aes computational hydraulics for civil engineers

8/11/2019 AES Computational Hydraulics for Civil Engineers

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74

HYDRAULIC ELEMENTS

5X,'UPSTREAM PIPEFLOW. SUGGEST USiR as-EXAMINE ASSUMED',/,SX,'PIPEFLOW FLOWOEPTBS FOR POSSIBLE CRITICAL DEPTH OR , / ,5X,'SOPPIT CONTROL IN UPSTREAM PIPS, OR PRESSURE',I,SX,'PLOW POR BOTH DOWNSTRE M D UPSTREAM PIPEFLOW.')GOTe 3000

C OPEN-CHANNBL PLOWCC DOWNSTRE M FLew IS SUBCRITICAL OR CONTROL EXCEEDS CRITICAL DEPTH,CC [KONTROL-ll-> DOWNSTRE M CONTROL; LET DEPTH2-DEPTHZ,FOR DEPTH2}YYC(21210 CONTINUE

IP(DEPTB2.LT.YYC(2GOTe 250l{ONTROL-lIP(DEPTHl.LT.YYC(lGOTO 230

C CHECK FOR W SHOUT DUB TO LATERALS OR DELZ-DBCPWRITE (NT, 6WRITE (lI r, 99l)

991 FOllllAT( SX, 'CIIECK FOR JUNCTION WASHOUT DUB T LATeRALS OR .C 'JUNCTION DROP,')

WRr' ' (NT, 979WRITE (lI r, 980)CALL PPM(DELZ,DEPTBl,DEPTB2,R,OO,YYC,YYH,ANGLE,PL,TEST,NT)IF (TESi'.Li' 01)GO TO 992WRITE(tlT,6JWRITE (lI r,993)

993 FOllllAT(5X,'*JUNCTION DROP IN ELEVAi'ION OR LATERAL PRESSURE-',C 'PLUS-MOMENTUM',I,5X,'CAUSES UPSTREAM PLOWS TO DOKINATEC'HYDRAULICS.',1,5X,'SUGGEST REANALYZB JUNCi'ION FOR HYDRAULICC 'COll'rROL. ' J

GCTO 3000992 WRITE(NT,911J971 FORMAT(SX,'*DCWNSTREAK PIPEFLOW DEFTB IS ASSUKED AS HYDRAULIC

C I CONTROL' )GCTO 300

C CHECK FOR JUNCTION W SHOUT230 WRITE (NT,5J

WRI'rE (lI r, 979)WRITE(NT,980)CALL FPM(DELZ,DEPTS1,DEPTH2,R,QQ,YYC,YYN,ANGLE,FL,TESi',NT)WRITE (N'1',972)

97Z F O R M A T ( S X , U P S 1 R E ~PIPEFLOW IS SUPERCRITICAL, ND DOWNSTREAM',C J,SX,'PIPEFLOW IS SOBCRITICAL OR UNDER PRESSURE,')IF (TEST.LT.O.)WRITE (Ni', 973)

973 FORM T (SX, "DOWNS'l'REAM FLOW DOMINAfES JUNCTION HYDRAULICS',C /,SX, SYDRAULIC JUMP MUST OCCUR UPSTREAM OF JUNCi'ION.')

IF(TESi'.Li'.O.)GOTO 300WRIT (NT, 974 J

974 FORMAT(5X,"UPSi'REAM FLOW DOMINATES JUNCTION HYDRAULICS')C [KONTRaL-51-> UPSTREAM FLOW IS SUPERCRITICAL ND W SHOUT OCCURS

KONTROL-5

UPSTREAM FLOW IS SUBCRITICAL;LET DEPTB2-YY


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HYDRAULIC ELEMENTS

C >UPSTREAM CONTROL

410 SIGN-I.DTOpnc (2)DLOWO.GaTO 45

c BEGIN DEPTH-DETERMINATIONC:420

450

DOWNSTRE M CONTROL:DTOP2.*RII)*.995DLOWnC(I)DG-. 5* (DTCP+DLOW)

WRITE(NT,S)WRITE (NT, 979)WRITE(NT,980)WRITE (NT, 6)IF(SIGN.LT.O.)GOTO 500

C. DOlrnSTREAM CONTROL.DO 475 J - l , l lCALL FPM(DELZ.DG.DEPTH2,R,CO,YYC,YYN,ANGLB,FL,TBST,NT)IF(TEST)460,2000,470

460 DLOW-CG

GOTO 475470 DTOP-DG475 DG-.5*(DLOW+DTOP)

GOTO 2000C: UPSTREAM CONTROL.500 DO 525 J - l ,13

CALL FPM(DELZ,DBPTHI,DG,R,QQ,YYC,YYN,ANGLE,FL,TEST,NT)IF (TEST) 510,2000,520

510 DLOW-DGGOTO 525

520 DTOP-DG525 DG-.5*(DLOW+DTOP)2000 CONTINOE

C OUTPUT RBSULTS

21012102

2100C

C3000C187C

CC

WRITE (NT,5)IF (KONTROL.LT.3)WRITE(NT.2101)IF (KONTROL.EO.3)WRITB(NT.2102)IF (KONTROL.EO.4)WRITE(NT.2101)IFIKONTROL.EO.5)WRITE{NT,2102)FORMAT(SX, DOWNSTREAM CONTROLASSUMED AT JUNCTION )FORMAT(5X, UPSTREAM CONTROL ASSUMED AT JUNCTION )WRITE (NT,6)IF {KONTROL.EQ.l.OR.KONTROL.EC.5)WRITE(NT.2100)DEPTHl,DGIF (KONTROL.NE.J.ANO.KONTROL.NE.5)WRITE(NT,2100)DG,DEPTH2FORMAT(5X, COMPUTBD UPSTREAM PIPEFLOW DEPTa(F T) _ , F 6 . 3 , / ,5X, COMPUTED DOWNSTRE M PIPBFLOW DEPTH(F T) ,F6 .3)

CONTINUE

FORMAT(16 ( * ) )

RETURNEND


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HYDRAULIC ELEMENTS

c ---------------------------------------------------------------------SUBROUTINE FPM(2,D1,D2,R,Q,YYC, YN,ANGLE,FL,TEST,NT)

c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -C SUBROUTINE DETERMINES, {TEST] - (FPM(IN)-FPM(OUTllc

DIMENSION R(4),Q(4),YIC(4),YYN(4),ANGLE(41,FL(41

DELTA(YY,RR)-ACOSRR-YI1/RRlAREA(YY,RRI-RR*RR*(ANG-.S*SIN(2.*ANG))AJ-1.M - I .CJ-O.DC-a.ANG-CELTA D1 ,R I IF-J .1415926/180.AI-AREA(D1,R(I))AZ-R 2)*RI2)*3.141593XI-Z. *R 21IF(DZ.GE.Xl)GOTO JANG-DELTA(D2,R(ZIIA2-AREA(D2,R(2)I

l T-.5*(D1+D2+FL(1)+FL(2))IF Q 3).LT 01)GOTO 20

c-------LATERAL. LINE.3ANG-DELTA(YYN(3),R(3Al-AREA(YYN(3),R(3D3-YIN(3)IF(YIC(3).GE.YYN(JGOTO 20

C . MILD FLOWXoT-FL(J)IF(YYC(3).GE.X)GOTO 5A3-R 3)*R 3)*3.141S93Xl-R 3) *2.IF(X.LT.X1)GOTO 10OJ-XlIF X.GT.xIIDJ-XIF(D3.GE.xl)GOTO 20

5 ANG-DELTA(YYc(3),R(3)A3=AREA(YYC(J),R(lllD3-YYC(3)

OTO 2010 ANG-DELTA(X,R(l))AJ-AREA(X,R(l))DJ-X

C-------LATERAL. LINE.420 IF{O 4).LT 00I)COTO 50

ANG-DELTA( YN(4),R(4"A4-AREA(YYN(4),R(C)1D4-YIN(4)IF(YYC(4).CE. YN(4)IGOTO 40

c: MILD FLOwX-T-Ft 4)IF(YYC(4) .CE.XIGOTO 25A4=R(C)*R(4)*3.141593X1=R(4)*Z.IF(X.LT.XIIGOTO 30D4-XIIF(X.GT.Xl)D4-XIF(D4.GE.XIIGOTO 40

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HYDRAULI C ELEMENTS

25 ANG-OELTA(YfC(4"R(4"A4-AREA[ YC(4),R(4D4-ryC(4)GOTO 4

30 ANG-DELTA(X,R(4U-AREA(X,R[4D 4 1

40 CONTINUE50 TEST-(Z+DI-D2)"(Al+A2)"16.1-Q(2)"Q(2)/A2+Q(1)*Q[1)"COS(ANGLE(l)"

C F)/Al+Q[J) Q[3) COS (ANGLE [J) P)/A3+Q(4, "Q(4)COS(ANGL (4) "P l/A4WRITE(NT,lOO)Dl,D2,D3,04,TEST

100 PORKAT(10X,4PIO.3,Pll.O)

RETURNEND


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HYDRAULIC ELEMENTS

PROGR M D T ENTRY

---OATA ENTRY FOR GRADUALLY VARIED FlOW WATER S U R F ~ C O E T e R ~ l N A T I O NFOR CONSTANT SLOPE RECT/TRAP/V-SHAPED OR PIPE---PAGE 1

E n t ~ rconsUnt channeL sloge SO; A L ~ O ~ A e l eVALUES ARE t .00001) TO (.Q9 J

Ent 'r length CFEET) 01 channel with CQnsUnt sLoge W > XL:ALLO.ABLE VALUES ARE Cll TO Cl00000l

Enter constant cnannel ftow CFS) :sa> 1;.:ALLO.ABLE VALUES ARE C.Ol l TO Cl000000 J

Enter channeL fr1etion factorCMannings) :=*> RN:ALLO.ABLE VALUES ARE C 008 ] TO C 9999 l

Enter ,h.nneL control-depthCFEET) 2 . )(NOTE: IF COl IS ENTERED. CRITICAL DEPTH IS ASSU ED

AS CONTROL:ALlO.ABLE VALUES ARE COl TO Cl00D l

TYPE: EXIT to leave progra_ ; TOP to go to top of pageMAIN to go t o maln .enu

YcaNT

---DATA ENTRY FOR GRADUALLY VARIED FLOW WATER SURFACE D E T E R ~ I N A T I O NFOR CONSTANT SLOPE RECTANGULAR CHANNEL---PAGE 2

Enter . a x 1 m u ~nuaber o f i t . ~ v . l sta oeuSl d in ~ r o f i l e a._> NNALLOWABLE VALUES ARE C10 l TO (1COO 1

Ent , h n n o t b dth(FEET) _ > 8:ALLO.ABLE VALUES ARE COl TO Cl0DD l

TYPE: EXlT to leave progrilll ; TOP to go t o top o f pageSACK to go back one page

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80

HYDRAULIC ELEMENTS

~ A T AENTRY fOR ADUALLY VARIED fl.OW WATE. SURFACE D E T E R ~ I N A T I O NfOR CONSTANT S I O P ~TRAPfZOIOAI HANNEL--PAGE Z

Entfr m mum number of t n t ~ r V l l lto b.used in pro1 i {e > NN:.ALLOWABLE VALUES U C10 l TO (1000 l

Enter , h . n n e l ~ a s e ' l l i d t n ( F E E T ) ,. ''''> " I ":AL.L.OWASL.E VAL.UES UE CO] TO (1000 ]

Enter chinnel Z v . lu ===> "t"(NOTE: Z QUOTIENT OJ: (HOIllZONTAL)/ (VERTICAL>':AL.L.OWASL.E VAL.UES UE [0] TO [100 J

TYPE; EXIT to lu 'V. progr ; TOP t o go to top of pol;.; lACK to go blek one page

---oATA ENTRT FOI GRADUALLY VARIED FLOW WATER S U ~ F ~ C EOETERMINATIOHFOR CONSTA.T SL.OPE (Vl -SHAPED C H ~ E L P A G EZ

Enter maximum number of i ~ t e r v i l sto beused in pr o f i le . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . : : Os> NH:'L.LOWASL.E VAL.UES ARE [10 J TO [ICeO J

Entel cn.nn_l % v.lue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . o . o . o . o ===> ..z .(NOrE: QUOTIENT 0 (HCRIlONTALJ/(VERTICALll: A L ~ O W A e LVALUES ARE (0] TO [100 ]

TYPE: EXIT to leave prograla ; TOP ta gg to tcp of page; SAC)( to 90 b a ~ kone p ~ g .


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HYDRAULIC ELEMENTS

PROGRAM 6

C SUBROUTINE GVF(KTYPElC

C ANALYSIS OF GRADUALLY VARIED FLOW W TERC SURFACE DETERMINATION

NT NUTC

COMIION /NOT/NOT

C INITIALIZE REQUIRED INPUT VARIABLESZ-O.O

CC

B .OOl0 0 . 05 0 0 .0XL-O.RN O.

YCONT-O.NN ODlAM O.

C READ DATA INPUTREAD FREE 5lS0,XL,O,RN,YCONT,NN,DIAM,B,Z

IF KTYPE.NE.B)GO TO 151CALL GVFPI NT,DIAM,SO,O,XL,RN,YCONT,NN)GO TO 153

151 CALL GVFCH NT,Z,B,SO,O,XL,RN,YCONT,NN)153 CONTINUECC

RETURNEND

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c ---------------------------------------------------------------------SUBROUTINE GVFCB(NT,Z,B,SO,Q,XL,RN,YXNT,NN}c ---------------------------------------------------------------------CC ANALYSIS OP GRADUALLY VARIED PLOW W A ~ E RC SURFACE DETERMINATION

C C O K K O N / N U ~ P / N U T P , I S V

C FUNCTION O ~ P I N I T I O N SAREA(YY)-YY*(B+Z*YY)PER(YY)-B+2.*YY*SQRT(1.+Z*Z)YCTP(YY)-1.-o*Q*(B+2.*Z*YY)/(o*AREA(YY) **3.)YNMP(YY)-I.-o*Q*CON/(AREA(YY)**l.llll/PER(YY)**1.l333)DL(YY)-YCTP(YY)/(YNMF(YY)*SO)FPM(YY)-GAM*(YY*YY*(S*.5+Z*YY/3.)+Q*Q/(o*AREA(YY)ENEROY(YY)-YY+Q*Q/(2.*G*ARSA(YY) **2.)

IF(B.LE.O.)S-.OOOlCC------CONSTANTS

GAM-02.4G - n . lCON-(RNll.486)**2./SOW R I ~ E(NT, 187

5 FORMAT(15( - WRITE (NT,200)

200 FORMAT(5X, GRADOALLY VARIED FLOW PROFILE INPUT I N F O R M A ~ I O N I )WRITE (NT,5)W R I ~ E ( N T , 2 0 2 ) S D , X L , Q , R N , Y X N T , N N , B , Z

202 FORMAT(5X, CONSTANT CHANNEL SLOPE(FEET/FEET) ,F8.6,I,C 5X, CHANNEL L E N G T H ( F E E ~ )- , r12.2,I ,C SX, CONSTANT CHANNEL FLOW(CPS) , 1 1 2 . 2 , / ,C 5X, CONSTANT CBANNEL FRICTION FACTOR(MANNING) ,F8.6,1,C 5X, ASSUMED CHANNEL C O N ~ R O LDEPTH(FEET) , F 8 . 2 , I ,C 5X, MAXIMUM NUMBER OF INTERVALS IN PROFILE ,16,1,C S X , C O N S ~ A N TCHANNEL SASEWIDTB(PEET) - ,FI0.2,I,C 5 X , C O N S ~ A N TCBANNEL Z FACTOR - ,F10.4)

C-----------------------------------------------------------C PROFILE DETERMINATIONNN-NN 2UPIT-5000.DOWN-O.YC-IOOD.DO 520 1-1 ,22IF(CTF(YC514,521.515

514 DOWN-YCGCTO 520

515 UPIT-YC520 YC-(UPIT+OOWN) *.5521 I F ( Y ~ N T . E Q . O . ) Y K N ~ ~ Y C

U P I ~ ~ 5 0 0 0 .

DOWN-O.YN-IOOO.DO 530 1 - 1 2 2IF(YNMF(YN523.531.524

523 OOWN YNGOTO 530


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HYDRAULIC ELEMENTS

524 U P I T ~ , { I53 YNo(UPIT+OOWN) * ,5531 CONTINUE

~ I T E { N T , 5 3 3 ) Y N , Y C

533 FORMAT(5X, NORMAL OEPTH{FEET) 0 , P 9 . 2 , / ,C 5X,'CRITICAL OEPTH(PEET) - ,F9 ,2 )

535 IF(YN,LE,YC)GOTO 550C

CIF(YKNT.LT.YC)GOTO 545

SIGN--l.DYo(YKNT-YN).99S/NNI


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84

C

HYDRAULIC ELEMENTS

DX_DY*(DL(Y)+DL(Y2)+4.*DL(YINT+SIGN*I*DY/3.SL-SL+DXIP(SL.GT.XL)GOTO 582Y-Y2E-ENERGY(Y)FH-PI H(Y)IP(I.EQ.NN-l.AND.SL.LT.O.)SL-XL

1580 VV-SQRTE-Y)*64.36)580 WRITE(NT,564)SL,Y,VV,E,FH

CC

GOTO 1000

582 Y-Y2-SIGNZ.DY*(SL-XL)/DXE-ENERGY(Y)FH-FPII(Y)VV-SQRTE-Y)64.36)WRITE(NT.564)XL.Y,VV,E.PIIGCTO 1600

1500 CONTINUEWRITE (NT,1505)

1505 FORMAT(/lX, WARNING. PROFILE DEPTB INCREIIENT IS . TOO SHALL. , j ,

C6X, REATTEIIPT PROBLEII WITB A SLIGHTLY DIFFERENT CONTROL DEPTH ,j,C 6X. OR A FEWER NUIIBER OF PROFILE INTERVALS. )1600 CONTINUE1000 CONTINUE

C FORMATSC180 FORMAT(76( )187 FORMAT(76( )C

RETURNEND


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HYDRAULIC ELEMENTS

PROGR M : D T ENTRY

---oATA ENTRY FOR GR OU LLY VARIED 'LOW W TER SURFACE D e T E R ~ l N A T I NFOR PIPE--f AGE Z

Enter xieu. nunber of intervals to btu3ed ~ pr o f i le ==*> NNAll.OWASCE VACUES ARE [10 J TO [1000 J

Enter CQnstant p i ~ diam.t.rCINCHESJ z=_>:ALLOWASLE VALUES RE [3] TO (24Q l

TYPE; EXIT to le . . . . prag r.a ; TOP to go to top of p a ~ e; e.l.CK to go back ont pag t

orAM

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HYDRAULIC ELEMENTS

PROGR M 7

C SUBROOTINB GVFPI(NT,OIAM,SO,O,XL,RN,YINT,NN)CCC ANALYSIS or GRADUALLY VARIED FLOW W TERC SURFACE DETERMINATIONC

CC

OELTA(YY)-ACOSR-YY) R)AREA(YY)-R*R*(ANG-.5*SIN(2.*ANGPER(YY,-2.*R*ANGTW(YY'-2.*R*SIN(ANG)YCTP(YY,-1.-o*O*TW(YY) (GOAREA(YY) **3.)YNMP(YX)-1.-o*O*CON/(AREA(yy)*o3.3333/PER(yy)*o1.3333)OL(YY)-YCTP(YY)/(YNMF(YY)*SO)FPM(YX)aCAM*(O*O/(G*AREA(YX+YBoAREA(YY)ENERGY (YX)-YY+QoO/(2.oG*AREA(YX)*2.)

C CONSTANTSGAM-n G-32.2CON-(RN/1 86)*2./S0WRITE(NT,187)

6 FORMAT(16('-'I)WRITE (NT,200)

200 PORMAT(5X,'GRADOALLY VARIED FLOW PROFILE INPUT INFORMATION,')WRITE (NT.6)WRITE(NT,202)SO,XL,O,RN,YINT,NN,OIAM

202 FORM T (5X, 'CHANNEL SLOPE(FEET/FEET) - , p8 . 6 . / ,5X,'CBANNEL LENGTB(FEET) - , F1 2 .2 .1 .

C 5X,'CONSTANT CHANNEL FLOW(CFS) - ,F12 .2 , / ,C 5X,'CONSTANT CBANNEL FRICTION PACTOR(MANNING) - .F8.6,I ,C 5X,'ASSUMED CHANNEL CONTROL DEPTB(PEET) - ,F8.2,1.C 5X,'MAXIMOM NUMBER OF INTERVALS IN PROFILE - ,16,1,C 5X,'CONSTANT PIPE DIAMETER(INCBES) - ,Fa .3)

C-----------------------------------------------------------C PROPILE DETERMINATIONC

LOGIC-ONN-2*NNDIAM-DIAM/12.R-DIAN/l.DMAX-.94*DIAN

512 UPIT-DIAKDOWH O

YC-DMAX/2.DO 520 1-1,22ANG-DELTA (YC)IF(YCTF(YC514,521,515

5 4 DOWN YCGOTe 520

515 UPIT-YC520 YC-(OPIT+DOWN) *.5521 IF (YC.GT.DIAN)YC-DIAM

IP(YKNT.EO.O.)YKNTYCTEST-.49a*DIAM*o2.6667*SO**.5/RNIF(O.LT.TEST)GOTO 522WRITE (Nt,5221)

5221 FORMAt(5X,'-)NORMAL PIPEFLOW IS PRESSURE FLOW',


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YN-DIAII 2.GOTO 531

HYDRAULIC ELEMENTS

522 UPIT-OMAX

523

524530531

533C

5331C

534535

CC

DOWN-D.YN-OMAX/2.00 530 1 - 1 , 2 2ANG-OELTA(YN)IP(YNMP(YN))523,531,524DOWN-YllGOTO 530UPIT-YNYN-(UPIT+OOWN)-.5CONTINUEDl lAX-.82*DIAM

IP(YN.LE.DIAII)WRITE(NT,533)YN,YCPORMAT(5X. NORMAL DEPTB(PEET) , P 9 . 2 , / ,5X. 'CRITICAL DEPTII(PEETI .F9 .21IP(YN.LT.DIAII.AND.YN.GT.OMAX)WRITE(NT,5331)PORMAT(5X. NOTE.GIVEN NORM L DEPTB IS LOWER VALUE r TWO POSSIBLE,/,SX.'SUGGEST CONSIDERATION OP W VE ACTION, UNCERTAINTY, ETC. )IF (YN.GT.DIAIII WRITE (NT. 5341 YCFORMAT(5X, 'CRITICAL DEPTB(PEETI ,P9 .2 )IP(YN.LE.YC)GOTO 550

IF(YKNT.LT.YC)GOTO 545

IP(YKNT.LT.YN)GOTO 5351IF (YN.GE.DMAXILOGIC-lIF(LOGIC.EQ.lIGOTO 2IF (YKNT.GT.DIAMIYENT-DIAMGOTO 5359

5351 IF (YN.GE.DMAX)LOGIC-2IF(LOGIC.EQ.2)GOTO 2000

5359 SIGN--l.DY-(YKNT-YN) .99B/NNKODE-lGOTO 560

545 SIGN-I.C

C

C

DY- (YC-YltNT) NN

KODE-2GOTO 560

550 IP(YKNT.LE.YC)GOTO 555C

C

IP(YN.GE.DMAX)LOGIC-.IP(LOGIC.EQ.4)GOTO 2000IF (YltNT.GT.DIAII)YKNT-OIAIISIGN--l.DY- (YitNT-YCl/NNKOOE-lGOTO 560

555 SIGN-I.IF(YKNT.LT.YN)GOTO 5559IF (YN.GE.DMAX)LOGIC-S

IF(LOGIC.EQ.51GOTO 20005559 OY-(YN-YKNTl .99B/NN11:00-2

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560

HYDRAULIC ELEMENTS

SL O.IF(ABS(OY).LT 0005)GOTO 1500Y-UNTANG-DBLTA(Y)E-ENERGY(Y)CALL YBAR(y,DIAR,YB,NT)

FM-Pl M(Y)C OUTPUT

262263C

WRITE(NT,l80)I P ~ O D E . E Q . l I W R I T N T , 2 6 2 ) Y ~ N T

IF(KODE.EQ.2)WRITE(NT,263)YKNTFORMAT(5X, DOWNSTREAR CONTROL ASSOMED DEPTH(PT) - , PS.2)FORMAT (5X, UPSTREAM CONTROL ASSUMED DEPTB(PT) - ,PS.2)

WRITE (NT,180)WRITE (NT,254)

264 FORMAT(5X, GRADOALLY VARIED PLON PROfILE COMl UTED INPORMATION, )IIIIITS(NT,6)IIIIITS (NT, 2 U )

261 PORMAT(2X, DISTANCE PROM',6X,'PLOWDEPTB',3X,'VLOCITY',6X, 'SPECIFIC' ,8X,C PRESSORE+ ,/,3X, CONTROL(PT) ,9X, (PT) ,6X, (PT/SEC), ,

5X, ENERGY CPT)C 4X, MOMENTOMCPOOHOS) )VV-SQRTC(E-Y)*64.J6)WRITECNT,564)SL,Y,VV,E,PM

C-------PROPILE CALCULATION564 FORMATC2FI5.3,Pll.3,FlS.3,2X,PlS.2)

C

DO 58 r-I,NN,2YZ-YKNT+SIGN*OY*CI+I)ANG-DELTA (Y)TEMPI-DL(Y)ANG-DELTACY2)TEMl 2-DL(Y2)ANG-DELTACYBNT+SIGN*I*DY)TEMP3-DL(YBNT +SIGN*I*DY)DX-DY*(TEMPl+TEMl'2+4.*TEMl'3)/3.SL-SL+DXIF(SL.GT.XL)GOTO 582Y-y2ANG-DELTACY)E-ENERGYCYCALL DAR(Y,DIAM,n,NT)FM-rPMCY)IFCI.EQ.NN-I.AND.SL.LT.O.)SL-XL

1580 VV-SQRT(E-Y)*64.36)580 WRITE(NT,564)SL,Y,VV,E,FM

CGOTO 1000

5S2 Y-Y2-SIGN2.*DY*CSL-XL)/DXANG-DELTACY)S-ENERGY(Y)CALL YBAR(Y,DIAM,YB,NT)FM-PPM(Y)


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1000

1500

15 5

2000

2005

2100C

HYDRAULIC ELEMENTS

VV.SQRT( (E-lC) 54,36)WRITE(NT,564)XL,Y,VV,E,FMCONTINUBGOTO 2100CONTINUBWJtITE(NT.1505)FORKAT(/lX,WARNING,PROFILE DEPTH I N R E ~ E N TIS TOO SMALL. ,

C/6X, REATTEMPT PROBLEM WITa A SLIGHTLY DIFFERENT CONTROL DEPTH ,I.C 6X, OR A FEWER NUMBER OF PROFILE INTERVALS, )

OTO 2100CONTINUEWRITE(NT,6)HIUTE(NT,200S)FORHAT(5X, PLOW PROFILB OEPTBS ARB GREATBR TH N 8 2 0 I A M E ~ E R .

C I,SX, SUGGEST CONSIDERATION or SEALED FLOW IN THIS RE CH DUE TO ,I,C 5X, W VE ACTION, UNCERTAIN1 Y, ETC, )

CONTINUE

C FORIIATSC180187C

FORIIAT 76 . FOlUIAT 76 . ) )

RETURNI lNl)

89


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102/142

HYDRAULIC ELEMENTS EXAMPLE PROBLEMS

Proolem 5.1 .2 .

Determine normal depth and c r i t i c a l depth data for a 48 inch BCPwith a s lope of 0.010 f t f t and a flow o f 100 cfs . Use aManning's f r i c t i o n fac tor o f n = 0.013. Note t h a t f low i s

su p e rc r i t i c a l . Fr > 1) .

CRITICAL DEPTH

NORMAL EPTH

4 ' R.CP. 0-0.010

. PIPEFLOW HYDRAULIC INPUT INFORMATION

PIPE DIAMETER FEET) = 4.000PIPE SLOPE FEET/FEET) 0100PIFEFLOW CFS) = 100.00MANNINGS FRICTION FACTOR = .013000

CRITICAL-DEPTH FLOW INFORMATION:

CRITICAL DEPTH FEET) 3.03

CRITICAL FLOW AREA SQUARE FEET) = 10.212CRITICAL FLOW TOP-WIDTH FEET) = 3.429CRITICAL FLOW PRESSURE + MOMENTUM POUNDS) = 2765.09CRITICAL FLOW VELOCITY FEET/SEC.) 9.792CRITICAL FLOW VELOCITY HEAD FEET) = 1.49CRITICAL FLOW HYDRAULIC DEPTH FEET) = 2.98CRITICAL FLOW SPECIFIC ENBRGY FEET) 4.52

NORMAL-DEPTH FLOW INFORMATION:

NORM L DEPTH FEET) = 2.46FLOW AREA SQUARE FEET) = 8.09FLOW TOP WIDTH FEET) = 3.894FLOW PRESSURE + MOMENTUM POUNDS) = 2931.64FLOW VELOCITY FEET/SEC.) 12.353FLOW VELOCITY HEAD FEET) = 2.370HYDRAULIC DEPTB FEET) = 2.08FROUDE NUMBER 1.510SPECIFIC ENERGY FEET) = 4.83

91


103/142

92


Problem 5.1.3.

Determine normal depth and crit ical depth data for a 48 inch RCPwith a slope of 0.010 f t / f t and a flow of 150 cfs using aManning s frict ion factor of n

=0.013. Note that a circular

conduit flowing a t a depth of 82% of the pipe diameter conveys thesame discharge as a conduit flowing fu l l . Consequently, thecomputer output suggests the designer may wish to consider theconduit flowing full .

o

"Eo

'll

d~Q

-

R I T f ~ LDill : :::":: ... ~NORMAL DEPTH

4' R.C.P $0=0.010 \. )D- Depth o Flow d =Diameter of Conduit

. . .

PIPEFLOW HYDRAULIC INPUT INFORMATION

PIPE DIAMETER FEET) = 4.000PIPE SLOPE(FEET/FEET) .0100PIPEFLOW CFS) = 150.00MANNINGS FRICTION FACTOR = .013000CRITICAL-DEPTH FLOW INFORMATION:

CRITICAL DEPTH FEET) = 3.60CRITICAL FLOW AREA SQUARE FEET) = 11.901CRITICAL FLOW TOP-WIDTH FEET) = 2.412CRITICAL FLOW PRESSURE + MOMENTUM POUNDS) = 4923.58CRITICAL FLOW VELOCITY(FEET/SEC.) 12.604CRITICAL FLOW VELOCITY HEAD (FEET) 2.47CRITICAL FLOW HYDRAULIC DEPTH FEET) = 4.93CRITICAL FLOW SPECIFIC ENERGY FEET) = 6.06NOTE,GIVEN NORMAL DEPTH IS LOWER VALUE OF TWO POSSIBLE.SUGGEST CONSIDERATION OF WAVE ACTION, UNCERTAINTY, ETC.

==_== _ c... = = . = = = = ~ = = = = = = = = = = = = = = : = = = = = = = = _ = = = = = = = = = = = = = = =NORMAL-DEPTH FLOW INFORMATION:

NORMAL DEPTB FEET) = 3 . 7FLOW AREA SQUARE FEET) = 11.57FLOW TOP WIDTH(FEET) 2.722FLOW PRESSURE + MOMENTUM POUNDS) s 4932.98FLOW VELOCITY (FEET/SEC.) - 12.968FLOW VELOCITY HEAD FEET) = 2.611HYDRAULIC DEPTH FEET) = 4.25FROUDE NUMBER 1.109SPECIFIC ENERGY FEET) = 6 .08


104/142


Problem 5 1 4

Determine normal depth discharge of a 48 inch RCP on a s lope of0.010 f t / f t with a flow depth of 3 feet Use a Manning s f r i c t ionfac tor of n = 0 013

. . _ _-_._-----PIPEFLOW HYDRAULIC INPUT INFORMATION

FIFE DIAMETER FEET) = 4 000FLOWDEPT8 FEET) s 3 000PIPE SLOPE(FEET/FEET) = 0100MANNINGS FRICTION FACTOR = 013000 > NORM L DEPTH FLOW CPS) = 130 99

NORMAL-DEFTH FLOW INFORMATION.

NORM L DEPTH FEET) 3 00FLOW AREA SQUARE FEET) = 10 11FLOW TOP WIDTH FEET) = 3 464FLOW PRESSURE KOMENTUM POUNDS) = 4137 36FLOW VELOCITY (FEET/SEC.) = 12 956FLOW VELOCITY READ FEET) = 2 607HYDRAULIC DEPTB FEET) = 2 92FROUDE NUMBER = 1 337SPECIFIC ENERGY FEET) a 5 61

Problem 5 1 5

Determine the diameter of circu lar conduit required to discharge144 c f s when f lowing f u l l Assume s lope of pipe i s 0.010 f t / f tand the Manning s factor of n = 0.013

. _ ---------- .- . . ----- . . ._.---_ . . . . . . -- . . . . . . . . - . _ _._-_.-PIPEFLOW HYDRAULIC INPUT INFORMATION

PIPE SLOPE(FEET/FEET) = 0100PIPEFLOW CFS) = 144 00MANNINGS FRICTION FACTOR = 013000>SOFFIT-FLOW PIPE DIAMETER FEET) 4 004

93


105/142

94


Problem 5 1 6

Determine the slope t ha t s required for a 48-inchdiameter pipe to convey 200 cfs when t i s flowing ful l .Manning s f r ic t ion factor of n = 0.013.

4-foot)Assume a

. . . .

PIPEFLOW HYDRAULIC INPUT INFORMATION

PIPE DIAMETER FEET) = 4.000FLOWDEPTH FEET) 4.000PIPEFLOW(CFS) = 200.00MANNINGS FRICTION FACTOR = .013000>SOFFIT-FLOW PIPE SLOPE(FEET/FEET) .0194

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = ~ = = == = =


106/142

_ _ _ . HYDRAULIC ELEMENTS EXAMPLE PROB.:L:::E 'M 'S'-

Problem 5.2.1.

Determine normal depth and c r i t i c a l depth data for a concretel i ned t rapezoidal channel having a Z o f 2, a basewidth of 6 f t .longi tudinal s lope of 0.002 f t / f t and conveying s o cfs . Use aManning s f r i c t i o n fac tor of n : 0.015. Note t h a t flow i ss u b c r i t i c a l (F r < 1).

NORMAL DEPTH

~ C R I T I C A LE P T H -Z 2

I 6 1

9S

_._ .- _ . ____ _ _ _----._-- _ _--CHANNEL INPUT INFORMATION

----------------------CHANNEL Z(HORIZONTAL/VERTICAL) = 2.00BASEWIDTH(FEET) = 6.00CONSTANT CHANNEL SLOPE(FEET/FEET) .002000UNIFORM FLOW(CFS) = 500.00MANNINGS FRICTION FACTOR .0150

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =


> NORMAL DEPTH(FEET) = 4.26

FLOW TOP.- WIDTH (FEET)=

23.0461.83LOW AREA (SQUARE FEET) -HYDRAULIC DEPTH(FEET) = 2.68FLOW AVERAGE VELOCITY(FEET/SEC.)UNIFORM FROUDE NUMBER - .870PRESSURE + MOM NTUM (POUNDS) =AVERAGED VELOCITY HEAD(FEET)SPECIFIC ENERGY(FEET) = 5.274


B 09

14444.791.015

CRITICAL FLOW TOP-WIDTH(FEET) 21.89CRITICAL PLOW AREA (SQUARE FEET) = 55.41CRITICAL FLOW HYDRAULIC DEPTH(FEET) = 2.53CRITICAL FLOW AVERAGE VELOCITY(FEET/SEC.) = 9.02CRITICAL DEPTH(FEET) = 3.97

CRITICALFLOW PRESSURE MOMENTUM[POUNDS) =

14307.55AVERAGED CRITICAL FLOW VELOCITY BEAD(PEET) 1.264CRITICAL FLOW SPECIFIC ENERGY(PEET) = 5.237


107/142


Problem 5.2.2.

Determine normal depth and c r i t i c a l depth data for a concretelined trapezoidal channel having a Z of 2, a basewidth of 6 feet ,longitudinal slope of 0.005 f t f t and conveying 500 c f s . Use aManning's f r i c t io n fac to r of n = 0.015. Note t h a t flow i ssupercr i t i ca l ( Fr > 1).

NORMAL DEPTH :;..;;;r

I 6 I

****************************************************** CHANNEL INPUT INFORKATION

CHANNEL Z(HORIZONTAL/VERTICAL) = 2.00BASEWIDTH(FEET) = 6.00CONSTANT CHANNEL SLOPE(FEET/FEET) = .005000UNIFORM FLOW(CFS) = 500.00KANNINGS FRICTION FACTOR = .0150

========================================================a=c=================NORMAL-DEPTH FLOW INFORMATION:

> NORMAL DEPTH{FEET) =FLOW TOP- WIDTH(FEET) =FLOW AREA(SQUARE FEET) =

3 .4219 .69

43 . 99HYDRAULIC DEPTH{FEET) = 2.23FLOW AVERAGE VELOCITY{FEET/SEC.) =UNIFORM FROUDE NUMBER = 1.340PRESSURE MOMENTUM{POUNDS) =AVERAGED VELOCITY HEAD(FEET) =SPECIFIC ENERGY(FEET) = 5.430

11 .37

14878.122.006

~ ==== ===============================CRITICAL-DEPTH FLO,I INFORMATION:

----------------------------------------------------------------------------CRITICAL FLOW TOP-WIDTH(FEET) = 21.89CRITICAL FLOW AREA (SQUARE FEET) = 55.41CRITICAL FLOW HYDRAULIC DEPTH(FEET) = 2.53CRITICAL FLOW AVERAGE VELOCITY(FEET/SEC.) = 9.02CRITICAL DEPTH(FEET) = 3.97CRITICAL FLOii PRESSURE MOMEN,UH (POUNDS) - 14307.55AVERAGED CRITICAL FLOW VELOCITY HEAD(FEET) 1.264CRITICAL FLOW SPECIFIC ENERGY(FEET) = 5.237


108/142


Problem 5.2.3.

For a concrete l ined t rapezoidal channel with a flow depth of 4feet determine the discharge rate. Assume a Z of 2 a basewidthof 6 f ee t longi tudinal slope of 0.005 f t f t and a Manning s

fr ic t ion factor of n = 0.015.

97

. . . .

CHANNEL INPUT INFORMATION

NORMAL DEPT8(FEET) = 4.00CHANNEL Z HORIZONTAL/VERTICAL) = 2.00BASEWIDTH FEET) = 6.00CONSTANT CHANNEL SLOPE(FEET/FEET) = .005000MANNINGS FRICTION FACTOR - .0150

============================================================================

NORMAL-DEPTH FLOW INFORMATION.

NORMAL DEPTH FLOW CFS) =FLOW TOP- WIDTH FEET) =

692.2622.00

FLOW AREA SQUARE FEET) HYDRAULIC DEPTH FEET) = 2.55FLOW AVERAGE VELOCITY(FEET/SEC.)UNIFORM FROUDE NUMBER = 1.365PRESSURE MOMENTUM POUNDS) -AVERAGED VELOCITY HEAD FEET) =SPECIFIC ENERGY FEET) = 6.373

56. 00

12.36

22241.032.373

=================================E E==S=====================================

CRITICAL-DEPTH FLOW INFORMATION:----------------------------------------------------------------------------

CRITICAL FLOW TOP-WIDTH(FEET) = 24.68CRITICAL LOW AREA SQUARE FEET) = 71.62CRITICAL FLOW HYDRAULIC DEPTH(FEET) = 2.90CRITICAL FLOW AVERAGE VELOCITY(FEET/SEC.) = 9.67CRITICAL DEPTH FEET) = 4.67CRITICAL FLOW PRESSURE MOMENTUM POUNDS) = 21282.92AVERAGED CRITICAL FLOW VELOCITY HEAD FEET) 1.451CRITICAL FLOW SPECIFIC ENERGY (FEET) m 6.120


109/142

98


Prd:llem 5.2.4.

Calculate the slope required to discharge 500 c f s in a concretelined trapezoidal channel having a flow depth of 4 feet. Assume aZ of 2, a basewidth of 6 f ee t and a Manning s f r i c t io n fac tor of0.015 f t / f t

.


NORMAL DEPTH FEET) = 4.00CHANNEL Z HORIZONTAL/VERTICAL) = 2.00BASEWIDTH FEET). 6.00UNIFORM FLOW CFS) = 500.00MANNINGS FRICTION FACTOR = .0150

D ~ D SNORMAL-DEPTH FLOW INFORMATION:

> CHANNEL SLOPE FEET/FEET) = .00261FLOW TOP- WIDTH FEET) = 22.00FLOW AREA SQUARE FEET) - 56.00HYDRAULIC DEPTH FEET) = 2.55FLOW AVERAGE VELOCITY FEET/SEC.) = 8.93UNIFORM FROUDE NUMBER - .986PRESSURE MOMENTUM POUNDS) = 14308.88AVERAGED VELOCITY HEAD FEET) = 1.238SPECIFIC ENERGY FEET) = 5.238

========================================= ==================================

CRITICAL-DEPTH FLOW INFORMATION:----------------------------------------------------------------------------

CRITICAL FLOW TOP-WIDTH FEET) = 21.89CRITICAL FLOW AREA SQUARE FEET) = 55.41CRITICAL FLOW HYDRAULIC DEPTH FEET) = 2.53CRITICAL FLOW AVERAGE VELOCITY FEET/SEC.) 9.02CRITICAL DEPTH FEET) = 3.97CRITICAL FLOW PRESSURE MOMENTUM POUNDS) = 14307.55AVERAGED CRITICAL FLOW VELOCITY HEAD FEET) = 1.264CRITICAL FLOW SPECIFIC ENERGY FEET) = 5.237


110/142


Problem 5.2.5.

Determine the basewidth required for a concrete t rapezoidalchannel to convey 500 cfs a t a flow depth of 4 feet. Assume the Zi s 2 the longi tud ina l slope of 0.005 f t f t and a Manning sfriction factor of n = 0.015.


NORM L DEPTH(FEET) = 4.00CHANNEL Z HORIZONTAL/VERTICAL) = 2.00CONSTANT CHANNEL SLOPE(FEET/FEET) = .005000UNIFORM FLOW CFS) = 500.00MANNINGS FRICTION FACTOR = .0150

99

~ ~


> BASEWIDTH FEET) = 2.89FLOW TOP- WIDTH FEET) = 18.89

43.57LOW AREA SQUARE FEET) =HYDRAULIC DEPTH(FEET) = 2.31FLOW AVERAGE VELOCITY(FEET/SEC.)UNIFORM FROUDE NUMBER = 1.332PRESSURE MOMENTUM POUNDS) =AVERAGED VELOCITY HEAD FEET) =SPECIFIC ENERGY FEET) = 6.045

11 . 4 8

15226.212.045

s c ~ _

CRITICAL-DEPTH FLOW INFORMATION.

CRITICAL FLOW TOP-WIDTH(FEET) = 21.12CRITICAL FLOW AREA SQUARE FEET) = 54.72CRITICAL FLOW HYDRAULIC DEPTB(FEET) = 2.59CRITICAL FLOW AVERAGE VELOCITY(FEET/SEC.) = 9.14CRITICAL DEPTH(FEET) = 4.56CRITICAL FLOW PRESSURE MOMENTUM POUNDS) 14665.52AVERAGED CRITICAL FLOW VELOCITY BEAD (FEET) 1.297CRITICAL FLOW SPECIFIC ENERGY FEET) = 5.854


111/142

100


Prcblem 5.2.6.

Determine the s ide slopes Z) o f a concrete t rapezoidal channeldischarging 500 cfs a t a flow depth of 4 fee t . Assume a channelbasewidth of 6 f ee t longi tudinal slope of 0.005 f t f t and aManning s fr ic t ion factor of n = 0.015.

.

CBANNEL INPUT INFORMATION

NORMAL DEPTB FEET) = 4.00BASEWIDTH FEET) = 6.00CONSTANT CHANNEL SLOPE(FEET/FEET) = .005000UNIFORM FLOW CFS) = 500.00MANNINGS FRICTION FACTOR = .0150

= = = = = = = = = = = = = = = = = = = = = = ~ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =


1 .05 > CHANNEL Z-FACTOR =FLOW TOP- WIDTH FEET) =FLOW AREA SQUARE FEET) =

1 4 . 3 740.75

HYDRAULIC DEPTH FEET) = 2.83FLOW AVERAGE VELOCITY(FEET/SEC.) =UNIFORM FROUDE NUMBER = 1.284PRESSURE MOMENTUM POUNDS) =AVERAGED VELOCITY HEAD FEET) KSPECIFIC ENERGY FEET) = 6.338

12.27

16277.762.338

======_======= a =================================================== a=


CRITICAL FLOW TOP-WIDTH FEET) = 15.59CRITICAL FLOW AREA SQUARE FEET) = 49.46CRITICAL FLOW HYDRAULIC DEPTH FEET) a 3.17CRITICAL FLOW AVERAGE VELOCITY(FEET/SEC.) = 10.11CRITICAL DEPTH FEET) = 4.58CRITICAL FLOW PRESSURE MOMENTUM POUNDS) = 15818.05AVERAGED CRITICAL FLOW VELOCITY HEAD (FEET) = 1.587CRITICAL FLOW SPECIFIC ENERGY FEET) = 6.168


112/142


Problem 5.2 .7 .

Given a t rapezoidal channel with a s lope of .014 f t / f t abasewidth of 5 feet, and a Z of 2, discharging 250 cfs , determinewhere a hydraul ic jump w i l l occur when the channel changes to as lope of 0.0015 f t / f t . Assume a Manning s f r i c t i on fac tor ofn = 0.015 and a channel length of 1000 f ee t .

Step 1 . Determine normal depth data for a t rapezoidalchannel with a slope of 0.014 f t / f t .

step 2. Determine the normal depth pressure plus momentumof a trapezoidal channel with a slope of 0.0015 f t / f t .

Step 3. Knowing t h a t t he depth of f low i s 2.00 f e e t a t thegrade break from step 1), determine a gradually varied flowprof i le for the channel. Note t ha t the jump will occur wherethe P M from step 2 equals the P ~ from step 3

, ,(CRITICAL DEPTH

' NORMAL DEPTH LINE~ - - - - - - . - - -.

ONTROLSE TION

-.. . . . . . .-------if -Assumedjump shape :

: 10C\I

SoaO.0015MILD SLOPE

115

101


113/142

102


Step 1: Determine normal depth data for a t rapezoidal channelwith a slope of 0.014 f t / f t

. . . CHANNEL INPUT INFORMATION

CHANNEL Z HORIZONTAL/VERTICAL) = 2 00BASEWIDTH FEET) = 5 00CONSTANT CHANNEL SLOPE FEET/FEET) = 014000UNIFORM FLOW CFS) = 250 00MANNINGS FRICTION FACTOR = 0150

================================================= ==========================


2 00

NORMAL DEPTH FEET)=

FLOW TOP- WIDTH FEET) =FLOW AREA SQUARE FEET) =

13 0018 01

HYDRAULIC DEPTB FEET) = 1 39FLOW AVERAGE VELOCITY FEET/SEC.) =UNIFORM FROUDE NUMBER = 2 078PRESSURE MOMENTUM POUNDS) =AVERAGED VELOCITY HEAD FEET) SPECIFIC ENERGY FEET) = 4 993

1 3 B8

7682 562 992

=============== ==========================================================


CRITICAL FLOW TOP-WIDTB FEET) = 16 74CRITICAL FLOW AREA SQUARE FEET) = 31 92CRITICAL FLOW HYDRAULIC DEPTH FEET) = 1 91CRITICAL FLOW AVERAGE VELOCITY FEET/SEC.) = 7 83

CRITICAL DEPTH FEET)=

2 94CRITICAL FLOW PRESSURE + MOMENTUM POUNDS) = 6191 97AVERAGED CRITICAL FLOW VELOCITY HEAD FEET) = 952CRITICAL FLOW SPECIFIC ENERGY FEET) = 3 B88


114/142


Step 2: Determine normal depth and pressure plus momentum of atrapezoidal channel with a slq;>e of 0.0015 f t / f t

. . .CHANNEL INPUT INFORMATION

CHANNEL Z HORIZONTAL/VERTICAL) = 2 00BASEWIDTB FEET) = 5 00CONSTANT CHANNEL SLOPE{FEET/FEET) = 001500UNIFORM FLOW CFS) 250 00MANNINGS FRICTION FACTOR = 0150

= = = ~ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = . = . ~ = = =


NORMAL DEPTH FEET) = 3 44FLOW TOP- WIDTH FEET) = 1 8 7 740 92LOW AREA SQUARE FEET)

HYDRAULIC DEPTH FEET) = 2 l8FLOW AVERAGE VELOCITY FEET/SEC.)UNIFORM PROUDE NUMBER = 729PRESSURE MOMENTUM POUNDS) =AVERAGED VELOCITY HEAD FEET) =SPECIFIC ENERGY FEET) = 4 022

6 11

6506 47580

=============================== __ ==_.== ======================:=========CRITICAL-DEPTH FLOW INFORMATION:

CRITICAL FLOW TOP-WIDTH FEET) = 16 74CRITICAL FLOW AREA SQUARE FEET) 31 92CRITICAL FLOW HYDRAULIC DEPTH FEET) 1 91CRITICAL FLOW AVERAGE VELOCITY FEET/SEC.) = 7 83CRITICAL DEPTH FEET)

=2 94

CRITICAL FLOW PRESSURE MOMENTUM POUNDS) = 6191 97AVERAGED CRITICAL FLOW VELOCITY HEAD{FEET) 952CRITICAL FLOW SPECIFIC ENERGY FEET) = 3 888

103


115/142

104


Step 3: From step 1 we know that the flow depth i s 2.0 feet at thegrade break. Determine a gradually varied f low p ro f i l e for thechannel. Note t h a t a jump wi l l occur where the pressure p lusIIIOIlElltum from step 2 equals the pressure plus momentum of step 3.

.GRADUALLY VARIED FLOW PROFILE INPUT INFORMA1 ION,

CONSTANT CHANNEL SLOPE FEET/FEET) .001500CHANNEL LENGTH(FEET) = 1000.00CONSTANT CHANNEL FLOW(CFS) 250.00CONSTANT CHANNEL FRICTION FACTOR(MANNING) a .015000ASSUMED CHANNEL CONTROL DEPTH (FEET) 2.00M XIMUM NUMBER OF INTERVALS IN PROFILE 15CONSTANT CHANNEL BASEWIDTH(FEET) 5.00CONSTANT CHANNEL Z FACTOR D 2.0000NORMAL DEPTH FEET) 3.44CRITICAL DEPTH(FEET) 2.94

UPSTREAM CONTROL ASSUMED DEPTH(FT) = 2.00============================================================================

GRADUALLY VARIED FLOW PROFILE COMPUTED INFORMATION,

DISTANCE FROM F L O ~ I E P T HVELOCITY SPECIFIC PRESSURE+CONTROL FT) FT) FT/SEC) ENERGY FT) MOMENTUM (POUNDSj

000 2.000 13.885 4.995 7685.5816 509 2.062 13.281 4.S03 7464.5032.762 2.125 12.717 4.637 7266.174S.705 2.1S7 12.190 4.496 7088.8864.274 2.250 11.696 4.375 6931.1279.399 2.312 11.233 4.272 6791. 5793.997 2.374 10.798 4.186 6669 06

107.970 2.437 10.389 4.113 6562 53121.206 2.499 10.003 4.054 6471. 06133.565 2.561 9.639 4.005 6393.80144.883 2.624 9.295 3.966 6330 01154.955 2.686 8.970 3.936 6279 02163.524 2.749 8.662 3.914 6240.24170.263 2. Sl1 8.371 3.900 6213.12174.744 2.873 8.094 3.891 6197 18176.392 2.936 7.831 3.888 6191. 97


116/142


Problem 5 3 1

A tr iangular shaped concrete channel with a z of 1.5 having aslope of 0.003 f t f t conveys 20 cfs Determine normal depth andcrit ical depth data for the channel assuming a Manning s frictionfactor of n = 0.015.

NORMAL DEPTH

1 5

. . A . CHANNEL INPUT INFORMATION

CHANNEL Z(HORIZONTAL/VERTICAL) = 1 50BASEWIDTH(FEET) = 00CONSTANT CHANNEL SLOPE FEET/FEET) = 003000UNIFORM FLOW(CFS) = 20 00MANNINGS FRICTION FACTOR = 0150


> NORMAL DEPTH FEET) 1 75FLOW TOP- WIDTH(FEET) =FLOW AREA(SQUARE FEET) =HYDRAULIC DEPTH FEET) = 87FLOW AVERAGE VELOCITY FEET/SEC.)UNIFORM FROUDE NUMBER = 826PRESSURE MOHENTUH(POUNDS) =AVERAGED VELOCITY HEAD(FEET) =

5 244 57

SPECIFIC ENERGY(FEET) = 2 043

4 38

335 52298

= = = ~ = = = = = = = = = = = = = = = = = = = = = = ~ = = = = = = = = = = = = = = = = = = = ~ = = = = = = = = =

CRITICAL-DEPTH FLOW INFORMATION:----------------------

CRITICAL FLOW TOP-WIDTH FEET) = 4 85CRITICAL FLOW AREA (SQUARE FEET) = 3 93CRITICAL FLOW HYDRAULIC DEPTH FEET) = 81CRITICAL FLOW AVERAGE VELOCITY FEET/SEC.) = 5 09CRITICAL DEPTH FEET) = 1 62CRITICAL FLOW PRESSURE MOMENTUM(POUNDS) = 329 55AVERAGED CRITICAL FLOW VELOCITY HEAD(FEET) = 403CRITICAL FLOW SPECIFIC ENERGY(FEET) = 2 021


117/142

106


Problem 5.3.2.

Determine t he normal depth and c r i t i c a l depth data for atriangular shaped concrete channel conveying 20 cfs . Assume a Zof 1.5, a channel slope of 0.010 f t f t and a Manning s f r i c t i o nfac tor of n = 0.015.

.L::CRITICAL OEPTlL r r -.-

NORM L EPTH

~ ,


CHANNEL Z HORIZONTAL/VERTICAL) = 1.50BASEWIDTH FEET) = .00CONSTANT CHANNEL SLOPE FEET/FEET) = .010000UNIFORM FLOW CFS) = 20.00MANNINGS FRICTION FACTOR = .0150

= = = = = = = = = = = = = = = = = = = = = ~ - = ===================== ============== = = = = = = = ~ = =NORMAL-DEPTH FLOW INFORMATION:

1.39 NORMAL DEPTH FEET) =FLOW TOP- WIDTH FEET) =FLOW AREA SQUARE FEET) =

4.172.90

HYDRAULIC DEPTH FEET) = .70FLOW AVERAGE VELOCITY FEET/SEC.) ~UNIFORM FROUDE N U M B ~ R= 1.457PRESSURE MOMENTUM POUNDS) =AVERAGED VELOCITY BEAD FEET) =SPECIFIC ENERGY FEET) = 2.129

6.90

351.16.738

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = ~ = = = = = = = = = = = = = = = = = =

CRITICAL-DEPTH FLOW INFORMATION:CRITICAL FLOW TOP-WIDTH PEET) = 4 . 8 5CRITICAL FLOW AREA SQUARE FEET) = 3.93CRITICAL FLOW HYDRAULIC DEPTH FEET) = .81CRITICAL FLOW AVERAGE V E L O C I T Y F E E ~ / S E C . )= 5.09CRITICAL DEPTH FEET) = 1.62CRITICAL FLOW PRESSURE MOMENTUM POUNDS) = 329.55AVERAGED CRITICAL FLOW VELOCITY H E ~ D F E E T ) .403CRITICAL FLOW SPECIFIC ENERGY FEET) = 2.021


118/142

HYDRAULIC ELEMENTS EXAMPLE PROB= L= EccM = S=

Problem 5.3.3.

Compute the discharge rate n a triangular shaped concrete channelhaving a flow depth of 2 feet. Assume a Z of 1.5, a channel slopeof 0.010 f t f t and a Manning s fr ic t ion factor of n = 0.015.

1 7

. . .

CHANNEL INPUT INFORMATION----------------------------------------------------------------------------

NORMAL DEPTH FEET) 2.00CHANNEL Z HORIZONTAL/VERTICAL) = 1.50BASEWIDTH FEET) = .00CONSTANT CHANNEL SLOPE(FEET/FEET) = .010000MANNINGS FRICTION FACTOR = .0150_ cNORMAL-DEPTH FLOW INFORMATION:

NORMAL DEPTH FLOW CFS) =FLOW TOP- WIDTH (FEET) =FLOW AREA SQUARE FEET) aHYDRAULIC DEPTH FEET) = 1 .00FLOW AVERAGE VELOCITY(FEET/SEC.)UNIFORM FROUDE NUMBER = 1.544PRESSURE MOMENTUM POUNDS) =AVERAGED VELOCITY HEAD (FEET) =

52.586.00

6.00

8.76

1142.631.193

SPECIFIC ENERGY FEET) = 3.193============================================================================


CRITICAL FLOW TOP-WIDTH FEET) 7.14CRITICAL FLOW AREA SQUARE FEET) = 8.50CRITICAL FLOW HYDRAULIC DEPTH FEET) = 1 .19CRITICAL FLOW AVERAGE VELOCITY(FEET/SEC.) = 6.19CRITICAL DEPTH FEET) = 2.38CRITICAL FLOW PRESSURE MOMENTUM POUNDS) = 1051.24AVERAGED CRITICAL FLOW VELOCITY HEAD (FEET) .594CRITICAL FLOW SPECIFIC ENERGY FEET) = 2.975


119/142

108


Problem 5.3.4.

For a t r i angu lar shaped concrete channel conveying 20 c f s ,determine the channel slq:>e required to maintain a flow depth o 2feet. Assume a channel Z = 1.5 and a Manning S fr ic t ion factor ofn ,. 0.015.

.


NORMAL DEPTH(FEET) = 2.00CHANNEL Z(HORIZONTAL/VERTICAL) = 1.50BASEWIDTH(FEET) = .00UNIFORM FLOW(CFS) = 20.00MANNINGS FRICTION FACTOR .0150

= = ~ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = ~ = = = = = = = = = = = = = = = = = = = = = =


CHANNEL SLOPE(FEET/FEET) = .00145FLOI l TOP- WIDTH (FEET) = 6.00FLOW AREA (SQUARE FEET) = 6.00HYDRAULIC DEPTH FEET) 1 .00FLOW AVERAGE VELOCITY(FEET/SEC.) 3.33UNIFORM FROUDE NUMBER = .587PRESSURE MOM NTUM (POUNDS) = 378.79AVERAGED VELOCITY HEAD(FEET) = .173SPECIFIC ENERGY(FEET) 2.173

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = ~ . = = = = == = = = = = = = = = = = = = = = = = = = =

CRITICAL-DEPTH FLOW INFORMATION.

CRITICAL FLOW TOP-WIDTH(FEET)=

4.85CRITICAL FLOW AREA (SQUARE FEET) = 3.93CRITICAL FLOW HYDRAULIC DEPTH(FEET) = .81CRITICAL FLOW AVERAGE VELOCITY(FEET/SEC.) = 5.10CRITICAL DEPTH(FEET) = 1 .62CRITICAL FLOW PRESSURE MOMENTUM(POUNDS) = 329.55AVERAGED CRITICAL FLOW VELOCITY HEAD (FEET) = .403CRITICAL FLOW SPECIFIC ENERGY(FEET) = 2.021


120/142


Problem 5 3 5

Determine the channel side slopes (Z) necessary for a triangularshaped concrete channel to convey 20 efs a t a flow aeptb of 2 feetand having a longi tud inal s lope of 0.010 f t / f t Assume a

Manning s friction factor of n = 0 015

CHANNEL INFur INFORMATION

NORMAL DEPTB(FEET) = 2 00BASEWIDTH FEET) 00CONSTANT CHANNEL SLOPE(FEET/FEET) = 010000UNIFORM FLOW CFS) = 20 00MANNINGS FRICTION FACTOR 0150

NORMAL-DEPTH FLOW INFORMATION,

} CHANNEL Z-FACTOR = 72FLOW TOP- WIDTH (FEET) = 2 69FLOW A R ~ S Q U A R EFEET) = 2 89HYDRAULIC DEPTH(FEET) = 1 00FLOW AVERAGE VELOCITY (FEET/SEC.) = 6 93UNIFORM FROUDE NUMBER = 1 221PRESSURE MOM NTUM POUNDS) = 388 65AVERAGED VELOCITY HEAD FEET) = 746SPECIFIC ENF.RGY{FEET) = 2 146

109

===_====_==== ================================================_========c====CRITICAL-DEPTH FLOW I ~ F O R M A T I O N :

CRITICAL FLOW TOP-WIDTH{FEET) = 3 13CRITICAL FLOW AREA SQUARE FEET) = 3 39CRITICAL FLOW HYDRAULIC DEPTH{FEET) 1 0BCRITICAL FLOW AVERAGE VELOCITY(FEET/SEC.) 5 91CRITICAL DEPTH{FEET) = 2 11CRITICAL FLOW PRESSURE MOMENTUM POUNDS) = 381 51AVERAGED CRITICAL FLOW VELOCITY HEAD (FEET) = 542CRITICAL FLOW SPECIFIC ENERGY{FEET) = 2 70B


121/142


122/142


Problem 5.4.2.

Using the da ta from 5.4.1, assume flow s car r ied evenly on bothsides of the street.

STREETFLOW MODEL INPUT INFORMATION

CONSTANT STREET GRADE(FEET/FEET); .010000CONSTANT STREET FLDW(CFS) 5.00AVERAGE STREETFLOW FRICTION FACTOR[MANNING) ;CONSTANT SYMMETRICAL STREET HALF-WIDTH[FEET)CONSTANT S ~ M M E T R I C LSTREET CROSSFALL[DECIMAL)CONSTANT S ~ M M E T R I C LCURB HEIGrH[FEET ; .50

.01500020.00

.017000

CONSTANT S ~ M M E T R I C LGUTTER-WIDTH[FEET) 1.50CONSTANT S ~ M M E T R I C LGUTTER-LIP[FEET) = .03125CONSTANT SYMMETRICAL GUTTER-HIKE(PEET) = .12500FLOW ASSUMED TO FILL STREET EVENLY ON BOTH SIDES

STREETFLOW MODEL RESOLTS:

STREET FLOWDEPTB(FEET) .32HALFSTREET FLOODWIDTH(FEET) 11.33AVERAGE FLOW VELOCITY(FEET/SEC.) 2.06PRODUCT OF DEPTH VELOCITY = .67


123/142

112


Problem 5.4.3.

Using the s t ree t cross section of Problem 5.4.1, determine thedepth of flow for 35 cfs assuming the flow i s carried evenly onboth sides of the street

. . . . . .

STREETFLOW MODEL INPUT INFORMATION- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

CONSTANT STREET GRADE FEET/FEET] .010000CONSTANT STREET FLOW CFS]. 35.00

.01500020.00

.017000

AVERAGE STREETFLOW FRICTION FACTOR MANNING]CONSTANT SYMMETRICAL STREET HALF-WIDTH FEET] =CONSTANT SYMMETRICAL STREET CROSSFALL DECIMAL)CONSTANT SYMMETRICAL CURB HEIGTH FEET] - .50

CONSTANT SYMMETRICAL GUTTER-WIDTH FEET] 1.50CONSTANT SYMMETRICAL GUTTER-LIP FEET] - .03125CONSTANT SYMMETRICAL GUTTER-HIKE FEET) .12500FLOW ASSUMED TO FILL STREET EVENLY ON BOTH SIDES

STREET LOWING F U L L ~

~ = = = = = = = = = = = = = = = = = = = = = = = = a = = = = = = = _ = ============== ======================STREETFLOW MODEL RESULTS;

NOTE; STREETFLOW EXCEEDS TOP OF CURB.THE FOLLOWING STREET FLOW RESULTS ARE BASED ON THE ASSUMPTIONTHAT NEGLIBLE PLOW OCCURS OUTSIDE OP THE STREET CHANNEL.THAT IS ALL PLOW ALONG THE PARKWAY, ETC., IS NEGLECTED.

STREET FLOWDEPTH FEET] .52HALFSTREET FLOODWIDTH FEET) = 20.00AVERAGE FLOW VELOCITY FEET/SEC.) 3.89PRODUCT OF DEPTH.VELOCITY = 2.02

: = = = = = : = = = = = = ~ = = c ~ = = . = = = = = ~ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =


124/142


125/142

114


Problem 5.5.1.

Dete :mine the upstJ:eam and downstJ:eam flow depths fo : the jWlCtionshown. Note that a ze :o flow depth in d t input assumes normal

depth.

LEGEND

54 RCPII

71 OOcfs~ r

II

~ So=0.004

NOL NORM L DEPTH LINE

COL CRITICAL DEPTH LINE

l FLOWl.INE El.EVATIONRCP REINfORCEO CONCRETE PIPE

o PROfiLE~ : ; r P O S S I 8 L EW TER SURF CE

JE.3Q /t l

NIlL- - 7 - -\ua COL

IOZ II

' 1 l5499.5


126/142


127/142

6


Problem 5.5.2.

Determine the upstream and downstream flow depths for the previousproblem assuming tha t the 48 inch RCP flowline matches the 54 inch

RCP flowline.

PIPE-FLOW JUNCTION INPUT INFORMATION

PIPE

UPSTREAMDOWNSTREAM

LATERAL tLATERAL 12

FLOW(CFS)

70.001 0 0 .0 0

25.005.00

DIAMETER(INCHES)

48.0005 4 .0 0 03 0 .0 0 01 8 .0 0 0

SLOPE(DECIMAL)

.00400

.00400

.00500

.00600

MAINLINE FLOWDEPTH INPUT INFORMATION:UPSTREAM PIPEFLOW DEPTH (FEET) , .00DOWNSTREAM PIPEFLOW DEPTH(FEET): .00

FRICTIONFACTOR

.0130

.0130

.0130

.0130

ANGLE(DEGREES)

.000

.00020.00045.000

FLOWLINEELEVATION

100.00100.00101. 00102.00

=.= = = = - ~ =.... = = = = = = = = = = = = = = ~ = = = = = = = = = = = = = = = = = = = = =PIPEFLOW

NORMAL ANDCRITICAL DEPTH INFORMATION,

PIPE

UPSTREAMDOWNSTREAM

LATERAL tLATERAL 12

CRITICAL DEPTH(FEET)2 .5292.9381 .703

.860

NORMAL DEPT(FEET)

2.6343 .0 5 61 . 790

. 8 5 0

PRESSURE-PLUS-MOMENTUM DETERMINATION BASED ON VARIABLE,"BALANCE" (Z+DI-D2)*(Al+A2)*G/2.-Q2*02/A2+01*Ol*COS(ANGLEl)/Al+Q3*Q3*COS[ANGLE3)/A3+Q *Q4*COS[ANGLE4)/A4

CHECK FOR JUNCTION WASHOUT DOE TO LATERALS OR JUNCTION DROP,PIPEFLOW FORCE-PLUS-MOMENTUM DETERMINATION (NEGLECT MINOR LOSSES)

UPSTREAM DOWNSTREAM LATERAL.1 LATERAL.2 BALANCEDEPTB(FT) DEPTB(FT) DEPTB(FT) DEFTH(FT) (FT'*4)

2 .634 3 .0 5 6 1 .845 .850 - 2 8 1 ."DOWNSTREAM PIPEFLOW DEPTH IS ASSUMED AS HYDRAULIC CONTROL

CHECK IF JUNCTION SEALS DUE TO DOWNSTREAM CONTROL.PIPEFLOW FORCE-PLUS-MOMENTUM DETERMINATION (NEGLECT MINOR LOSSES)

UPSTREAM DOWNSTREAM LATERAL.l LATERAL.2 BALANCEDEPTB(FTl DEFTH(FTl DEPTH(FT) DEPTH(FT) (FT* 41

4 .0 0 0 3.056 2.528 .850 23 .'UPSTREAM FLOW ASSUMED NOT SEALED.

PIPEFLOW FORCE-PLUS-MOMENTUM DETERKINATION(NEGLECT MINOR LOSSES)UPSTREAM DOWNSTREAM LATERAL.l LATERALf2 BALANCEDEPTH (FT) DEFTH(PT) DEPTH (FT) DEPTH (FT) (PT '4)

3.254 3 .0 5 6 2 .1 5 5 850 -203 3.617 3 .0 5 6 2 .3 3 7 850 -1 0 8

3.799 3 .0 5 6 2 .4 2 7 850

-49 3 .889 3.056 2 .473 850 -18 3 .9 3 5 3.056 2 .495 .850 -2 .3.957 3 .0 5 6 2.507 .8 5 0 7 .3 .9 4 6 3 .0 5 6 2 501 850 3 3.940 3 .0 5 6 2.498 850 O3.937 3 .0 5 6 2 .4 9 7 .850 l .3.939 3 056 2.497 850 O3.940 3 .0 5 6 2.498 850 O3.939 3 .0 5 6 2.498 850 O

DOWNSTREAM CONTROL ASSUMED AT JUNCTION

COMPUTED UPSTREAM PIPEFLOW DEPTH(FEET) = 3.939COMPUTED DOWNSTREAM PIPEFLOW DEPTH(FEET) 3.056


128/142


Problem 5 5 3

Analyze the junction structure shown with supercri t ical flowupstIeam and downstream. 1\gain note that a zero flow depth shownfor data input means normal depth of flow.

POSSIBLE WATER5URF ACE

30

PROGRAM ASSUMESHYDRAULIC JUMPOCCURS UPSTREAM

OF STRUCTURE

PROGRAM ASSUMESCRITICAL DEPTHAS CONTROL

5 PROF ILE

7


129/142


130/142


Proolem 5.5.4.

Analyze the following junction structure assuming normal depth offlow upstream and downstream

II

60cl ll o

I

PROGRAM ASSUMESSOFFIT CONTROL

4S RCP

PROGRAM ASSUMESNORMAL OEPTH

E 48100

119


131/142

12


. .

PIPE-FLOW JUNCTION INPUT INFORMATION

PIPE

UPSTREAMDOWNSTREAMLATERAL lLATERAL 12

FLOWCFS)60.0090.0025.00

5.00

DIAMETER(INCHES)

48.00048.00030.00018.000

SLOPE(DECIMAL)

.00400

.00400

.00500

.00600

MAINLINE FLOWDEPTH INPUT INFORMATION:UPSTREAM PIPEFLOW DEPTH FEET). .00DOWNSTREAM PIPEFLOW DEPTH FEET): .00

FRICTIONFACTOR

.0130

.0130

.0130

.0130

ANGLE(DEGREES)

.000

.00020.00045.000

FLOWLINEELEVATION

100.00100.00101. 00102.00

============ ===========================================

PIPEFLOW NORMAL AND CRITICAL DEPTH INFORMATION:

PIPE

UPSTREAMDOWNSTREAMLATERAL HLATERAL t 2

CRITICAL DEPTHFEET)2.3342.8761 703

.860

NORMAL DEPTHFEET)2.3733.2451 .7 9 0

.850

PRESSURE-PLUS-MOMENTUM DETERMINATION BASED O VARIABLE.BALANCE Z+DI-D2)* Al+A2)*G/2.-02*02/A2+01*Ol*COS ANGLEl)/Al

+Q3*03*COS ANGLE3)/A3+04*04*COS ANGLE4)/A4

CHECK FOR JUNCTION WASHOUT DUE TO LATERALS OR JUNCTION DROP:PIPEFLOW FORCE-PLUS-MOMENTUM DETERMINATION(NEGLECT MINOR LOSSES)

UPSTREAM DOWNSTREAM LATERAL.l LATERALt2 BALANCEDEPTH FT) DEPTH FT) DEPTH FT) DEPTB FT) FT*4)

2.373 3.245 1.809 .850 -369 .DOWNSTREAM PIPEFLOW DEPTH IS ASSUMED AS HYDRAULIC CONTROL

CHECK IF JUNCTION SEALS DUE TO DOWNSTREAM CONTROL:PIPEFLOW FORCE-PLUS-MOMENTUM DETERMINATION(NEGLECT MINOR LOSSES)

UPSTREAM DOWNSTREAM LATERALtl LATERALt2 BALANCEDEPTH FT) DEPTH(FT) DEPTH FT) DEPTH FT) FT 4)

4.000 3.245 2.623 .850 -33 .

UPSTREAM WATER DEPTH EXCEEDS PIPE DIAMETER:.SUGGEST REANALYZE JUNCTION AS UNDER PRESSURE-FLOW CONDITIONS.


132/142


Prcblem 5 5 5

Determine the upstream and downstream flow depths for the junctionshown assuming norml depth upstream and downstream.

- ,

'

4S RCP

100 cIsa

50=0 006

L 481 /

COL

\ L 4 2

99.5

42 RCP

IOOch

So=O OIO

-.en

121


133/142

122


~ . . w . . _

PIPE-FLOW JUNCTION INPUT INFORMATION- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ~ -- - - - - - - - - - - - - - - - - - - - - -

PIPE

UPSTREAIIDOlrnSTREAIILATERAL nLA'l"ERAL . 2

FLOWCFS)

100.00100.00

.00

.00

DIAMETER(INCHES)

48.00041.000

.0000 0 0

SLOPE(DECIMAL)

.00600

.01000

.00000

.00000

MAINLINE FLOWDEPTR INPUT INFORMATION;UPSTREAM PIPEFLOW DEPTB FEET); .00DO OliSTREAII PIPEFLOW DEPTH FEET): .00

FRICTIONFACTOR

.0130

.0130

.0000

. 0000

PIPEFLOW NORMAL AND CRITICAL DEPTH INFORMATION;

A N G ~ E

(DI GREESI.000. 0 0 0.000. 000

F L O W L I N ~

ELEVATION100.00

9 9 . 5 0.00. 0 0

PIPE

UPSTREAMDOlrnSTREAIILATERAL HLATERAL t2

CRITICAL DEPTHFEET)3.0303.068

. 0 0 0

.000

NORMAL DEPTHFEET)2.9632.850

.000

.000

PRESSORE-PLOS-MOMENTUM DETERMINATION BASED ON VARIABLE."BALANCE" ~ ( Z + D 1 - D 2 ) ( A l + A 2 ) G / 2 . - Q 2 Q 2 / A 2 ~ 1 Q l C O S ( A N G L E 1 )+Q3*Q3*C05 ANGLE3)/A3+Q4*04*COS ANGLE4)/A4

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ~ - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - -U P S ~ R E A MFLOW lS SUPERCRITICAL: CHECK FOR HYDRAULIC JUMp;PIPEFLOW F O R C E ' P L U S - M O M E N T U ~DETERMINATION(NEGLECT MINOR LOSSES)

UPSrEEAM DOWNSTRE M LATERAL.l LATERALi2 BALANCEDEPTH (FT) DEPTH FT) DEPTB(FT) DEPTR(FT) FT**4)

2.963 3.068 .000 .000 4* U P S T R E ~FLOW DOMINATES JUNCTION HYDRAULICS:"NO HYDRAULIC JUMP OCCURS AT JUNCTION.

P I P E P ~ O WFORCE-PLUS-MOMENTUM DETERMINATION/NEGLECT MINOR LOSSES)UPSTRE IoI DOWNSTRE IoI L TEIl LU LATERALt BALANCED E P T R ( F ~ )DEPTH FT) DEPTH{FTj DEPTH/FTj (F T ' )

~ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -2.963 1.534 . 000 .000 -1027 2.963 2.301 .000 000 -177 2 .9 6 , 2.685 .000 000 -37 2.963 2.877 . 000 .000 6 .2.963 2.973 000 000 1 2.963 2.925 .000 000 -2 2.963 2.949 .000 000 O2 . 9 6 3 2.937 000 000 -1 2 . 9 6 3 2.943 .000 .000 O.2.963 2.946 .000 000 O2 .963 2.947 . 000 000 O2.963 2 . 9 4 8 000 .000 O2.963 2 . 9 4 8 . 0 0 0 000 O

UPSTREAM CONTROL hSSUMED AT JUNCTION- - - - - - - - - - - - - - - - - - - - - - - - - - - - - ~ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

COMPUTED UPSTREAM PIFEfLOW DEPTP(FEET) = 2.963COMPUTED DOWNSTRE M PIPEFLOW DEPTH(fEET) - 2.947

= = = = = = = ~ = = = = . = . = ~ . ~ . = = ~ = = = = = = = = = = = = = = ~ = = = = = = ~ = = = = = = . = = . = = = = = ~ = =


134/142


123

Problem 5.6.1.

Determine the gradually varied flow prof i l e for a 78 inch RCPflowing partially flow with 300 cfs, which changes from a slope of0.004 f t / f t t o 0.0035 f t / f t Assume a channel l en g th of 500 f e e tand a Manning s f r ic t ion factor of n = 0.013.

. .Q.. :

/...:--:. 1 MI PROFILE, DEPTH---.. 'F NORMAL

N o r ~d e ; t h / ; ; , ~ - - c R i i i C A LO E P T H : : : ; t - ~- ll:CD.. :

SO-0.0040MILO SLOPE So-0.0035

M I L o E RMILD SLOPE

CONTROLSECTION

iQI II

)

. . .GRADUALLY VARIED FLOW PROFILE INPUT INFORMATION,

CHANNEL SLOPE(FEET/FEET) = .004000CHANNEL LENGTH (FEET) = 500.00CONSTANT CHANNEL FLOW CFS) = 300.00CONSTANT CHANNEL FRICTION FACTOR MANNING)ASSUMED CHANNEL CONTROL DEPTB(FEET) =MAXIMUM NUMBER OF INTERVALS IN PROFILE =CONSTANT PIPE DIAHETER(INCHES) = 78.000NORMAL DEPTH FEET) = 4.84

CRITICAL DEPTH(FEET) = 4.65

.0130005.15

15

= = ~ = = = = = = = = = = = = = = = = ~ = = = = = = = = = = = = = _ = = = = = = = = = = ~ = = . ~ = = = E =_ = = = = _ = = = = = = = = = = = = = = =

DOWNSTREAM CONTROL ASSOMED DEPTH{FT) = 5.15= = = : = = : : = ~ = : = = = : = = = = . = = . = = = = ~ = = = = = ~ . = = = = = = = ~ = = = = = = = = = == = = = = = = = = = = = = = = = = = = = =

GRADUALLY VARIED FLOW PROFILE COMPUTED INFORMATION:

DISTANCE FROMCONTROt. (FT)

.00014.00928.38643.19158.50774.43691.111

108.7161 2 7 .5 0 4147.B41170.320195.B85226.334265.666326.519500.000

FLOWDEPTB(FT)

5.1505.1305.1095 .0895.0685 .0485 .0275.007

4 .9 8 64.9664 .9454 .9254.9044.8844 .8644.857

VELOCITY(FT/SEC)

10.63610.67110.71910.7611 0 .8 0 31t).84110 .89010.935

10.98011 .02511.07111.11B11 .16511.21311 .26111.277

SPECIFICENERGY (FT)

6.9086.9016.8946.8886.8826.8766.8706.8656.8596.8546 .8506 .8456.8416.8386.8346.833

PRESSURE+MOMENTUMPOUNDS)

10295.3110282.6810271.6610261. 0210250.7710240.9210231. 4810222.4510213.10205.6210197.8610190.5210183.6210177.1710171.1810169.37

in


135/142

124


Problem 5.6 .2

Given t h a t a 78 inch RCP carrying 200 cfs changes from a slc:pe of0.0015 f t / f t to a slope of 0.0021 f t / f t determine the gradual lyvar ied flow pro f i l e assuming a pipe length of 3000 fee t and aManning s f r ic t ion factor of n = 0.013.

Normal deDth IIneM 2 PPOFILE

,., NORMALDEPTH,

/ \' I- - - -/ \- cRiT CALDEPTH 'u '- r


136/142


Pt:oblern 5.6 .3 .

Determine the water surface of an M3 profi le in a 78 inch RCPdischarging 300 cfs as i t changes slope from 0.0067 f t / f t to aSlope of 0.0040 f t / f t . Use a pipe length of 500 feet and aManning s friction factor of n = 0.013. Note that the flow depthis only calculated to cri t ical depth. A hydraulic jUmp will occurwhere the pressure plus momentum of the M3 profile equals that ofnormal depth flow.

/

.J ).r...E..R. .CAlDEIin t - - '_-IH Normal dOPth IIno


137/142

126


. . . . ~ . . ~ ~ . . . . . . . . + . .PIPEFLOW HYDRAULIC INPUT INFORMATION

PIPE DIAMETER FEET) = 6.500PIPE SLOPE(FEET/FEET) .0040PIPEFLOW CFS) = 300.00MANNINGS FRICTION FACTOR a .013000


CRITICAL DEPTH FEET) = 4.65CRITICAL FLOW AREA SQUARE FEET) = 2 5 . 4 0 4CRITICAL FLOW TOP-WIDTH FEET) = 5 . 8 6 6CRITICAL FLOW PRESSURE + MOMENTUM POUNDS) 10128.91CRITICAL FLOW VELOCITY FEET/SEC.) = 11 . 8 0 9CRITICAL FLOW VELOCITY BEAD FEET) = 2.17CRITICAL FLOW HYDRAULIC DEPTH FEET) 4.33CRITICAL FLOW SPECIFIC ENERGY FEET) = 6 . 8 2

= = = = = = = = = ~ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = ~ == = = = = = = = = = = = = = = = = = = = = =


NORM L DEPTB PEET) = 4.84FLOW AREA SQUARE FEET) = 26.51FLOW TOP WIDTH FEET) 5.666FLOW PRESSURE MOMENTUM PDUNDS) =FLOW VELOCITY FEET/SEC.) =FLOW VELOCITY BE D FEET) =HYDRAULIC DEPTB FEET) 4.68FROUOE NUMBER = .922SPECIFIC ENERGY FEET) =

10165.4811.316

1 .9 8 8

6 .8 3


138/142

I tD

'


Problem 5.6.4.

Determine an Sl gradual ly var ied flow p ro f i l e in a 78 inch Repflowing par t i a l ly f u l l with 300 c f s . Assume the pipe slopechanges from 0.0057 f t / f t to 0.0035 f t / f t . a Manning s f r i c t io nf ac tor o f n = 0.013 and a pipe length of 500 f t . Note tha t flowdepth is calculatd to cr i t i ca l depth only. Actually a hydraulicjump wi l l occur in t he steep sec t ion where the pressure plusmomentum of the gradual ly var ied flow p ro f i l e equals t ha t ofnormal depth flow.

/ '1

I I -5 PROFILE' NORMAL DEPTH---.....- - -

7- - - . -

'Norma' depth line

====- CRITICAL DEPTHNote. Hydraulic jump nol shown)'' I

127

it>

l i t5 0 - 0 . 0 0 5 7

5 0 ' 0 . 0 0 3 5 \. )STEEP SLOPE

~MILD SLOPE

CONTROLSECTION

I ~

GRADUALLY VARIED FLOW PROFILE INPUT INFORMATION:

CHANNEL SLOPE(FEET/FEET) = .005700CHANNEL LENGTH FEET) = 500.00CONSTANT CHANNEL FLOW CFS) 300.00CONSTANT CHANNEL FRICTION FACTOR MANNING)ASSUMED CHANNEL CONTROL DEPTH (FEET) =MAXIMUM NUMBER OF INTERVALS IN PROFILE =CONSTANT PIPE DIAMETER INCHES) = 78.000NORMAL DEPTH(FEET) = 4.23CRITICAL DEPTH(FEET) = 4.65

= .0130005.15

10

DOWNSTREAM CONTROL ASSUMED DEPTH FT) = 5.15


DISTANCE FROM FLOWDEPTH VELOCITY SPECIFIC PRESSURE+CONTROL (FT) (FT) (FT/SEC) ENERGY (FT) MOMENTUM POUNDS).000 5.150 10.636 6.908 10295.31

7.561 5.100 10.737 6.891 10266.9114.704 5.050 10.842 6.876 10242.0521. 384 5.000 10.949 6.863 10219.5927.545 4.950 11. 060 6.851 10199.6233.121 4.900 11.175 6.841 10182.2338.024 4.850 11.293 6.832 10167.5242.149 4 BOO 11.416 6.825 10155.5545.357 4.750 11.541 6.820 10146.4547.468 4.700 11.671 6.817 10140.3048.240 4.650 11.806 6.816 10128.91


139/142


128

. ************* * * ~ * * . * * ~ * * * * * . . . . .PIPEFLOW HYDRAULIC INPUT I N F O R M A T I O ~

PIPE DIAMETER FEET) = 6.500PIPE SLOPE FEBT/FEET) .0057PIPEFLOW CFS) = 300.00MANNINGS FRICTION FACTOR = .013000


CRITICAL DEPTH FEET) = 4.65CRITICAL FLOW AREA SQUARE FEET) = 25.404CRITICAL FLOW TOP-WIDTH FEET\ = 5.866CRITICAL FLOW PRESSURE ~ O ~ E N T U ~ P O U N D S )= 10128.91CRITICAL FLOW VELOCITY FEET/SEC.) = 11.809CRITICAL FLOW VELOCITY HEAD FEET) 2.17CRITICAL FLOW HYDRAULIC DEPTH FEET) = 4.33CRITICAL FLOW SPECIFIC ENERGY FEET) = 6.62

NORMAL-DEPTa FLOW INFORMATION,

NORMAL DEPTB FEET) = 4.23FLOW AREA SQUARE FEET)

=22.67FLOW TOP WIDTH FEET) = 6.197

FLOW PRESSURE + MOM NTUM POUNDS) =FLUW VELOCITY FEET/SEC.) =FLOW VELOCITY HEAD FEETJ =HYDRAULIC OEPTH FEETI 3.69FROUDE NUMBER = 1.203SPECIFIC ENERGY FEETI =

10264.8913.118_2.672

6.90


140/142

HYDRAULIC ELEMENTS EXAMl'L l ROBLEMS

129

Problem 5.6.5.

Given that a 78 inch RCP conveying 300 cfs changes from a slope of0.0066 f t / f t to a slope of 0.010 f t / f t determine the watersurface pro f i l e asuming a pipe length of 500 f t . and a Manning sf r i c t i on factor of n 0.013.

LLCRITIC L DEPTH_

~ ~ ~ N O R M A LDEPTHD

8 )() So-0.0066

STEEP SLOPE

n

GRADUALLY VARIED fLOW PROFILE INPUT INFORMATION:

CHANNEL SLOPE(FEET/FEET) = .010000CHANNEL LENGTH(FEETJ 500.00CONSTANT CHANNEL FLOW{CFS) 300.00CONSTANT CHANNEL FRICTION F A C T O R ~ A N N I N G IASSUMED CHANNEL CONTROL DEPTH(FEET) =MAXIMUM NUMBER OF INTERVALS IN PROFILE CONSTANT PIPE D I ~ E T E R I N C H E S )78.000NORMAL DEPTB(FEET) 3.52CRITICAL DEPTH(FEET) 4_65

.0130004.00

15

= = = K = = = = ~ = = = = = = = = = = = = = = = = = = ~ C = = = = ~ = = = = = = = ; = = = = = = = = =UPSTREAM CONTROL ASSUMED DEPTH(FT) = 4.00


DISTANCE FROMCONTROL (FT)

.0008.171

17 .3822 7 8 0 2

39.64253.17668 .764

8 6 .8 9 3108.243133 .812165.143204.813257.637334.353468.865500.000

f LOWDEPTH(FT)

4.0003 .9683.9373.9053.an3.8423.810

3.7783.7473.1153 .6833.6523.6203.5883.5573.556

VELOCITY(FT/SEC)

13 .99914.13214.26714.4051 4 . 5 4 614.69014.837

1 4 . 9 8 715.14115.29815.45915.62315.79115.96316.13916.143

SPECIFICENERGY (FT)

7.0457.0717.0997.1291.1617.1947.230

7.2687.3097.3517.3977.4447.4957.5487.6047.605

PRESSURE+MOM NTUM (POUNDS)

10458.6010492.8610529 . l l10567.4010607.7810650.3110695.03

10742.0010791.2710842.9210896.9910953.5511012.6611074.3911143.6511145.11


141/142

130


Problem 5.6.6.

Determine the gradually varied flow prof i le for a 78 inch Repflowing partial ly ful l with 300 cfs which changes from a slope of0.0170 f t / f t to a slope of 0.010 f t / f t . Use a pipe length of 500feet and a Manning's fr iction factor of n = 0.013.

-1 f

n ~ -C fB J A l OE \D

\ _ - , T H (T { ? - . . . . . .~ f f \ ~ N o r m a ldepth line \NORMAl

OEPTH \ ' " *i 53 PROFIL.E. /SooO.OI7'O }: l

of

S o 0.010T PSLOP MILDER STEEP SLOPE

CONTROLSECTION

. . . . GRADUALLY VARIED FLOW PROFILE INPUT INFORMATION:

CHANNEL SLOPE(FEET/FEET) = .010000CHANNEL LENGTH(FEET) = 500.00CONSTANT CHANNEL FLOW(CFS) = 300.00CONSTANT CHANNEL FRICTION FACTOR(MANNING)ASSUMED CHANNEL CONTROL DEPTB(FEET) =MAXIMUM NUMBER OF INTERVALS IN PROFILE =CONSTANT P I P ~D I A M ~ T ~ R ( I N C H E S )= 78.000NORMAL DEPTH(FEET) = 3.52CRITICAL DEPTB(FEET) = 4.65

.0130003.00

15

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

UPSTREAM CONTROL ASSUMED DEPTH(FT) = 3.00GRADUALLY VARIED FLOW PROFILE COMPUTED INFORMATION:

DISTANCE FROMCONTROL(FT)

.00021.597

44.22468.05093.288

120.212149.181180.682215.398254.326299.0093 5 2 . 0 2 5418.187500.000

FLOWDEPTH(FT)

3.0003.0353.0703.1053 . 1 3 93.1743.2093.2443.2793.3143.3493 . 3 6 43.4183.450

VELOCITY(FT/SEC)

20.03619.73819.44919.1671 8 . 6 9 418.62818.36918.11817.87317.63517.4031 7 . 1 7 716.95716.762

SPECIFICENERGY (FT)

9.2389.0888.9478.8138 . 6 8 68.5668.4528.344B.2428 .146B.0547.9697. BB67.616

PRESSURE+MOMENTUM (POUNDS)

12834.0912693.4412558.2112428.2012303.2512183.1612067.7911956.9511850.4911748.2911650.2111 5 5 6 . 1111465.8511 3 8 7 1 0

; = = = = = = = = = = = = = = = = = = = = = = = = = a = = = ~ = = = = = = = = = = = = = = = = = = = = = =


142/142

REFERENCES

Brater, E.F. and King, H.W. Handbook of Hydraulics for theSolut ion of Hydraulic Engineering Problems, Sixth Edit ion , Md;raw-Hill Book Co., New York, (1976).

Daugherty, R.L. and Fran z i n i , J .B. , Fl u i d Mechanics withEngineering AWlicat1ons, McGraw-Hill ook Co., New York, (1977).

Hromadka I I T.V., Clements, J.N., and Sa lu ja , H., ComputerMethods in Urban Watershed Hydraulics , Lighthouse Publications,Mission Viejo, California, 1984.

Hromadka I I T.V., Clements, J.N., and Guymon, G.L., -Guidelinesfor Interact ive Software in Water Resources Engineering,- WaterResources Bulletin, Feb. (1983c)

Hromadka I I T.V., Durbin, T.J. and DeVries, J . J . , ComputerMethods i n Water Resources , Lighthouse Publicat ions , MissionViejO, California, (1985).

Kouti tas , C.G., Elements of Computational Hydraulics r PentechPress, (1983).

aes computational hydraulics for civil engineers

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