- -·d1 � ], . Bra --f'Y UNITED STATES

DEPARTMENT OF THE INTERIOR

BUREAU OF RECLAMATION

HYDR AULIC COMPUTATIONS TO AID IN THE

DESIGN OF STATI ON 1097+60 WA STEWAY

FOR THE HEART MOUNTAIN CANAL

SHOSHONE PRO J EC T, WYO M ING

Hydraulic Laboratory Report No. Hyd.-221

BRANCH OF DESIGN AND CONSTRUCTION

DENVER, COLORADO

DECEMBER 5, 1946

u.� IT,_,;:, ,:.-.:-r,, T�,::; l,t.L .:-,nTrdr ,\ 1 OF T11L u� l'SrU .. O:l.

i3ij i'Lt,U ,JI hr: CL,_;\L,T 101i

:.r,,i-.c,1 .Jl � -s.i. 0'1

1 L nu 1..,onstruction r.,n,;i116E:>r.Lr.6 dl'-t :_;eolo,;icd. Control

uH .. f'-t.;;"'e .... rcn vi vis.Lon �0nver, Colort...Co ut. Cei,lt>er ) , J. }46

Lc·bon, tor:7 t .. e,.ort rm. ;.:;.::1 nyor,:u.lic Lt,norbtory Com, 1iJ..ed by: J. ri. joums 1:.nct

Fi. d.. BL. ck-.,, ell Hevi�wca by: J. �- Jridley

.:.:ubj cct: ,1y-11'L,L<J..ic co:n ,uktions to [,.i.ci in t:1c ,;:...:...;i�n of ::Jtc.-tion lj)?/-60 ·,-;t...�tE:,V,D:f for tne nt:1.rt .!ow1t .... in Ct..ttc.:i--.:.;nosrunc Project, ·i,yo1<1in5•

Inc.ro<,uction. ri.yc.trLU.Lic com_ul.Lt.Lons \',en, ll1< .. .::c in L1,e uenver

.,Jun.L-.i.c Li...bon ... to;:-y du.rir.�: J,·iril oi' .i.';1_;8 to i,io in tnto o -sie,'11 of

.::itc.ti·:m �,..1;7/.JJ 'f:c.ste;·:,.y for trw ric:..rt :'i1ountc.in Ci..n: . .L, ::,nosnont: r'roj£,ct,

in tiie L.borc.tory.

l'ne ori,"".i.rn ... l .:iu:oLf, or trio -,�c,..;te·,-,L·J Li si,own in }· i:;urc 1. ;:,tLtion

JfJJ or tn_, ·;,,,vtc.1.1.!y i.:, on tile c:..1:c1 c..,nt,u·lir,u 1..t c�.11c. ... ::itLtion 1.J)?/84.

T,;-c' 1�·,.-�,tt;,n.,:,· f .. !JY.'. ;...=; contro.1..1· a oy t'..'.) rt:ct1..u_,).:..1.c..r 0 t·i., .. ::;. 1.11 opr:;11 cnute

Tut. 10.1.lo .. lL,.:'. r(;co1:.i'!':E;11ue:, c.tir:1en.,;ions i',,:;;l'e ;1eter;.1ir:•.'c. b.: corrt;.>:,rin6

to1;:; .1:,-:...n,'.,(J....i.C )..'I'O,J':rtic:·,,; or' t.1,i:s str·uctu cc· ,, i tn t110,.;;<-' of t .. ·,.,ro>.i:111.. tely

11wstewL.y Culvert. The ex�eriruental oischbr6e n. tin6 curve for the

cuLvert inlet w�s �etermin�d by test on the model culvert of the

w&stev;c;.y of the Grc,vity Me.in Cw11,l, Sktlon l6i/30, Gile, VL.lley Project,

,,_ri:.::.orn.,., wnich wti.s unlier test c:.t tne time in the ::i..L.bori::tory. The arrange­

ment of tne two culverts 11na the c1}ii>ro&cn Chi.illnels ·.vere essentif.lly the

stJne except that the roof entrE,nce was sqm .. re for the HeHrt :,1ount&in

Culvert wid rounded for the Grc.vity Muii1 C&rn ... l Culvert. The entrEince

w&s rectt..n6'--llc:.,r in the model. The rJode,l. reµresented culvert openings

6 by 7.5 feet to a 1:.:.4 scltle for the Grcivity Mf::.in Canel and openings

4 by 5 feet t0 1:; l: 16 seal� for the Hebrt Mountccin design. F'i?01re �

shows tne exp�ri�entLl w&�i&�dy discnu.rge rL.tin� curve converted to . . .. . prototype qu&nti ties for tne Heu.rt ,vlou.ntc..in Wasteway. .From tnis curve, the

W!.isteway will C1;:trry 5b0 seconci-feet for the ffil:!.Ximum can1:..l w1:,ter surfe.ce

elevL.tion of 5171.1), or for the design cti.nal dischar6e of 554 second-feet,

the cL.nal w&ter surf&ce elevation will be 5171.05. This di�chLrge curve

m;_,_y be useu to determine tne ct..m.l w1;. ter surf&ce el0vc:tion when any stbted

flow L-; checked cma diverted by me1;;ns of the wt..st�v,uy. Tne experiment1:..l

VbLUes of tae coefficients of contrt..ction Ena aischarge ere .lotted

c..g1:oinst heao in F'i:.:,-ure J for the i-iet:.rt ::.:iountbin Vlistew&y.

Comr.,utc:.tion for me1:,.n cross-sectioncl velocity t.t St&tion ;.:/43 .Ul.

Tne velocity in the cnute at Station .:./-40 .ul w1:.s corn;0uted by tne Design

Section by starting witn the �no•n velocity &t Stt..tion J/-J3.13 und

tre�tinl successive short rec;cnes �sis customLry for fLow in steep

cnutes. As b checK, tne L.ssumption is mLde thL.t tne flow will be non­

hCCeh:rating -:..t St1...tion �/48.01. From Mo.nning' s eyuLtion, u velocity of

37.�I feet u. second w1:;.s obtc..ineci, which compLres very fEI.vorably with

37.4 feet a second as computed by the first method.

Computution for verticul curve, Station �/43.01 to �/14.45.

LJeriv1;,tion of" tne equc.tion for the tn,jectory in the cnute, beginning at

St1:.ttion ,._/-40.Jl, is &s follows:

y : X t!:ill i/J t g . V ;;,_ �d ,:_ O cos 'P

,:_ X (1)

wi1ere x is tne riorizonthl coordim,te, y the vertic&l coorairn,.te, ¢ the

::;lope &ngl.e of the chute ( referred to the hori�ontrsl) 1:..t the beginning

of tne curvt' , VO

Uie mee.n cro s s-sectione.l velocity for the maximum

disc ilc. rge con<1itiQn at the beginning or the curve , bnd g the acceleration

of gr;.vity , T he VL,llecito Drun St1ill1-v1:.y , which w&?. tested in the laboratory , �Jo sses sed h trc..j e ctory n ear the end of the chute very similc, r to the Jro.,:,osea rie,::.rt ,fountain design . The oi-.i.. �im.ll tr&j ecto ry of the V&lleci to S1Jillwuy w:....s bu s eo on FormulE. ( 1 ) . Tnis tn:,.j �1 ctory wa s found to b e e:>. c e s s ively steep , sine.:; tiie w1:,ter SJ.:irang free of tne cnute floor downstreb.ll1 from this

vertical curve . Tne com;-mted mean velocity , V 0

, con �iderin 6 c.1.ll losses in tr1e c 1 Jut e , b.t tne beginnin g of the tr1:,j ectory Wb.::l com_..1utod to be 5 -;i feet &. ::;econd 1 or the Vc.:..1.lE: cito Spillway . ii flatt er traj e ctory , bt. s c<.l on the theo reticc..L mean velocity of 82 . 5 feet a s e cond , which Wb.S colll1mted by n� 6lecting b ll lo sses , proved satisfa ctory . The equation for the sati sf& ctory

tr�j ectory �roved to b e :

Y : X tan ¢ f g X --rr-------2V cos.c: .¢

�

wnere V i s the tncoreti ca.l velocity nt Station ;,:f43 , Jl .

The r�tios of the square s of the two velocities are : 2

V =

Suostituting ( 3 ) into

( 3� .5, )A:

V 59 °

( � )

2 ( approxima t e ) = 2 V

Y = x tan ¢ /. g

4 v/· co/¢

( 2 )

( J )

( 4)

Inspection s.'.1ow s that if hci lf the va lue of g i s used in Equation ( 1 ) ,

tne r ,0:· su.1. t s e.re iuentic&l with tnose of Ec:un.tion ( 4) . In tne propo sed c. sign o.f rl.cbrt r1lount&in Wastewuy , 1/:.:: g was used in Equation ( 1 ) so the tri, j e c tory is sufficiently fla t to prevent any sprin ging from the cnute bottom o. t l:,ile ve:::-ti cc.l curve .

Tne velocity useci in L!_]Uc.J tion ( 1) was the mean v eloeity of the c .r-0 3 .,-s e ctiun . .:iiuce tue 1nt ximum velocity i s con sider&bly greater than the mob.n v � .1.o ci ty , a tr, . j e ctory desioied for the me&.n velocity will

ue too stee:J for tile m_. :; s of wb ter flowing in the area of m1:..x imwil

vslo c i ty , ,:, s w1.1 .s verified by tne Vall e c l to S�, i .J.lwE..y te::it s . for this reason , it see,!!s ..LO t:,ic�.i th1, t the trc. j ectory should be desi �ed for the maximum

r, . taer tnvn tne &ver,1 ;e:e ve.loci ty o!' the cro ss-section a t the beginning of

3

the tn, j e ctory . The r& tlo of me xi mum to me&n velocity for the fol.iowing

thre e structure s i s :

( 1... ) V2..1.J..cci to .:::i 1; illway ( model me1...suremen t) Vm1::.x . /Vmeb.11 = 65/55 = 1 . 18

t b ) i:Ju.1.J. Lc.:ke uccm S:. il.Lwc..y ( moclel meti. surement)

Vrnax . JV mec,n = 66 . J/59 .4 :: l . 16

( c J 0outh C c:.n�, l Chute , U n com,;e1 n5re Proj e c t \ fi elu rne!isurement )

V·ui...X� Vm"' '-'11 = 3,; . 8/�8 . l = 1 . :.::0

Fro:n tne ::; e :'.!leu surer:ien t s , inol ce1ti0ns are trui t t,he v el.ocity to use in i:,.1uc...tion , l ) should be abou t "-0 µercent 6rel. ter th1m V

0• Equb.tion ( 1 )

toen becomes :

y . x tan ¢ t 6 ( 5 )

1 , ccoroin5 t o thi s 1::.m,ly si s , Equ1:ttion ( 1 ) , usin 5 the mean velo c i ty and 70

ins te&a of 50 percent of g , m1:1y be used in computing the traj e ctory . E>:perimen t s should be conducted to sup,:iort thi s s ta t ement . Entrc inment

of ti.ny 1.:;. i r ;; ill £,ad u. Safety f1:1ctor, s ince velocities wil.L be lowe r .

1 ,ne�le of fl&re o f the chute, S tation "-.j.-:34. 45 t o ,3/65 . 88, en tering

the s ti.1J. in ,;-b1... sin . Tne economical widths of cnu te &nd stil.1.ing-bc, sin

&re deter�1in ed from cost consit.l.eru tion s . The cnute must be fl&..red a.t

its lo ·r. er enci ::uch thc..t ti1ere will be c.c uniform rii s tribution of depth

of flow en terin5 the stil.1.lng-b1.,.sin . There mus t be a spreb d in5 of the

flow from tne narrow c nute section to the wider stil �ing-busin sect ion

1...t such u rL.te ti1b t the uepth l1i stribut ion r�mt-ins relE..tively uniform .

;:iuch s,.Jret.o.lnb uncier n1:.tur1.1.l force::i l s probably 1:..fi' �cted by the s evercl

nydr1.tu.1.i c j.Jropertie;; involved , but i ts rLte is known to be very closely

rc_;_"'- t eu to tne veloc i ty . The tneoreti ct.l mew-1 vel.o ci ty at tne entrc.,.nc e

to th"' stillin5-bbsill f or tne Dt::er Crec,1< Dam b1-1illwc.y wr.. s 7.3 . 1 f ee t E..

...; ecorw ·.vuicn i s t.!.J,?roxlm2.tely t11e ::ib.We c. S t ru., t for the Heart iJountt:in

�j.J l.LJ.w1.,.y . Te::its on the �ouel oi tne Deer CreeK S0illway s no� ed thbt

tne :Ill-'xi rnum to t:11 bn6le of flt...re , in 1JL .. n , to ma. in tttin & w1iform aej.Jth

aistri bution tJ t the , JOOl E:ntn ... nce v, 1::. s 11 degre e s . U s in 5 11 d egre e s for

t:w ne ;: ... rt . . iountt.in d e s L;n ,?lu:es tne beginning of the flare a t

.:;t1- t i on �f -}0 , 1 . Uni0 �; s tneri:: ure o tncr d i s bdvun t5 6e s , 1:. reauct ion in

cost u nLi goou. ,Jool. �· ctlon wll.1. resu.1.t by ueginn in6 tne flure c.t hbout

4

Sta tion 'L/- 15 .

Slope of tile chute leu.ding into the still.ing-basin, Sta tion ti./.94 .45

to J/65."88 . General experiments n&.ve been conducted in the laboratory

on chute sloµ e s ran6in� from 1:1 to the ho ri zontal . Ther e h� s been

.1.ittle a.ifferen ce in the length of the j u.rap or the tailwc.ter required

to maintL .. in the j ump for the seven. l sloµ e s test&cl . A stee�er slope

than J : l, now ever , reduc e s the effectivenes o of the jump in dis s ipating

ener.D7 of tne flowin'g wuter wnicn Wb.S inai cated by deeper s cour when

no block s o r sills were used . With block s and & si ll, or � a entuted

sill ��one , the ctVera6e depth of scour wa s a bout the s&me for &�l slopes .

nydn,.u l i c cons ider&tions would indicu te u 1-1/�: l slo11e. Economic

consideru tions, now eve r , snow ti1e s teeper slope to be the mo re desir&ble .

For a givru1 elev&tiori of tne stilling-b�sin, the fl�tter sloµes will

re.:iuire nigher ret1:tining-w&lJ.s, � 6re&ter l ength of cnute floor to be

a e s i 6neci ag&inst UJlift pres sure, end mo re excav& tion, thus incre&sing

the cost. The cen trifu6c..l forces at the j unction of the sio1)e with the

ba s in floor are greater for steeper slope s, but the struc ture i s usually

exc e ssively strong lit t!lis point.

C hute blocks. Sme.11 block s plc. ced on the c hute at the entrance

to the stli.lin6-bu.sin a re effective in formin6 h more eff i c i ent j ump.

In sucn cuses , the incoming j et i s corru6at ed into & number of sm& ll

j et s , each t->roduc lng its own sy stem of edd i e s, tnu s resulting in a .gre&ter

di s s ipt.tion of energy. Wi th th0 numerous jets E:ntering the pool in &

corrugated ;i ,, ttern , i-'c,rt of the hi�h-velo c i ty j et i s lifted f rom the floor,

whi ch a.lso b cids to the effectiven e s s of the jwnp. P.ei,eu.ted experiments

rn, v e snown crmLc blo cks to be effec tive in reduc in6 .s cour beyond the end of tne stillin�-ba s in , but tnu t furtner reauction in scour is very sli�ht

with b.1.o cJC heignt s t?;ret; ter th&.n the theoretic1:1 l D1 de1Jth enterin g tr1e rk,s in. v1, in the CL .. s e of He1.:..rt :,,loun tc..in rh,stE:wuy, i s &c1u1:tl to () • .33, whi c h

r e sults i n a. blo cK hei 6nt of atl[iroxima tely 5 in ches , prototy µe . I t i s

very tJrODb.ble t h& t tl!i 1:; unusually tJJin .;11ec, t o f v, a ter flow in6 a. t hi gh

velocity will contain 1-. ni �n percen t1:, 6e oi' entn .. in ea 1:. i r. For ti1at' rea son,

the de 1 J t n of ·.n. tbr enterln ,; the µool mt..y be u s much 11. s lJu f) erc,3n t ,;ret..ter

t,1,.n tiie trkoreti c[... l c,e,;tn , unu so 1 -in cn i 1l ;h c nu te blo c.i<. s ure recommended .

T c .,, t s DbV b ciuo .;n tnc.. t ,c ·,vidtn of b J..oc,.; uppro:x imh t8ly e,.iuul to tr;e ileigbt i s

u e .;; t . BJ.oci s L,. incr1es ,�ide, arn,.nc;ed t.. 5 s uown i n Yi 6-ure 4 , E.re recommended .

5

Since the velocity is much lower at the sidewalls , b.1.ocks ;,h.ced here have

proved of little use.

Stil.1ing-b&.sin floor blocks . my arr&.ngement of buffle blocks on the

stillin g-basin floor will, of course , aid in the dissip,1 tion of energy in

the pool. Blocks with vertical upstream f&.ces are more effective th&n

tnose with sloping upstream fa ces , so thci.t sm�ller si zes of vertical face

blocks muy be used to produce the same re sults. However, the vertical

upstream f�ce blocks will receive gre�ter impact as the high velocity

carries through on the floor �ith littl e retardation. This calls for facing

on the block s , reinforcement, und !:l11Choru5e. The results of model tests

of three structures , with the mv.ximum cbu te velo city approxim · tely the same

ci s for the Heci.rt i11ountain Wasteway , indicate that c. row of blocks about

one-sixth the theoretical D2 height pl&. ced a, Jproximu tely c: t the downstreliill

two-thirc:.s point of the stilling-bt,sin results in the best jump performb.!lce.

Sin ce the theoretical v�lue of D� is 11 feet , b block height of � feet was

chosen. It is recommended that row of basin floor blocks , &rranged &s

shown in F'igure 4 , be in corporated in the design.

Stil.iing-basin floor elevat ion. The proper elevation of the stilling­

basin floor wili be determined by the use of results from model studies of

two s imilar structures of the following hydn,.ulic properties : ( & ) discharge

of 106.6 second-feet a foot width, Vi of 73.2 feet <> secon d , D1 of 1.457 feet;

theoretical D2 of :a . 3 feet; ( b ) discharge of 160.0 SE=cond-feet o. foot width,

v1

of 75.l feet a second , D1 of ;c..13 feet and theoretical D� of ;.;6.0 feet.

The me1isured minimum D2 depth for a good j ump wu s 18.0 feet for ( a) and �;.; feet

for ( b ) , which �re 84.5 and 84.6 p ercent of the theoretical , re spectively.

Tr1e pos sibility of h�ving less deµth than the jump theory indic&tes , without

causing the j ump to sweep out , i s at le�st �artly due to the influence of the

blocks in maintaining the jump in the basin. The theoretical D� for the

structure in question is 11.0 feet , and 8 5 _f)ercent of this i s 9 . 3 5 feet.

The end of the tr�nsition at elevation 5089.50 i8 considered u control

over whi ch water flows at critical depth, whi ch is approximately �.25 feet.

Con sidering the head ht thi s point to be J/ 2 de , gives a water surfa ce

approximately 3.35 feet for mc.: Y.imum di.;:;che.rge , and the required difference

in stilling-pool floor and con trol elevation s becomes 6.0 feet. From these

considerations , the floor llb.Y be safely raised ;:..09 feet to elev�tion 5083.50,

6

.-..s sno·Nn on fi��re 4 . T .'."ie j umi1 i'or tne t,t.; �. teu structure swept out oi' the;

bi., Sir, ·:. nen trw tt..i1. M .. ter -..: t: pt n w1... s reduc E.-c!. to t .. ��ro;dmt tely 75 i-Jercent of

tne t11eor�ti cLl D� - On tni s b1... sis , the e1.evL tion 5003 . 50 �ool provices

.... n ex c e s s of l. 1 feet L 5t. in st the j wnp swee.i:1in 6 out of ttH, bi :::;in . In the

te.,ted structure s , tne diff erence in elevhtion between t rw st.il.J.. in,;-b1.. sin

f loor &nci riverbec: -.;.own stre,..m wt..s .3 feet . The b-foot '.l iff erence in the

He& rt .1Iount1.. in desi ::,n snou L.: ,;ive &cd ed s:..fety t..61.. inst tne j ump sv:ee�J in g

out .

;..no ther L., ctor efft: c t i vd.y reuuc .i.n 5 tae re. , ui r{::d D;.:.

cepth is the

intl.uen c e of en tn .. in eo fa ir in tne c hute flow . Vlitr , tne ni gt1 velocity t.na

smE;ll r1 e: - tn en terin� tne pool , LV,, ilL ble ct� t1:. on tl:le 1:. bsori! ti. on of 1.. ir

woulc .i.nui c c.te tlic. t tne f1.ow m& y con tL,in mu c n &s 5C � c r c en t b i r .

lntrouucin,; tni ::., v,d.ue in ti le j ump momentum eqw. tion results in c,

r�cuction of D, by b �proxim1.. tely d;.:. percen t , wnl cn �ives &n t..uued e� ce ;:; s ,:.

t&il\\ t... ter ciet->tt1 of h.i:Jt,iro.x im1...tely l . 7 feet u5c. in s t tne j ump s ·,\ '-- "' l in; out ,

f ne D� aeJtn o f ) . 3 5 feet i s , thErefore , ubout. � . 5 to J . 0 feet in e�cess of

thi:: t , ... t wui c! l tne j umµ wi1.1. sweep out .

0tL.i. .l.i.n6- Ln. sin .Len 5th . Tue l.:-n 6t11 o f tm, ;:; ti.1.1.in .;-hc- s iu s 1,ou1.a

be ;;.u.l 1 i c i ent.L,Y 1.on� to _. rE:ven t ex ce.:3.:,ivu ..,ro ;:. lon ,10·,m s tre1..:u . Tlle L:n �;t�

of b::..;.; .in i;:; usuc. .J....L.j' m1, ,ie e.1w .. l to tne lcn ;tn of the � ump . r ,le .J..cn -;tn of

the: j wnp c.-l1G. b sin c;;..n b e s nortenc·o w 11e:n c nu tL, :..r,u i;. 1' ron u.:..o cl<s �. re u s ea .

The resu.l t, :;, on t r, f:' two stru c ture::; men t.i on ec in t1,e � r e c t,clin ., ::.; ect 1on

inui cc-- te tw .. t t1 b:..sin 1::n,;tn four t imes tae t, l .iWi.. tcr , ,e t , tr1 for :.. ,_;ood

j um;; '- t mc.:>.imum :.li scn. .... rbe e}.tt:nus t:,E:; i'U..L. .L l ccn ,.;tn of tnE j um1, Vv nen t LO cks

bre emt11.oyc • On t . i i!:: bi.:i s i s , tne 11.in i.num 1. en _;th of 1_,1.. sin is J? . ,. feBt , or ,

suy 40 feet . T ne 15 feet of trunsi tion &t tne end of the bt sin i s

con :, L.: erc .. · c;;;irt..bJ.e L l1U i t n .i. .1. _ D t-rvs a;:; 1.. n c.�..1l tion t o tne b , sin .len,;tn .

r·or e conomic reLson ::, , i t i .:, r t, com::i c nc.80 tr1: . . t t ne s tillln,;-b,, s in !)c 5 , ,orten ed 10 feet over tne ori� ini...l --i c .:; i "'--n , ;:;ince st. ti s i' uc tor:; j um"i : Jerformc.n c e m1.:.y

be -:c}.i-- e c tea for Lhe snorter bt sin . V, lt ; i tnc si 1orter b, sin e n d n.i. r;Her floo r ,

s�me sL.v in g in ex c�vb tion C L n b E: ruL1.i zeci .

Tn .. ir: ing-w: . .J..1 rdi r';hts . Tht.; ::: i. C le,H. l.i s o i' ti 1e c r ,u t (::: c rc n 1 ,e r2auced ut

leL �t :.. roo t ner. r tn� uuu of � ft(.; c nutc , ;:;ln c e tnt: :n;.. ;. irnuu ;, i.. t er ,:e, t : 1 v: .i.11

cot be more ti� n l f oot . Tne stillin ;-b�sln tr� lnin �-� � l i s nLv e Lbout 4 1 ·eet

fre 1::bo ..... ro ,, !lc:D tne L.ow i s cri t i ca 1. � t the enci of tue tn,nsi t ion . Sin c e

some s courin ,I; must 1 ccur doNn stre,, ;u Lefore tne ue 1,th w i .Ll b e cri ti cul c t tile

7

en ,i 0 1 t.nt:: s .1.'.) 1 , i r , ,� 1 .1.0 ,)r , : nu to ,. J..Lo,1 tor ::,omc s 1. 1 i�: !:l l!i.n .. ; in th� ; lOol , no

rc:uuc t .i.01 in tr: i 1 1 :;..i, , ,- ·1, t • .1.l n ,: i , n c. is n·Coin:nc:nu ,_:Ci .

, .ni:,l e: .i. ._, ,_ e, ._ , , scou.:r . I t i s v er-J , ·ro bL.blJ t:1c t 11.2 1 vy , ,1 e .u .. - , , .i. , cec

ri,:ir1:c;1 , . t the enc o t' tnt bi . s in ·1, i 1 .1. n.;sult in no :,,COL,r L :v&n 1,i t ri con linaous

o,:,er .... tion o t t(1e mc;.l',ililLL'.l Ji.:,cn::-. r ,;£- . rtoi; t::v is r , ir ··i <Jlocities :.. re ::;ui 'fi ciently

ni .::::h to resul t in s cour in ,.; , the curren t 0 1 tne ,.;;rounr: I'<-' 1.J.. (. I' , i'orrnca unc1 er

t !1P. :;;trei. ::: i e::, vin 5 trie .:; 1.o iJGG. tr,. nsitior i f loor , ,,il .1. ,:,ov s ffii.:.teri t. ..L u,.., s t rcuI,l

6i v in :; : 1rotE:: ctio11 to tne e:u toff WL..J..l re.. t! t8r tm,.11 s cour '::: t t: r le 1 �-Wt·. y from

tni s ,•. 1:.ll .

8

oo,£ ois

A cL.

z C

.J Q.

_o-ii · " 9·ez1; �"v���-�·� _ ' ;!

t-8'C:i lli t3 J- - - -90,>S l 3 � - ­

«6£1Sl3 i­S > 1 >1S 13 ! t,Q�Pl':: 1 3 =l

86',t1�13 K>Sttif lfiS�

� PC:091«; IT�:-09·091s 13 f · · ··

£81)9JS1l £r8£+0 DIS ; �

.9,,S 980£ • t, O,$' · - -

'\'> eec;1•11 01sf

"' .J

ii:: 0 f

-,.9-,�I

... T] 'ID

¥ ; : � = ' � �- �

� ' , , iv>-.··�

· t

.i- . 0 C

-,), :i

C

0 i= u "' Ill

CD I CD z 2 ... �

FIOU11£ I

-...

!1171

' .. 5170

0 !H69 • +

2 z

� 5168 t,.;; (/)

I cl z u

5157 z

� - t- 516& a::

C( w %

z 2 � j 5 .. 5 LA.I ..J w u; 3

51&4

I IIQ

I I

1162

0

r 1uun� � I I I

Max. Canal w. 1. 1111.1• _9 _ _ _ _ _ •• Q• ilO 5.F.

j

I �

J

I

/ 7

I I

I I

I

/ . V

,L. � Top of Culvert El. 51a!U9 ,.-• . -

V ..... . �

/ /

/

/ -.·�·

SHOSHON E P ROJE C T - WYOMING HEART MOUNTAIN CANAL

STA. 1097 +ao WASTEWAY _ __ . .. R AT I NG CURVE

2- 4 ' X 5' SQUARE ENTRANCE . .. G ATE OPENINGS

WASTEWAY DISCHARGE IN SECOND FEET

Jo I .la . I I . I . ·400 :Mft IOO

. ..

I

. �

.. �

� Ill

10

9

8

7

6

f s

!

! -1 3

2

� t I � � / · I I I,

I---+---+--�--�- I I /

I H C I I �

/ H I

/ -+--��--+----+--�---...--#--+--�---4--____;-+-...-�

!° i lJ - ,___ - - --- - - - - V I I t I : - - - o - - - -

/ ,

,,, ., ,, � �.�, � , --:-:-,�/Q ) l Note: I

v V Cc measured experimentaliy ' C computed from Qa CA� t------t---+--+-v----,tAF---+---+--�--+-----hi_,.l--�---J using mea•red Q and Ho

v /

�...

------� Cc ---l,....----'" ----�

-� C L-----�� ·-----

�

0.4& .50 .52 .54

. ,.

.56 .58 .60 .62 .64 .66

COEfflCIHTS 't; AND "ff SHOSHONE PROJECT HEART MOUNtAIN CANAL

STA. 109 7+ 60 WASTEWAY

COEFFICIENTS FOR SQUARE ENTRANCE CULVERT GATES WITH PARTIALLY

SUBJ-ERGED Fl.DN 2-�x!5' GATE OPENINGS

,.. I@

11 c,,

- - - - - - . ,0 - ,0 1

I I I< - - - - - i I �-I - - - - - -->-1 I II � I

I I � - - - - .. al @L I - - - - - >ii

I

z � ..J Q.

•

I I

� I

in

c · N

I , . ' • ' .,. 1 / ,· .

z •o 0

� I t-.., 0 C • � > 0 IO l&I � ..J l&.I "' ,

According to Torricelli ' s theorem, water discho.rging from fill orifice

und er o huad, H , h� s a theoretical velo city equ&l to the velocity acquired

by u bou.y fullin6 freely " in vacuo" through u vertical ah;tE:...nce , H , thut is :

V t = 'Y� g H or

H =

2 V t /'ig

The expression Vt /2g is termed the velocity head .

( 1)

( �)

Because of the effects of friction and vi scosity , the mean velocity of

a j et is always less than the theoretical velocity . Expressed by symbols :

Cv = Vof't ( 3 )

Therefore , from ( l) Vo: Cv 1/ r 2gH (4)

If A' is the cross-sectionul area of the j et at vena contracta and A

is the area of gate opening,

C - A '/ A C - ( 5 )

Cc d ecre&ses a s contruction is reduced and e.i-Jproaches unity for an opening

with wel�-rounded corners .

The dis cn&.rge from EJ.ny ga te opening is equal to the product of the

cro ss-section�l area of the j et at the venu contracts , the meun ve�ocity at the

same section and a coeffi cient, Ca , which represents the effect of velocity of

approctch; thut i s ,

or Q = C A r� g H where C = Ca Cc Cv

( 6)

Tne vi,.lues of Ca and Cv are difficult to obtain experimentully , and

these coefficients are of theoretical r&ther than practical value . The value

of C c mt=:.y be re1.;. ci.i.ly obtE in cod by met.;3urin g tuc E- re,. of ti1e j et Lt t t .:1e venu

coutrL ct1:1 . Nwneri cul VL .i.u8s of C u.re obtt . .i.n ed b;,i me , . . surint; the: J i J c r11.;.r c;e

l 'ro.n : ·.r 1 Oyening or' �nown ,1.i.men., ions tJ.n d the !50Verning 1 ,res-::;ure het-ta .

l'ne coefficien t C E, s 5iven by for!.mh. ( b) .i.nclud '-' s tne eff'" ct of

v e.LOc i ty of ap_f)rouch , .Lo s s of he,,d due to fric tion 2..nd vi scosi t:r , end

contres cti on . The knov,lo::a,;e: of tne coeffi c.:ien t i s not �-ufi" icient to j ustify

tr,e usG of --.:. forffiul"" w ,�i c r: contain s SE::_),,Ti:. te term::; to correct for velo city

of & _ -.Jrot.c r . , .:i.03 s of rw1.,.d due to fri c t ion E..nd. vi scosi ty , :-:nd con tn,.ctlon .

in l- i c:;u1·e lA for wLi ch tne fJ.ow i r. termed 1-'c. rtiL. ll? subillerg,�u . l t !- , - 1 e ir�,

t i1.t. t for s'-'- te s of tnit: type con ditions influen cin e s .i. c:e ,. ni.:: bo -L �om c,:-n tr'-, c tions

C.L V G very .Little e:t "fec- t on C .

::'H:,v'r- tion 1.st tnu vonc con t-rL c tL t :1 t-: orcti c::..1.ly i,;ive.:: tne t;ro}-' t:r .i to u J e in

f '.)r::1ult. ( 4 ) . T r,e oi s tut C C C cD WL. ::i r:1c 1..sureu e.x,_ eri,n t:r. t1, J..ly in tns 1 : 16

;�,ou cl 01· tv, o 4- by ) -l'oo"t 6;:.. tt: Op(;llint�S i 'or .:;ever�.L v�.1.uc::. 01· H0

•

1 ieL.Cl for 0-ny stL.tcc: .J i s cnc.rge i s tnen �lven by :

l-i H - C D 0 C ( 7 )

to o tr ,er C:L t L sl :.::. ,; ::; , ,. cu.::·vt, ·,. t- ::: l,rl ·.,.-1, 6.i.v .Lu�; tr,t. e.-. • E:ri::iei ,t.� _ _ L V;; .lut o l' C c for vt.:.riou:; v1:. .1.ue s of tne r,_tio o i ' .:i.,te ope11inv; 1..1 , .J'.d the he&,:'. on ti1e 51:.te

s ill H0 • From tnis cur·.· e , s11o;rn r.,r. Fi :_;ure lJ.. , C c CL!l b e: d et-er,:: .'..ned for ;_r1y

J.;/rl0 ri. tio vi r ti c 1 1 ;_,_ '-lo s �; trw �ff" e cti v e t1e1..d tr) be cornt-'11t � ·ct by f .) r:r.ul.u l 7 ) .

T 1:.e 1 1 C II cu eve fo r v1:;.rious v :..; l 11e s 0.l ] 1/i-!0

L, .... a. so s ! lO ,,n on 1- i :ure l.i-, . T he

u i .::i C tlurge from �ny r<r,o\•,n ;:>t'-' o;)en in6 c,nd n6;;; G of m.ter ub-'.:lvE: t c.e 6,, te sill

rn1..y b ,� com t ,uten hy use of forr:1uh ( b i .

plottea on l- i .;u.ce ,._J;. .

I t .L s be1. i 0vcc' tt i . . t tnc •no •...:.el ac.t.::. converteo to 1 . rototy pe '...:i..ti "titi.es

F . \'. . 31 1 . i . . < ! cll . ·e .o: · k, in T 1·1::. r ; G , c t- ! on s ,. J ------ -- ---

ot dDcric .:.n uoci ct ·J 91' C, ivi.L t.r:;;in ecn, , Vol . lv.:: , l Jfl , Lnc. t 1... 0 u rc ..;ult

of l , 500 C .' • • · erimen t;:; 01 : si.}.. : : tO '.J.<.;1. 5 co in 1 , :.. rE;ci ·,, itr, prototy_ · e n, su ..... ts , tne

r... tio of (,:p/c�m Vf:ri -c-u 1, s 1,._

· 5 , or trn.t 1 'rouc e 1 o t::o i:..: el .LL. 'h , . , · 1. 1. i cs _ to .::: • 5

: i s c r�c.crge tiJrou. ;!1 s 1.ul c e s . l'ne 1.:.ven . . �c dE: t , , rt.ure of C.: ,/'-<m from l wi, s z·

i ounu

�o:ne ·-;ue s tion re11,t- in s regE: rl 1ing e:� , ,,,.u s ion of tr1e ·:oY r ,erirn en t"' l nat11 for

tue on"" �c:.· te size to other 6r, te sizes . Velo city of a ,-'iJ ro1.:..chJ en tr;:..n ce J.o::;s

£..nu contrft,. ction L .c e ;,.1rob&.bly 1.. .d 1 :ffectecl by the btt te :J i ze ;., no s o:..,J � . no-.,1Jver ,

Kin/' t"::....s j 'ouno t :1� t tr1e combi!1 cu .1.nf lueuc e of c.i:h-. s e f(,I ctors on t : �a c.i i �c :1.u rge

from bn orifice is not �ore t2&n �bout 5 �ercent of t�e to tb l ai� Cilli r�e , so

�ny v&ri&tion in diJ cn& r �� for the 3ev c:�: g�t6 s i z e s due to the s e r� ctors �ill

)rob&bly Le no more tr.Ln .1. or :.:. �.> erc:ent of t11e d i ::: c tL..: r�c for t:1e !? : · _ cri1r, cnt.;:; l

s i z -:: s c...nci sh1-, �JC S to deter"iinc tt«0 correctness o:� tni s 3tc te1:1ent .

*King , H . � : . , !lc.ndbook 0f ! !vdrc.1c1lics , Third •oi ti0n, pp . 4u-55 .

3

.: ·.7,;,-

.0 -- ... __ ""-0.9 - . ""--

o.e

0.7

0.6

0.5

04 Qj-£

03

0. 2

0. 1

0 . 48 . 50

-----....__ ... - --.... ---..... r---.._

� --.....

� ��

� ¾ - - *----1

I

I I I I I I

Ho I I I I I I I '

rmv,n,,l.

I I

- 1 I I I I

I

H I

I

I h -

I

........_ _ 'f. _ _ _ _ _ _ _ CcD 1 j

I

r---.._ r--.......

� �

.,, ., , �

- o

f i I J

1 , ' \

"c" i,;· --......

r---.._ r----.... -......... "

r---....

"' " � �

'� \

' � "' \ � -"' \ '

, .. I' ' \ ' . \ I'' � '

- ' \ II '-l

\' .. .52 .54 _56 . 58 .60 .62 .64 .66

SHO SHONE P ROJE CT Cc measured exper imeta l ly HEART MO UNTAIN CANAL C computed from Q= CAv'lijH GATES WI TH SQUARE ENTRANCES

using measured Q and Ho COEFFICIENTS OF CONTRACTION IN TERMS OF 0/Ho PARTIAL LY SUBMERGED DI SCHARGE

:!! G> C: :a "' -)).

• •

1 5 I I I • 1 f 7 1 '#. ,' r r '"'•" .,. 1).., ii J."' .... ·, I '}' �-, I ,,

· 1 4

1 3 I I I I / IJ J , !! I //I / I / / I / A / I / I ,.v ,1 I JL I I

1 2

1 1

1 0

�0 : 1 I 1- / WIY�

L I ;�;%�Ti.1��r ,

7

6

5 I I ! K f t'I I µ ,4 < I 1 1 1 1 1 1 1 1 I

I 2 3 4

5 6 7 8

9 10 I I 1 2 1 3

14 15 16 1 7

18 19 20

· �

2 - 3' X 3 ' 2 - 41 IC 3 1

2 - 3 1 >< 41

2 - 5 1 X 3 1

2 - 31 I( 5 I

2 - 41 X 4 1•

2 - 5' x 4' 2 - 4' x s ' 2 - 6' x 4 ' 2 - 4 X 6 '

2 - 6 1 x 5 ' 2 - 7 1 X +' I

2 - 61 X 5 1

2 - 51 X 6' 2- 7' x 5' 2 6' X 6 2 5' x 1 2 7' X 6 1

2 61 X 7

1

2 7' X 7 ' SHOS H O N E PR O J E C T • W YO M I N G HEA R T MOUNTA IN CAN AL

\,I I Ill(// r: I I '- D I S CH AR G E C UR VES - SQUARE ENTR ANCE _..._____j _ _...,_--1 r ' R ECTA N GU L AR GA T ES - PAR T I A L LY

3 0 200 400

SUBM E R G ED D I SC H A R G E

600 800 1 000 1 200 �$CHARGE I N SECOND FE ET

14-00 1 600

-···

"Tl Gi C: � fl1

----------------------------------------------'�

'

\

' -

&

IJ

" I

"\

f •

\_

I , J

' J '

I i

' .

\

c..