hydraulic computations to aid in the design of …prototype qu&nti ties for tne heu.rt...
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- -·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
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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
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9
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,,, ., ,, � �.�, � , --:-:-,�/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 /
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0.4& .50 .52 .54
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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
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� 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
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\' .. .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
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1 2
1 1
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7
6
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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
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