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TA '416 .B87 HYD-399 1955 C.2
UNITED ST ATES DEPARTMENT OF THE INTERIOR
BUREAU OF RECLAMATION
PROGRESS REPORT II
RESEARCH STUDY ON STILLING BASINS
ENERGY DISSIPATORS,
AND ASSOCIATED APPURTENANCES
Hydraulic Laboratory Report No Hyd-399
ENGINEERING LABORATORIES
COMMISSIONER S OFFICE DENVER COLORADO
June 1 1955
DATE DUE
GAYLORD PRINTED IN U.S.A.
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. til -~ l>efth ::.- • • • • • ... ..•.. -~. •/,.ie' • -. ~ • • Length, .-1' ~ •. ;J. •• : ..... ; .•.. _.,. ., ·,,. ., .. • .. •· ·• • • ..
Water -~ .azd -~·~ai :·; ~ .• ·. ·.- • , • .. ,-.,.
• • • . . .. . .. . ...• · ........... ,. . .. ~'.C&tiOll. ot ·1e.ita ~ 3) • •· ·• • • • •
SMl·M-·~---.... : ...... :-..,...-a Stn~•, ··oa--- .vaa.,- -.11m· •---•·-_(JJadil-: tt,3. . .
Devel.oJ;mttt !ea.ta: F:tnal. Tesibs · • • •.
• • • •
• • • •
........ • ~.;\j:,.;·· • ~ • . . ·"· ..... .
• • • • • • ... ...
De-tlecto:r bloc!ks • • • • • • • • • • • • • • ~- .water 4ept11. • • • • .. • •. • • • .., • • • .... length and em a1ll • • • • • • • • • • PertoZIIIIIICe ••••••• •-~~~. ·• •••
Pert'~e Deaign •••
• •
, • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • ••
ii
. ,, ,a
63 . 63
63 66 66 66
67
. 6r( 61
',;- :·
wave SUppzesso.:rs . • • • • • • • • • • ........ Batt !Ylle· Wave SUJpl'ea-sor • • • • • • • • • • umeri,ass !Jpe lfa• 8apJre,'sor • • • • • • • •
• • • • • • • • • Performance •.••• , •••••••• GeDenJ. tesip ~ • • • • • • 8-.Ple problell; kauQla 4 • • • • • •
5. StiJJ:lng Basin nth 81'Qptng ~ (:Basin V}·
.. • • • . . .. • • • • • •
Intl04uetioa • • .• • • • • • • • • • • • • • • • PftviOllS'--l:Qerimental WoJIJt • • • • • • • • • • .. 83DP1D&" JltilOa ·--Teats • • • • • • • • • • • • • • •
Tail. water Dep.bb. (ease D) • • • • • • • • • • Length ·of ."J'mQ· f~ D) • • • • • • • • • • • Bxpression tor· cJli(U,'.on Slfp1ag .Q1"0ll (.CalM tJ).
-.1'a1Q ~teffwtltc:s,·-(0. · B) • • • • • • • • ~tal --1ta '(Cale B); • • • • • • -. ·• Length of t1'mlg) (Case B) • • • • • • • • • • •.
_·. -·}<··
t~'·61
1',. 11· _., •.. ••
Practical Applica-t-:1.cms • • • • • • • • • • • • • 100
Existing St-metm:ea ••••••••• Evaluation of SJ.opillg .A»roDB • • • • • Sloping. Q1'0il -vesus Hor.tZODtal· ~ Jttect ·Of -Slope at mm-te • • • • • • • ·Rec~ •••••••••••
• • • • . ... . . ...... • • • • . ~ ...
6. StliUng :Basin-tor Pti,e or Optn Cllalmel. 8111i1e'ts Ko Tail Wat'er ReqUiftcl (Basin VI)
~- •· . . . . . . . . . . . . . . . . . . . . . Introduction · • !'eat Prececlure ·
• • • •
• • • • • • • • • i • • • • • • • • • • • • • • • • • • • •
l[Jdraulie MOaelE. -•••••••••••••.• Developmaa't; Of Jlas.1n • • • • • • • • • • • • •
. Pert~ or !as-in • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • • • • • • • • • • ......... •· ........ .
l,l2-/·.
ll2 113,_
1 2 3 4 5 6 7 8 9
10 11 12 13 14 15
J.6 17 18 19 20
21 22 23 24 25 26 27
28 29 30 31 32
33
34 35 36
37
38 39
-P~ ~
Test Flumes A and B • • • • • • • • • • • . • • • • ,. • • • • 5 Test Flumes C and D • • • • • • • • • • • !' • • • • • • • • 6 Test Flumes E and F • • • • • • • • • • • • • • • • • • • • 7 Definition of Symbols (Basin I) •• • ••••• • ••••• 13 Ratio of Tail Water Depth to Dt ............. • 15 Length ~f JUJII) in Terms ot DJ. Basin I) • • • • • • • • • • 17 Length of Jump in Terms ot D2 Bas1n I) • • • • • • • • • • 18 Loss of Energy in Jump on BoriZC>Dtal Floor • • • • • • • • • 21 Jump Forms • • • • • • • • • • • • • • • • • • • • • • • • • 22 Definition of Symbols (Basin II) •••••••••••••• 28 MilWIIWll Tail Water D.epths (Bas:lns :t, II, and III) • • • • • 35 Length ot Jump on Horizontal. noor (Basins I,. II and III) • 37 .Approximate Water Surface and Pressure Prot:Uea {BatJin II) • 39 Recommended Proportions (Basin II) • • • • • . • • • • • • • • !JO curves tor Detel'lllination of velocity BDteri.Dg Basin. tor
Steep Slopes • • • • • • • • • • • • • • • . • • • • • • • • l,.2 SAF Stil.ling Basin • • • • • • • • • ·• • • • • • • • • • • • lt6 Record of .Appurtenances (Basu Ill) ••••. • • • • • • • • 48 Recommended Proportions (Basin Ill) • • • • • • • • • • • • 49 Height ot Battle Blocks . and Sill (Basin III) • • • • • • • • 53 ApproxiJDate Water SUrfac:e and Pressue Profiles
(Basin III) • • • • • • • • • •. • • • • • • • • • • • • • 56 Tail Water and Jump Height eurvea (Example 3) ••••••• 59 Record ot .Appurtenances (Basin IV) •• ·• • • • • • • • • • • "64 Proportions -tor Stilling Basin IV ••••••••••••• 65 Drop Energy Dissipator (Type IV) • • • • • • • • • • • • • • 68 Raft Wave SUppJ:essor (Type IV) ••••••••••••••• 70 Performance of llnde~s Wave 5\1;P.Pnssor •••••••••• 72 Hydraulic Perto1'iD&nce--Wave Su!Jpnasor tor Friant~rn
Canal.. • • • • • • • • • • • • • • • • • • • • • • • ·• • • 7.4 Underpass Suppzessor--Wave Height Recoms--carter Lake • • • Underpass Suppl'essor--B)draulic Cbuacter.latica •••••• Forms ot Jump on Sloping Apron ••••••••••••••• .Ratio ot Tail Water Depth to D1 (Basin V, Case D) ••••• Length ot Jump µi Terms of Tail Water Depth (Basin V,
75 77 85 89
Case D) • • • • • • • • • • • • • • . • • • • • • • • • • • 90 Length of Jump in Terms ot ConJugate Depth D2 (Basin V,
Case D) ••••••••••••• ·• • • • • • .. • • • • • 91 Shape Factor K in JUIIQ) :ro1'1111& (Basin V, case D) • • • • • • 93 Profile Characteristics (Basin v, case B) ••••••••• 91a. Tail Water Requil'ement tor Sloping Aprons (Basin V,
Case B) • • • • • • • • • • • • • • • • • • • • • • • • • 99 Caapar1son or Elcisting Sloping A1>l'OD Designs with cur.rent
Experimental Results (Basirt V1 Case B) •••••••••• 102 Existing Basins with Slopµig A,pzons (Sheet 1 ot 2) •.•••• 103 Existing Basins with Sloping Aprons (Sheet 2 ot 2) • • • • • loll.
iv
Bo. -Ito 41 IJ2 43 44 .. ,
l 2 3 4 5 6 7 8 9
10 11
South Canal C:tmte, Station 25+19~ tJ~ Pn,Ject • • •
:Basin ActiC>at SOtlta euaJ. -~. lhr«eC!li#lli-.. ~~ • • .; • .. l1Qact Tne 'lll8rs, a.ss:1.~~ (Basin VI.} • • • • • • • ·.-;. • • ~cal. Pert~ , ____ ff) • • • • . • • • • • • • • • • .•
Compartson ot BDergJ tcrsses--~ ~ and BasiD VI • • .
Ension and EmergeDC7 ~ (Ba&d.D VI) • • • • • • • • •
'!maJ
StilliDg ;aasU with Bonzontal Floor (Jasin I) • • • • • • •
Madel Daul.ta- cm Bxtsttag TJpe- II B.181Da • • • • • • • • • •
Ver:t.ficattoa Testa on '1'n,e II !aaitls ••••••••••• •
Ven.ticat1on 2ests 011 TY.PB m Bas1,na • • • • • • • • . • • •
Results ot -.;ample 3 ••••••••••••••••••••
Waw Betght Reduction "1.t)t U~s ~ W&ft Suppnssor •
Effect of tJme.Z',P&Ss l,eng.tll 011 Waft aem.ct1on • • • • • • • •
St:tl.1'ng JaaSU with Sl.olJ~ Al*OA.( .. iD V·, case D) • •• •
St111Sng Baaw with S;J.opit.Dg Ai,toJ.l ~-'.t" case B) ••••
Jsistillg S-t4~ Basins with Slt,p:Lng ~ • • • • • • • •
Stilllng Bariu Dim.ens-ions (Basin Vi) •••••••• • •• -.
...
~--· -~--
,1· .. ,
. ~ ·S!U.118 . DIP___,,_ '11 9 ...«OB
Cc-.i1ssioaer1s otfice Engilleering ~ Deaver1 Coloraclo June 1, 19"
-- QI ~- .,•
.Altbollgb. tbe 8u1'eau ot· Reclamation has designed aml eonq.-.e• tecl bmdze4a ot djJl;ltag bM$DS --~ enagy- ~~-~1ml: ~, .,m- .-'!I-- .Junet-ion Vi:th ap~, oa-t1-t: ~-, and ~ s-w.ucture•; -!it ·:4-e- ~-·mceaa&17' 1D maDf' -qsea. to -.u -4el. stucU.es or ,_.,~ a.tm~, · to be cerWn tbat -ate.e ¥ill OP.mite as anticipated. -.e nuon.-b. · .. theee .mpetttive teats., in. man¥ .cases, is that a tacwr ot --~ . exists, which 1D .-tnqect is mlated to an inCQ!q>lete ~ot tbe overall ~:matica et tbe __._lie ~ .. &114 other t,:pes · ot ener.- 44~•~- ·· . · ·
~---~• ..... atuddiea made on 1114-1w4ual st-i.uetuns . OftZ' a perio4 ot ·ieiln, .V .d:iffeDmt Pl~, fOl'_,Mffefltn'b. ~ ot 4edgl\en, v1• e.uh :•tnctu-,:e ~ a .cll-ttuent,"'~· duisn ~tatioii tor tovu..,.. •~ _.zesd.ted .1n a col.le*O.Ji of .. aata,-,r~ .. • 8DJ' ldottb& ~-:to·Jle. ~, inccma\lstent, --•th t::d.ti ~ _:·_ cozmeetmg lius-. . --. ... 1a1-,. :r..~- into ·Wle works -•t ~:,. revealed tbe tact ~ ._.. l1*s vea act1ml Jy nol181stent.
To :tU1 the.~ tor ~to~. )V&'aulic design ~o~t~on ·cm st1ll1Dg ba&-iDIJ ciid ene-igy· ~aat.».•rs • labo:mtory :lm.tiated a ., :re~arch s,rcgnm-a -ti• .--1 aa~ect. 9le prol,ra ve.s begutl ••~-*; rather academic stuq ot tbe 1qilraulic 3UQ, observing all 1tJaBeS 88· 1-,· occurs 1n open channel tlov. With a 'bffal.er understanding ot thts phenomenon it was 'the1.te,poNible to-~ to the more ·pmct$clil asp,cts ot st1J11ng basin desigb-.
~ Labol'&'tol7 Beport l'O-. B)d-38>; ProP.lJ• ll!PGrt, Beaearch Study. on ~~ Baaina &114- Bleket Dias~tors; dated Juzre U, 1954. J. B. Bradley is now 'B)draulic Engineer, Bllfl!lm Gt Public Roa4a1 Wash1Dgton, D. C.
1
Existing knowledge,. tm!ht~ labo:i-atory and .tielci teats collected t:rona lf1dnu.lic Iabo11Ltory ·reco1'6s ·• ·experience over • ·23-year period, was used to esfabl.1s1i ·., direc:!t -~ to -i;be pr&cUcd. problems encountered in eydraulle design.. ~$ of tests were $~performed on both available and specWJ.¥ const,m~ted equii-nt to · obtain a fuller umter'&tanMng ot the citlta at ~- atld to close· ·'th.& 1l1ilii loopholes. Testing am amly.sis were SJD~ett to -e'stablish ~: · curves 1n critical regflres, providing suttieien~ understanat1·ng of'• ·· hydraulic jump in its many forms to establish ·workab-le des·igb_ ~-. Since all the test points were obtai:ned by the &$lie ~somiel, usirig· standards established be:f'ore tesiiing ·began, aml/ '$-'itli'C'e l'eSUits 811&-:C~ ~: clusions were evaluated from the- same "'atum, ~-- pmsented ue consistent and reliable.
This report, therefore, is the resul.t of the :t1rst inte'~d attempt to generalize the design or ati.Uing basd.ns1 e~ icBsstp't(jn, and associated appUrtenances. General design rull,'& ate t>N'.SeD.~0'-iC>: -that the necessary ditDensions ·ror a particular sttta~~ ~-lbe eas-*, and quickly ·detel'mined, and tbe selected 'Values c!J,e'd.(eclO-'tiY' -otbe\r' :. • designers ~ thout th.Ef need tor exceptional jud_.nt. ot -e~bsiift previ011s experience.
Although Dlllch. ot the original data an- Pl'e.•nted---:tn ·tabw;a,r -· form, the report emphasizes design procedures ntbe~'tban "t11e ~~ aspects ot the data. Certain de-s-ign p~cedures-1 nc01111ended .;ln the .. - · · past, have been sat1st'actorily -prcven, while· others' :iuwe1,bfe~ ~ or discarded in f'"avor of improved method&.. Satisfe:t!t"ctt-y ··'e~t1f#i11~ are given tor proeeduns, which in the past w:re- cox,.starea.~~-••li't.J tor example, it is nov· ~ understood·wq ce~·-~c -~-, -~ •1•. require a stilling basin onlf 2. 5 t:lDles the downs~• dei,..th ~- .-. 0 ~-while other jumps require basin' lSngths· 1J..5 times. tlie depth•of(~l:'$iJ/'.·-·'·. :·-(· In most instances desiSQ rules and procedur.es ~ clearltsta'hed in simple terms with limits t':l:Xed in a ·de1"1Dite -•~ In other · cases, however, 1 t is necesaaey to st&te ;,Pl'O(:edu1'e~- -aml l:b1¢ta- 1n ·; . . broader terms, maldng it. necessary to caref'UllU nidl 'the' ec~: ,· te~. ·t.
Proper use of the materiel in tbi.si re~~- 1"1.lll, ·elim1nate 1:he' · · need for hydraulic ·mQdel · tests on mny indiViduat .'ft~tu~s I P&-rbt-ai-· larl.y the· smaJ ler ones. Struetuws obt&ined by fGlloW'i.Jlg the recom,.. mendations 1n this report will be cons&rvati.ve in that they will '"c()!).tain a desirable factor of safety. However, "to furtber reduce stmcture · sizes,· to account for unsymmetrical. conM.t:Lons of approach or getaway, or to evaluate other unusual conditions not covered in this di-scusaion., model stud~es will stiil prove beae:ticial. ·
2
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six IIWlbers cerzesp,jlA· w-··· --~-._ a,. W's_ .... ·· ·t .. ffItems 7 throuah 13 ,rW;·be ~ted.:u~-~--·f ... :. · ... , . ·?f·
~1. 4-ft1m98~at*r~u.,_.._~~:.:2. fflll:k\'g ·1-tzl"1dW11MJ~:-, ·. . · ., · . -~ ~:~ ~: ·
'oloeks ·ait tbe .,_. _end··aia~ra:, -.-.~ll 4%':" ·-,~-- W;~~~f.;t-8UGh •• am ottu u..a--·bip.4a·,id, ..... ~.·-:0
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-----~ ... .,_, ~~ :lt° to· ,. i.ir, .. : ~-=~ •.. =ii,.;_ -.i:: ..IIOlrll&I ·l.en.gth. . .. : . ~ '-~- ·.') .
a. StUMrii ·- t.R·"U'Wrai• daif8: --~ .. re~saio• is •llil*Ctec1o
. ··· : ..... . . ~:. -
- 9. ftt:Llli,gblldn tor tiw~:--~ can accf~ both f1"ee ad ---- t).,o\r . . ... ' ·. . ·. ..... • . .. - :, . . • . . : :.1 •• :· : \, ...
10. s~ttling' bUU1 tor use o:n ld;th-.l'lel4 mtlet 'WOZb;· _uit~.,_ hOll.av·Jet valws. . . . . . . .
U. Slottecl bu~ :rw' -111!11Uma ad lair- -.:rta:u, 4-8 ~ · .J._:
12. ~-~--,. ~- 41111B ·---- ..... ·of--·· .. _ ... - ... ,. . . water ex.lats. . . . . . . '
13. Plip lmelrSt Yltich· cttac__.s above tlle tail wa'tei-.
,":'.
.· . ..
St:1 l Jing basin8 a1'e defined as stmctu,na 1D which all or part of a hydraulic "'*'or~ enetil/t·~d'tiei4 action- k .QODf:lsled.- .: ·. O~ stmctures, such .as bllc'keta Qr. ~t 411•~•, ~' .ciesl~-- ·. , ... energy 4iH1Pato-n. . , . :. . -j\
BXPEBIMJli'!AL IQUIPlll!:E
. Five test f'lulles were used at one time o.r ~r-•,~• .,;_. the e~ c1&'ba :recpdi'e;d 1n the :~n~ -~ ~~--.,._ .-:~-· · and B, ftg\li-e 1; F~s C .• D4: ,.,. 2; ·,and ~ P., J',...: ·~~.tt· ., , .. arrangement SboWn ·.-s ·n,.u. -E,. Pigpa- .3,- -ac~al.ll! ·-qceuptei ~!- ,,. . ,
Flume D duriJJ,g one. stage 0-t ·the- test-in&; .-lut i't ~ • -- _,. . <,. ·. a sepante flume for~ of retennce. la.ch~- seftedi.'t·• ··:. ,. _;::;;- f. purpose either 1D veritying s1milari:ty or ex.tending tbe -~ af-:U.~:. .. experimeJl;ts. Flumes .1: ·1, C, D, -4 .B @.Dta~ ~~~~- ~:/. -. _·. f that the .-Jet _..Rd -. a,~j131ng '--•in-., en~ ~,,1#fe ~tP-1-• , _ _.;
~ =• ~~!!4' IL":1~c~ : c::; .!-~!j~~=~ · . .- .. was hon,~.-
- . . . . ,. . ·,.. . . '. ···.: :· ,-. . The experiments 'Wen ~4 in-a edstiing DIQ4el .t. f4e.-.;.. ..
Trenton DBDl spillway, F:S.-gmie lA, _..111 a. .,.U. tia~ ,fm'd .__,. ~- ,_-:-ity. This was not _an 1~-~~~ ~r~n1;..~<tr.·~ ,~•- '._-:;· as tbe ~im.Dg walls on -. omi~ ~ -•~ttg.::. '-'· ~~--~--. =caused the distribution of flff &~g tht a+,;:f;W.'08 ·-sh ·to.·-lbu{·. . · With ea.ch ~ in dis~:Ji .• noue~lea~, ~•;'~ ot ·etu~it:. sene4, a pu.r:,ose in tbat it, atct.ed 1D --'ting 4~.,i ... ~ ~.-... --: ,, underway.
. _.Te~s were $hen ~:t.:AUea.·s.n a glaas-ata.ea:·~o-:~ · · 2 feet wide and 40 feet -long iii Vh1ch , ... a,ef'la,r ,aec\lQh ,,.. ~,· , Flume B, Figu;11e l. The· ·crest Of .the oved'1ow sect:1on ·,ras 5~5 f4!ri .... ·. the floor, While the dQlfnstxeBDl ~e was ~n. a ale;,pe of 0.7:1. The-.·.-·: · capacity was about 10 efs. .
Later, the work w-aa. c$1rl'~d · on e.t- the ba~ at -. 'Clmte 1-6. -inches wide having a slope of 2 h,bnmntal to l ~~- -~ • ~- ot approximately 10 feet, Flume ~, F~ 2. !mle -at.ill~- basin had.· a glass wall on one s:l.de. The aJ.•~•• c~i~7 _WM 5 cf_a ..
Tbe largest scale experiments wen made on. a gJ.a•s~i-.:lab'~ :-°_
oratory flume 4 feet Wide and .80 t~e:t;- J.o.q,, _in wbieh an .. nerf'all -c~ . with a slope of o •. 8:1 vas iastaJ.lecl, tluJiie D,-Pie;ue 2. The 41.'0t. ~- · _. heac:lwater to taU water-~ this .. case._.. app~ly' J2 teet,. am!·• mav:Jnn1m discharge was 26 eta. ·· ·.,. . · · · ' · .. . .. ·-· .
FIGURE 3
TEST FLUME (E) Width 4 feet, Drop o. 5-1. 5 feet, Discharge 10 cfs
TF.ST FLUME lF\
The downstream end ot the above flume was also utilized for testing small overflow sections 0.5 to 1.5 f'eet in beight. The max1mm discharge used was 10 cfs. As stated above, this piece of' equipment will be designated as Flume E, and is shown on Figure 3.
The sixth piece of equipnent was a tilting flume Yhich could be . adjusted tor slopes up to J.2°, Flume F, Figure 3. This flume was l toot wide by 20 feet long; the head available was 2.5 feet, and the flow was controlled by a slide gate. · Tbe discharge capacity was about 3 cfs.
Each piece of equipment contained a head gage, a tail gage, a scale for measuring tbe length of the jump, a point gage tor measuring the ~verage depth of flow entering the Jump, and a means of' regulat.~ the tail water depth. The discharge in all cases was measured through the laboratory venturi meters or portable venturi-orifice meters. The tail water depth was measured by a point gage operating in a stillingwell in most of the cases. The tail water depth was regulated by an adJustable weir at the end of each flume.
It is felt that the design information to be piesented will be found economical as well as effective, yet an effort was made to lean toward the conservative side. In other words, a moderate factor of safety has ·been included throughout. Thus, the illf'o:mation is considered suitable for general use with the follow1ng provision:
It should be made clear at the outset that- the information here_in is based upon SJIIIIIStrical and un~om action in tbe stilling basin and buckets. Should entrance cond1tions or &PP\lrtenances mar the head of any of these structures tend to produce asymmet17 of f'lov down the chute an.a. in the stilling basin, these generalized designs may not be adequate. In this case 1 t ~ be advisable to :make the basin in question of a more symmetrical nature, more conservative, or 1 t may be Wise to invest in a model study. Also, should greater economy be desired than these generalized designs indicate, a IICldel study is recommended.
8
SEC'l'I01i 1 '·
GDERAL IllVESTIGilIOlf OF TJIE B!DRAULIC JUMP OB HORIZOl'l'AL AP.ROB
(BASIH I)
Introduction 'Iv •. :
'·
A t:re:mendous amount of experimental, ·as well as theoretical, work bas been performed in cmmection with the hydraulic 3lDllP on a horizontal apron. To mention a few of the experimenters who contributed baskc informati:io there are: Bakbmetett an~ Matzkel 9, Safra:nez3, Woycicki , Chertonos , Einwachterll., Elmsl.2, Jlindsl.4., J'orcheimer21, JCennison22., Kozeny23, Rehbock24., Schoklitsch25., Woodval'd2E>, and others. There is probably no phase of hydraulics that has received more attention, yet., froa a practical viewpoint there is still much to be learned.
As mentioned previously, the first phase of the present stuq was academic 1n nature consisting of correlating the results ot others and observing the hydraulic jump throughout its various phases; the primary pur,pose being to become better acquainted· with the overall Jump pheDOJDenon. The objectives 1D mind were: (1) to detel'llline the applicability of the ~c jump formula for the entire range of ccmditions experienced 1D design; (2) as only a limited amunt of information exists on the length of Jum;p., it was desired to correlate existing data and extend the range of these detel'minations; and (3) 1t was desired to observe the various for.ms of the jump and to catalog and evaluate them.
Current Experimentation
To satisfactorily observe the hydraulic ·jump throughout its entire~ required a.testing program 1n all of the six flumes shown on Figares l., 21 and 3. This 1.Dvolved about 125. tests, hble 11 at discharges fl'OJll 1 to 28 cfs. The mmber of fl.mies used enhanced t.be value of the results in that it was possible to observe the degree of' similitude obtained for· the various scales. Greatest reliance was naturally placed on the results from the larger scales, or larger flumes, as it is well known that the Junq, action in small models occurs too rapidly tor tl)e. eye to toll~ details. Incidentally., ·· the length of Junv;, obtained from tbe t.vo mJ Jer flumes, A and P, vas consistently shorter than that observed tor the larger flumes. This was the :result ot out-of-scale frictional resistance on the floor and side walls. As testillg advanced and this deficiency became better understood, some allowance was made for this effect in the observations.
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Experimental Results
Detini t1ons of the s,mb<)ls used 1D connection Yith the ~lie Jump on a horizontal floor are shown on Figure ~. The procedure followed in each test of this series was· to f'irst establish a tlov. The tail water depth was then ~ increased until the front of the jump moved upetream. to Section 1, indicated on Figure 4. The tail water depth was then measured, the length of the jump recorded, and the dep:th, of flow entering the jump, D1, was obtained by averaging a generous number ot·point gage measurements taken 1Daned1atelyupstream from Section 11 Figure 4.. The results of the measurements and succeeding conq,utations are tabulated in Table 1. The measured quantities are tabulated as follows: total discharge (Column 3), tail water depth, which shou1d be the conJugate depth in this case (Column 6), length ot Jump ( Column ll), and- depth of flow entering jump ( Column 8). Column l indicateE· the test flumes 1n which tbe experiments were performed, and Column I;. shows tbe width of each flume. All compi~ tations are based on discharge per toot width of flume, or q., and unit discharges are shown in Column 5. · The velocity entering the jump V1, Column 7, was compu:ted by dividing q (Column 5) by D1 (Column 8).
The Frou.de Humber
The Froude rm:mber, Column 10, Table 1, is simply:
(1)
where F1 is a dimensionless. parameter, V1 and D1 are ft1ocity and depth of flow, respectively,. entering the JWIP, and g is the accel.eraticm of' gravity. The law of s1il:1lltude st.ates that where gravitational forces predominate, as they do 1n open cbaouel phenomenon, the Frou.de ~r should be the sue value in model and prototype. Although energy COil• versions 1n a hydraulic jUm:p bear some relation to the Reynolds DUll'ber, gravity forces predominate, and the Frou.de mmber is very useful tor plotting stiJ Jing basin characteristics. BabJonetett and Matzkel demonstrated this application in 1936 when they relatef2st1111ng basin characteristics to the square of' tbe Froude number, -• They te1'1118d this expression the ld.Detic flow factor. t!Dl
The Fl'Ollde nwuer Y1ll be used throughout this presentation. As the acceleration of gravity is a coutant, the term. 8 cOlllcl be omitted. Its inclusion makes the expression dimensionless, however, and the f'om. shovn as (1) is preferred. .
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At>Pllcab1l1ty ot lbdrauJ.ic Jump Fol'IIB1l.a
The theory ot the h1draullc Jump in hor:l.zontal channels has . been treated thoroughly by others ( see Bibl1ogra.I>h1'), and Will not be repeated here. The expression tor the hydraulic Jum:,p, based on pressure-1110111en:twa, occurs in~ forms. The toll.ov1ng tom is most comm.only used in the Bureau:15
. l>1 f »12 2V12 »1 »2•·2+ '/,;-+ g (2)
This may also be written:
Carry:!.Dg D1 over to the left side of tbe equation aDl1 substituting F12 for V12, ,
gl)l
D2 Ji/4 + '812 .;_ - - 1/2 + »1
or
D J1 + 8F12 - 1) if• 1/2 (· (3) 1
Expression (3) sbcYs that the ratio ot co~gate depths 1s str:l.ctly a function ot the Frowle number. The ratio~ is plotted With respect to the Froude DWlber on Figme 5. The line, which is virtually straight except for the lower eD41 represents the above e~~e,ioli tor the hydraulic ,'NlllPi while the points, which are exper:lmental, &1"\9 ~rom Columns 9 and 10, Table 1. Tbe agreement is quite good tor the entire range. There is an unsuspected character:l.stic, · hove-ver, which should be mentioned here but will be enlarged on later.
Although the tail vater depth, recorded in Colmm 6 ot Table 11 was sutticient to bring the tront of the jump ~o Sec"tion l (Figu.re It.) in ~ test, the ability of the 3UJ1G1 to l'ell&in at.Section 1 for a slight lowering ot tail vater depth became more clitticult tor the higher and lower values ot the Froude number. The JW1.P was least sensitive to variation 1D tail water depth 1D the Jl:1.ddle range, or values ot 11 tram 4.5 to 9.
111-
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• I!' J lx HYDRAULIC JUMP STUD'IES ~ RATIO OF TW DEPTH
I d TO D1 /
STILLING BASIN r / ./
I I I I I I I I I I I I/ I I I I I I I I r I I 0 2 4 • • lO 12 '4 18 18 20
F1=~ 437 ~
Length of Jump
The length of tbe Jump, Col.um ll, !able 1, was the most difficult measurement to determine. In cases where chutes or overtalls were used, the front of the JWI.P was beld near the inwrsection of the chute and the horizontal floor, as shown on Figure Jt.. The length of Jump vu •asured troa this point to a point dOVDStream where either the high• velocity Jet began·to leave the floor or to a point on the surface iaaediately dowDatreaa froa the roller, whichever was the longer. In the case of Jrlwle F, where the flow discharged f!'CIIR a gate onto a horizontal· floor, the front ot the J1D1P was llllintained Just clownatreaa tram the com;pleted contraction ot the entering Jet. The point at Yhich the high-velocity Jet begins to rise troa the floor is not fixed, but tend& to ahitt upstreaa am downstream. Thia is also tl'lle of tbe roller on the aur.f'ace. It was at first ditticult to repeat length obsenatioas within 5 to 10 percent by either criterion, but with practice satisfactory meaauzementa became possible.
A B7Stem devised to •aaure velocities on the bottaa, to aid 1n detenrln1ng the lengtn of JuQ, proved 1Jiadequate and too laborima to allow completion of the program planneA.. Visual observations, therefore, proved to be tbe moat satisfactory as well as the most rapid method for determ:t n:lng the l~ngth measurement. It was the intention to Judge the length of the JWI.P troll a practical standpoint; other words, the end of the jump, as chosen, would represent the end of the concrete floor am side walls ot a conventional stilling basin.
The length ot .1UJ1P has been plotted in two ways. The nrst is perhaps the better method vhile the secODd is the more common. · · The f'irst method is slmvn OD Figure 6 where the ratio length of Jump to D1 (Col.wlm 13 'fable 1) is plotted with respect to the Frowle mmber, (Colmm 10) tor results from. the s1.X test flumes. !he Nsulting CU1'ft is fair.q flat, which is tbe principal adT&D.tage ga.1ned by the uBf! of these coord1nates. The second method of plotting, vbere the ratio of length ot Jump to the · con3Ugate . tail water depth D2 ( Column 12) is pl.otted vith respect to the Froude mmber1 is presented OD l'igme 7• Thia latter method of plotting Y:l.l.l be usecl throughout the stuq; .'l'be points represent the experimental values.
In addition to the curve established by tbe test P,Oints, curves representing the resu1ts ot three other experimenters are shawn on Figure 7. The best 1movn am most -vide.q accepted curve for length. ot Jwa;p is that o't Bakbme+.ett and Matzkel vbich was detend.ned from. experillents made at Colwnbia University. 'fhe greater portion ot tbia curve, labeled 1, 1s at variance with the present experimental results. Because ot the Wide use tbia curve has exper:l.eDcecl, a rather coa,plete e~lanat1on is presented Nprding the disagreement.
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The ex:periJllents of Bakbmeteff' and Matzke were pertOJ.'lle4 in a tlwae 6 inches vi.de, with limited head. The depth of tlcnr eDter.l.ng '.the Jump was ad.Justed by a -vertical slide gate. The :max1mm discharge was approximately 0.7 eta, and the thickness of tbe Jet entering the .11Dw., D1, was 0.25 toot for a Froude DWllber of 1.911,. The results up to a Frowle nwnber of 2.5 are in agreement with tbe present experiments. · !o. increase tbe Froude DIDlber, it was necessary tor BaJrbmeteft aA4 MatZke to clecrease the gate OIJ8n1Ds• The extreme case involved a discharge. ot O.JA cfs and a value of Dl ot 0.032 toot, tor 11 • 8.9, which is mch . smaller than any discharge or value of D1 used in the preae:at experimants. Thus, it is reasoned that as tbe gate opening decreased, in tbe 6-inch-vide flume, frictional resistance in the ~ban:Ml donatream . increased·out ot proportion to that which would have occurred in a larger flume or a prototn,e structure. fills, the .1UQ .tol'Jllld in a shorter length than it should. In labora-t;or., J•ngaage, this is mom. as •scale effect,• and is construed to •u that prototJ:pe action is DOt faithfully zeproduced. It is quite c•rtain that t.bis was the case for the •Jor portion of the BabJnnetett-M&tzke curve. In tact, they veze somewhat dubious concerning tbe small scale u;perillenta.
To contim t!le above conclusion, it was fOIID4 that results tram Flume r, which was l foot wide, became erratic when the 'Yll1ue of' J>1 approached 0.10. Figw:es 6 aDd 7 sbav three points obtained with a -.alue of J>1 ·of approxiately 0.085. !!!lie three points are give~ the sJlllbol x and tall short Of t1'te recammended curve.
The· two rea::ln::lng curves, labeled 3 and 4, on 11gun 7, portray the S11111e t:rnd as the curve obta::I.Dec1. f1'0JI the current ex;peri-: •nts. The criterion used bJ each exptrillenter tor Judgillg· -tme length of tbe .1um;p 1a undoubtedl.J' zeapo1181,le for the di&Jlacement. 1'be CUft
labeled 3 vaa obta::I.Ded at the Technical Wliveraitf ot l!erlill on a flume 1/2 mt.er ~ by 10 mters long. The curve labeled 4 .Y"IS determined from expermmta performed at the Federal ~titute ot·!l:eclmology, Zurich, ·Switzerland, on a flume o.6 ot a •ter vi4e and 7 •tera long. Tbe cune numbers are the same as the :reference numbers in the Bibliograp!Jt which -refer- to the work.
As cu be observed frcm Piguze 7, the test reaul~s fraa Flumes B, c, D, I, and P plot sufficientq well to establish a aiJagle . curve. The tiff paints ~ Flume A, aenoted bJ squares, apJear somewhat erratic and plot to the right ot tbe general curve. Henceforth,. ~terence to :rtgan 7 will concern ~ tbe recClmlmldecl curve '11bich is conaic1ered applicable for general use.
19
Energy Absorption 1n Jump
With tbe experimental information available, it is oDly' a matter of computation to determine the energy absorbed 1n the jump. Columns 14 through 18, Table 11 list the. computations, and the symbols may be defined by consulting the specific energy diagram on Figure Ja.. Column 14 lists the total energy, E1, enwring the · Jum,p at Section 1 tor each test. This is simply the depth of f'low, D1, plus tbe velocity head computed at the point ot measul'ement. . The energy leaving tbe Jump, which is the depth of flow plus the velocity liead at Section 2, is tabulated in Column 15. The differences 1n the values of Columns 14 and 15 constitute the loss of energy, in f'eet of water, attributed to the conversion, Column 16. Column 18 lists the percentage of energy J.ost in tbe Jump EL, to total energy entering Jump, E1. This percentage is plotted with respect to the Froude DUJD.ber and is shown as the curve to the left on Figure 8. For a Froude number of 2.0, which would correspond to a relatively thick Jet entering the jump at low velocity, the curve shows the energy absorbed in the Jump to be aboot 7 percent of the total energy entering. Considering the other extreme, for a Froude number of 19, which wolll.d be produced by ·a relatively thin Jet entering the Jump at very high velocity, the absorption by the· J,-p wduld amount to 85 percent of' the energy entering. Thus, the ~lie Jump can perform over a wide range of conditions. There are poor ~s and good Jumps, with the most satisfactory occurring over the center portion of the curve.
.Another method of expressing the energy absorption in a Jump is to express the loss EL, in terms of D1• The curve to the right on Figure 8, shows the ratio~ (Columl 17, Table l) plotted against the Fl'Ollde number As there a~ those wbo prefer this method of' plotting, the _latter curve has been included.
Forms ot the Hydraulic J\m§)
The ~lie Jump may occur 1n at least tour different distinct forms on a horizontal apron, as shoVn on Figure 9. Incidentally, all of these forms are encountered in design. The internal characteristics of the Jump alld the energy· absorption 1D the Jump vary with each f'orm. Fortwiately- these forms, some ot which are desirab1e and some undesirable, can be cataloged conveniently with respect to the Froude number.
The form shown in Figure 9A can be·expected when the Froude number ranges from 1.7 ~o 2.5. When the Froude number is unity, the water would be flowing at critical depth; thus a jum;p could not- fprm. This would correspond to Point O on the specific energy diagram of Figure 4. For the values of Froude number between 1.0 and J..1 there is only a slight difference in the conjugate depths DJ. and »2• A slight rutf'le on the water surface is the onl.y apparent feature that
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· ·EFFECTIVE BUT ROUGH HYDRAULIC JUMP STUDIES STILLING BASIN I
JUMP FOR.MS
I
diff'erentiates this f'roa flow Vi th unitom velocity distribution. AJJ the Froude number approaches 1.7, a series of mall rollers develop on the surface as indicated in Figure 9A, and this action remains mch the same but With further inten~itication up to a valw;t of' about 2.5. Actually there is no particular stilling basin problem involved; the water surface is quite smooth, the velocity throughout is fairly unitcma, and the energy loss is J.av.
Figure 9B indicates tbe tn,e of' Jump that may be enc01111tered at values ot the Frotlde DUlllber f'ram 2.5 to 4.5. 'l'his is an oscillating tne of' action, so cammon in canal structures, where the entering 3et oscillates from bottom to surface and back again with no regw.ar period. Turbulence occurs near the bottom one instant a.ad entirely on tbe surface the next. Bach oscillation proclUces a large wave of' irregular period which, in the case of' canals, can travel tor miles doing unlimited cJemage to earth banks and riprap. The case 1s ot sufficient im;(lortanae that a separate section, Section 4, :baa been devoted to tbe practical aspects of' design.
A well stabilized.~ can be expected for the. range of' Proade D\Dllbera between 4.5 aDd .9 (Figure 9C). ID tliis range, the downstrea extrend.ty of' the surface roller, and the point at which the higb• velocity Jet tends to leave the floor practically occur 1n tbe sama vertical plane. The Jump is well balanced and the action is thus at its best. !he energy absorption 1n the JWII> tor Frollde DWliben fl'Olll 4.5 to 9 rauges fro& lf.5 to 70 percent (Figure 8).
As the Prou.de mamber increases above 9, the form of the JW1Qi1 graduaJ.q ebange11 to that showD 1n Figure 9D. This 1s the case where V1 is very high, D1 is comparatively sall, and the difference in conJugate depths is large. The high-velocity Jet no loDE,19r carries through for the full M!ngth of the Jump. In other words, the downstreaa extremity of' the surface roller nov becomes-the determ1n1ng factor 1n Judging the length of the .1um;p. Slugs of water rol 11ng clown the front face of' the Jump intem:lttentl.1' fall into the high-velocity Jet generating.· additional waves dow:nstreaa, and a l'OUgb. surface can prevail. Figure 8 shows that the enera dissipation tor this case may reach 85 pe~at.
The limits of' the F:roude muiber given above for the various forms ot Jump are not·detin1te values,·but overlap somevllat depending on local f'actors. · Retul"Aing to Figure 7, it is found tbat the length curve catalogs the various phases of' the JUJIG) quite well. Tbe flat portion ot the curve indicates the range of' best operation. !rhe steep portion ot the curve to the left definitely indicates an 1Dternal change 1D the tom of' the .1UIIIP•. In tact, two changes are manifest, the tom shown 1n Figure 9A and the t01'Jl1 which migbt better be called a transi_tion stage, shown in Figure 9B. The right end ot the curve on Figure 7 also indicates a change in f'orm, wt to less ~nt.
23
Practical Considerations
As stated previously', it was the intention to stress the academic rather than the practical viewpoint in this section. An exception has been made, as this is the logical place to point out a: few ot the practical aspects of st1JJ1ng_'basin design using horizontal aprons. VieW'ing the four f'orms of Jump Just discussed, the toll.owing is pertinent: ·
1. All forms are encountered in stilling basin design.
2. The form in Figure 9A requires no· ·ba:ft1es or special consideration. The only requiremsnt necessaey is to provide the proper length of pool, which is relatively short. This can be obtained tran Figure 7.
3. The form in Figure -9B 1s one ·o-r the most diff'icult to handle and is :frequently' encountered in the design of canal structures, diversion dams, and even outlet works. Baffle blocks or appurtenances 1n the basin are o-r little value. Waves are the main source of diff'iculty and methods tor coping With them are discussed in Section It-. The present information my prove valuable in that it will help to restrict the use of' Jumps in the 2.5 to 4.5.Froude number range. In many cases its use· cannot be avoided, but in other cases, altering o-r dimensions my bring the J~ into the desirable range.
4. lo particular difficulty is encountered in the torm shown on Figure 9C. Arrangements of baffles and si~s Will be found valuable as a mans of shorteniDg the length of basin.
5. As the Froude number increases, the Jump becomes more sensitive to tail water depth. For numbers as low as 8, a tail water depth greater than the conjugate depth is advisable to be certain that the Jump W'ill stay on the apron. This phase Will be discussed in more detail iD. the following sections.
6 ~ When the Frau.de number is greater- than 10, a stil."ting basin my no lo~r be the most economical dissipation device. · The difference in conjugate depths is great, and, generally speaking, a ver:, deep basin with high tra:ln1ng walls is required. ~ cost of' the stilling basin may not be commensurate vith the results obtained. A bucket type o-r dissipator my give com.parable results at less cost.
Water-surface Profiles and Pressures
Water-surface profiles for the jump on a horizontal floor were not measured as these have alreaq been deteimaed by Bakbmetett and Matzke.,l Bewman and L&Boon.,19 and Moore.27 18 It bas been shown by several experimenters that the vertical pressures on the ·f'loc:>r of the stilling basin are virtually the same as tbe . vater-surtace i,rotile - '· voulc1 indicate. Al though there w1ll be more air entraiment and bulk1Dg in the prototype., making the freeboard of training vaJ.ls less thaD indicated in the model., pressures obtained fl'OJIL· Jll0dels are auft1eient~ accurate tor design purposes.
CODClusions
'l'he foregoing e:x;penments and discussion serve to associate the FJ'OUde number witJl stilling basin design vhei,t it ott~n ·JIBD7 advantages. The ratio of co~te.depths., the J.eragtb. ot .1.WIP> the tne of:· Jump to be expected., and the losses involved bave all been related to this DUJDber. 'l'he principal advantage ot this- f'om of presentation is tbat one my see the ,entire. picture. at a glance. 'l'!1e for,egoing 1Dtomat1.on is basic to the understanding of the hydraulic JUD!l). The fo~ sections deal with the more practical aspects., such as ll0dify1Dg the · Jump by ba:rtles and sills to increase stabili ~Y and shorten the length. An example follows which may hel,p clarity the 1Dtormation so far presented. ·
Application of Results (Exanq>le l}
Water flowing under a sluice gate discharges into a rectangular stilling basin tbe same vid~ as the gate. The _average velocit," and the depth of f'low after contraction of the Jet is camplete ue: V1 • 85 ft/sec and D1 • 5.6 feet. Determine ~ conjugate tail water depth., the length of basin required to confine tbe Jump.,- tbe effectiveness of~ basin.to dissiP&te energy., and the t~ of' jUJII) to be expected.
-::::=::::::8:::5 = • 6 .34. ../32.2 X 5.6
Entering Figuze 5 with this value
»2 -· 8.5 »1
25
The conJugate tail water- depth
D2 • 8.5 z 5.6 • 47.6 feet
Entering tbe l'eCO!llancled cum on Figure 7 with a Jrmcle DUllber ot 6.34 · ·
L . iii. 6.~
Length ot basin necessary to cODtiDe the Jump
L • 6.13 X Ji.7.6 • 292 feet
Ellterillg F1gme 8 With the above ftllae ot the J'roucle mmber, it is fOIUld that the energy absorbecl in tbe .11BQ is 58 P81'Cellt ot tbe energy entering. ·
By COD8Ultiltg Figare 9 it is QPUeD~ tba1; & . ft17 a&t1s:ractor., .1\UQ can be expectecl. ·
SECTIOI 2
STILLDG BASIi FOR BIGB DAN AID EAR'J.'11 DAM SPILLWAYS MD LARGE CABAL STRJCTUDS
(BASU II)
DTRO.DUCTIOB
St1~ basins are seldom. designed -to confine tbe entue length of the 1Q'draul1c .1UilP on the pawd &pl'OD as was asSU11tcl in tbe foregoing section; tint, tor economic :reasons and secoadJ,1', because there are mans tor madit7,I.Dg the JWQ characteristics to obtain caaparable or better performance in shorter lengths. It is poaaibl.e to reduce the Jump lengtb bJ' the :I.Dstallat1on of accessories such as blocks, battles, and sills in the st11J1ng bas1D. ID a441tion to ahortentng the Jump, the accesaor:tes eurt a stabilizing effect aml 1D same cases increase tbe factor ot aatet7.
Section 2 concerns still1Dg basins which have been ill common use on high daa and earth daa spillwap, and large canal structures, and will be denoted as Basin II (F1gure JD). !he basin contaiDa chute blocks at tbe upstnaa end and a clentatecl sill near the downstrea end. llo battle piers are used in Basin II because ot the relative~ high veloci~iea entering the Jmq,. b pr:lDcipll &:la vu to (1) .pae:ralize the cleaip, and (2) detel'Jline the range ot operating conditions tor which this basin 1a best suited. The f1rat obJective was not difficult as the Bureau has designed an4 constncteclauy of these basins, aaae ot vhich were checkecl' "'1th IIOdels. Tlle principal task consisted ot consul.ting laborato17 records and tabulating the reau1ts. ~ accomplish the MCODd obJectiw required add1t1onal. laboratory ex»eriments.
A11AL'18IS OF EIISTllG DAB
:B.tllgjnn1ng nth the first p.baae (ll, the capacities am cl1aeD• s10Ds ot 36 st.1lJ1ng basins tor earth clams, small overtlov 48118 and large canal stNctures, which b&'9'e been tested b7 :moae1s, are listed in !ab1e 2. The model stuclies were made in several laboratories bJ' many indirlduala over a 23-Je&r period. Each 1Dd1v1clual was moze or less free to exper:Lment Yith IIOdels· of these st:mctures as be saw :tit. !fbe tiilal clesigna, tabulated 1D. Table 2, represent ail agreement between designer and exper:llleate .. · 'for each case. Tims, the tabulation shoald be itl.eal for selecting a generalized clesigD 'for Basin II.
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Results of Compilation
With the aid of Figure 10, most of the s,mbols used in Table 2 are self-explanatory. Tbe use of baffle piers is limited to Basin III. Column 1 lists the reference material used in compiling the table. Column 2 lists the maximum reservoir elevation, Column 3 the maxi.mLml tail water elevation, Column 5 the elevation of the stilling basin f'1oor, and Column 6 the maximum. discharge for each spillway. Colum 4 indicates the height of' the structure studied, sbowing a maximum t'all from headwater to tail water of' 179 feet, a m1n1mnm of' 14 feet, and an average of' 85 feet. Column 7 shows that the width of the stilling basins varied from 1,197.5 to 20 feet. The discharge per foot of basin Width, Column 8, varied from 760 to 52 cfs, with 265 as an average. The
computed velocity, V1, (hydraulic losses estimated in some cases); entering the stilling basin (Column 9) varied from 108 to 38 feet per second, and-the depth of flow, D1, entering the basin (Col.wan 10) varied from 8.80 to o.60 feet. The value of' the Froude number (Column 11) varied from 22.00 to 1&..31. Columnl2 shows the actual depth of' tail water above the stilling basin floor, which varied from 6o to 12 feet~ while Column 14 lists the computed, or conjugate, tail water depth for each stilling basin. The conjugate depths, D2, were obtained from Figure 5. The ratio of the actual tail water depth to the conJugate depth is listed tor each basin in Column 15~
Tail water depth. Tbe ratio of' actual tail water depth to conjugate depth shows a max:1111m of 1.67, a m1n1nnun of O. 73, and an average of 0.99. In other words, on the average, the basin floor was set to provide a tail water depth equal to the conjugate or. necessary depth.
Chute blocks. The chute blocks used at the entrance to, the stilling basin varied in size and spacing. Some basins contained nothing at this point., others a solid step, but in the majority or cases a serrated device., known as chute blocks., was utilized. The chute blocks at the upstream end of the basin tend to corrugate the jet, littu6 a portion of it fl;"ODl the floor, resulting in a shorter length of' jump than would be possible without them. These blocks also tend to improve the action 1n the jump. The proportioning of chute
blocks bas been the subject of mch discussion. The tabulation in Columns 19 through 24 of Table 2 shows the sizes which have been ).lsed. Column 20 shows the height of the chute blocks, while Column 21 gives the ratio of height ot block to the depth D1. The ratios of' height of block to D1 indicate a maximum of 2.72, a minimwll of 0.81., and an average
ot 1.35. This is somewhat higher than was shown to be necess&r7 by the verification tests discussed later; a block equal to Di in height is sufficient.
30
The rid th of tbe blocks is shown ill Colman 22. Col.um 23 gives the ratio of width ot the block to height, with a wx1mnm of 1.67, a :min1nnm ot o.!ell., and an average of 0.97. The ratio of width ot block to spacing, tabulated 1n Coham 24, shows a •rfnm of 1.91, e. JD1n1:nnm of 0.95, and an average of 1.15. The three ratios iDdicate that the proportion: height equals width, equals spacing, equals »1 should be a satisfactory standard tor chute block design. The ride variation shows that these dimensions are not critical.
Dentated sill. Tl:le sill 1D or at the end of the basin vaa either solid or had same tom ot dentated arrangement, as 4esignatecl 1D Column 25. A dentated sill located at the end ot the apron 1s rec01111&nded. '!he shape of the dentates and tbe angle ot the sills varied considerably 1D tN spillways tested, Colmms 26 through 31. The position ot the dentated sill also var1ecl and this is 1m11cated bJ" the ratio ~I 1n Column 26. · The distance, x, is •asured to tbe
dovnstreaa edge of the a1ll, as illustrated ill Pigue 10. The ratio
X -L varied tron 1 to 0.65, with an average ot 0.'17. II
The heights ot the c:lentates are given 1D Column 27. The ratio ot height· of block to the conjugate tail water depth is shoVa 1n Col.mm 28. !beae ratios show • wximm ot 0.37, a mnimm ot o.08, aD4 an average of 0.20. '!he width to height ratio, Column 30, shova a :mexi:nnJII of 1.25, • 111n1:nDI of 0.33, and an average of 0.76. '!he ratio of width of block to spacing, Col.mm 31, sbolrs a nilx:hlDI of 1.91, a JD1n1:nm of 1.0, and an average of 1.13. For tbe sake of general1zat1011, 1.he tollov1ng proportions are reccaaended: (1) height of dentatecl sill • 0.2D2, (2) width ot blocks • 0.15])2, and (3) spacing ot blocks • 0.15»2, vhe~ l>2 is the conJ,igate tail vate:r depth. It is recommemed that the dentated s1ll be placed at the downstream end of the &prOD..
Columns 32 through 38 show tbe proportions of additional battle blocks used on three of the stil.11ng be.sins. These are not necessary and are not reccmmended tor this type ot bas1n.
Additional details. Column 18 1ndicates the angle, With the horizontal, at wb1ch &· high-velocity jet enters ~ stilling ~ill for each ot the spillways. The -.xuam angle vas 34 and the minimam 14 •. The effect of the vertical angle of the chute on the action ot the hydraulic Jump could not be e~ted frm the information aftilable. This factor rill be considered, hoWeve:r, 1D Section 5 1D connection with sloping apron design.
31
Column 39 designates the cross sec~ion of the basin. In all but three cases the basins were rectangular. The three cross sections that were trapezoidal bad side slopes varying f'rom 1/4:l to 1/2:1. The generalized designs presented in this report are for stilling basins with rectangular cross sections. Where trapezoidal basins are used., a model study is strongly recommended. ·
Designers have been. concerned over the type of Y1Dg wall which should be used at the end of' stilling basins. Column.40., Table~ .. indicates that in the majority of' basins constxucted for earth dam spillways the wing walls were normal to the t1"&'.in1ng val.ls. Five basins were constructed without Wing walls using a rock blanket for protection. The remainder utilized angl1 ng v1.ng walls or warped transitions downstream f'rom the basin. The latter are common on canal stru.ctures. The object., of course., is to build the cheapest wing wall that will afford the necessary protection. The type of Ying wall is usually dictated by local conditions such as width of the chazmel downstream, depth to foundation rock, degree of' protection needed., etc., tbus Ying walls are not amenable to generalization.
VERIFICATIOB TESTS
It was early learned that the information on Table 2 did not cover the entire range of operating conditions desired. There vas insufficient information to determine the length of basin for the larger· values of the Froude number; there was little or no inf'o:rmation on the tail water depth at which sweepout occurs., and the information available was of' 11 ttle value for generalizing water-surface profiles. It was, therefore., necessary to perf'orm a set of experiments to extend the range and to supply the missing data. The experillents were made on 17 Type II basins, proportioned according to the above ru.les., and installed in Flumes B., C., D, and E ( see Columns l and 2, Table 3). . Each basin was Judged at the discharge :for which it was designed; the length was ad.Justed to the minimum that would produce satisfactory operation, and the absolute mn1nmm tail. water depth for acceptable operation vas measured. The basin operation was also· observed for flows less thail the designed discharge and found to be satisfactory 1n each case.
Table 3 is quite similar to Table 2 Vi.th the exception that the length of basin LII ( Column 11) was determined by experiment, and the tail water depth at which the jump Just begau. to sweep out of the basin was recorded ( ColUllll 13) •
•
32
Tail Water Depth
'l'he solid line on Figure ll vas obtained :from the hydraulic
Jump :formula ~ • 1/2 ( V 1+8F2-1) and represents conjugate tail water D1
depth. It 1s the same as the line shown on Figure 5. The dash lines on Figure 11 are merely guides drawn :for tail water depths other than
conjugate depth. The points shown as dots were obtained tl"Clll Column 13 ot Table 2 and constitute the ratio o:f actual tail water depth to D1 tor each basin listed. It can be observed that the majority- of the basins were designed tor conjugate tail water depth or less. The JD:1.n1-=- tail water depth tor Basin II., obtained :from Column llt- ot Table 3, is shown on Figure ll. The curve labeled "Minilllm 'l'W Depth Basin II" 1.ndicates the point at which the front. ot the jump aoves away- trom the chute blocks. In other words., any aaditional loveriDg ot the tail water would cause the Jump to leave the basin. CODSUltiDg l'igure ll it can be observed that the margin ot safety tor a Frollde mmber ot 2 is O percent; while tor a mmber ot 6 it increases to 6 percent., tor a number of 10 it d1lll:1nishes to 4 percent., and tor a number ot 1.6 it is 2.5 percent. '1'o be certain that this is understood., it will be stated another way. The JUJQ> will no longer· operate proper~ when the tail water depth approaches o.98D2 for a Froude number of 2 or o.9'1,~ tor a number of 6 or o.96~ tor a mmber ot 10, or 0.975»2 tor a DWlber ot 16. !be argill of safety is largest 1n the middle range.· For the two extremes of the curve it is advisable to provide a tail water greater tbaD. co$gate depth to be sate. For these reasons the Type II basin should nner be designed tor less than conJ,agate depth and a m:f n:fnDD safety factor ot 5 percent ot D2 is rec01111ended.
There are several other considerations in regard to tail water which are mentioned as a reminder. First., tail water curves are usual.11' extrapolated for the discharges encountered in design., so they can be 1n error. Secondly., the actual tail water depth usually lags, 1n a temporal sense, tb&t at the tail water curve tor rising flow and leads tbe curve tor a falling discharge. Bxtra tail water should thereto:re be provided 1:r reasonable increasing increments of discharge 11m1t the pertomance ot tho stl'llcture because ot a lag in buildiDg up tail va~r depth. Thi.Ml.y, a tail water curve may be such that the aost adverse condition occurs at less than the mex:Sam clesigned discharge; and fOllrthq, tell;porary or pemanent retrogression ot the riverbed davnstreaamay be a tac~r needing cons1derat1oa. These factors., some of which are difficult to evaluate, are all 1111:portut 1D stilling basin desigD., ud suggest tbat an adequate factor ot saf'et7 is essential. It 1a advisable to constnct a jump height cune, superilQ,K>sed on the tail water curve., tor 'each basin to determine the moat adverse operating condition. Tb.is proce4ure Yill be illustrated later.
34
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0,7
5
I 1
0,2
0
,75
I
8,3
0',75
I 9
,5
I
0,7
5
I 6
,5
0,7
5 I
5,3
211
0.6
11
Varied
UIJ.
Wl
15,13 0
.97
12.02
o.96 9
,70
0
,94
8,39
0,93
17
,04
0
,97
1
5,ll
0,9
5
13,75 0
,97
1
3,6
0
0,9
7
13
.21
0
,97
19,35 0
.97
1
7,8
) 0
,98
1
5,3
1
0,9
9
13
.89
0
,98
12,75
0,9
7
11
.32
0
,96
6.,S
0
,94
9
,02
8
,90
The ftritication tests repeatedly c1emonstra:ted tbat there ia no simple remedy tor a deficiency 1n tail water depth. Increasing the length of basin, which is the remedy often at~ in the f'ield, v1ll not c~nsate tor det1cienc7 in tail water depth. :ror these reasons, ca?"e should be taken to consider all factors that -,- attect the tail vater at a future date. A stilling basiD that does not pertom :,roper~ carmot be .1ustif'ied in the light ot lll0lle7 saftt. b7 skimping, regardless of' the 8IIOW1t.
IA!yth of Basin
The necessary length of Basin II, cletel'Jl1Ded by the wr1t1cat1on tests, is shown as tbe 1ntened1ate cune on Pipre 12. The squares 1nd1.cate tbe test poiDts (Cohums 10 and 12 of hble 3). The black dots represent existing basins (Col'U11DS ll an4 17, Table 2). ConJugate depth was used 1n the ol'd1nate ratio rather tban actual tail water depth since it coald be co.mp,tted for each case.
The dots scatter considerably but an aftrage curve 41'&VD thror&gh these poillts voald be lower than the -Basill II cune ~ In :r1111re 12, therefore, it appears that 1D practice a basin a'bal.lt 3 times the con.-,Ugate depth is artuaJJ7 used when a basin ~bout 4 times the con-3ugate is recomended f'raa the ftritication tests. It abolll4 be remembered, havner, that the shorter basin8 were all model teatecl and. every opportunity was taken to reduce the basin length. The extent an4. depth of' bed erosion, vave heights, favorable f'lood f'nquencies, tlOCld chlration and otber factors were all used to justify reducing the basin length. Lacking def1D1te lmovl.edge ·Of' this type 1n deaipiDg a ltas1n tor field conatru.ction without model tests, _ the lcmpr 1Das1ns indicated by the verification teats cune are recoaaendecl.
The 'f7pe II 'basin curve has been arb1trar1.ly teniD&ted at :rroude mmber Jt., as the 3UJ1.P ,_,. be 1Ul8table at lower mmbera. The clmte blocks bave a tendency to stabilize tbe Jm.P- and recluce the 4. 5 limit discussed f'or Ba.sill I. For bas1ns having Fl'Ollde nmibers below 4.5 see Section 4.
Water-nrtace Profiles
Water-surface profiles were meae~ cluriDg the teats to a14 1n com.piting uplitt pressures umler tM basin apron. As the vater surface in the stilling basin teats f'1Dctuated rapidly 1:t 'VP.fl felt tbat a high 4egree ot accuracy in •asanment na not neceBs:'\l"J.. Tb.is vaa tOIIDd to be tru.e when. tbe approximate vater-aurtace profiles obta:1Decl were plotted, tben generalized.. It was toand tbat the profile u, tlle basin c011ld be closely approximated by a straight line meldng a . angle CX. with tlle bori.zontal. ft.is line can also be considered to be a pressure protile.
li}_l_
30
2
2•
2
2
2
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I
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I
;
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z
FIGURE 11
-
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, / II
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V •' ,,,,
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I/ , / V
I I ~v V V ,'
Dz,.l(vl+SF!-1) I/ I/ / !/ - , ) I / 01 t 17'"· ,-•• v I
• .' / -j',l / II' II'/ If 'V V .' __,_
I/ Ii ,j ' I/ •' , , ,
' ·-1, v,
/ I' IV , '[ll<. ·~Minimum TW Depth I 1, , , L' jBasin n I - ,- ,-
I ~ I V .1~, I ~/ I v~ V / ,r;, t11in1mum ·rw Depth
9 I/ l/11-, / ' ,• Basin Ill Ii , .. ,i, "1
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J / ,. ·~ . ,, x Verification tests basin I (Table I) II, J
., . ,, • Existing type n basins (Tobie 2)
I I/ ""' I~ o Minimum T w - type n basin (Tobie 3)
/lh /~ o Minimum T W - type m basin (Tobie 4)
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F,=..l!i-Vgo;-
HYDRAULIC JUMP STUDIES
STILLING BASINS 1,II AND ill
MINIMUM TAILWATER DEPTHS
....
.
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4a
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ump
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16
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The angle OC. (Column 24, Tab1e 3) observed in each ot the verification tests has been plotted Vi.th respect to the Fl'Ollde maber on Figure 13. The slope increases Vi.th the Froude number. To use the curve in J'iggre 13, a horizontal l1ne is drawn at conjugate depth on a scale drav1ng of the basin. A vertical l1ne is also drawn t1"011l the \19Stream face ot the dentated sill. Begtnu1ng at the point ot intersection, a sloping line is constructed as shown. The above procedure gives tbe approximate vat.er surface and pressun profile tor con.)lgate tail vater depth. Should the tail vater depth .be greater than D2, the profile Will resemble the uP119rmoat line on Figgre 13; the angle remains UDCbanged. This information appl.ies only tor the Type II basin, constructed as recommended in this section.
COBCIDSI0E
The following ru1ea are recommended tor gemrallzation ot Basin II, Figure l!i.:
1. Set apron elevation to utilize full conJugate tail water depth, plus an added factor ot safety it needed. AD additional factor ot safety is advisable tor both lov and high 'V'alues ot the Froude number ( see figure ll) • A ndn1mun margin ot safety ot 5 :percent ot »2 is rec0111118nded.
2. Basin II may be effective down to a Fl"Ollde muaber ot J., but the lower values should not be. taken f'or granted (see Section 4 tor values less than 4.5).
3. The length of basin can be obtained frca the intermediate curve on Figure 12.
If.. 'l'he beight ot chute blocks is ·equal to the depth ot tlov entering the basin, or »1, Figure llf.. The Vidth and spacing should be equal to approximately D1,; however, this may be var:l.e4 to eU:m1ute the need ot fractional bl.ocks. A space equal to~ is preferable
. ~ . along each wall to reduce spray and maintain desirabl.e pres~s.
5. The height ot the dentated sill is equal to 0.2D2 , while the mx1mm width UC,. spacing ·reco.mmended is apprc>ldate~ 0.151>2. In this case a block is recc:mnended ad.1acent to each side wall, figure lli-. The slope ot the contimous portion ot the end sill is· 2:1. In the case of' narrow basins, which waald iDVOlft cml,1' a few dentates accOl'ding to t.\e above rule, it is advisab1e to reduce the width am the spacing so long ae this is clone proportionately. Beducing the width am spacing ~tuaJJy ill,pro9es the performance in narrow basins, thus, the minimum width and spacing ot the dentates is governed only by structural considerations.
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ute
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6. It is not necessary to stagger the chute blocks and the sill dentates. In f'act this practice is usually 1Dadviaab1e f'rom a construction standpoint.
7. The verification tests on Basin II indicated no perceptible ehange in the stilling basin action With respect to the slope of' the chute preceding the basin. The slope of' chute varied tram o.6:l to 2:l in these tests, Column 25 1 Table 3. Actually, the slope of' the chute does have an effect on the ~raulic Jump in some cases. This subject will be discussed in more detail in Section 5 with regard to sloping aprons. It is recommended that the sharp intersection between chute and basin apron, Figure 141 be replaced With a curve of' reasoD&ble radius (R > 4D1) wben the slope ot the chute is 1:1 or greater. Chute blocks can be incorporated on the curved f'ace as readily as on the plane surfaces.
Following the ab<m.· rules Will result in a sate, conservative stilling basin tor spillways Vi th f'all up to 200 f'eet and f'or flows up to 500 cf's per foot of' basin Viclth, providing the jet entering the basin is reasonably un11'orm both as to velocity and depth. For greater falls, larger unit discharges, or possible asJD11118tr;y, a model study of' the spec11'1c design is reccmaended.
Aids 1n Computation
Previous to presenting an exanu,le illust::-ating the •thod of' proportioning Basin II, a chart Will be presented which should be of' special value tor pre11m1M-r;y computations, The chart IIISkes it possible to determ1De V1 -and D1 With a f'air degree of accuracy, tor chutes having slopes of' o.8:l or steeper, where computation is a difficult and arduous procedure. The chart presented as Figure 15 represents a composite of' -experience, computation, and a limited amount of experimental inf'o:rmation obtained f'rom prototype tests on Shasta and Grand Coulee Dams. There is much to be desired in the way of experimental confirmation; however, it is felt that this chart "ls sufficiently accurate for prel1:m1n8J7 design. A concerted effort will be made to obtain ad:41tional experimental information whenever possible.
The ordinate on Figure 15 is tall from reservoir level to still1ng basin floor, while the abscissa is tbe ratio of actual to theoretical velocity at entrance to the stilling basin. The theoretical velocity VT a \/ 2g(Z-B/2) (see Figure 15). The actual velocity is the term desired. The curves represent dUf'erent heads, :e:, on the crest of the spillway. As is reasonable, tbe larger the head on the crest, the more nearly tbe actual velocity at the base of the spillway 1rl:,ll approach the theoretical. For example, with H • a.<> :f'eet and Z • 230 f'eet, the ·actual wloci ty at the base of the dam voulc1 be 0.95 of the caapited theoretical velocity; while w1 th a head of' lO feet on the cres-t~, the actual velocity vould be 0.75 V-r. The value of D1 is com:pu:ted by divicling the Ullit discharge by the actual velocity obtained troaFig11re 15
41
FIGURE 15
I I I ;
uol-lHH-4---l-1-1,-1--+-H-,-+--++,-+--t--H,H-lrt--Jt-1-t'iH-t
I II
so,M-_-i-_-1-~---1-i-_-1-.i,-_+-i-l~+-c~i-.:l-i-luL4..i:t,1j,1=l·tt=t=t=l!·J~l=t~~""!,!!!f!!:!!!!~---------------it ---f
•e.J-+--l-+-+-,-1Hi-1-'1H-+1-+-i1 r-ri+-\-+t1-t+1 ·r+t 1 -t+--t---1 t:-:_-~- ----------t l I I ·.-. I I
I '/)-.'• I I
4 •ol-ll...--lH-4-1--4-+·-11--Hf+--t--f-1tl-+i-t-':'t-tH1H---, · · · · : : I Z v \ ',1, I I
'' .0-,, I I I .·i:,·
440,1-4-4--+-+-+--11-+-+-~1--+t-+-t--Ht-t-tt--t--t-1 · . · ·: v.r~) I I 1 • • .-.
0 ,f>; I I • , I I
' ' ' •. I I
1- 42 I \ ·,(), 'i,: I l Ill I • •. • : I
~ 400 ~ I ~ 1 ::o. ',;_. : : a,: I .. fJ: : I
O 1 --1-+-+-+-l-H-I-H'f,+.-+:+-+ '-+-+-+-t--tH'H+-tt-t--i ·: .-. ' .• I : 0 ....... .,. 1
~ •• , I ' ..........--::-. · o· · : . 1 .,.
- 1--i--l-l---1,--1,--1,4!--i-+1--Hf+--ll-+--++-+--l-i-t-Ht-H--I :~ . . . . . y
Z I I \ V,r,•:.·4!· .•·,a, .;,. ,•
iii HO 1 \ D1 •• • ''
: \ , u, 340W~l-ll--l-4-4-t---1-4--+---11 HC"'M-4-+-tl-++t-<t+--'i z _. I I ..J 12:d-+--i--l---l-+-+-,-1~,+-++,+--H-+-+-t-tHI-Ht1t-tt-; ~ I
II! i \ \ \ e •.-· , , , , \ _. I-IH-1,-+-+-+--4--'rt-l-Hr-HIH-\t-++1 H:-tt--tt--1
~ 2,_.w-+-+-+-+-+--t--Hrl-+-,-it--HH-t-t--tt--t-tt-1t'"-l ILi ... \ a,: 2aol--+-+-+-H~-+-+-+-+.-\+--H-\t-H\+""ft1H-ttt'"'l1""-1 0 > ' \ :; 240 \ , ,
::: ~Hl-+-+-+-+--+-~\-+-+--'t-~ -1-41,-i, \-+-++HH-IH--;
a,: 220 ' 11 2 -+--+-+--+--+-+-+-+-'v-t-~'\..-t--t-~014--il-ll-+H,-H-~ ~ \ ,d
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... \
... \ . ' ~ 1aol--i--1-1---1---1--1---1--1--+-w-1 -+--H,+--H-t0--tr1---t1r-H1111"-i
II
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,ao 11 , , , 1\1 x~· ... \ 111 ' 1 I
1401--1--1--H~---1--i---l--l--+--+-+-+--r, +-"11,t'Hl\'ht-;-+'HHH
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\ ' \ l11 I
1001-+--I-IHl--l-1-4-4--1--+-Fc+.>.J--+-"Hrt'ri-x-itlt-HIH ', .S,) \
+--+-+--+-+-t-t-~~1\.--t'<\T'"rs,., \ \ \ I
aol--1--1-if-lf-l'-t-+-+-+--t--t--t-';~:-t--,\.;-;- , \ \
' ' aol-1---1-11--11--1-i-l---1--+-+-+--+--+-+--l''rt \~\r+\-tttli
I\ \ 40,l--1--~-l--l--1-+++-+-+-HH-+-1-~l\-llltl\,~ 'J\\III
.. 'I\ 'lol--l--J-..jl--l~--1--1--+-+-++++++-+-r-1"1-..:-\li'il
o-",, -..1, 1--1--1--l---lf-l--+-...I-+-+-+-+--+--+--+--++• I .... r--. 0 o., 0.2 O.• O,. 0.D 0.8 < .t o.a OlJ
YA_(octuol) v, l theoretical)
PROTOTYPE TESTS x Shasta Dam o Grand Coulee Dom
HYDRAULIC JUMP STUDIES
CURVES FOR DETERMINATION OF
VELOCITY ENTERING STILLING
BASIN FOR STEEP SLOPES
0.8:1 TO 0.6:1
The chart is not applicable tor chutes flatter than 0.6:1 as frictional resistance assumes a4ded 11lportance in this range. 'flleref'ore, it Will be necessary to cc,mpite the draw-down curve as usual starting at the gate sectionvhe't"e critical depth is known.
Insuttlation, produced by air :troa the atmosphere 111 ,cl ng vith the sheet of' water during the tall, need not be considered in the )Qdrau• lic Jump c~tations. Insuttlation need be considered principalq in the desisn of chute and stilling basin valls. It is not possible to construct valls sufficiently high to confine all spray 811d splasll; thus, the best that can be hoped :tor is a height tbat is reasonable and commensurate _With the mter:Lal and terrain to be protected.
APPlication of Results (Example 2)
'l'he crest of an overfall daa, having a downstl'eam slope o:t o. 7: 1, is 200 feet above the horizontal floor of' the stilling basin. The head on the crest is 30 feet and the maYinm discharge is 480 eta per toot ot stilling basin Width. Proportion a '!ype II stilling basin :tor these conditions.
Entering_Figu.l'e 15 vith a head o:t 30 feet over the crest and a total tall ot 230 feet,
VA f; • 0.92
'l'he theoretical velocity VT• J2s(230~. 117.6 tt/sec·
The actual velocit7 VA• v1 = 117.6 x 0.92 • 108.2 tt/sec
The Froude number .
»1 = '(j_ ~ 1~ 2 = 4.44 feet
Vl. 108.2 ... 1. F1 = - = --;::::::::::::::::=== • 9 •"""" V 81)1 V 32.2 x 4.44
Entering Figure 11 vith a Froude number o:t 9.04, tbe solid line gives,
'l'W Di• 12.3
As 'l'W and n2 are syn0110110Us in this case, tbe con.,ugate tau water depth,
The minimua tail vater l1ne tor the Type II basin on Figure 11 shows that a factor o:t satet7 o:t about 4 percent can be expected :tor the above Froude number.
Should it be desired to pron.de a margin o:t satet7 ot 7 percent, the tollow1Dg · procedure JDa7 be. tolloved: Consulting the line tor minimwll TW depth :tor the Type II basin, Figllre 11,
TW Di • 11.85 :tor a Frowle DWlber ot 9.011,
The tail vater depth at which sweepout is incipient:
'l'Wso • 11.85 x 4.~ • 52.6 feet
AM1ng 7- percent to this t1.gure, the at111:lng basin apron should be positioned tor a tail vater depth ot
52.6 + 3.7 • 56.3 feet or 1.0302
The length ot basin can be obtained by entering the intermediate curve on Figure l2 with the Frowle number ot 9.011;.
1xx· - • 4.28 l>2
L]:1 • •.28 x 54.6 • 234 teet (see Figure 14)
The height, width, and spacing o:t the chute blocks as recomended is D1, thus the dimension can be Ja. teet 6 1.nches.
The height ot the dentated sill is 0.2D2 or 11 feet, vhile the Width and spacing of the dentates can be 0.15D2 or 8 feet 3 inches.
SECTION 3
SHORT STILLDG BASilf FOR CAlfAL STRJCTURES, SMALL OUTLET WORKS, ARD SMALL SPILLWAYS
(BASIB Ill)
DTRODUCTIOl'f
Basin II often is considered too conservative and consequently
overcostly tor structures carrying small discharges at moderate veloc-
i ti~s. This can be especially true in the case ot canal chutes, drops,
wasteways, and other structures which are constructed by the dozen cm
canal systems. Any saving that can be effected in decreasing the size
ot these structures can amount to a sizable sum when Jlllltiplied by the
mmber of structures involved. There is, ot c01l1'Se, another consider
ation which should be kept in lliJJd. It the dimensions ot a particular
structure are reduced to the point where it no longer operates satis
factorily, this mistake Y1ll be repeated many times over. In this
section a generalized design is developed tor a class ot smaller struc
tures in which the velocity at the entrance to the basin is moderate or
low (5 to 6o feet per second, corresponding to an OYerall head of about
100 teet). Purther economies 1n basin length are accanplished With
battle piers.
The :most effective ,ray to shorten a stilling basin is to
m.oclUy the Jump by the addition ot appurtenances in the .basin. One
restriction i.Qosed on these appurtenances, however, is that they 11111st
be self-cleaning or nonclogging. This· restriction thus limits the
appurtenances to blocks or sills which cali be incorporated on the
stilling basin apron.
Tbe Depart.men~ ot .Agriculture 816 developed a very short
still1Dg basin designated "The SAF Bas1n," tor use on drainage struc
tures such as the Soil Conservation 5ervice constructs. The SAF basin,
Figure 16., tits the needs tor which it was developed but does not pro
rtde the factor of safety necessaey for Bureau use. This was ·demon
str.ted by constructing and testing several bas1ns proportioned to SAi'
specifications. It was discovered, however, that the arrangement of
this basin had excellent possibilities, and that by cbang:tng dimensions,
such as the length, the tail water depth, the height and 1ocation ot the
battle bl.ocks, etc., tbe desired degree of conservatisa could be
obtained.
FIGURE 16
HYDRAULIC JUMP STUDIES
SAF STILLING BASIN
I
, II ',
'
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!
In addition to the foregoing tests, numerous experiments vere performed using various types and arrangements ot battle blocks on tbe apron in an effort to obtain the best possible solution. Saae of tbe baffle blocks tried are shown on Fig11re 17. The blocks were posi tionecl in both single and double rows with the second row staggered with respect to the first. Arrangement •a• on Figure 17 consisted of a solid bucket sill which was tried in several positions OD tbe apron. This sill required an excessive tail water depth to be ettective. The solid sill was then replaced Vi th blocks and spaces. For certain heigb:t;s, widths, and spacing, block. "b" performed quite well, resultini in a water surface i=a1m1Jar to that shown on Fig11re 20. Block "c" vas ineffective for &fl7 height. -The velocity passed over the bloclt at abollt a lt.5° angle, thus was not impeded, and the water surface downat1'eaa vaa very turbulent with waves. The stepped block "d" was also ineffective both tor a single row and a double row. The action was much the same as tor "c.• The cube "e" was effective when the best height, width, spacing, and position on the apron were found. The front of the' ~ was almost vertical and the water surface downstreaa was quite flat and smooth, much like the water surface shown on Fig11re 29. Block •f,• which is the same shape used in the SA'F basin,. performed identical.ly Yi th the cubical block "e. • The illportant feature as to shape appeared to be tbe vertical upstream f'ace. The foregoing blocks were arranged 1D single and double rows. The second row in each case was of little · value, sketch "h," Fig11re 17.
Block "g• is the same as block "fff with the comers rounded. It was found that row,01ng the corners greatly reduced the effectiveness ot· the blocks. In tact a double row ot blocks with rounded corners did not perform. as well as a single row of' blocks "b, It "e, It or "t. It NJ bl.ock •f• is usually preferable from a construction stand.J)oint, it was used througboUt the remaining tests to dete:rm:I.De a general design With respect to height, width, spacing, and position on the apron.
In addition to experimenting with the battle blocks, varia• tions were tried With respect to the size and, shape of the clmte blocks and the end sill. It was found that the clmte blocks should be kept small, no larger tban »1, i:f' possible. The end sill had little or no ef'tect on the jump proper vhen ba:f':f'le piers are placed as rec011111ended. The basin as fillally developed is shown on Figure 18. This basin is principally an impact dissipation devit"e whereby the baffle block.a are called upon to' do most o:f' tbe work.. The. clmte blocks aid in stabilization of the Jump and the aolid type end sill 1s tor scour control.
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At the conclusion of the development work, a set of verification tests was made to eYAJ11:Jne and record tbe performance of' this basin, which will be designated as Basin III, over the entire range of operating condi t1ons that may be met in practice. The tests were made on a total of 14 basins constructed in Flumes B, c, D, and E. The conditions under which the tests were run the dimensions of' the basin, and the results are recorded on Table 4. The headings are identical with those of' Table 3 except for the dimensions of' the baf'fle blocks and end sills. The add1 tional s:ymbols can be identified from. Figure 18.
STILLING BASIB PERFORMANCE AID DBSIGI
Stilling basin action was quite stable for this design; in fact, more so than for either Basins I or II. The front of the Jmu.> was steep and there was less wave action to contend with downstream than 1n either of the former basins. In addition, Basin III has a large factor of safety against jump sveepout and operates equally well for all values of the Fr011de number above 4.o. The verification tests served to show that Basin III was veey satisfactory.
Basin III should not be used where baffle piers will be exposed to velocities above the 50 to 6o feet per second range Without the full reslization that cavitation and resulting damage may occur. For veloc1 ties above 50 feet per second Basin II or hydraulic model studies are recommended.
Chute Blocks
The recommended proportions for Basin III are shown on Figure 18. The height, width, and spacing of the chute blocks are equal to n1, the same as was recommended for Basin II. Larger heights were tried, as can be observed from Column 181 Table 4, but are not recommended. The larger chute blocks tend to throw a portion of the high-velocity jet over the baffle blocks. Some cases , Ul be encountered in design, however, where D1 is less than 8 inches. In such cases the blocks may be made 8 inches high, which is considered by some designers to be tui:, minimum size possible from a construction standpoint. -rhe width and spacing are the same as the height, but this may be varied so long as tbe aggregate width of' spaces approximately equals the total Width of the blocks.
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Baffle Blocks
TllC llell)lt or tn@ baf'rl.a bl.04:U ~rea.sea vi~ tbe J"rw4c: number as can 'be o'bservecl f'rom Columns 22 and 10., Table 4. The heigh-t, 1n terms of D1, can be obtained from. the upper li.De on Figure 1.9. The width and spacing can vary so long as the total spacing is equal to the total width ot blocks. The most satisfactory Yidth and spacing vere :found to be three-f'ourths of the height. It is not necessary to stagger the baffle blocks Yi.th the chute blocks as this is often difficult and there is little to be gained from a h.Jdraulic standpoint.
The baffle blocks are located 0.802 downstream from the chute blocks as shown in Figure 18. The actual positions used 1n the verification tests are shown in Column 25, Table 4. The position, height and spacing of tbe baf'f'le blocks on the apron should be ~red to carefully, as these diulensions are important. For eX&lij)le, if' the blocks are set appreciably upstream from the position shown, they will produce a cascade with resulting wave action. On the contrary, if' the blocks are set farther downstream than shown, a longer basin will be required. Likewise, if the baffle blocks are too high, they can produce a cascade, while if' too low a rough water .surtace Yill result. It is not the intention to give the impression that the position or height of the battle blocks are critical. Their position or height are not critical so long as the above proportions t,re followed. There exists a reasonable amount of leeway in all directions; however, one cannot place tbe battle blocks on the pool f'loor at random and expect &D1'thiD8 like the excellent action associated Yi.th the Type III basin.
The baffle blocks may be in the form shown on Figure 18, or they may be cubes; either shape is effective. The comers of the baffle blocks are not rounded, as the sharp edges are effective 1n producing eddies which in turn aid in the dissipation of energy. It is advisable to place reinf'orcing steel back at least 6 inches from the block surfaces when possibl.e, as there is some evidence that steel placed close to the surf'ace aids spall.ing. ·
End Sill
The height of the solid end sill is also shown to var:,Yith the Froude number although there is nothing critical about this d:llllension. The heights of' the sills used 1n the verification tests are shown in Columns 27 and 28 of Table 4. The height of the end sill in terms of' D1 is plotted Yi th respect to the Froude number and shown as the · lower line on Figure 19. A slope of 2:1 was used throughout the tests.
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Tail Water Depth
The SAF :rules suggest the use of a tail water depth less thaD. full conJugate depth, D2• As in the case of Basin II, full conjugate depth, measured above the apron., is also recommended tor Basin Ill. There are several reasons tor this statement: First., the best operation for this stilli~ basin occurs at full conjugate tail water depth; secondly., 1:f less than the conjugate depth is usl!!d1 the surface velocities leaving the pool are high, the .1UJllP action is 1mpa1red., and there is a greater chance tor scour downstream; and thirdly, it the ba:Ule blocks erode w1 th· t:lllle, the add1 tional tail water depth will serve to lengthen the interval between repairs. On the other hand, there is no particular advantage to using greater than the conJugate depth, as the action in the pool will show little or no iml>rovement.
The margin ot safety tor Basin III varies from 15 to 18 percent depending on the value of the Froude mmber, as can be obsened by tbe dotted line labeled, "M1D1DDD Tail Water Depth--Basin III," on Figure 11. The points, from which the line vas drawn, were obtained from. the verif'1cat1on tests, Columns 10 and 14, Table 4. Again, this line does not represent com,plete sveepout, but the point at which the front ot the Jump moves away from the chute blocks am the basin no longer functions properly. In special cases it may be advisable to encroach on this wide margin of safety, however, it is not advisable as a general :rule tor the reasons stated above.
Length of Basin
The length ot Basin III, which is related to the Froude number can be obtained by consulting the lower curve on Figure 12, page 37. The points, indicated by circles, were obtainf:tcl from Colunms 10 and . 12, Table 4, and indicate the extent of the verification tests. The length is measured from. the downstream side of' the chute blocks to the downstream edge of the end sill, Figure 18. Although this curve was determined conser'latively, it will be found that the length of Basin III·is less than one-half' the length needed for a basin w1 thout appurtenances. Basin III, as was true of Basin II., may be ef':tective for values of the Froude number as low as 4. 5, thus the length curve was terminated. at this value.
Water Surface ·am. Presau:re Prof'Ues
Approximate water-surface profiles we:re obtained tor 'Basin m during the verification tests. The fl'Ollt of the Jump was so steep, Figure 20, that only tvo measurements were necesaary--tbe tail water depth and the depth upstream fl'Oll the baf'f'le blocks. 1'J:le tail water depth is shovn in Colmm 6 and the upstream depth is recorded in Column 29 of Table i.. The ratio of the upstream. depth to ccmJugate depth is shovn in Column 30. As can be observed, the ratio is •ch the same regardless of the· value of the Froude mmber. Tbe aftrage ot tbe ~tios in Col.mm 30 1a o. 52. Thus it w:l.ll be asSWled tbat tbe depth upstre• :rrma the baffle. blocks· is one-half the tail vat.er clepth.
The profile represented by the crosshatched area, Figure 20, is tor cODJugate tail water dep+...b.. For a greater tail vat.er clepth Dz,
the upstream depth would be !!. For a tail water dept,ll leas than COD•
3Ugate, Dy, the upstream c1eJ.i woulcl be approximately ;z. There aneara
to be no particu.lar significau.ce to the tact that this ratio is one-halt.
The information on Figu:re 20 applies only' to Basin I~, proportioned according to the rules set forth. It can be asBUllll!td that tor all practical purposes the pressure and water-surface profiles are the same. The:re will be a lncallzed increase in pressure cm the aproza immediately upstreaa from each battle block but this bas been taken into account, more or less, by extending the d1agraa to fllll tail water depth beg1un1ng at the upstream face of the battle.blocks.
:RECOMMDDAl'IOIS
The f'ollowins rules pertain to the design of the T)pe III basin, Figure 18:
1. The stilling basin operates best at full ccmJugate tail water depth, D2. A reasonable factor of safety is involved at conjugate depth tor all values of the Froude DWlber (Figme 11), but it is recommended that the designer no,; make a general practice of encroach1ng on this margin ot &atety. ·
2. The length of pool, which is less tban one-halt the length of the natural jull;p, can be obtained by consulting tbe curve for • Basin III on Figure 12.
3. Stilling !a.sin III may be effective tor value& o~ tbe Froude nuaber as low as 4.0 but this cannot be stated tor certain ( cODSUl.t Section 4 for vallles under 4.5). ·
55
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4. Height, Width, and spacing of chute blocks should equal the average depth of flow entering the basin, or »1 • Width of blocks may be decreased, providing spacing is reduced a like amount. Should Di prove to be less than 8 inches, make the blocks 8 inches high.
5. The height of the baffle blocks varies with the Froude number and is given on Figure 19. The blocks may be cubes or they may be constructed as shown on Figure 18 so long as the upstream face is vertical and 1n one plane. This- feature is important. The Width and spo.cing of baffle blocks are also sbown on Figure 18. In narrow structures where the specified width and spacing of blocks do not appear practical, block width and spacing may be reduced, providing they are reduced a like amount. A half space is reconaended ad.)acent to the walls.
6. The upstream face of the baffle blocks should be set at a distance of o.~ troa the doWnstream face of the chute blocks (Figure 18). This dimension is also 1-Pc)rtant.
7. The height of the solid sill at the end ot the basin can be obtained f'rom Figure 19. The slope is 2:1 upward 1n the direction of flow.
8. There is no need to round or streamline the edges of t2le chute blocks, end sill or baffle piers. Str-B&l inj ng of baffle piers may result in loss of halt ot their ettectiveness. Small chamfers to prevent chipping ot tbe edges is pel"llissible.
9. As a reminder, a condition of excess tail water depth does not justify shortening the basin length.
10. It is recommended tbat a radius of reasonable length (R > lm1) be used at the intersection of the chute and basin apron tor slopes of 4~0 or greater. .
u. As a general :rule the slope of the chute has little effect on the jump unless long flat slopes are involved. This· phase Will be considered in Section 5 on sloping aprons.
As the Type III basin is short c012pled1 the above rules shoald be followed closely for 1 ts proportioning. If the proportioning is to be varied from that recomended1 or if the limits glven below are exceeded, a model study is advisable. Arbitrary limits tor the Type III basin are set at 200 eta per toot of basin Width, or 100 feet ot fall, until experience demonstrates otherwise.
57
Application of Results (Example 3)
Given the following COlllPllted values for a saall overf'lov dam
Q. q V1 D1 eta cfs ft/sec tt -
3,900 78.0 69 1.130 3,090 61.a 66 . 0.936 2.,022 40.45 63 o.642
662 13.25 51 o.260 and the tail water curve f'or the r1 ver., identified by the solid line on Figure 21., proportion a Type III basin tor the most adverse cODdition utilizing tull conjugate tail Yater depth. The tlov is s,-etrical and the width of' the basin is 50 feet. (The pg.rpose of this exam,l)le is to demonstrate the use ot the Jump height curve.)
The first step is to conq,ute the Jump height curve. As V1 and Di are given., the Froude number is COJD.Plted and tabulated 1n Column 2, Table 5, below:
Table 5
Q D2 D1 D2 J\1111.p he11!!t elevation cfs F1 Di ft ft Curve a Curve a• - (2) (3) (4) (5) (l) (6) (7) 3,900 ll.4~ 15.75 1.130 17.eo 617.5 615.0 3,090 12.02 16.60 0.936 15.54 615.2 612.7 2,022 13.85 19.20 o.642 12.33 612.0 609.5 662 17.62 24.5 0.260 6.37 606.1 603.6
Entering Figure ll (page 35) with these values of the Froude number values of 2! are obtained for conjugate tail water depth from the solid D1 . line. These values are also ~ and are shown listed in Column 3. The conJugate tail Yater. depths t~~ the various discharges., Column 5., vere obtained by miltiplying the values in Column 3 by those in Column 4.
If' it vere assumed that the most adverse operating condition occurs at the maximum discharge of 3,900 cfs, the stilling basin apron sboul.d be placed at elevation 617.5 - 17.8 or elevation 599.7.
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With the apron at elevation 599.7 the tail water required tor conjugate tail water depth tor each discharge would follow the elevations listed in Column 6. Plotting Columns 1 and 6 on Figure 21 results in i."urve a, which shows that the tail water depth is inadequate tor all but the maximum discharge.
The tail water curve is unusual in that the most adverse tail water condition occurs at a discharge of approximately 2,850 cts rather than maximwa. As full conjugate tail water depth is desired for the most adverse tail water condition, it is necessary to shift the jump height curve downvard to match the tail water curve for a discharge o't 2,850 cts (see Curve a•, Figure 21); ·The coordinates tor Curve a• are given in Columns 1 and 7, Table 5. This will place the basin floor 2. 5 feet lower, or elevation 597.2 feet, as shown in sketch on Figure 21. . Although the position ot the basin floor was set tor a discharge of 2,850 eta, the remainiDg details are proportioned tor the MX1mnm discharge 3,900 eta.
Entering Figure 12, page 37, with a Froude number of 11.a.2,
Lx11 n;- • 2.75, and the length ot
basin require~ LJ:n • 2.75 x 17.&> • 48.95 feet. (Rotice that conJugate depth was used, not tail water depth.) The height, Width, and spacing of' chute blocks are equal to D1 or 1.130 feet (use 13 or 14 inches). · - -The height of the battle blocks for a Froude llWllber of' 11.42 (Figure 19, page 53) is 2.51>1•
h3 • 2.5 x 1.130 • 2.825 feet (use 2, inches). The width and spacing of the battle blocks are preferablY three-fourths of the height or
0.75 X 34 • 25.5 inches.
60
From Figure .l8 (page 49), the upatre• tace ot the battle blocks should be o.8D2 trom the downstrea tace ot the chute blocks, or ·
o.8 x 17.80. 14.24 feet.
The height of the solid end sill (Figure 19, page 53) is 1.6oD1, or
~ • 1~60 x 1.130 • 1.81. feet (use gg 1Dches).
The fiDal. dimensioDs of the basin are abovn on 11.&Dre 21, page 59.
"
61
SECTION 4
STILLIIG BASIi DESIGI .ARD WAVE SUPPRESSORS FOR CANAL STHJC'lURES, OUTLET WORKS A1ID DIVERSIOB DAMS (BASIB IV)
DTRODUCTIOI.
ID this section tbe cbaracterist1.cs ot the h1dl'aulic jump and tbe design ot an adequate stilling basin tor Froude numbers between 2.5 and 4.5 are discussed. This range is encountered principally in the design of canal stl'llcturea, but occa.sionally diversion daas and Olltlet works fall in this category. In tbe 2.5 to 4.5 Froude number range, the JUJIG) is not f'ully developed and the previously discussed me:t;hods of design do not apply.. The main problem concerns the waves created in the ~lie Jump, wk:ing tbe design of a suitable. wave suppressor a part of the stilling basin problem.
FOllr means of reducing wave heights are discussed. The first is an integral part of the e.·1.illing basin design and should be used only in the 2.5 to 4.5 Froude number range. The c.econd may be considered to be an alternate design and may be used over a greater range of Froude ILWDbers. These types are discussed as a part of tbe stil.liDg basin design. The third and fourth devices are CODSidered as appurtenances which may be included in an original design or added to an existing stl'llcture. Also, they may be used in any open channel f'lov-vay without considerati~ of the Froude mmber. These latter devices are described under the heading Wave Suppressors.
For low values of the Frollde number, 2.5 to 4.5, the entering Jet oscillates inte:rmi ttently tl'Olll bottom to surface, as 1ndicated in Figure 9B, page 22, with DO particular period. lach oscillation generates a wave which is difficult to dampen. In narrow stl'llctures, such as canal.a, waves may persist to some degree for .miles. As they encounter obstl'llctions in the caoal, such as bridge piers, turnouts, checks, and transitions, reflected waves may be generated vhich tend to ~n, modify., or intensity the orig1Dal wave. Waves are destl'llctive to earth-lined canals and riprap and produce ulldeairable surges at gaging stations and in measuring devices. Stl'llctures in thi~ range of . Froude numbers are tbe ones that require the most maintemmce. In tact, it 1:las been necessary to nplace or rebuild a number of existing stl'llctures 1::1 this category •.
62
On wide structures, such as diversion dams, wave action is not as pronounced since the waves can travel laterally as well as parallel to the direction ot f'low. The combined action produces some dampening effect but also results in a choppy water surface. These waves may or may not be dissipated in a short distance. Where 011tlet works, operating under beads of 50 feet or greater, fall Within the range of' Froude numbers between 2. 5 and 4. 5, a model study of' the stilling basin is inq>erative. A model stud_i,, is the only means of' including preventive or corrective devices in the structure so that proper perfo1'111BDCe can be assured.
STILLING BASIN DESIGN--FROUDE NUMBER 2.5 'l'O li-.5
Development Tests
The best way to combat a wave problem is to eliminate the wave at its source; in other words, concentrate on altering tbe condition which generates the wave. In the case of' the st.i J J 1ng basin preceded by an overfall or chute, two schemes were apparent tor el.1m1.• Dating waves at their s011rce. The first was to break up or el1111uate the entering Jet, shoWn on Figure 9B, by opposing it with directional Jets deflected from baffle piers, or sills. '!'be second was to bolster or intensity the roller, shown 1n the upper portion of' Figure 9B, by directional Jets deflected f'rom large chute blocks. ·
'fhe first method was unsuccessful in that the number and siztt of' appurtenances necessary- to break up the roller occupied so mch volume that these in themselves posed an obstruction to the f'lov. This conclusion was based vn tests in which vari011s shaped baf'f'le blocks and guide blocks were systematically placed in a stilling basin 1n combina• tion with numerous types of' spreader teeth and deflectors in the chute. 'fhe program involved dozeut! ot tests, and not until all conceivable · ideas were tried was this approach abandoned. A few of' the basic ideas tested are shown on Figure 22, a, b., c, f, g, and h.
Final Tests
Deflector blocks. The s,ieond approach, that of' attenq,ting to intensity the roller, yielded bet.~r results. In this case, large blocks were placed well up on the chute, whi1e nothing was installed in the stilling basin proper. The object in this caee was to direct a jet at the base of the roller in an attempt to strengthen it. Arter a nwaber ot trials, the roller was actually intensified which did improve the stability of the Jump. Sketches d and e on Figure 22 indicate the oilly schemes that showed promise, although many variations were tried. Af'ter finding an arrangement that was ef'f'ective, it was then attempted to make the field construction as sim.ple as possible. The dimensions and proportions of the deflector blocks as finally adopted are shown on Figure 23.
63
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. BASIN IV.
I
The object in the latter scheme was to place as few appurtenances as possibl.e in the path of the fl.ow, as vol.ume occupied by appurtenances helps to create a backwater problem, tlms requiring higher training walls. The number or deflector blocks shOVD on Figure 23 is a minimum requirement to accan;plish the purpose set forth. The width of the blocks is shown equal to D1 and this is the maximum width recommended. From a hydraulic standpoint it is desirable that the blocks be constructed narrower than indicated, preferably o.75D1• The ratio of block width to spacing ehwld be :maintained as 1:2.5. Tbe·9rtl"9me tops of the bl~ka &1'9 mli above i:he floor oft.he ei::illine; 'b•oi1h -r. llJ.t;X;kD m:r a.:pper.u- uo be mtller hlgh f:Lild, 1n some cMes, @rtl'@Mly l&~, 'hu+. tM.e !A 61!1Mn·U.al ·as -eLe Jet DUSt p~ at ~ \,a,se ot tllc roller to be errect1ve. TO acrommMate tlle var1.ous Elopes or <!hutes anc3. ogee shapes encountered.1 a ru.le bas been established that the horizontal length of the blocks should be at least 2D1• The upper surface of each ~lock is sloped at 5° in a downstream direction as it . vas found that this feature resulted in better operation, especially at the lower discharges.
Ta11 water depth. A tail ·water depth 5 to 10 percent greater than the conJugate depth is strongly recommended for tlie above basin. Since the jump is very sensitive to tail water depth at these low values ot the Froude number, a slight deficiency · 1n ~11 water depth may allow the jum,p to sweep completely out of the basin. Many of the difficulties that have been encountered in small field structures in the past can be attributed to this aspect of the jump for low numbers. In addition, the jump pertorms much better and wave action is diminished it the tail water depth is increased to approximately l.lD2•
Basin iength and end sill. The length of this basin, which is relatively short, can be obtained from the upper curve on Figure 12. Ko add.1tiona1 blocks or appurtenances are needed in the basin, as these will pl'OYe a greater detriment then aid. ·The addition of a small tri~ angular sill placed at the end or the apron for scour control is desirable.
Performance. If designed for the maximum discharge, th1s stilling basin will perform satisfactorily for all flows. Waves below the stilling basin will still be in evidence but will be of the ordinary variety usually encountered with jumps of a higher Froude number. This design is applicable to rectangular cross sections only.
66
ALTERHAT.I!: STILLIIIG BASD DESIGW•-SMALL DROPS
Performance
An alternate basin for reducing wave action at the st,urce tor values ot the Froude number between 2. 5 and II,. 5 is applicable to small drops in canals. The Froude number in this case would be computed the same as tbou.gh the drop were an O'lertlow crest. A series ot steel rails, chaimel irons or timbers in the form ot a grizzly are installed at the drop, as shown on Figure 2a.. The O'lertalling jet is separated .into a number of long, thin sheets of water which tall nearly wrtically into the c&ll&l. below. Energy dissipation is excellent and the usual wave problem is avoided. It the rails are tilted downward at an angle ot 3° or more, the grid is self-cleaning.
Des1p
Two spacing arrangements were tested 1n the laboratory: 1D the first, the spacing was equal to the Yidth ot the beams, and 1n the second, the spacing was two-thirds ot tbe beaa Width. The latter was the more effective. In the first, the length ot grizzly required was about 2.9 times the depth ot flow (y) in the canal upstream, while in the second, it was necessary to increase the_ length to approximately 3.67. The following expression can be used tor computing the length ot grizzly:
:w - 9 ~- CWB J20
(If.)
where Q is total diecharge, C is an experimental coetticient, W is the width of spacing 1n feet, 1' is the number ot spaces, g is the accelera• tion of gravity and y is the depth ot tl.oir in the canal upstreaa ( see Figure 24). The value ot C tor the two arrangements tested was o.21t-5.
In this case the grizzly makes it pose1ble to avoid the hydraulic ~. Should it be desired to maintain a certain level in the canal upstream, the grid may be tilted upward t,, act as a check; however, this a.rraDF.ment may pose a cleaning problem..
WAVE SUPPRESSORS
!rhe two stilling basins described in the firi:.t part ot Section If. my be considered to be wr:\ve suppressors, althollgb. the suppressor effect is obtained from tb., necessary features of the s-t:.1Jl1ng 'basin. It greater wave reduction i~ required on a proposed structure, or if a Ya'Y8 suppressor is required to be added to an existlng flow-way, the two types discussed below may prove usetul. Both ot these tn,ea are applicable to most open cbame1 tlow-vays hav1Dg rectangular, trapezoidal,
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or other cross-sectional shapes. The first or raft type may prove more economical than the second or underpass type, but rafts may not provide the degree of wave '!'eduction obtainabl.P. With the underpass type. Both types may be used w1 thout regard to the Froude number.
Raft Type Wave Suppressor
In a structure of the type shmm in Figure 25, there are no means f'or eliminating waves at their source. Te&ts showed that appurtenances 1n the stilling batiin merely produced severe splashing and created a backwater effect, resulting in subm trged flow at the gate tor the larger flows. Submerged f'lcw reduced the effective head on the structure, and in turn, the capacity.· Tests on several suggested d'!vices showed that rafts provided the best answer to the wave problem when additional submergence could not be tolerated. The general arrangement of the tested structure is shown in Figure 25. The Froude number vaned f'rom 3 to 7, de~nding on tbe head behind the gate and the gate opening. Velocities in the canal ranged from 5 to 10 feet per second. Waves were 1.5 feet high, measured from trough to crest.
During the course of the experiments a number of rafts were tested; thick rafts with longitudinal slots, thin rafts made of perforated steel plate, and others, both floating and fixed. Rigid and articulated rafts were tested in various armngements.
The most effective raft arrangement consisted of two rigid stationary rafts 20 f'eet long by 8 f'eet wide, made from. 6- by 8-inch timbers, placed in the canal downstream from the stilling basin (Figure 25). A space was left between timbers and lighter cross pieces were placed on the rafts parallel to the f'low, giving the appe~ce of" nany rectangular holes. Seve,:e.J. essential requirements for the re.ft were apparen1;: (1) that the rafts be perforated in a regular pattern; (2) that there be some deptl", to these holes; (3) that at least two rafts be used; and ( 4) that the rafts be rigid and held stationary.
It was found that the ratio of hole area to total area of' raft could be from 1:6 to 1:8. The 8-foot width, W on Figure 25, 1,; a minimum. dimens1.011. The rafts must have sufficient thickness so that the troughs of the waves do not break free from the underside. The top surfaces of' the rafts are set at the mean water surface in a f'ixed position so that they cannot move. Spacing between rafts should be at least three times the raft dimension, mes.sured parallel to the flow. The f'ir"it raft decreases the WM.Ve height about 50 percent, while the second raft effects a further reduction. Surges over the raft dissipate themselves by flow dowmrard throl.•.gb. the holes. · For tlas specific case · the waves were reduced from 18 to 3 inches in height.
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Under certain conditions wave action is of concern only at the maximum discharge when f'reeboard is endangered, so the rafts can be a permanent insi.allation. Should it be desired to suppress the waves at partial flows, the rafts may be made adjustable, or, in the case of trapezoidal channels, a second set of rafts my be placed under tbe · first set tor partial flows. The rafts should pertOl'lll equally veil in trapezoidal As well as rectangular channels.
The recommended raf't arrangement is also applicable tor sup.. pressing waves with a regular period such as wind waves, waves produced by the starting and stopping or pumps, etc. In this case, the pos~tion of the downstream raft is important. The second raft should be pos1• tioned downstream at some fraction of' the wave length. Placing it at a tull wave length could cause both rafts to be ineffective. Thus, for narrow canals it may be advisable to make the second raft portable. 3ovever, if it becomes necessary to make tbe rafts adjustable or · portable, o"' if a moderate increase in depth in the stilling basin can be tolerated, c~,nsideration should be given to the tn,e of wave suppressor discussed below.
Underpass TY!]e Wave Suppressor
General description. By tar the most effective wave dissipator is the short-tube type of UDderpass suppressor. The mme "short-tube• is used because the structure bas man:,- of the characteristics r-f the .· short-tube discussed µ, hJdraulics textbooks. This wave suppassor IB7 be added to an exiating s ""' ucture o .. · included in the original cOllStruction. In either case it provides a sightly structure, permanent in nature, which is economical to construct and effective in operation.
The recommendations tor this stncture are based on 'three sepa:?"&te model investigations, each having different tlcnr conditions and wave reduction requirements.
Essentially, tbe structure consists of a horizontal root placed 1il the f'lov cbannel Viiih a headwall sufficiently high to cause all tlaw to pass beneath the roof. The height ot the root above the channel floor may be set to effectively reduce wave heights tor a considerable range of' flows or chamlel stages. The length of the roof, however, t:\etemines the amount of wave suppression obtained for any particular roof setting.
Performance. The effectiveness of this wave auppressor is illustrated in Figure 26. In this instance it was desired to reduce wave heights entering a lined canal. to prevent overtopping of tbe cODal liDing at near max1nim discharges. Below 3,000 second-feet, waves were in evidence but did not overtop the lining,. For larger discharges, however, the s~illing basin produced moderate waves which were actually intensified by the 'Short transition between the basin and the canal..
71
FIGURE 26
Without suppressor - waves overtop canal.
Suppressor in pla( - Length 1. 3D2, submerged 30 percent
Performance of Underpass Wave Suppressor 1:32 Scale Model Discharge 5,000 Second-feet
These intensiQ&td waves overtopped the lining at lt-,000 second-feet and became a real problem at 4,500 second-feet. Anxiety developed when it became known that water.demands 1'0Uld soon require 5,000 second-feet, the design capacit-y·ot the canal. Tests were rnade With a suppressor 21 feet long using discharges fro:m 2,000 to 5,000 second-feet. The suppressor was located between the st1111ng basin~ the canal.
Figure 27, Test 1, shows the results of tests to detel'Dline the optimu:m opening between the· roof and the channel floor using the rn•:dnun discharge, 5,000 second-feet. With a 14-foot opening, waves were reduced f:ro:m about 8 f'eet to about 3 ·feet. Wafts were reduced to less than 2 feet with an opening ot 11 feet. Smaller openings· projuced less wave height reductions, due to the turbulence created at the underi,ass exit. Thus, it may be seen that an opening ot t:ro:m 10 to l2 feet produced optinml results.
With the opening set at 11 feet the suppressor effect was then determ:1ned for other discharges_.· These results are shown on Figure. 27, Test 2. Wave height reduction was about 78 percent at 51000 second-feet, increasing to about 81,. percent at 21000 second-feet. The device became ineffective at about 1,500 second-feet when tbe depth of flow became less than the height of the roof.
To determine the effect of ·suppre,:sor length on the wave reduction, other factors were held constant While the length was varied. Tests were made ·on suppressors 10, 21, 30, and 40 feet long for discharges ot 21 3, 4, and 5 thousand second-feet, Figure 27, Test 3. Root lengths in tel'lia ot the downstream depth D2 tor 5,000 second-feet were 0.62D2, l.3D>2, and 2 •. 5D2·, respectiveq. In tema of a 20-tootlong . underpass, halving the root length al:mos~ doubled the downstream wave height while doubling the 20-toot length almost hal'Ved the resulting Ya:ve height.
The same tJPe of wave suppressor was succes~ful.ly used in an installation where it was ne~essary to obtain optinma wave height reductions, since :rlov tro:m the underpass discharged di:rectq into a Parshall flume in which it was desired to obtain accurate discharge measurements. The capacity of the structure was 625 cubic feet per second bat 11;; was necessary for the underpass to function for low· flows as well as tor the Nx1mnm. With an ~rpass 3-5D2 long and set. as shown in Figure 28, the wave reductions were as shown in Table 6.
73
FIGURE 27
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TEST NO. I TO DETERMINE MOST EFFECTIVE
ELEVATION FOR ROOF - ~-sooo cfs.
16
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WAVE SUPPRESSOR FOR FRlANT - KERN. CANAL
RESULTS OF HVDRAULIC MODEL TESTS
74
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Table 6
WAVE HEIGHTS IN FEET--PROTOTYPE Maximum Head Discharge : 625 : 550 : 400 : 200 : 100 in cfs :Upstream*:Downstreem*: U: D: U: D: U: D: U: D . . . .
Wave heights: H3. 8 : 1n feet : plus :
0.3 • • • • • • • • . . . . . . . . :4.2:0.3:4.5:0.4:3.6:0.4:1.7:0.3 • . • . : . • . . • . • . • •
*Upstream station is at end of stilling -basin. Downstream station is in Parshall flume. HRecorder pen reached limit of' travel in this test only.
Figure 28 shows some of the actual wave traces recorded by an oscillograph. Here it may be seen that the maximum wave height., measured from minimum trough to maximum crest did not occur on successive waves. Thus, the water surface will appear smoother to the eye than is indicated by the maximum wave heights recorded in Table 6.
General design procedu!!. To design an underpass for a particular structure there are three main considerations: First, how deeply should the roof be submerged; second, how long an underpass should be constructed to accomplish the necessary wave reduction; and third, how much increase in flow depth will occur upstream from the underpass. These considerations are discussed in order.
Based on the two installations shown on Figures 27 and 28, and on other experiments, it has been found that maximum wave reduction occurs when the roof' is submerged about 33 percent, i.e., whl!n the under side of' the underpass is set 33 percent of the flow depth below the water surface for maximum discharge, Figure 29C. Submergences greater than 33 percent ( for the cases tested) produced undesirable turbulence at the underpass outl.et resul.ting in less overall wave reduction. With the usual tail. water curve, submergence and the percent reduction in wave height Will become less, in general, for smaller than max1:mnm discharges. This is illustrated by the upper curve in Figure 29C. The lower curve shows a near constant value for less submergence, but it is felt that this is a somewhat special case since the wave heights for less than JUX:hnum discharge were smaller and of shorter period than in the usual case.
It is known that the wave period greatly affects the performance of a given underpass, with the greatest wave reduction occurring for short period waves. Since the designer usuall.y does not kn~ in advance the wave periods to be expected, this factor should be t!l1:adnated from design consideration as far as possible. Fortunately, wave action below a stilling basin usuall.y has no measurable period but consists of a miXture of generated and reflected waves best described as a ~oppy
76
.
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HYDRAULIC CHARACiTERISTI-CS UNDERPASS WAVE SUPPRESSOR
14
water surface. This tact makes it possible to provide a practical solution from l1mi ted data and to el1nd.nate the vae period f'rom considera- · tion except 1n this· general way: waves mat be of' the ftriety ordiliarily found downstream. f'rom h1dr&Ulic jumps or energy dissipatora. These usually· have a period of not more than about 5 seconds. tonger period waves may require special treatment not covered 1n this discussion. Fortunately, too, there generally is a tendency tor the W&'ft period to become less with decreasing discharge. Since the suppressor provides a snater percentage reduction on shorter period 'Waft& 1 this tends to of'f'set the characteristics of' the device to give leas wave reduction f'or reduced submergence at lover discharges. It is therefore advisable 1D the usual case to submerge the underpass about 33 i,ercent for tbe maximum discharge. For less submergence, tbe wave reduction can be estimated trom Figure 29C. · . ·
The llinimml length of underpass required depends on the 1111101l1lt of' wave reduction considered· necessary. If' it is auf'f'icient to obtain a DC'Dlnal reduction to prevent overtopping of a canal lining at near maximum discharge or to prevent waves f'rolll attacking cbam,el, banks, a length lD2 to l.5D2 will provide f'rom 6o to 75 percent wave height reduction, pl'OYided the initial waves have periods up to about 5 seconds. The shorter the wave period the greater the reduction tor a given underpass• For long period waves I little wave reduction may occur because of the p1,ssibil1 ty of tbe wave length being nearly as long ~ longer than thf.t underpass, with the wave passing untouched beneath the UDde!'ll8.8S•
To obtain greater than 75 percent wave reductions, a longer underpass is n."tcessary. Under ideal conditions an underpass 2D2 to 2. 5D2 in length may provide up to 88 percent wave reduction to~ wave periods up to about 5 seconds. · Ideal conditions include a velocity beneath the underpass of' less than, say, 10 feet per second and a_J.ength of channel 3 to ~ times the length of the underpass downstream from tbe underpass which may be used as a quieting pool to still the small turbul.ence waves created at tbe underpass exit.
Wave height reduction up to about 93 percent may be obtained by using an underpass 3 .5D2 to lt.D2 long. Included in this length is a lt.:l sloping root extending from the underpass root elefttion to the tail water surface. The sloping portion should not exceed about one-quarter of the total length of underpass. Since slopes greater than 4:1 ~o not provide the desired draft tube action they shollld not be used •. Slopes flatter than lt-:1 provide better draft tube action and are therefore desirable.
..o
S1Dce the greatest wave reduction occurs 1D the first D2 ot underpass length, it may appear advantareous to construct tvo Short· undel"l,asses rather .than one long one. In the one case teated, tvo · underp.uses each· lD2 long, ¥1th a length 5D2 between tbell, gaw an · added lO percent wave reduction advantage over one umte~s 21>2 long. Tbe extra cost of auotber headwall sllould be conad.de?ed, J:aawenr. .
Table 7 summarizes the U1011Dt of wave reduction -obtaiDable for various underpass lengths.
Table 7 EFFECT OF UIDERP.ASS LE1IJTH OB WAVE Rl!;DUC'l.tOR
For Underpass Submergence 33 Pere.•nt and · Max:Jm,m Velocity BQeath 14 ft/sec
• Underpass length : Percent wave reduction*
• • •
lD2 to l.5D2 • 60 to 75 • • •
2D2 to 2.51)2 • 80 to 88 • • •
3.5 to 4.®2 • "90 to 93 •
*For wave periods up to 5 aecollis .• · HUpper lillit onl1' ¥1th draft tube tne
outlet.
'lo detel'lline the backwater ettect of placing tbe uudel"JIIUJ• 1D tbe cllannel, Figu_:re 29B Y11l prove hel.pful. · Data tl'OII ·tour diffennt underpasses were used to obtaiD the tvo curves shown. .Altbough tlle te•t poj.Dts from which the curves were drawn shoVed -,.nor 11lconsistenc:les, probably because factors other than those considered also affected the depth of water upstre• from the underpa.ss, it is belined tbat the submitted curves are sutticient:q ac~te tor design PQl'llO&es. ~pre 29B shavs two curves ot the discharge coefficient •c• versus avenge velocity beneath the underpass, one tor UDderpaas · lengths of ~ to 202 aD4 the other ·tor lengths 3D2 :to 4»2• Intermecliate values may be interpolated although accuracy of this order is. not uauall7 :required.·
79
Sample problem, Example 4. 'l'o illustrate- the use ot the prececling data 1n designing an underpass, a sample problem Y1ll. be helpful.
Assume a rectangular channel 30 feet Wide and 14 feet deep :f'lows 10 feet deep at maxtmum discharge, 2,J&oo cfs. It is estimated that waves Yill be 5- feet high and of tbe ordinary variety hav1Dg a . period less than 5 seconds. It is desired to reduce the heipt of the waves to approximately 1 foot at wx:fJDWD 41scharge by 1nstal.l1Dg an underpass-type wave suppressor Without increasing tbe depth of' water upstream. from the under.pass more than 15 inches.
. To obtain :ma1dn1m wave reduction at •tjmnm '1ischarge, the underpass should be submerged 33 percenii. Therefore, the depth beneath the underpass is 6.67 feet with a corresponding velocity of 12 ft/sec, (V • 30 2~?,67). 'l'o reduce the height of the waves f'~ 5 to 1 toot,· an 8o percent reduction in wave height is indicated, and,. from Table 7, requires an underpass approximate]¥ 2D2 1n length.
From Figure 29B, C • 1.07 tor 2D2 and a -velocit,' ot 12 ft/sec. From the equation gl. ven on Figure 29B:
2 400 2 Total bead, h + hy • ( Q ) 111 ( 8 02 2f 07 200) • ;i.95 feet CA{ig . • X • X
h + hy is the total head required to pass the flow and h represents the bacltwater effect or increase in depth of water upstream. from the underpass. The detemination of values for h and hy is done by trial and error. AB a first determination, assume that h + hy. represents the increase in head.
~n, chaunel approach velocity, V1 • f • (l.O !1~5130 • ~-7 ft/sec
"-- • (V1)2 • (6.7)2 0 ~of t -v- 2g 64.4 :I ·•. 00
and h • 1.95 - 0.70 • 1.25 teet
To refine the calculation, the abd9e COIDPlltat;lon is repeated us:!.ng the new head
V1 • (io !•~5)30 • 7.1 ft/sec
by• 0.72 foot
and h • 1.17 feet
Further retine•nt is wmeceaaary •
Tlms, the average water surface upstream fl'Clll the Ulldel'lt&Sa is 1.2 feet bigber than the tail water which satisfies the assumecl design requirement of a Nx1mnm backwater ot 15 inehes. ~ length of the underpass is 21>2 or 20 f'eet, and the waves &1"9 n4ucecl 80 percent to a ma:x1n1m height ot approx:laateq l toot. .
. If :Lt is desired to reduce the waft heigh.ta still further, a longer underpass is :required. Usillg hble 7 ud Figure 29B as in the above problea, an underpass 3. 5 to 4.0D2 or 35 to Jao . feet in length reduces the waves 90 to 93 pe:rcent, wlking the aawnstream waves appl'OXimateq 0.5 toot high and creating a backwater, h, of' 1.61 f'eet.
In using the above heads, al.lovance shollld be made for waves and surges which, in effect, aze above the CCllll;Pllted water surface. onehalf the wave height or more I mea&U1"8d fl'Oll crest to trough, ahoulcl be allowed above the cODLp1ted surface. Full wave height voald provide a more conservative design tor the usual short period waves encomrtered ill flow channels. ·
The headwall ot the underpass should be extended to this same height and a. seawall overhang placed at the top to turn wave spray back into the basin. An alternate method would be to place a cover, say 2D2 long, upstream tram tbe underpass headwall.
To insure obtaiDing the max:tnm wave reduction for a guen length of underpass, a 4 :l sloping roof should be provided at the downstream end ot the underpass, as indicated on Figure 28. This slope may be conside~.;d. as part ot the overall length. The sloping roof' will help reduce the JDB.:x:1nm wave height and v1ll also reduce the frequency vith which 1 t occurs I providing in all respects a better appearing water surface., ·
A close inspection of' the submitted data Vlll reveal that slightly better results were obtained 1n the teats than are cla:lmed in the example. This was done to illustrate the aegree ot consenatisa requil'ed, since it should be understood that tbe problelll of wave reduction can be very complex it wmsual conditions prevail.
81
The data and sample problem given here are for cOllditions within tbe limits described. From these data it should be possible to design a wave suppressor tor general use with a good degree of accuracy. Care should be taken, however; that the data are not extended be,ond. the 11m:1ts given. When any dollbt exists, a model study shoul4 be made, particularly if' tbe wave reduation 11111st be accomplished because of a measuring device located imediately clownstream from tbe suppressor. Additional mdel tests will be required to be certain that the llm.lted amount of data, troa which these conclusions were clra.Wn1 represent tJPicerJ. problems encountered 1D the design of field structures.
82
SECTIOlf 5·
STILLIIG BASIB WITH SLOPING APRON (BASIB V)
IITRODUCTIOB
Much has been argued, pro and con., concerning the advantages and disadvantages of' stilling basins Yi.th sloping aprons. The discussion continued indef'ini tely simply because there was not sufficient supporting data available from which to draw conclusions. It· was decided in this·study, therefore, to investigate tbe sloping apron basin sufficiently to answer the many debatable questions and also to provide more definite design data.
Four flumes., A., B, D, and F, Fi.gures l., 2., and 3., were used to obtain the range of Froude numbers desired f'or the tests. In the case of Flumes A, B, and D, floors were installed to the slope desired, while Flume F could be tilted to obtain slopes from 0° to 12°. Theslope., as referred to in this discussion, is the tangent ot the~ between the floor and the horizontal., and will be designated as "-·· Five principal measurements were 118.de in these tests, namely: the dis• charge, the average depth of' flow entering the Jump., the length of the jump, the tail water depth, and the slope of' the apron. ·The tail water was adjusted so that the front of' the junq, formed either at the intersection of the spillway face and the sloping apron or., in the case of the tilting flume, at a selected point.
The jump tbat occurs on the sloping apron takes ma.ny. forms depending on the slope and arrangement of ~ apron, the value of' the Froude number, and the concentration of flow or discharge per foot of width; but from all appearances, the dissipation is as effective as occurs in the true lcydraulic jump on a horizontal apron.
PREVIOUS EXPERIMENTAL WORK
Previous experimental work on the sloping apron bas been carried on by several experimenters. In 1934, the late C. L. Yarnell of the United States Department of Agriculture sur.errised a series of experiments on the hydraulic jump on sloping aprons. C&rl Kindsvater5 later compiled these data and presented a rather cOJlq>l.ete picture, both experimentally and theoretically, tor one slope, namely: 1:6 (tan (J • 0.167). G. B. H1ckox5 presented data tor a series of el9)erimelits on a slope of 1:3 (tan (J • 0.333). Bakbmetetf1 and Matzke6 performed experiments on slopes ot O to 0.07 1D a flume 6 inches wide.
!
Fram an academic standPoint, the.Jump my- occur 1n several vays on a sloping apron, as outlined by Kindsvater, presenting separate and distinct problems, Figure 30. Case A is a Jump on a horizontal apron. In Case B, the toe ot the jump forms on the slope, while the end occurs over the horizontal apron. In Case C, the toe ot the Jump is on the slope, and the end is at the junction ot the slope and the horizontal apron; while in case D, the entire 3WIIP forms on the slope. With so many possibilities, it is easily understood why experimental data have been lacking on the sloping apron. Messrs. Yarnell, Kindsvater, BeJrbme+.ett, and Matzke limited :their experiments to Case D. B. D. R1ncUMb7 ot the University of California concentrated on the solution of' Case B, but his experilllental results are complete for only one slope, that of' 12.33• (tan f, • 0.?17). . · . .
SLOPIBG APROI' TESTS
Fram a practical standpoint, the scope of the pres~nt teat program need not be so broad as outlined 1n Figt&re 30. For eXBlll,l)le, the action in Cases C and D is tor all practical purposes the same, if' it is assumed that a horizontal floor begins at the end of' the jump tor Case D. The first of the current experiments to be described 1n this chapter involves Case D. However, sufficient tests were ma4e on Case C to verify the above statement that Cases C and D can be considered as . one. The second set. of' tests will deal with Case B. Case B is virtually case A operating with excessive tail water dept):.. As the tail water depth is ·rurther increased, Case B approaches Case C. The results of' Case A have already been discussed in the preceding chapters, and Cases D and B will be considered here 1n order.
Tail Water Depth ( Case D)
Data obtained from the four flumes used in the sloping apron tests (Case .D experiments) are tabulated 1n Table 8. The headings are very much. the same as those in previous tables, but Will need some
· explanation. Column 2 lists the tangents of' the angles of' the slopes tested. The depth of' f'J.ow entering the Jump, »1, Column 8, was measured at the beginning of' the . .1UDIP in each case, corresponding to Section 1, Figure 30. It represents the average of' a generous number of' Point gage measurements. The velocity at "bhis same point, VJ-_, Column 7, was computed by dividing the unit· discharge, q (Col.UJIID 5), by D1• 'l'he length of' .1WllP, Column 11, was measured in the flume, bearing 1n mind that the object of' the test was to obtain i)ractical data for stilling basin design. The end of the .1UDIP was chosen as the point where the high velocity Jet began to lift froa the. floor, or a Point on the · 1evel tail water surface imediately downstream. from the surface roller, whichever
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....
..,___ ________________;
I 4 l l 11 I: I Slope I Q I V :Diacbarge: '1'W :Velocity1 I :Length: , I Da I I I It Teat :ot apron: Total : Width 1:per toot :'hil-vater:enter1111:uter1ug: '1'V 11 ..!J._: ot : L 1 !!2_ 1Coa,1vaate1-''IV I L 11bqe n-: tan - :diacharge1ot bqiJ11ot buiD : depth I .11111p I .1\IIIP I 1"i : 1 - 8ft. I .,Ullp I w I Di l!l'V ~ I Ii : 1li lt'utor : : cte tt : eta : tt I tt/aac I tt I ' : -l, I tt I • I I ft I . I I {l) I (2) (3) (4) I (5) · (6) : (7) : (8) : l9) I (10) 1 (U) 1(12)1 (13)1 (1H 1(15)1(16)1 (17) x : 0.661 2.b?ii ,;a· : o.41ci o:$ 'i·- 1.ss d,.6"§ 'iio.oo: ·1,.1$ ', 1.66 ,, .• ilis1 a.201· a.lit6 • ,t.fi.!:4·.n. 1.,0· -I I 2.250 I o.i.61 o.'6() : 8.09 I 0,o,7 : 9,821 5:91 I 2.90 15,181 7,90: 0,450 :1.24r6.451 2.50 I 2.500 I 0,512 o.'89 : 8.26 I 0,062 I 9,501 5.85 I 3.10 15,261 7.851 o.1186 :1.2116.381 2.~ I 2,750 I 0,~ 0,629 l 8,42 I 0,067 I 9,391 5,73 I 3,30 :5,251 7,701 0,516 :1,22:5.401 2,45 I 3,000 I 0,615 0,660 I • 8,5" 0,072 I 9,171 5,61 I 3,Jio 15,151 7,551 0,5" 11,2116,251 2,45 1 3.250 1 o.666 o.69'J 8.65 o.m : 9,011 5.49 1 3.45 :4.971 7.40: 0.570 11.2i!l6.o,1 2.50 3,,00 I 0,717 0,744 8,74 0,082 I 9,071 5,]8 I 3,60:14,841 7,20: 0,590 ll,2616.l0: 2,80 1,,00 4,350 I 0,]45 0,474 7,67 0,045 :10,531 6,37 I 2,40 :5,061 8,6o1 0,387 :1,22:6,201 ·2,,0 2,500 I 0,575 0,61.2 I 8,i.f 0,068 I 9,44: 5,72 3,20 :4,98: 7,701 0,523 :1,2316,12t 2;50 3.500 1 1 0.805 0,792 1 8.85 0.091 : 8,701 5,17 4.oo :5,051 6.90: o.628 :l,2616.371 2.75 l I I I I I I I I I I I 0,096 I 2,000 I 4,830 I 0,414 0,560 I 7,96 0,052 110,77: 6,15 2,50 :4,471 8,201 0,426 11,3115,871 2,04 I l
2,500 I I 0,518 0,652 7,97 0,065 110,031 5,51 3,60 :5,521 7,45: 0,484 11,3517,441 2,28 3,000 I I 0,621 0,745 I 8,28 0,075 I 9,93: 5,33 3,20 :4,301 7,101 0,532 11,4016,011 2,40 3,500 I I 0,'(25 0,835 8,53 0,085 I 9,82: 5,15 3,60 :4,311 6,90: 0,586 :1,42:6,15: 2,50 4.ooo I o.828 o.~ 1 8.63 o,096 : 51.79: 4,90 4.oo 14.26: 6.50: o.~ :1.5116.411 2.75 I I 0,135 2.000
2,,00 3.000 3.500
' I : I I I I l·I I ; 4,810 I 0,416 0,620 I 6,93 0,060 110,33: 4,99 2,50 14,061 6,601 0,396 ll,56:6,321 2,15
: 0.152
: : 0.185'
: o.218
I 4,000
1.500 2,000 2,500
I 3,000
I I I I 4,35() I
I 1,500 I 4,350 2.000
I 2,500 :
1.750 : 4.350 2,250 I
I I : 0.280 1.250 : 4.350
1,500 I I I l.750 :
I : 0.052 1,000 2,000 : 1,500 I 2,000
2.500 3.000 3.500 i..ooo 4.500 5.000 5,500 I 6.000
: 0.102 , 1.000 l.,500 2.000 2.500
I 3,000 3.000 3.500 4.000
I 4,500 : 5.000 5.500
0,520 0,710 I'· 7,5" 0,069 110,291 5,06 3,00 14,231 6,751 0,466 11,5216,441 2,07 0,~ 0,895 I 7,80 0,080 110,061 4,86 3,20 13,971 6,401 0,512 11,5716.251 2,15 0,728 0.905 8.09 0.090 110,061 4,75 3.60 13,981 6.301 0,567 11.60:6.341 2,22 0.832 o.985 8.58 0.097 :10.151 4,85 3.90 13,961 6.401 o.621 11.5916.281 2.19 I I I 11 I 11 I 0,]45 0,'40 I 6,'" 0,055 I 9,821 4,71 I 2,10 13,891 6,201 0,34?.,. ll,5816,161 1,94 0,460 0,663 6,76 0,068 I 9,751 4,57 I 2,55 13,851 6,101 0,41S ll,6016,151 2,00 0,575 0,790 7,57 0,076 :10,391 4,84 I 3,10 13,92: 6,451 0,490 11,6116,331 2,00 0,690 0,900 7,67 0,Q90 110,001 . 4,50 I 3.40 :3,781 6.00: 0,5"° :1,6716,301 2,10
0.345 0.460 0.575
0,402 I 0,517
o.a87 0.345 0,402
0.500 0.750 1,000 1.250 1.500 1.750
I 2,000 : 2.250 I 2,~ I 2,150 : 3.000 : I 0,500 I 0,750 I' 1.000 : 1.250 : 1.500 : 1.500 : 1.750 : 2.000 : 2.250 : 2.500 I 2,750
0.6oo 0.720 o.840
0.700 o.862 o.620 0.675 0.752
0.855 1.010 1,160 1.300 1,426 1.570 1.693 1.813 1._920 2,0QO 2,110
0.970 1,180 1,354 1,543 1,724 1,720 1.890 2.040 2.152 2.300 2,450
: : S : I : ,: I : 6,05 I 0,057 :10,531 4,47 I 2,15 :3.58: 5,901 0,336 ll,7816,40: l,83 6.57 I 0,070 :10,291 4,38 I 2,60 :3,611 5,80: 0.406 11, 7716.40: 1,83 7.01 : o.082 110.24: 4.31 : 3.00 :3,57: 5.70: 0.467 :1.80:6.421 1.a, I I t: It : I: 6,00 0,067 :10,f51 4,08 I 2,30 13,29: 5,45: 0,365 11,92:6,301 1,70 6,63 0,078 111,051 4,19 I 2,70 :3,13: 5,55: 0,433 11,9916,241 1,73
4,70 4,79 4,79
17.24 16.30 16.39 17.12 17,05 17,16 17.09 17.05 17.01 17,08 16.95
U,61 I 15,63 I l5,87 : 16.23 I 16.48 : 16.30 I 16,36 I 16,53 : 16.42 : 16,45 : 16.18
I I 0.061 110.16: 0,072 : 9,381 0,084 I 8,95:
0.029 0.046 0.061 0.073 o.088 0.102 0.117
I 0,l:!ll : 0.!47 I 0,161 I 0,177 I I 0.032 I 0,~ : 0.Cf63 : o.m : 0.091 : 0.092 : 0.107 I 0,121 I 0,137 I 0,152 : 0.170
I I 129.481 :21.961 119.021 117.81: :16.201 :15,391 :lli.471 :13.73, :13,06: :12,551 :11,92: I I :30,31: 124.581 121.491 120.041 :18.95: :18,70: 111.661 :16.86: 115,71: 115.13: 114.41:
86
I I I I 3,35 I 1,60 12,581 4,251 0,259. 3.15 : 1.80 :2.67: 4,051 0.292 2,91 : 1.95 :2,59: 3. 70: 0.311
: : : : 17,85 I 4,10 :4,79124,751 0,718 13.i.«) I 5,10 :5,05118.45: 0,849 11.69 : 6.10 :5,26:16.10: 0.982 11,16 I 6,50 :5,00:15,351 1,121 10,13 I 7 ,50 :5,26:13,85: 1,218 9,46 I 8,00 :5,10:12,95f 1..321 8,80' I 8,90 :5,26:12,10: 1,416 8.27 : 9.60 :5.29111.301 1,492 7 .82 I 9,80 15,10110,60: l,558 7.50 :10.50 :5.20110.20: 1,642 7,10. :11.00 15,211 9,65: 1,708
I I I : 15,40 : 4,20 :4.33121.251 0.680 12.57 : 5.20 14.41117,301 0.830 11,lli I 6,10 14,51:15,351 0.967 10.30 : 6.80 14.40:14.151 1.088 9.63 : 7.60 :4.41:13,201 1.200 9.47 : 7.50 :4.36:12.95, 1.191 8.81. : 8.20 :4.34112.101 1.293 8,37 : 8.80 :4,31:11.40: 1.379 7,82 : 9.40 14.37:10.601 1.452 7.44 -- :10,00 :4.34:10.101 1.536 6.91 :10.60 :4.33: 9.35: 1.590
: I : :2.39.16.18: 1.44 :2.3116.17: 1.44 :2.4216.271 1.46 I I I :1.19:5. 711 2,94 11.19:6.011 2.80 :1.1816.21: 2.78 11.16:5.80: 2.45 11.1716.15: 2, 70 :1.19:6.06: 2 .80 11.2016;281 2.92 11.2216.44: 3.10 11.2316.29: 3.20 11.2316.401 3.20 :1.2416.44: 3.30 I I I 11.4216.17: 2.51 :1.4216.'"1 2.50 11.4016.31: 2,44 :1.42:6.24: 2,50 11.4416,34: 2.56 11.44:6.30: 2.58 11.46:6,34: 2.75 11.4816.38: 2.72 :1.4816.47: 2,70 :1.5016.51: 2, 75 :l,54:6.67: 2.85
Tft1e 8--Cad;1-cl
ll'l'ILI.tllJ - lll'l'Jl SU>PDIJ APROlr case», :eeau v
! Slope :' Q V !n1ao!.rs.! '1'lf !v.~u,! »!k ! I :~: I ! »a ! : ; IC • I 'hat 1oi- &Pl,"OIU 'total : Wi4th :per toot 1Nl-vatff:e11tering1uteriug1 '1'lf 11 J1_1 ot I L I D2 1Coll,ftlp.w: 'l.'W I L 1Sbape , ti- tan - :411chup1ot buu:ot buill I · upth I ~ I ,1mp I ~ I 1 • .SDJ. I .11JIIP I W I· Df 1'1'11 ~ I !Ii' I 1'i 1:r.otor ' (1) 1 (9) : (J.G) I ft 1(12)1(13) 1 ft 1(1.5)s(lA)1 (17) I I I I 11 I I ~- . I ·
.,
I O,ll.3 I I
0,100
0,174
0.200
0.150
I 0,100 I I I 0,0,0
. 2,,00 3,000
I 3,,00 I I 4,000 I I 4,,00 I I· 5,000 I 5,500
2.eoo I 2,,00
3,000 3.500 4,000 4,,00 5,000 5.,00
I 2,000 3,000 4,000 5,000 6,000
I I 4,000 I 3,970 I 6,000 I 8,000 I 10,1)()()
l
I I
I
, ~ I ~.,oo 6,750 I
I 1,980 l 1,000 2,800 I
2.980 3.s,o
I 3,850 I 1,780 I
1,9'+0 3.8"(0
·: 3,620 : 1.aeo I 3.910 2.300 I
1,250 1,,00 1,750 2,000 2.250 2.,00 2,750
1,000 1.250 1,,00 . 1.750 2,000 2,250 2.,00
I 2,7,0 I I 1.000 I 1.,00
2.000 2,500 3,000
1,007 1,,U 2.0l.S 2.518 0.567 1.134 1,700
1,980 I 2,800
2.980 3.8,o
3.850 1,780
1,940 3,870
3.620 i.~ 3.910 2,300
. 1,737 1,940 2.120 2,270 2.i.ao 2,590 l!,750
1.750 2,000 2,150 2.370 2.600 2,720 2.8510 3.100
1,900 2,330 2.820 3.270 3,&(e
1,530 1,888 2,200 2.630 1.200 1:n.0 2,100
I I 13•33 I 13,59 I 13.51 I 13.57 I 13-51 I 13,55 : 13,59 I l3.'5
.I I 11,63 I 11.63 I l2.3' I 12,38 : 12.35 I • I 18.64 I 19•12 I 1!1.75 : 2().li. I 18.510 : 18,29 I 19.'4
1,452 7.17 1,663 I 7 .69
2,035 I 8,32 2.460 8."8
2,095 I 7.97 1,260 6.93
1.180 I 6,i.c» l,6Ji8 I !jl,38
I 1.357 I 7,62 1,306 : 12.38 1.291 : 6.66 0-~M I 5.87
87
I , I , , I ·, I • I , I , I , I , 120,681 9.0, 6;51013,97112,4cfr 1;~2 11,67:6,Qs 1,95 119.021 8,11 7,,013.86111.0.,1 1-.ua 11.1216.~1 2.o-.1 117,971 T,61 8.2013,87110,301 1.21, 11.-rti.16.t,1 2,03 117,011 7.27 8.7013.831 9,e,1 1.310 11.73,6.61u 2.01 116.031 6.75 9-.2013.801 9.101 1.m 11.7616,701 2.08 IJ.5 ,421 6,]9 9, 1013, '741 8,651 1,4'4 tl,, 7816,6'f1 2,08 11.l..861 6.09 10.2013.ns 8.201 1.511 11.8116.731 2.10
I I I I I I I 11 1 0.075 123.33, 8.60 · &.001;.i.::i111.75: 0.881 11.99:6.au 1.11 1 0,092 121,741 T,89 6,60i3.~110,70c 0.984 12.0316.711 1,76 I 0,111 119,371 7,J.5 7,3013,IJC>I 9,101 l,'1f7 12,00r6.781 1,73 : 0,129 118.371 6.65 8.00,3.381 9,00l 1.161 l2,04'16,891 1. 76 I 0,J.118 117,'71 6,19 8,3013,19t 8.351 1,236 l2,1016,7l: 1,79 1 o.166 116.391 5.86 9.10:3.34, 7.e,, 1.303 ,2,o,16,98r 1.78 I 0.Ja 1l5,7l1 5,,S I 9,6013,321 7,501 l,380 12,0916,961 1,79 I 0,203 :15,211 5,30 I 10,00.3,821 7,101 1,4i.1 12,l.516,!141 1,81 I I I I I I I 11: I 0,086 122,091 6,98 I 5,6012,9'1 9,451 0,813 l2,]416.891 l,5' : 0.129 118.061 5.70 I 6.51012.961 T,65: 0.987 12.3616.991 1.56 I 0,162 117,411 5,i.c, I 8,1012,8"(1 7 ,25t 1,174 12,4016,901 1.,-7 I 0,202 IJ.6,191 4,85 I 9,2012,811 6,45: 1,303 12,5117,061 1,59 I 0,243 IV.,8e1 4,41 I 10,00:2,77: 5,801 1,409 12,5617,0,: 1,59 I I I I I I I I I I I 0,0'4 128,331 14,14 I 6,6014,31119,,01 1.0,3 :1,4516,27: 2,65 t 0,019 123,901 11,99 I 8,20t4,]1+1J.6,,01 1,303 11.,4,16,29: 2,65 I 0,102 121,'71 10,90 I 9,'70:\.41:V.,951 1,525 :1,4lu6,36: 2,65 I 0.la, 121,041 10,04 I ll,,Ot\,]7113,751 1,719 11,5}16,69: 2,S, I 0,030 11Jo,001 19,23 I 4,'f5:3,96126.701 0,801 11,50:"5,931 2,75 I 0,dl!a . 127,,S: 12,SJ4 I 7,8014.56117 ,901 1,109 11,5417,031 2,90 0,067 124 ,14: 11,67 I 9,1014,331J.6,l.01 1.i.oo 11,,016,50: 2, 78
I
0.276 0.JQ
0.358 0.454
0.483 0.257
I 0,303 I 0.524 I I 0.475 : o.v.7 : 0,587 I 0~392
I I I 5,261 I 4,571 I I I 5,68:
5.421 I
4,331 i..90:
3.89: 3.lJl.1
I 2.861 8.881
I 2,201 I 2,41:
I I I 2,41 I 4.31t12,961 3,001 0.828 2,24 I 5,0Ch3,01: 2,801 1.018
: : : 2.45 5.8012.85: 3.0,1 1.092 2,22 I 6,70:2.72: 2,75: 1,248
: : : 2.02 5.9012.Se1 2,45: 1.183 2,41 I 4.00a3.171 3,001 0,771
I I I 2.05 3.7013.11J1 2.50: 0.757 1,80 I 4,8012,911 2,151 1,J.26.
4 : t. 1,95 I 4,30:3,17: 2,351 1.lJ.6 5.69 I 6.80:5,21: 7 ,65.: 1.124 1,53 I 3,6012,791 1,801 1,0,7 1,65 I 2,80:2,971 1,95: 0. 764
I I : 11,75:5,19: 1.88 11.6314.91: 1,76 : : : :1.86:5.31: 1,72 :1,97:5,37: 1.81 : : : 11.77:4.99: 2,10 11.6315.191 2.00 I I I 11.56:4.891 2.93 ' 11."614.261 2.55 I I I 11.22:3.S,: 3.00 ,1.16:6.0,: 3.90 I 11.2213.411 3.20 11.2313.671 3-2~ !
occurred farthest downstream..• The length ot tlJe jum.p1 as tabulated in Column 11, is the horizontal dis~e from Sections l to 2, Figure 30. The ~ water· depth, tabulated in Column 6, is the depth masurecl at the end ot the jump, correspolld:lng to the depth at Section 2 OD Figure 3(). .
The ratio~ (Column 9, Table 8) is plotted With respect tQ the
Froude mmber (Column 10) tor sloping aprons haYing ~nts 0.05 to 0.30 OD Figure 31. The plot tor the horizontal apron (tan f, • 0) is the 88118
as shown in Figure 5. · Superimposed on Figure 31 are data troa ICind.svater,5 Hickox,5 Be-bkmetett,l and Matzke.6 The agreemnt is Within experimental error.
The small chart on Figure 31 was constructed using data t:rom the larger chart, and shows, tor a range of apron· slopes, tbe ratio ot te41 water depth tor a continuous sloping apron, to conjugr,te depth tor a horizontal apron. · As indicated on. the sm.L. sketch in Figure 31,· D2 · and TW are identical tor a horizontal apron. . The conjugate depth, D2 listed 1n Column 14, Table 6, is the depth necessary f.or a Jum.p to tol"Jll on an imaginary horizontal· floor beg:lnn:ing at Sectian 11 Figure 31.
'.rhe small chart, therefore, shows the extra depth, required tor a .1UJllP ot a given Frollde number to tom on a sloping apron, rather than OD a hor:Lzontal apron. For eX&IQle, if the tangent ot the slope is 0.10, a tail water depth equal to 1.4 times the conjugate depth (D2 tor a horizontal apron) will occur at the end ot the jump; while it the slope is 0.30, the tail water depth at the end of the jump will· be 2.8 times the conjugate depth »2• The conjugate depth D2 used 1n cODDection with a sloping apron is merely a convenient reference figure which .has no other meaning. It will be used throughout this discussion on sloping aprons.
Length of JpmP (Case D)
The length of jum_p for the Case D experiments has been presented 1n two ways. First, the ratio length of jump. to tail water depth, Column 12, was plotted with respect to the Froude nwiber on Figure 32 for sloping aprons having tangents troa Oto 0.25. Sec~, the ratio of length of Jump to the conjugate tail water depth, Col'Ullll 16; Table 8, has been plotted with respect to the Froude mmber f'or tbe same range of slopes on Figure 33. Although not evident on Figure 32, it can be seen from Figure 33 tllat the length of' jump on a sloping apron is longer than tbat which occurs on a hori1&0Dtal floor. For
. L exam,ple, for a Froude nwnber of 8, the ratio D2 var.Les from 6.1, tor a
horizontal apron, to 7 .o, for an apron with a slope of 0.25. Length determinations from. IC1ndsvater5 for a slope of O .l.67 are also plotted on Figure 32. The points shoV a wide spread.
417
FIGURE 31
Tont 0.30 0.15 0.IO 0.15 0.10 O.OI so.--,,-,.-,.-,--.-.,....~--,,-,-..,....,....,--,..:..,.,..,....,....,17'"T..,.....,....-.....,,.......,..;;1 ..,.....-....;.,.......,-,-..,....,....,~ ..............
I ' "J
1-11-1-i--t--+-+-+-t--+--+<•. 1-HH;'+. -t---H/++-it-+-,+-H+'+-H-11,..,.._/++-HH~..+-+-+-+-+--I HI-H-+-+-+-+-+-1-+-+--+..o+-+-l-f,-i--+-..-.1--+-+-,1+--1---1-1~-+--1--h'-,t.....1~-+-+-17.,,_+-,t.....1~-+---10 J I ,
IV I , I/
11t-H-t+++-H--+-++-+..:.+.9 J,:.+-+~HH4+-l~/+-l-.i,,11r...i--1-HH-l-'+-HH-+-h4--'-l--l I " ,
' ' J I J
V O / I '
14,t-...... -+-+--+-+-+-t-+-+--+--+++ '-+-+-+-HH-+-+1--1--~~/-l-+-H-,.1-+-+-+-H""""-+-+--i-~ / , / I/ 111 I , I/ I I
' J 17 11 t-H-+-+--+-+-+-t-+-+_..,J-+-+-I'' Hl-hl'-+/-+-+-+-t-t,-1+-iH-+,61--1--+-t-t-.4--+--+--+-+-l-lH--I I / I J a , I/
' I I ' ., IOHH-++++-H-t--f,j1!+--t+1+-I-Jt-+-:11'1++-b11ia+-+H-,.1-I-HH-#-1+-l-+-H-+-+++-l--l /0 / ., j
7 .J J IV J ' • / 17
0 I I I • I • /
~ I • • I A I/ j;...: III-H-+-+-+-+-+-1-11-l-llif--1-1"9.=I,-* ,-1--0-+,11H--t-~F-,1-,-,~ ...... _._...._.,,,,4,..._-'--'-,!,16-'-_._..,_,,..,l-'-_._-'--,,120.
0 ' 0 / A ' • I Ill I/
/ J ' / -~'
t-t,..·----+·l-f-JJ-1"-.-+-+-,l--ll-'I,_}_. iV I ,7 , J ~ 111H-++-I-H'l-1+-A..1 .:,...+11+--+1-HbY.~l-..s·~~l-++-.l-+-I li/ I ,...,
I' -Ol-ll---l--l-+-l+l,lalll-J,A.!l;J".,1,'.-. JJJ~ '-1,.t-1-1-i.;,-''-+-l-+4-11-11---l--l--l I• r. I J x;,- 11 /
I ' r, ' . ' ' ., . 1 1 IJ 11
aHH-+H1'wH+.ffi ,._'4--Jl/4--H I ~ I
_cp
r, , t 1 ';---~--- "'7-t-H'Hf1ff"1I*"+-HH-+-r.i ,.. ••. -----L...----------r,tI
,ao.--......-...--/.....---.---.
-2111---+---+,-l-+----i----1
.201--+-+-+----1----1 .. J !· 151,,_ -+--1-1---+--i----1
.101---1-++-+--lf---l
.os1----+if""'--+----+--1---1
90'~~,-_,ei-,;..~3...;_.-1-.......15 T: TAILWATER DEPTH RELATED TO CONJUIIATE DEPTH FOR
SLOPING APRONS
SYMBOL. A 0 ,, X
•
TA, t SOURGE o.oao-0.0&1 Flumea A,B&F 0.100 Flumes A,B,D&F 0.155 Flume A 0.1110-0.114 Flumas A,BaF o. 187 Klndsvoter
+ 0.174 Flume F • 0.185 Fl111111 A D 0.100•0.218 Fl- A,B&F * 0.18!1 • 0.280 Flumes AaB 0 0,311 Hcko1 ), 0.0 Boklllnellff a Matzke A O.D48 llakhmllleff & Motzlre • 0.010 Bokllmetelf a Matzlle o~,.__.1_._~_._..._,1,-1......,_._ ....... ~-------------------------1 0 2 4 8
HYDRAULIC JUMP STUDIES . STILLING BASIN V (CASED)
HY.DRAULIC JUMP ON SLOPING AP.RON RATIO OF TAILWATER DEPTH TO. D1
89
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Several mathematicians and experimenters have developed . expressions for the hydraulic Jump on sloping aprons, 2 5 6 13 so the.re is no need to repeat ~ ot these derivations here. .An expression presented by IC1ndsvater5 is the :more common and perhaps the more practical to use.
- l (5)
All s)'Dlbols have been referred to preViously, except tor the coef'f'icient K, a dimensionless parameter called the shape factor, which varies with the Froude number and the slope ot the apron. Kindsvater and Hi~ox evaluated this coefficient tram the profile of' the .1UJ1G> and the measured floor pressures. Surface profiles and pressures were not measured in the current tests but, as a matter of interest, K was computed f'l'Olll Expression 5 by substituting experimental values and solving f'or K. The resulting values of' K are listed in Co.lumn 17 of' Table 8, and are shown plotted with respect to the Froude number for the various slopes on0 Figure 34A. Superimposed on Figure 34A are data from. Kindsvater tor a slope of' 0.167, and data f'rom. Hickox on a slope of 0.333. The agreement is not particularly striking nor do the points plot well, but it should / be remembered that the value JC is dependent on the method used for determining the length of jump. The current experiments indicate that the. Froucl.e number has little effect on the value of K. Assuming this to be the case, values of ind1Vidual points for each slope were averaged and K 1s shown plotted with respect to tan - on Figure 34B. This phase is incidental to the study" at hand and has been discussea only as a matter of' record.
Jump Characteristics (Case B) . Case B -is the one usually encountered in sloping apron design where the Jum.P forms both on the slope and over the horizontal portion of the apron (Figure 30B). Although this form of jump may appear quite complicated, it can be readily analyzed when approached f"rom. a practical standpoint. The primary concern ill slop~ apron design is the tail water depth required to move the front of' the jump up the slope to Section l, Figure 30B. There is little to be gained with a sloping apron unless the entire length of the sloping portion is utilized •.
Referring to the sketches on Figure 35A, it can be observed that f'or a tail. water equal to the conjugate depth, D2, the front of the jump Will occur at a point O I a short distance up the slope. Thie· distance is noted as lo and varies with the degree of slope. If' the tail water depth is increased a vertical. increment, A Y1, 1 t would be reasonabl.e to assume that the front of the jump would raise a corresponding increment. This is not t?Ue, the jump prof'ile undergoes an
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frictional resistance on tbe slope. The vel.ocity, V1, and the Froude number were computed at the sa:me location. The tests were made for slopes with tangents varying from. 0.05 to 0.30, and in some cases, several lengths of floor were used f'or each slope, as indicated in Column 15 of Table 9.
The resulting leng*"..hs and 'bail water depths, divided by the conjugate depth, are shown in ColWIIDS 13 and 14 of Table 9, and these values have been plotted on Figure 36. Tbe horizontal length bas been used rather than thf. vertical distance, A Y, as the former dimension is more convenient f'or use. Figure 36 shows that the straight lines for the geometric portion of the graph tend to intersect at a common point, l 'l'W ~ • 1 and D2 • 0.92, indicated by the circle on the graph. The change in the profile of the jump as it moves from a horizontal floor to the slope is evidenced oy the curved portion of the lines.
Case c, Figure 30, is the upper extreme of Case B; and as there is practically no difference· in the performance for Cases D and C, · data for Case D (Table 8) can again be utilized. By assuming that a horizontal floor begins at the end of the Jump in case D, Columns 15 and J.6 of Table 8 can be plotted on Figure 36. In addition, data from experiments by D. D. Rindlaub of the University of California, for a slope ot O .217, have been plotted on Figure 36. The agreement of the information from the.three sources is very satisfactory. Lellgth of Jump (Case B)
It is suggested that the length of jump tor Case B be obtained from Figure 33. Ac~, Figure 33 is for continuous sloping aprons, but these l.Et:t1.gths can be applied to Case B with but negligible error. In some cases the length of jump is not of' particular concem because it~ not be economically possible to design the basin to confine the entire jump. This is especially true vhen sloping aprons are used in conJunction vi th medium or high overtall spillways where the rock in the riverbed is in fairly good condition. When sloping aprons are des1.gmd shorter than the le~~.h indicated on Figure 33, the rock in the· river downstream must aet M part of' tbe stilling basin. On the other hand, when the quality t">f foundation material 1s questionable, it is advisable to make the apron·suf'f'iciently long to confine the-entire jump, Figure 33.
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HYDRAULIC JUMP STUDIES
STILLING BASIN V (CASE B)
Lv--·········-
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10
TAILWATER REQUIREMENT FOR SLOPING APRONS
.......
PRACTICAL APPLICATIOBS
Existing Structures
To determine the practical value of' the methods given tor the design of' sloping aprons, existing basins employing sloping aprons were, in effect, redesigned using the current experimental information. Pertinent data for 13 existing spillways are tabulated in Table 10. The slope of the spillway face is listed in Column 3; the tangent of' the sloping stilling basin apron is listed in Column 4; the elevation of the upstream end of the apron, or front of' the Jump, is listed in Column 7; the elevation of the end of the apron is listed in Column 8; the tall from headwater to upstream end ot apron is tabulated in Column 9; and the total discharge is shown in Column ll. Where outlets discharge into the spillway stilling basin, that discharge has also been included in the total. The length of the sloping portion of' the apron is g1 ven in Column 14; the length of the horizontal portion of the apron is given in Column 15; and the overall length is given 1:n Column 16. Columns 17 throagh 27 are computations similar to those performed in the previ011s table.
The lover portions of the curves of Figure 36 have been repro-· duced to a larger scale on Figure 37. The coordinates from Columns 26 and 27 of' Table 10 have been plotted on Figure 37 for each of the 13 spillways. cross sections of the basins are shown on Figures 38 and 39. Taking the stilling basins in the order shown on Figure 37, we find that the basin apron is not completely utilized tor the aY'f:an1m discharge eondi tion at the Shasta Dam. This discharge includes both spillway and outlet works. The tail water depth is more than sufficient for the j~ to utilize the entire st:.IJJ:.lng basin apron at Capilano L~m; and the full apron length is utilized at Friant., Madden, and lorn• Dams spillways. The entire apron length.will not be utilized tor the maximum discharge at Canyon Ferry Dam. In this case the apron was designed tor a discharge ot 200,000 cfs but the stilling basin will operate at 250,000 cf's without sweeping out. Keswick shows a deficiency in tail \.'8.ter depth for utilization of the entire apron, but this is compensated for, to some extent, by large spreader teeth at the upstream end of the apron. For the preliminary and final basin designs f:,r the Bbakra Dam spillway, both utilize practically the full length of apron. The jump will not occupy the :f'ull length of apron for-maximum discharge on Olympus, Fol.som, or Rihand Dams spillways. The jump will form. downstream f'roa the upstream end of the slope. The models ot the latter two structures actually showed this to be true. The f'ull length of apron will be utilized by the jump for the stilling· basin at Dickinson Dam. This was an earth dam spillway in which appurtenances were used in the basin.
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. All of the structures listed. in Table 10 and shown on Figures 38 and 39 were designed Vith the aid of model studies •. The degree of conservatism used in each case was dependent on local conditions and the imividual designer.
··· ·· '!'he total lengths of apron provided tor the above 13 existing structures are shown 1n Column· J.6 ot Table 10. The length of .jwllp for the m.x1mum discharge condition for each case is tabulated in Column 29 of the same table. The ratio of, total length of apron to length .of jump is shown 1n Column 30. The total apron length ranges from 39 to 83 percent of the length of Jump; or considering the 13 structures coll.ectiveiy, the average total length of apron ·is 6o percent ~~ the length ot the jump.
Evaluation of Sloping Aprons
: ~ convincing argument, quoted by the laboratory and others 1n the.:·past, .has been that sloping aprons shoilld be designed so that the JuDl,.height curve Mtches the tail water curve for all discharge conditiODS. This procedure results 1n ·wtJa.t has-.been designated a tailor-made \)aein. Sane ot the existing ~ins shown on Figures 38 and 39 were 4.esigned in .this manner. In light of the current experiments-, it was· discovered that th:18 course is not the ·most desirable approach. Instead, mtching tbe jump height curve ¥1th the ·tail water curve shoulcl be a secondary consideration, 9zcept for the mex1nam discharge condition.
Thus, the t1rst cons1deration·1n design 1s to detel'llline the apron. slope: that rill inTolve the Jldn1mm amount ·of excavation., the m1numm. Bm01U1t of concrete,· or both, ,for the D18-X1J11m1 discharge and tail water condition. This is the ·.prime consideration. Only then is the .1ump height ~eked to detel'Jline·'W'hether the tail water depth is adequate for· the 1ntel'Jllediate discharges. It will bP. found that the tail water depth usu~ exceeds the required 3WIQ? height tor the intermediate discharges. This may result in a s·lightly submerged condition tor intermediate discharges,· but. performance Will be. ·very acceptable. The extra depth Will provide a smoother water surface · in and downstream. from· the basin. Should the tail water depth be insufficient for intermediate flows, it Will be necessary-to increase the depth by increasing the slope, or reverting to a horizontal basin. It is not necessary tor the
. front of the Jump to form at the upstream end of the sloping apron for intermediate discharges provided the tail water del)th and the length of basin available for energy dissipation are considered adequate. Us-ing this -method, the designer is f'ree to choose the slope he desires, since
·tests showed -that the slope itself had little effect on the perf'omance of the stilling basin action.
105
It is not possible to standardize on sloping apron design nearly as much as f'or the horizontal aprons, as :much more individual judgment is requir:ed. The slope and overall shape of the apron 11111st be determined from economic reasoning, while the length must be judged by the type and soundness of' the riverbed downstream. The existing structures shown on Figures 38 and 39 should serve as a guide in proportioning future sloping apron designs.
Sloping Apron Versus Horizontal Apron .
A point, which it is f'elt bas been misunderstood 1n the past with regard to horizontal aprons tor high dams, can now be clarified. The Bureau has constl'llcted very f'ew stilling basins with horizontal aprons for 1 ts larger dams. It has been the consensus that the hydrm~lic Jump on a horizontal apron is very sensitive to slight changes in tail water depth. This is very tme for the larger values of the Froude number, but this characteristic can be remedied. Suppose a horizontal apron is designed for a Froude number of 10. The basin will operate satisfactorily for conJugate tail water depth, but as the tail water is lowered to o.98D2 the front of the jump will begin to move. By the time the tail water ia dropped to 0.96D2, the jump will probably be completely out of' the basin. Thus, to design a stilling basin in this n.:uge the tail -water depth :must be known with certainty or a f'actor of safety should be provided in the design •. To guard against a deficiency in tail water depth, the same procedure is suggested here as for Basins I and II. R~ferring to the minimum tail water curve for Basins I and II on Figure ll, the margin of safety can.be observed for any value of·the Froude number. It is recollllllended that the tail water depth tor maximum discharge be at least 5 percent larger than the minimum shown on Figure 11. For values of the Froude number greater than 9, a 10 per-. cent factor of safety may be advisable as this will not only stabilize the Jump but will improve the performance. With the additional tail water depth, the horizontal apron will perform on a par with the sloping apron. . 'rhus, the primary consideration in design need not be hydraulic but structural. The basin, with either horizontal or sloping apron, which can be constl'llcted at the least cost is the most desirable. Effect of Slo:pe of ~hute
A factor which occasionally affects stilling basin operation is the slope of chute entering the basin. The foregoing experimentation was sufficiently extensive to shed some light on this ·tactor. The tests showed that the slope of chute upstream. from the stilling basin was unimportant, as far as jump performance was concerned, so long as. the velocity distribution in the jet entering the Jump was reasonably uniform. In the case of steep chutes or short flat chutes, the velocity distribution can be considered normal. The principal difficulty is experienced with long flat chutes where frictional resistance on bottom and side val.ls is sufficient to produce a center velocity greatly
exceeding that on the bottom or sides. When this happens, greater activity results in the center of the stilling basin than on the sides producing an asymmetrical jump Yi th strong side eddies. This same ettect is also witneesed when the angle ot divergence or a c~te is too great tor the water to follow properly. .In either case the sur.t'ace of the Jump is unusually ro11gh and choppy and the positio?) .,r the front of the jum;p is not always predictable •
In~ case of earth dam spillways the.practice has been to make. the upstream portion unusually flat, then steepen the slope to 2:1, or that corresponding to the natural trajectory- cf the je1;, immecliately. pi,tceding the stilling basin. Figure lA, vh.ich shows the ·mod.el spillway tor. :Trenton Dam, illustrates this practice. , B11ng1ng an asymetrical Jet into the stilling basin at a steep angle usually does aid in· stabilizing the .1UQ. This is not effective, however, where very- long. flat slopes are inVolved and the velocity distribution is COlllPletely out of balance. ·
The most adverse condition has been observed where long canal chutes tel'llinate in st1111Dg basins. A typical example is the chute and basin at Station 25+19 on the South Canal, Uncompahgre Project, Colorado, Figure Jt.o. The operation ot this stilling basin .is not particularly objectionable, but it will serve as an 1llustra~1on. !rile above chute is approximately 700 feet long Yith a slope of 0.0392. The stilling basin at the end is also shown 011 Figure Jt.o. A· photograph ot the prototype basin operating at normal capacity ia shown on Figure 41. The action is of the surging type; the .11mP is unusually rough, with a sreat aaount of splash and spray. Two factors contribute to . the rough
. operation: the unbalanced veloci-cy- distribution in the entering jet, and excessive divergence of the chute in the ~teepeat porti011.
A definite 1-Provement can be accOlllPlished in future designs where long flat chutes are involved by utili~ing the Type III basin described in Section 3. The battle blocks on the floor tend to alter the asymetric.al jet, resulting in an ovei,µJ. 1-Provement in operation. This is the only corrective measure that can·be sugge~ted at this time.
Recommendations
The tollow1ng rules have been devised tor the design of slopingaprons as.developed from. the forego~ experiments:
1. Detemine an apron lirraDgement which Y11l give the greatest econaq tor~ max:tnnun discharge cond1tion. This is the governing factor and the · only justification tor u·a1ng a sloping apron.
·lO'r.
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2. Posit.ion the apron so that the tront of the Jump will form. at the upstream end of the slope for the max:1nann discharge and tail water condition by means of the information on Figure 37. Several trials will usually be required before the slope and location of the apron are coapatible with the hydraulic requirement. It may be necessary to raise or lower the apron, or change the original. slope entirely.
3. The length or the jump for max1Jmm1 or partial flows can be obtained from Figure 33. The portion of the j\µIIP to be confined on . the stilling basin apron is a decision for the designer. In making this decision, Figures 38 and 39 may be helpful. The average overa:.l apron in Figures 38 and 39 averages 6o percent of the length of Jwap for the maximum discharge condition. The apron may be lengthened or shortened, depending upon the quality- of the rock in ·the riverbed and <'ther local conditions. If the apron is set on loose material and the downstream channel is in poor condition, it may be advisable to make the total length of apron the same as the length of Jump. ·
4. With the apron designed properly for the maximmll discharge cond1tion, the next step is to be certain that the tail water depth and length of basin available for energy dissipation are sufficient for, say, l/4, 1/2, and 3/4 capacity. If the tail water depth is sufficient or in excess of the Jump height for the intermediate discharges, the design · is acceptable. If the tail water depth is . deficient, it may then be necessary to try a flat~r slope or reposition the sloping portion of the apron. It is not necessary that the front of the Jump tom at the upstream end of the sloping apron for partial flows. In other words, the front of the Jump may remain e.t Section 1 (Figure 30B), move upstream from Section 1, or :move down the slope for partial flows, providing the tail water depth and length of the apron are considered sufficient for these flow~s
5. A horizontal apron will perto:rm on a par with the sloping apron, for high values of the Froude .number, if the proper tail water depth is provided.
6. The slope of the chute upstream from a stilling basin has little effect on the hydraulic Jump so long as the velocity distribution and depth of flow are reasonably unifo:rm on entering the Jump.
7. A small solid triangular sill, placed at the end of the apron, is the onq appurtenance needed in· conJUJ1ction with the. sloping apron. It serves to lif't the f'low as it leaves· the apron and thus acts to control scour. Its dimensions are not critical; the moat effective height is between 0.05D2 .and O.lOD2 and a slope of 3:1 to . 2:1 (see Figures 38.and 39).
110
A spillway should be operated to produce as nearly a,mmetrical
flow in the stilling basin as possible. (This_ applies to all stUling
basins.) As,mmetry produces large horizontal eddies that C&1'1 C81'l7
riverbed material onto the apron. This material, motivated by the
energy- in the eddies, can abrade the apron and appurtenances in the
basin at a very surprising rate. These eddies can also undermine wing
walls and settle riprap. Asymmetrical operation is expensive operation,
and operators should be continually reminded of this tact •
Where the diacbarge over high sp1llways exceeds 500 cts per
foot ot apron Width, or where there is any f'o:rm of aa,mmetry involved,
a model study is advisable. For the higher values ·ot the Frou.de aumbe:r,
st, ll ing basins become increasingly expensive, and the perf'oZiUmce less
acceptable. '.rhus, wherv practical, a bucket type ot cUssi,a.tor riJa7· sel"V'e
the purpose better and more economically than a stilling basin.
lll
SECTION 6
STILI,lNG BASIN FOR PIPE OR OPEN CBAlfflEL OUTLETS NO TAIL WATER REQUIRED.
(BASIN VI)
The stilling basin developed in these tests is an impact-tne energy dissipator, contained in a relatively small boxlike structure, which requires no tail water for successful performance. Al.though the. emphasis in. this discussion is placed on use With pipe outlets., the entrance st~cture may be modified to use an open channel entrance.
Generalized design rules and procedures are presented to allow determining the proper basin size and all critical dimensions tor a range of discharges up to 339 feet per second and velocities up to 30 feet per second.* Greater discharges may be band.led by constructing multiple units side by side. Tbe efficiency of the basin in accomplishing energy losses is greater than a hydraulic jump of the same Froude number.
IM'RODUCTION
The development of this short impact-type basin was initiated by the need for some 50 or more stilling·structures on the Fl"&Dklin Canal, Bostwick Division, Missouri River Basin Project. The need was for relatively small basins providing energy dissipation independent of a tail water curve or tail water of any kind. Tbe demand for int'ormation on general design procedures for use on other projects prompted the laboratory to include further investigation of this basin in'the l;aboratory• s general research program. Continued research on this type of basin will be made as time and funds pemit.
-tlThe laboratory has developed two basins tor specific installations where. velocities were considerably higher. ~ basin was for 10 second-feet at 80 feet.per second, the other f'or 4 second-feet at 106 feet per second (see Bibliography, No. 33). SUfficient data are not available, however, to provide general design rules or procedures.
I
TEST PROCEDURE
Hydraulic Models
BJdraulic models were used to devel'>P the stilling basin, determine the discharge limitations, and obtain dimensions tor the various parts of the basin. Basins 1.6 to 2.0 f'eet wide were used in the tests. The inlet pipe was 6-3/8 inches, inside diameter, and was equipped vi th a slide gate Yell upstream from the basin entrance so thathe desired relations between head, depth, and velocity could be obtainThe pipe was transparent so that backwater effects in the pipe could. be studied. Discharges of over 3 cubic feet per second and velocities up to 15 feet per second could be obtained during the tests. Hydraulic model-prototype relations were used to scale up the results to predict performance tor discharges up to 339 second-feet and velocities up to 30 feet pex· second.
The basin was tested in a tail box containing gravel formed ·into a trapezoidal chamlel. The size of the gravel was changed several times during the tests. The outlet channel bottom was slightly wider than the basin and had 1: 1 side slopes. A tail gate was provided at the downstream end to evaluate the effects of tail water.
Development of Basin
The final J y evolved basin was the result of extensive tests on many di:t:ferent arrangements. A detailed discussidn of these tests is not given since they had little if any bearing on the final design except 1n a general way. This is discussed below. ·
With the many combinatiQns of discharge, velocity, and depth possible for the incom:f.tl,g flow, it became apparent during the early tests that some device was needed at the stilling basin.entrance to convert the many possible flow patterns into a common pattern. The vertical hanging battle proved to be this device, Figure 42. Regardless of the depth or velocity of the incoming flow (within the prescribed limits) the flow after striking the baffle acted the same as any other combination of depth and velocity. Thus, some of· the variables were ellminated from the problem.
. · The effect of velocity alone was then investigated, and it was found that for velocities 30 teet per second and below (for a 42-inch pipe) the performance ot tpe structure was primarily dependent on the discharge. Actually, the velocity of the incoming flow does affect the performance of the basin, but from a practical point of view 1 t could be eliminated from consideration. Bad this not be~n done, considerably more testing would have been required to· evaluate and express the effect of velocity.
113
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END SILL
..
For velocities of 30 feet per second or less the basin width W was found to be a function of the discharge, with other basin dimensions being related to the width, ·Figure 42. To determine the necessary width, erosion test results, Judgment, and operating experiences were all used and the advice of laboratory and design personnel was used to obtain the finally determined limits. Since no definite line of demarcation between a •too wide• or •too narrow" basin exists, it was necessary to work between two more definite lines, shown on Figure 42 as the upper and lower limits. These lines required far less Judgment to determine than a single intermediate line •
Various basin sizes, discharges, and velocities were tested taking note of the erosion, wave heights, energy losses, and general performance. When the upper and lower limit lines bad been established a line about midway between the two was used to establish the proper width of basin tor various discharges. The exact line is not shown because strict adherence to.a single curve would result in ditricult to use fractional dimensions. Accuracy o-r this degree is not Justifiable. Figure 43 shows typical performance of the recomended stilling basin for the three ~imits discussed. It is evident that the center photograph represents a compromise between the upper limit operation whi'c:h is very mild and the lower limit operation which is approaching the unsafe range.
Using the middle range of basin widths, other basin dimensions were determined, modified, "1),d made minimum by means of' trial and e;rror tests on the several models. Dimensions tor nine different basins -areshown in Table 11. These shou1d not be arbitrarily reduced since in the interes.ts of economy the dimensions have been reduced as -far as is safely possible.
Performance of Basin
Energy diseipa.tion is initiated by flow striking tbe vertical hanging battle.and being turned µpstream by the horizontal. portion of the battle and by the floor, in vertical eddies. The structure, therefore, requires no tail water for energy dissipation as is necessary for a hydraulic jump. basin. Tail water as high as d + J, Figure 42, however,Will improve the performance by reducing outl(~t velocities, providing a smooth water surface, and reducing tendencies toward erosion. Excessive tail water, on the other hand, will cause some flow to pass over the top of the baffle. This should be avoided if possible.
The effectiveness of the basin is best illustrated by cOJliP&ringthe energy losses within the structure to those which occur in a~lie jump. Based on depth and velocity measurements made in the approach pipe and in the downstream cbamlel ( no tail water), the change in momentum was cODQilUted as explained in Section 1 tor the hydraul.ic Junl).
115
ti
Su
gg
este
d
Max
imum
. Pi
:De
size
*
dis
char
ge
Dia
A
na
in
. (s
q f
t)
Q
w
B
L
(1)
(2)
(3)
(4)
(5)
(6)
18-
1.76
72
21**
5-
6 4.
:3
7-4
24
3.14
16
38
6-9
5-3
9-0
30
4.90
87
59
8-0
6-3
10-8
36
7.06
86
85
9-3
7-3
12-4
42
9.62
11
115
10-6
8-
0 14
-0
48 •
12.5
664
151
ll-9
9-
0 15
-8
5JI.
15.9(
)11.3
19
1 13
-0
9-9
17-4
6o
19.6
350
236
14-3
10-
9 19
-0
72
28.2
743
339
J.6-6
12-
3 22
-0
Tab
le 1
1
ST
ILL
DG
BA
SDf
DIM
EB
SI0
IS
Imp
act-
typ
e E
ner
gy
Dia
aip
a.to
r (!
Bai
n V
I)
Feet
and
in
ches
a b
C
d e
t (7
) (8
) (9
) (1
0)
(11
) (1
2)
3-3
4-1
2-4
0-11
0-
6 1-
6
3-11
5-
1 2-
10 1
-2
o-6
2-0
4-7
6-1
3-4
1-Jt.
o-
8 2-
6
5-3
7-1
3-10
1-7
o-
8 3-
0
6-0
8-o
4-5
1-9
0-10
3-
0
6-9
8-Jl
4:.1
1 2-
0 0-
10
3-0
7-4
10-0
5-5
2-
2 l-
0
3-0
8-o
ll-0
5-l
l 2-
5 1-
0 3-
0
9-3
12-9
6-l
l 2-
9 1-
3 3-
0
Inch
es
g
tw
tr
tb
tp
K
(13)
(1
4)
(15)
(J
.6)
(17)
(1
8)
2-1
6 6-
1/2
6 6
3
2-6
6 6-
1/2
6 6
3
3-0
6 6-
1/2
7 7
3
3-6
7 7-
1/2
8 8
3
3-l
l 8
8-1/
2 9
8 4
4-5
9 9-
1/2
10
8 4
4-l
l 10
10
-1/2
10
8
4
5-4
ll
u-1
/2
ll
8 6
6-2
l2
12-1
/2
12
8
6 . *
Sugg
este
d p
ipe
wil
l ru
n f
ull
whe
n v
elo
cit
y i
s 1
2 f
eet
per
sec
ond
or
ha
lf t
ull
whe
n v
elo
cit
y i
s
24 f
eet
per
seco
nd
. S
ize
may
be
mo
dif
ied
to
r o
ther
velo
cit
ies
by
Q
• A
V,
bu
t :r
ela
tio
n b
etw
een
Q a
nd
basi
n
dim
ensi
on
s sh
own
1111
st b
e m
ain
tain
ed
. ·
· ·
, *
*fo
r d
isch
arg
es l
ess
th
an
21
seco
nd-f
":!l
et,
ob
tain
basi
n w
idth
tra
m c
urv
e o
f F
igu
re 4
2.
Oth
er
· 3W
4w
w
di
men
sion
s p
rop
ort
ion
al t
o W
J H
•
4 ,
L a
J
, d
• 0
, etc
.
FIGURE 43
Lowest value of mmmumdi-scbarge - Coffespcmds to upper limit curve
Intermediate value of maximum discharge -Correspol;lds to tabular values
Largest value of maximum discharge - Corresponds to lower limit curve
Typical Performance at Maximum Discharges - No TaUwat·er Impact Type Energy Dissipator • Basin VI
The Froude number of the incoming f'low was computed using D1, obtained by converting the f'low area in the partly full pipe into an equivalent rectangle as wide as the pipe diameter. Compared to the losses in the hydraulic Jump, Figure 44, the impact basin shows greater etf'iciency 1n performance. Inasmuch as the basin would have performed Just as ef'f'iciently had the flow been introduced in a rectangular cross section, the above conclusion is valid. ·
B.ASIH DESIGN·
Table 11 and the key drawing, Figure 42, may be used to obtain dimensions for the usual structure operating Within usual ranges. How-· ever, a further understanding of the design limitations may help the designer to modify these dimensions when necessary f'or special operating conditions.
The basin dimensions, Columns 4 to 13, are a function of' the maximum discharge to be expected, Column 3. Velocity at the stilling basin entrance need not be considered except that it should not exceed about 30 feet per second.
Columns land 2 give the pipe sizes used in designs originat-. ing· in -the Commissioner• s Office, Denver, Colorado. These. may be changed as-necessary, however. These suggested sizes were obtained by assuming the· velocity of flow to be 12 feet per second. The pipes shown would then f'low full at maximum discharge or they would flow hall" full at 24 feet per second. The basin operates as well whether a small pipe flowing tull or a larger pipe flowing partially full is used. The pipe size may therefore be modified to fit existing co~.tions, but the relation between structure size and discharge should be maintained as given in the table. In fact, a pipe need not be used at all; an open clumnel having a width less than the basin width will perform equally as well.
The invert of' the entrance pipe, or open channel, should be held at the elevation shown on the drawing of Figure 42, in line with the bottom of' the baffle and the top of' the end sill, regardless of the size of the pipe selected. The entrance pipe may be tilted dowJiward somewhat without affecting performance adversely. A l1m1t of' 15° is a sugges~d maximum although the loss in etf'iciency at 20° may not cause
. excessive erosion. For greater slopes use a horizontal or sloping pipe (up to 15°) 2 or more diameters long Just upstream from the stilling basin.
Under certain conditions of flow a hydraulic jump may be expected to form in the downstream end of' the pipe sealing the exit end. If the upper end of' the pipe is also sealed by incoming f'low, a vent may be necessary- to prevent pressure fluctuation in the system. A vent to the atmosphere, say one-sixth the pipe diameter, should be installed upstream from the jump.
118
90
80
70
.JJ-LiJ Ill
tz Ill 60 u ~ la.I a. ~ 50
>c, ~ La.I
~ 40
z -Cl)
~ 30 ,.J
2.0
10
FIGURE 44
~ -/ ~
~ ~
Impact basin-- V / i,..---
"'"'v /
/ V V
/
V / I/ V
I ~ -Jump on horizontal floor .
, I j
I I 7 '
j
I I I I
I
. j
I I .
2. 4 6 8 10 12. 14 16 18 2.0
F - V1 I - "9D1
COMPARISON OF ENERGY LOSSES
IMPACT BASIN AND HYDRAULIC JUMP
The notches shown in the baffle are provided to aid in cleaning out the basin af'ter prolonged nonuse of the stncture. When the basin has silted.level tull ot sediment before the start of .the spill, the notches provide concentrated jets of water to clean the basin. The basin is designed, however, to carry the tull discharge, shown 1n Table ll, over the top ot the battle 1f tor any reason the epace beneath the battle becomes clogged, Fisure 45C. Perf'o:mance is not as good, na~rally, but acceptable. With ·the basin operating normally, the notches provide same concentration of flow passing over the end sill, resulting in some tend'!' ency to scour, Fisure 45A. Riprap as shown on the drawing vUl pro-r:l_de ample protection in the usual installation, but it the best possible performance is desired, it is rec0J11111ended that the alternate end sill and J.a.5• end walls be used, Figure 45B. The extra sill- length reAuces tlow concent~tion, scour tendencies, at d the height ot va~s in the downstream cbanne , .•
COICIDSIOJE AND ~OMMEBDATIOJE
The toll.owing proce~res and nles pertain to the design of Basin VI:
1. Use of Basin VI is 11.m1ted to cases where the velocity at the entrance to the stilling basin is about 30 feet per second or · less.
2. From the ma.Y1m,m expected discharge, determine the stilling baJJin dimensions, using Table ll, Columns 3 to 13. The use of 11111ltiple units side by side may prove economical in sOlile cases.
3. Canpute the necessary-pipe area from the velocity and discharge. The values in Table 11, Columns 1 and 2, are suggested si~es based on a velocity. of 12 feet per second and the desire that the pipe rm,. tun at the discharge given in Column 3. Regardless of the pipe size chosen, maintain the relation between discharge and basin size given in the table. .An open channel entrance may be used in place of a pipe. The approach channel should be narrower than the basin W1 tb invert elevation the same as the pipe. .
4. Although tail-water is not necessary tor successful operation, a moderate depth of tail water Will ·im,prove the perf'o.rmance. For best performance set the basin so that maximum tail water does not exceed d + j, Figure 42. .
5. The thickness of various parts of the basin as used in the Commissioner's Office, Denver, Colorado, is given in Columns 14 to 18, Table 11.
!
FIGURE 45
A. Erosion of channel bed-standard wall and end sill.
B. Less erosion occurs with alternate end sill and wall design.
C. Flow appearance when entire maximum discharge passes over top of baffle during emergency operation.
Channel Erosion and Emergency Operation f'or Maximum Tabular Discharge No Tailwater
Impact Type Energy Dissipator - Basin VI
6.. The entrance pipe or channel may be tilted downward about 15° without affecting performance adversely. For greater slopes use a horizontal or sloping pipe (up to 15°) 2 or more diameters long just upstream from the stilling basin. Maintain proper elevation of invert at entro.i,cc: as shown on the drawing.
7. If a hydraulic Jump is expected to tom 1n the downstream end of the pipe and the pipe entrance is sealed by incoming flow, install a vent about one-sixth the Pi:Pe diameter at any convenient location upstream from the Jump.
8. For best possible operation of basin use alternate end sill and 45 ° wall design shown on Figure 42. Erosion tendencies Will be l"educed as shown on Figure 45.
.
- BIBLIOGRAPHY
l. Bakbmeteff, · B. A. and Matzke, A. E. , "'!'be lcydraulic JUJll'P in Terms of n,aamic Similtlrity,~ Transactions .ASCE, Vol. 1011 p. 630, 1936
2. Puls, L. G., ''Mechanics of the Hydraulic JUJllP," ~au of Reclamation Technical Memorandum Bo. 623, Denver, Colorado, October 1941 .
3. Dr. Ing. !Curt Safranez, "Unwrsucl:mngen uber den Wechse1spnmg" (Research Relating to the Hydraulic Jump), Bausingin1eur, 1929, Hett. 37, 38. Transl&.tion by.D. P. Barnes, Bureau of Reclamation files, Den'Ver, COJ.orado. Also Cj,vil Engineer, Vol. 4, p. 262, 1934 ,
4.
5.
6.
7.
8.
Woycick11 K., "The Hydraulic Jmnp and its 'l'op Roll and the Discharge of Sluice Gates," a translation from Ge man by I. B. Hosig, Bureau of Reclamtion Technical Memorandum Bo. 435, Denver, Colorado, January 1934
Kinsvater, Carl E., "The Hydraulic Jump in Sloping Channels, tt Transactions ASCE, Vol. 1091 p. 1107, 1944 ;/
Bakhmeteft, B. A. and Matzke, A. E. 1 "The Bydraul1c Jump in Sloped Channels,• Transactions ASME, Vol. 60, p. lll, 1938
Rindlaub, B. D., lttJ!he Hydraulic Jump in Sloping Channels," The·sis tor Master of Science degree in Civil Engineering, UDiversity of Calife>rnia, Berkeley, California
Blaisdell, F. w., "The SAF Stilling Basin," united States De]la.rtment of Agriculture, Soil Conservation Serrice, st. AJlthony Falls Hydraulic Laboratory, Mimleapolis, Mi,Jmesota, December 1943
. 9. Bakbmetett, B. A., "The B,a.raulic Jump and Related Pbemmena," Transactions ASME, Vol. 54, 1932, Paper .APM-54-l :
10. Chertonosov I M. D-. (Some Considerations Regarding tbe Length of the Hydraulic Jump), Transactions Scientific ~esearch Institute of Hydrotechnics, Vol. 17, 1935, Leningrad. Translation from Russian in tiles ot Universit-y of Minnesota ·
11. Eimrachter, J., wossersprung and Decltwal.z~nlange (The lf1draulic Jump and Length of the Surface Roller) Wasserkratt und Wasserwirtschaft, Vol. 301 April 17, 1935
l2. Ell.ms, R. w., •couqJ11tation ot Tail-vater Depth of the B)draulic Jump 1n Sloping Flumes,• Transactions .ASME, Vol. 50., Paper 11yd. 50-5, 1928 -
123
13. Ellms, R. W., "Hydraulic Jump 1n Sloping and Horizontal Flumes, .. Transactions ASME, Vol. 54, Paper Hyd. 54-6, 1932
14. · Hinds, Juliap, nThe Hydraulic Jump and Critical Depth in the Design or Hydraulic Structures," Engineering News-Record,
· Vol. 85, No. 22, p. 1034, November 25, 1920 .
15. King, H. W., "Handbook or Hydraulics," McGraw-Hill Book Ca!IP&ll1, Second Edition, p. 334, 1929 ~
16. Blaisdell, F. w., ''Development and Hydraulic Design, Saint Anthony Falls Stilling Basin," Transactions ASCE, Vol. ll3, p. 483, 1948
17. Lancaster 1 D. M. 1 "Field Measurements to Evaluate the Characteristics ot Flow Down a Spillway Face With Special Reference to Grand Coulee and Shasta Dams, .. Bureau ot Reclam.tion Byd.raulj,.c Laboratory Report Hyd. 368·
18. Rouse, Hunter, Engineering Hydraulics, John Wiley & Sons, 19501 p. 571
19. Newman, J. B. and LaBoon, F. A. 1 "Effect of Battle Piers on the Hydraulic Jump," Master or Science Thesis, Massachusetts Institute of Technology, 1953
20. Higgins, D. J., 9The Direct Measure or Forces on Baffle Piers in the Hyl:lraulic Jump," Master of Science Thesis, Massachusetts Institute of Technology, 1953 ·
21. Forchhemier, Ueber den Wechselsprung1 ,The Hydraulic Jump, Die Wasserkraft, Vol. 201 19251 p. 238
22. Kennison, K. R., "The Hydraulic Jump in Open Channel Flow," Transactions ASCE, 1916
23. Kozeny, J. 1 Der Wasserspnmg, The Hydraulic Jump, Die Wasserwirtschaf't, Vol. 221 1929, p. 537
24. , Rehbock, T., . Di,e Wasserwalze al~ Regler des Ene:j-gie - llauslutltes der Wasserlaufe, The Hydraulic Roller as_a Regulator of the Energy Content o:f a Stream, Proceedings 1st International Congress for Applied Mechanics, Delft, 1924 ·
25. Schoklitsch., A., Wasserkratt und Wasserwirtschaft, Vol. 211 1926, p. 108 ·
26. Woodwud, s. M., "Hydraulic Jump and Backwater Curve., Engineering News-Record., Vol. 8, 1918, p. 574, Vol. 86, 1921, p. 185 · .
27. Moore I W. L. 1 "Energy Loss at the Base of a Free Overfall," Transactions ASCE, Vol. 109, 1943, p. 1343 .
28. "Hydraulic Model Studies, Fontana Project," Technical Monograph 68, Tennessea Valley Authority, p. 99
29. Rhone, T. J., "lf!nlraulic Model Studies on the Wave Suppressor Device at Friant-Kern Canal Head.works," Bureau of Reclamation Hydraulic Laboratory Report l[yd. 395
30. Beichley, G. L., "Hydraulic Model Studies of the Olltlet Works at . Carter Lake Resenoir Dam No. 1 Joining the St. Vra1n Canal,"
Bureau of Reclamation Hydraulic Laboratoey Report B'.yd. 394 31. Peterka, A. J., "Impact Type Energy Dissipatore tor Flow at Pipe
Outlets, Fnmklin Canal," Bureau of Reclamation 11:ydraulic Laboratory Report 11yd. 398 ·
32. Simmons, w. P., "Hydraulic Model Studies ot Outlet Works and Wasteway tor Lovewell Dam,• Bureau of Reclamation lcydraulic Laboratory Re1,0rt 11yd. i.oo
33. Schuster, J. C., "Model Studies ot Davis Aqueduct 'l'llrnouts 15 .4 and· 11.7, Weber Basin, Utah,• Bureau of Reclamation Hydraulic Laboratory Paper No. 62 ·
125
l.ln~~-~d States Department of the Interior .;·: .BUR.EAU OF RECLAMATION