submerged weir flow

8/2/2019 Submerged Weir Flow

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U. S. Department of AgricultureSoi l Conservat ion ServiceEngineering DivisionDesign Branch

DESIGN NOTE NO . 15%Subje c t: Submerged Weir Flow

Weir flow over a drop spillway i s either free f low or submerged flow.Free (unsubmerged we ir ) f low ex is ts when th e ta i lw at er surfa ce i s a t o rbelow th e cr es t of t h e weir . Submerged weir f low ex is ts when the t a i l -water surface i s above th e c r e st of t h e weir . The depth of submergencei s th e d if f ere nce i n e l eva t io n between t h e downstream water su rface andt h e c r e s t o f t h e w e ir .For f re e f low condi t ions t he d i scha rge through the we i r i s independento f t he t a i l w a t e r e l e va t i on and t h e de pth a t t he w e ir i s usua l ly t akenas c r i t i c a l d ep th , For submerged we ir flow, t h e d is ch ar ge may o r maynot be independent of th e ta i l wa te r e le vat io n. When t h e de pth o f sub-mergence i s 0.7 o f t h e c r i t i c a l d e pt h o r l e s s , t h e d i sc h ar g e i s usua l lyt a ken a s e qua l t o t h e f r e e d i s c har ge . For gr ea te r submergence, th e di s-charge i s determined by bot h t h e headwater and ta il wa te r dep ths ( se eFig. 1).

Energy Grade Liner n

Fig. 1H = Spec i f ic ene rgy head a t c re s t o f we i r, ft1H2 = Submergence over the crest = di f fe rence i n e leva t ion between

t a i lw a t e r and c r e s t o f w e ir , f t

*Prepared by H. J . Goon of th e Design Uni t, Design Branch, H y at ts v il le ,Maryland.


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L = Length of weir , f tC = D isch ar ge co e f f i c i en t f o r f r ee f l owQf - Discharge f o r f r e e f low = C L H ~ ~ ~ ~ ,f s Qfqf =- Discharge f o r f r e e flow per fo o t l eng th o f wei r = -, c f s / f tLQs E Discharge fo r submerged flow, c f s

Qsq E Discharge f o r submerged f low pe r f oo t le ng th of wei r = - c f s / f tS L 'The dis ch arg e f o r submerged flow i s t ak en a s

Qs = R Qfqs = R qf

where R i s assumed t o be a fu nc tio n of submergence r a t i o -., H-Figure 3.4, page 3.17 of NEH-11, Drop Spillw ays, giv es th e re l a t i o n be-

H2tween R and - This f igu re was p repared by ana lyz ing ava i l ab l e t e s tH,da ta of submerged flow over se ve ra l typ es of w eir s and ea rt h embankments.The da ta i nd ic at e a wide band of valu es of R f o r given va lues o f t hesubmergence r a t i o . Therefore , p re ci se re s u l t s should not be expectedfrom Figure 3.4. I f p r e c i s e r e s u l t s a r e n e ce ss ar y, a s e ar ch of l i t e r -a t u r e f o r d i scharge da ta f rom approp r ia te wei r s o r a model s tudy i sr eq u i r ed .Figure 3 .4 i s reproduced on Sheet 1 of ES-207. Observe t h a t when % andH2 a r e g iv en, H1 can no t be e xp l i c i t l y eva lua ted f rom Sheet 1, ES-207.Although H, may be s olv ed by cut- an d- try methods, it i s d e s i ra b l e t ot ransform th e graph of Sheet 1, ES-207 into a form such that H, can bee x p l i c i t l y e v al ua te d. The transformed graph i s given in Sheet 2 ofES-207. Thus

1. when H1 and q ar e g iven , Shee t 1 s used t o determine Hz ( s eeSExample 1, Sheet 3 of ES-207).

2. when q, and H a r e g iv en, H1 can be ex p l i c i t ly eva lua ted fromSheet 2, ES-207. ( s e e Example 2 ) .

3. when H, and H2 a r e gi ven, e i t h e r S heet 1 or Shee t 2 ma$ be usedt o de te rmine qs.


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Relation Between Submergence and DischargeSP'LLWAYS:Given HI and qs, determine Hz

" 2Values of 1

Energy Grade Lin e/ - I 7

I I rCrest Elevation

H1E Specific energy head at crest of weir, ft.H 2 - Submergence over the crest = Vertical distancebetween tailwater and crest of weir, ft.qs = Discharge for submerged flow per foot length ofweir, cfs /ft.q f z Discharge for free flow per foot length of weir,

cfs/ft.= 3.1 H~~

0.8 0.9 1(H2Values of ~1

REFERENCENEH-11 Drop Spi l lwaysPage 3.17-Figure 3.4

U. S. DEPARTMENT OF AGRICULTURESOIL CONSERVATION SERVICE

ENGINEERING D M S I O N - DESIGN UNIT

STANDARD DWG. NO.ES - 207S H E E T 2 OF3DATE 3 - 73


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,

REFERENCENEH-11 Drop SpillwaysPage 3.17-Figure 3.4

U.S. DEPARTMENT OF AGRICULTURESOIL CONSERVATION SERVICE

ENGINEERING DIVISION - DESIGN UNIT

STANDARD DWG. NO.ES- 207S H E E T L OF3DATE 3 - 73


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Relation Between Submergence and DischargeDROP SPILLWAYS:

Given: A drop s pi llw ay with submerged flow_CCDischarge coefficient , C = 3.1Specific energy head, H1 = 4.20 f tLength o f weir, L = 1 9 f tDischarge, Qs = 480 cf s

Determine: Submergence over the c r e s t , H2Solut ion: Qf =3.1 L H , ~ / ~3 . 1 ( 1 9 ) ( 4 . 2 0 ) ~ / ~5 0 7 c f s

Ekample 2

Given: A drop s pil lwa y with submerged flowLength of weir, L = 19 ftDischarge, Q, = 480 c f sSubmergence over the crest, H2 = 2.46 f t

Determine: Sp ec if ic energy head, H1- - = =Solution: qs - Qs 480 25.3 cfs/ft1 9

J- -1.7 1 (s he et 2, ES-207)H2

REFERENCENEH-11 Drop SpillwaysPage 3.17-Figur e3.4

U. S. DEPARTMENT OF AGRICLTLTLTRESOIL CONSERVATION SERVICEENGINEERING DIVISION - DESIGN UNIT

STANDARD DWG. NO.ES- 207S H E E T 3 OF3DATE 3 - 73


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submerged weir flow

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