-)) ' """"- ..... _,. - .......... ' -~- ' ~-- • J• •• , ~ • ,__., .... --- •••• < ~ ' ' ·- - , •• , ... ..._ ~- ·- .. ' -- ---· .... -----~- -- ·- .____ - ~,_._,..., ..... '--· ... -

.086 ----,'; or .020 .122 30.6 15 L!-O 2 () l)rf :J~, • ..Ju -- ::; . c.p

.0'(( 3r- ,-0 .016 .107 26. ~- 25 }r r.: - 7. ?!5 \_J ..----. .)oj ,- :J

. 034 88.25 .011 .086 21.8 5 60 1----, od -- .) • ;o

.113 26.55 .023 .131 33.9 23 26 +10.6%

.098 30.61 .021 .127 32.4 20 28 + 5.5%

.087 34. L~8 .019 .119 30. L~ 24 31 + 0.7%

.070 1.12.06 .016 .107 27.5 26 30 -11.5%

.057 52.63 . 01L~ . 09'( 24.9 22 36 -10.3%

.045 66. 6'{ .013 .092 23 .L~ 20 l!-O - 8.0%

.028 107. ]_lj. .009 .OTT 19.9 no nappe +llt.J.%

.056 h----, 7 r·-:J.). :J .01h .098 2l!-. 9 2h 50 61 - 7 • JO

.073 L~1. 09 .016 .107 27.5 27 1~ 0 9 lJ cl - ' .-p

.100 30.00 .021 .124 31.7 22 32 O%

.110 27.27 .022 .129 33.1 15 32 + 2 . 57b "'.J I-'

72

DATA FOR 42-INCH SIDE WEIR TEST

73

42-INCH SIDE WEIR TEST

H8ad Quantity Head Quantity Velocity Total Q2/Qr on Side \1-Jeir on Sup- Suppressed Flow

Side pressed Weir ''J c :ir \-Jeir

"'-t Q2 Ql (~s) 1.

r c:> "- 2 ( cf s) (ft) ( cr·s) (ft/sec) ~ .1.. ~-

.075 .309 .315 .66 1.37 .969 .3188

.061 .242 .294 .60 1.30 .842 .2874

. Ol+6 .175 .270 .52 1.19 .695 .2517

.076 .312 .313 .61 1.37 .920 .3391

.052 .204 .. 273 .so 1.20 .690 .2956

,-.-,5 . '~·..) .070 .228 .41 1.03 .470 .1489

Head o: s 1 de vr~ J :c

H ( rt)

~~ .. ,-,.-,'"'1!-~~···~ .• I-~· . ..,-.· •• -: ..C; -,

'075

.061

• Ol.J-6

.076

.052

.035

-- I J '/ _,_,_

L' C Cc( i 0. (.)

r::r( JCl :J • .)U

j6.09

Li-6. 05

67.31

100.00

J/ ~e0 -~-·- r"-,

1\]i __ l}";':-:, :,_.]-j

\: ;:~;·,i-, • (_'_; 1_,·

. OJ'(

.ens

.0}3

.orr

.013

.009

}? r· ~) -t)_ c ·; -~-·

J\ - ~' .1- J (; _t I ~ r

1Tl_~_ri11J 2 t) l-J~.~ ::Ut~:~~-· CC>/ -v·r · L~ 11 p::·•v/ll.

·-·~ --·-/ ,_ ··-· _ _ X J()()Q - .; .. ~...-.,.~-c. ~' ·'-' . --- -' .

._ '! l • _I r J. 30.0

.J.J.l.i 27.9

.100 .1

.121 29.7

.102 25.2

,083 21.1-~

J\. ~i - l_ c 0 ,..., ) -i ~-~; c.} J j

1J-;J ~~ t,c:r~~J [!.~)·:-,~:-~~ ~~--- t c·

2li

21

20

15

10

5

) I r::. i_)

Li:S

~0

l15

50

60

]) -: _· \ ~ _I ,:·) f; ("\ j_

I •--

"{.'_,

_f }~'();, C \) ~~~ C; t~ t r~' (1~

\l e~ 1 ~~:. c:, ;3

( c:!) -')

....... -- • . . j· ...

+ ~~ oc~ _..I • /')

+10. 1!}.;

-1·17 .ElJb

+10.3% /

21 I ' rJ ~- ·-t-. \.>;J

-10. 17;

'.] , .. ~-

'-·"·- ..

:: c) •

1

--, " l""o.. •

FOOTNOTES

21.

r l C?Q) S. r:l • 1'"' ~. \-~-u l~e spl ~Kays ror regulating sion canals. Transactions, A.S.C.E., Paper 1694, p. 1561-1588.

75

dive-:'-vol.

C_P;_l\OLLO, J A and N. /\. srr::.~\..LTSK-AL- r -, ~2o \ -:\ · _ • ", - _.__ \__:_::J :)) vlS-

cnarge over side weirs with and wit~ou~ baffles. Journal Boston Society of Civil Engineers, vol. 16, no. 1, p. 118.

_ J .• ~--:;~~:1\~ =~·'-'I., a::"d ::.::.B. TtJRN"ER (1929) Precise weir· measure-ments. Transactions, A.S.C.E., val. 93, Paper 1711, p.999-ll90.

1176. Herschel quotes from WOLF, R. (1860) Biographies relating to the history of civilization in Switzerland. Vol. III,

"1 r-7 /" p. ~tO·

p. ll'76. Herschel quotes from SEAI(ESPEARE_, Julius Caesar, Act II_, scene 2.

(1940) Lateral spillway channels. Transactions 2 (\..- ,- r ,.-..,

A.S.C.E., vol. 105, P er uo9, p. b0o-oL7.

'~:\\Y:::-'JH, E. (19Ltl..~) Flovv characteristics at rectang1..<lar open channel junctions. Transactions, A.S.C.E.; vol. 109, Paper 2223, p. 893-912.

iS_, E. ~ 1956) Flood protection of canals· py lateral spillways. Transactions, A.S.C E., vol 82, hY 1 5, Paper 1077_, p. 1077

, . . Ibid., p. 1077-5.

. CHOvJ_, V.T. ( 1959) Open-channel hydraulics .. NeH York, McGraw Hill, p. 340. ::

16. U.S. Department o~ the Interior~ Bureau of Reclamation,

76

Division o~ Engineering Laqoratories (1956) Hydraulic model studies of Eoulder Creek canal drainage inlet and overflow weir sections. Report no. Ryd. 407, p. 1-14.

l'{. WJRP~-IY, GLEKJ" ( 1950) Similitude in engineering, New York, Ronald Press. p. 41-42.

TULTS, H. r-)56) Flood protection of canals by lateral spillway. Journal or the Hydraulics Div­

. ision, A.S.C.E., vol. 82_, HY 1-6_, Paper l077J p. 1077-1

19. VE~~ARDJ JO}lli K. (1962) Elementary fluig me~hanics. 4th ed., New York, Wiley_, p. ~§~.

7?

Bil3LICGRAPEY

8:\.:-~2 r~•. H. (:sAo) Ls. tex•al spillway channels. Transactions~ A.S.C.E ~ vol. 105, Paper 2069.

C~-~0'.'.'_. V.r;}. (:::;_959) Open-channel cydraulics. New York~ McGraw Hill.

" n ·:""'\"!\ffjr.1..,.T ( "1 02-,) lfflli"""\ .,-! ""I ....-.. """"'• ,.,..., .. -, • ,.: __ ...

~'":0. JJ. ul'LL.lli .J.>' 5 l~,e Q-'-SCn=r0lDG-Cc.po.Cl vy

(1916)

(1950)

of s=..de:: W<:~irs. n Institute of Civil Er~gine­ers (london)) Selected Engineering Papers, no. 6.

Side channel spillways. Transactions, A.S.C.E.; vol. 89, Paper 1587.

Similitude in engineering. New York, Ronald Press.

N"II'II"c\10, H.H.R. (1928) Side spillways :for regulating dive:::·sion canals. Transactions, A.S.C.E., vol. 92, Paper 169~- .

•; - ', -0 'r 0 • ._,...._ -, ••,~

o_) .~ _; ~ \; ~~ :.._L.J:

. C. B. TURJ\lER ( 1929) Precise weir meas1J.re­ments. Transactions, A.S.C.E., vol. 93, Pc.per 1711.

(1956) Characteristics o:f side flow weirs.

I_..,..

. '

Tl-:.esis. University of Southern California..

:·o~~) R~o~· ~h~r~c~erl·s~~cs ~t recta~~u-~~r \. ....:..../ • • ..r... _._ vv \...i-.~o..~.c;;... C\.. v v.....~- ~ .... b ..J.,.c;,.

open channel junctions. Transactions, A.S.C.E., vol. 109, Paper 2223.

Cr'\.EC.~IIJ ~ :; . A. , and N. A. STEYSKAL ( 1929) Dis­cha~~c over side woirs wit~ and wi~hout b~ffies. Journal Boston Society of Civ~l

~ - r =~cince~s, vo~. ~o, no. ~.

·: \ .. :-· __,..,' \.. j

.. .,.,__ .J •• '·' J ,\..,• J.- -~ v

(1962) Elementary :fluid mechanics. New York, Hiley.

4thed.,

78

VITA

Ed[';ar SnovTden IV was born :May 15, 1934, in 1r·Jashington,

D. C. He graduated ~rom t~e Episcopal High School in

J:.J..,;.xandria, Virginia _ _, in 1952 and :from the University o~

Virsinia with the degree -of Bachelor o:f Arts in Mathematics

• - 9' r J..Yl J. ::;o.

Be was commissioned into the Regular Army as an officer

in the Corp·- of Engineers. He had engineer:ing assignments at

Port Campbell, Kentucky, Ui Jong Bu, Korea, and Fort Belvoir,

Virginia. During his Fort Belvoir tour of duty he was enroll-

0d in the School of Engineering, George Washington UniversityJ

~:;.nC. had "v. _.:; privilege to serve as White House Social Aid to

:eros:l.d8nt John F. Kennedy.

In 1963 he ·was assigned to· the University of Missouri

c:~·~ Ho:ila, enr·olled as an undergraduate student, and completed

·~1s requirements ror the degree of Bachelor of Science in

c·:L vil E:'1gineering in January-' 1965. He continued in the

~n J~rmary, 1965, he became a registered professional

cnzincer in the state of Missouri.

He 'i:Jas married to Miss Patricia May Spokes of' Rolla

in June of' tnat year.