08 open_channel (1).ppt

Monroe L. Weber-Shirk School of Civil and Environmental EngineeringOpen Channel Flow depthOpen Channel FlowLiqid !water" flow with a #### ######## !interface between water and air"relevant fornatral channel$% river$& $tream$engineered channel$% canal$& $ewer line$ or clvert$ !partiall' fll"& $torm drain$of intere$t to h'dralic engineer$location of free $rfacevelocit' di$tribtiondi$charge - $tage !######" relation$hip$optimal channel de$ignfree $rface (opic$ in Open Channel Flow)niform Flow*i$charge-*epth relation$hip$Channel tran$ition$Control $trctre$ !$lice gate$& weir$+",apid change$ in bottom elevation or cro$$ $ectionCritical& Sbcritical and Spercritical Flow-'dralic .mp/radall' 0aried FlowCla$$ification of flow$Srface profile$normal depth Cla$$ification of Flow$Stead' and )n$tead'Stead'% velocit' at a given point doe$ not change with time)niform& /radall' 0aried& and ,apidl' 0aried)niform% velocit' at a given time doe$ not change within a given length of a channel/radall' varied% gradal change$ in velocit' with di$tanceLaminar and (rblentLaminar% flow appear$ to be a$ a movement of thin la'er$ on top of each other(rblent% packet$ of liqid move in irreglar path$!(emporal"!Spatial" Momentm and Energ' Eqation$Con$ervation of Energ'1lo$$e$2 de to conver$ion of trblence to heat$efl when energ' lo$$e$ are known or $mall############M$t accont for lo$$e$ if applied over long di$tance$###############################################Con$ervation of Momentm1lo$$e$2 de to $hear at the bondarie$$efl when energ' lo$$e$ are nknown############Contraction$E3pan$ionWe need an eqation for lo$$e$ /iven a long channel of con$tant $lope and cro$$ $ection find the relation$hip between di$charge and depth4$$meStead' )niform Flow - ### #############pri$matic channel !no change in ######### with di$tance")$e Energ'& Momentm& Empirical or *imen$ional 4nal'$i$5What control$ depth given a di$charge5Wh' doe$n6t the flow accelerate5Open Channel Flow% *i$charge7*epth ,elation$hip 8no accelerationgeometr'Force balance4ld hl9: Stead'-)niform Flow% Force ;alanceWW $in 3abcdShear forceEnerg' grade line-'dralic grade lineShear force o? 8re$$re Coefficient for Open Channel Flow5==CV pp ==CVghlhl==CffSgSlV=l fh Sl =lh p 8re$$re Coefficient-ead lo$$ coefficientFriction $lope coefficient!Energ' Lo$$ Coefficient"Friction $lopeSlope of E/L *imen$ional 4nal'$i$& & ,efSh hlC fR Re = fhSRCll ===fhgSl RV ll ==f hgSRVl==f hgV SRl=& ,efSh hlC fR Re = -ead lo$$ length of channel& ,efhShRC fl Rel = = ==ffSgSlCV=!like f in *arc'-Wei$bach"==fhVSR gl=gVDLhl=f= Che@' Eqation !ABCD"Entrodced b' the French engineer 4ntoine Che@' in ABCD while de$igning a canal for the water-$ppl' $'$tem of 8ari$h fV C R S =AF: G C G C:smsmwhere C < Che@' coefficientwhere C: i$ for rogh and AF: i$ for $moothal$o a fnction of R !like f in *arc'-Wei$bach"=f hgV SRl=compare:.::F9 H H :.:::DB l9hd R For a pipe:.:== H f H :.::IF *arc'-Wei$bach Eqation !AD9:"where dD9 < rock $i@e larger than D9J of the rock$ in a random $ampleFor rock-bedded $tream$f < *arc'-Wei$bach friction factor=D9AfA.= =.:IloghRd _ 1+ 1 ] ,998 =dddARh

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=f=ll Vhd g==f9 =lhl VhR g==f9 =fhl VSlR g==fDf hVSRg=Dff hgV SR =A =.F=logA=f ,e fhR _ + ,Similar to Colebrook Manning Eqation !ADKA"Mo$t poplar in ).S. for open channel$!Engli$h $'$tem"A7=o=7IhS ,AnV A7=o=7IhS ,9K . AnV VA Q= 7 A I 7 =Ao hS ARnQver' $en$itive to n*imen$ion$ of*imen$ion$ of n n5 5E$E$ n n onl' a fnction of roghne$$5 onl' a fnction of roghne$$5!MLS nit$?">O?( 7LA7I;ottom $lope 0ale$ of Manning nLined Canalsn Cement plaster0.011 Untreated gunite0.016 Wood, planed0.012 Wood, unplaned0.013 Concrete, trowled0.012 Concrete, wood forms, unfnished0.015 Rubble in cement0.020 Asphalt, smooth0.013 Asphalt, rough0.016 Natural Channels Gravel beds, straight0.025 Gravel beds plus large boulders0.040 Earth, straight, with some grass0.026 Earth, winding, no vegetation0.030 Earth , winding with vegetation0.050 d < median $i@e of bed materialn < f!$rface roghne$$& channel irreglarit'& $tage..."C 7 A:ID . : d nC 7 A:IA . : d nd in ftd in m (rape@oidal Channel*erive 8 < f!'" and 4 < f!'" for a trape@oidal channel-ow wold 'o obtain ' < f!M"5@Ab'z y yb A=+ ( )A7 ==== P y yz b = + + A7 === A P y z b = + + = 7 A I 7 =Ao hS ARnQ)$e Solver? Flow in ,ond Condit$

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r y rarcco$ ( ) co$ $in= r A $in =r T '(4r r P = radian$Ma3imm di$charge when ' < ######:.KIDd( ) ( )$in co$ r r q q = 0elocit' *i$tribtion( ):AA ln yv y V gdSd _ + + ,A ln yd- =4t what elevation doe$ the velocit' eqal the average velocit'5For channel$ wider than A:d:.9 k 0on LNrmNn con$tant0 < average velocit'd < channel depthAy de=:.ICDd:.9d:.Dd:.=d0 Open Channel Flow% Energ' ,elation$=g0=AA=g0===x So=yAyx L fh S x = D###### grade line####### grade linevelocit' head;ottom $lope !So" not nece$$aril' eqal to E/L $lope !Sf"h'dralicenerg' Energ' ,elation$hip$= =A A = =A A = == =Lp V p Vz z hg ga ag g++ = ++ += =A =A == =o fV Vy S x y S xg g+D + = + +D(rblent flow ! A"@ - mea$red from hori@ontal datm' - depth of flow8ipe flowEnerg' Eqation for Open Channel Flow= =A =A == =o fV Vy S x y S xg g+ +D = + +DFrom diagram on previo$ $lide... Specific Energ'(he $m of the depth of flow and the velocit' head i$ the $pecific energ'%gVy E==+ Ef channel bottom i$ hori@ontal and no head lo$$= AE E ' - ####### energ'gV==- ####### energ'For a change in bottom elevationA =E y E - D =x S E x S Eo + +f = A'potentialkineticO pre$$re Specific Energ'En a channel with con$tant di$charge& M= = A AV A V A Q ===gAQy E + gVy E==+ where 4ow eqate pre$$re and momentm( )A ===A=p pF F g y y y r d + = - + ( )= = =A==(g y y y y y yV V V r d d r d - - - = - Wave Celerit'( ) ( ) ( )( (V V V y y V V y + + ( ( (yV yV V y V y yV yV yV yV + + + ( )yyV V V( ( ) V V V y g( ( )yyV V y g(= ( )=(V V gy (V V ! gy ! Ma$$ con$ervation''O'0O0-0w0-0w$tead' flowMomentm!VFrygV Wave 8ropagationSpercritical flowcG0wave$ onl' propagate down$treamwater doe$n6t 1know2 what i$ happening down$tream######### controlCritical flowcotch Weir;road-Cre$ted WeirSlice /ateF7 =D= tanAF =dQ C g % _ ,I7 ==IdQ C b g % _ ,I7 ===IdQ C b g% A=d gQ C by gy E3plain the e3ponent$ of -?= V g% Smmar' !A"4ll the complication$ of pipe flow pl$ additional parameter... #################0ario$ de$cription$ of energ' lo$$Che@'& Manning& *arc'-Wei$bachEmportance of Frode >mberFrHA decrea$e in E give$ increa$e in 'FrGA decrea$e in E give$ decrea$e in 'Fr