Open Channel Flow明渠流量讲解

OpenChannelFlowOpenChannelFlowLiquid(water)flowwitha____________(interfacebetweenwaterandair)relevantfornaturalchannels:rivers,streamsengineeredchannels:canals,sewer

linesorculverts(partiallyfull),stormdrainsofinteresttohydraulicengineerslocationoffreesurfacevelocitydistributiondischarge-stage(______)relationshipsoptimalchanneldesignfreesurfacedepthTopicsinOpenChannelFlowUniformFlowDischarge-DepthrelationshipsChanneltransitionsControlstructures(sluicegates,weirs…)RapidchangesinbottomelevationorcrosssectionCritical,SubcriticalandSupercriticalFlowHydraulicJumpGraduallyVariedFlowClassificationofflowsSurfaceprofilesnormaldepthClassificationofFlowsSteadyandUnsteadySteady:velocityatagivenpointdoesnotchangewithtimeUniform,GraduallyVaried,andNonuniformUniform:velocityatagiventimedoesnotchangewithinagivenlengthofachannelGraduallyvaried:gradualchangesinvelocitywithdistanceLaminarandTurbulentLaminar:flowappearstobeasamovementofthinlayersontopofeachotherTurbulent:packetsofliquidmoveinirregularpaths (Temporal)(Spatial)MomentumandEnergyEquationsConservationofEnergy“losses”duetoconversionofturbulencetoheatusefulwhenenergylossesareknownorsmall____________Mustaccountforlossesifappliedoverlongdistances_______________________________________________ConservationofMomentum“losses”duetoshearattheboundariesusefulwhenenergylossesareunknown____________ContractionsExpansionWeneedanequationforlossesGivenalongchannelof

constantslopeandcross

sectionfindtherelationship

betweendischargeanddepthAssumeSteadyUniformFlow-________________prismaticchannel(nochangein_________withdistance)UseEnergyandMomentum,EmpiricalorDimensionalAnalysis?Whatcontrolsdepthgivenadischarge?Whydoesn’ttheflowaccelerate?OpenChannelFlow:Discharge/DepthRelationshipPnoaccelerationgeometryForcebalanceASteady-UniformFlow:ForceBalanceWWsinDxabcdShearforceEnergygradelineHydraulicgradelineShearforce

=________Wcos

Wettedperimeter=__Gravitationalforce=________HydraulicradiusRelationshipbetweenshearandvelocity?______________toP

DxPgA

DxsinqTurbulenceGeometricparameters_________________________________________________________WritethefunctionalrelationshipDoesFraffectshear?_________Hydraulicradius(Rh)Channellength(l)Roughness(e)OpenConduits:

DimensionalAnalysisNo!PressureCoefficientforOpenChannelFlow?PressureCoefficientHeadlosscoefficientFrictionslopecoefficient(EnergyLossCoefficient)FrictionslopeSlopeofEGLDimensionalAnalysisHeadlosslengthofchannel(likefinDarcy-Weisbach)Chezyequation(1768)IntroducedbytheFrenchengineerAntoineChezyin1768whiledesigningacanalforthewater-supplysystemofPariswhereC=Chezycoefficientwhere60isforroughand150isforsmoothalsoafunctionofR(likefinDarcy-Weisbach)compareDarcy-Weisbachequation(1840)whered84=rocksizelargerthan84%oftherocksinarandomsampleForrock-beddedstreamsf=Darcy-WeisbachfrictionfactorManningEquation(1891)MostpopularinU.S.foropenchannels(Englishsystem)verysensitivetonDimensionsofn?Isnonlyafunctionofroughness?(MKSunits!)NO!T/L1/3BottomslopeValuesofManningnd=mediansizeofbedmaterialn=f(surfaceroughness,channelirregularity,stage...)dinftdinmTrapezoidalChannelDeriveP=f(y)andA=f(y)foratrapezoidalchannelHowwouldyouobtainy=f(Q)?z1byUseSolver!FlowinRoundConduitsyTArradiansMaximumdischargewheny=______0.938dOpenChannelFlow:EnergyRelationsenergygradelinehydraulicgradelinevelocityheadBottomslope(So)notnecessarilyequaltosurfaceslope(Sf)watersurfaceEnergyrelationshipsTurbulentflow(

1)z-measuredfromhorizontaldatumy-depthofflowPipeflowEnergyEquationforOpenChannelFlowFromdiagramonpreviousslide...SpecificEnergyThesumofthedepthofflowandthevelocityheadisthespecificenergy:Ifchannelbottomishorizontalandnoheadlossy-potentialenergy-kineticenergyForachangeinbottomelevationySpecificEnergyInachannelwithconstantdischarge,QwhereA=f(y)Considerrectangularchannel(A=By)andQ=qBABy3roots(oneisnegative)qisthedischargeperunitwidthofchannelSpecificEnergy:SluiceGate12sluicegateEGLy1andy2are___________depths(samespecificenergy)Whynotusemomentumconservationtofindy1?q=5.5m2/sy2=0.45mV2=12.2m/sE2=8malternateGivendownstreamdepthanddischarge,findupstreamdepth.SpecificEnergy:RaisetheSluiceGate12sluicegateEGLassluicegateisraisedy1approachesy2andEisminimized:Maximumdischargeforgivenenergy.SpecificEnergy:StepUpShort,smoothstepwithriseDyinchannelDyGivenupstreamdepthanddischargefindy2Increasestepheight?PACriticalFlowTdyyT=surfacewidthFindcriticaldepth,ycArbitrarycross-sectionA=f(y)dAHydraulicDepthycCriticalFlow:

RectangularchannelycTAcOnlyforrectangularchannels!Giventhedepthwecanfindtheflow!CriticalFlowRelationships:

RectangularChannelsFroudenumbervelocityhead=becauseforcegravityforce

inertial0.5(depth)CriticalFlowCharacteristicsUnstablesurfaceSeriesofstandingwavesOccurrenceBroadcrestedweir(andotherweirs)ChannelControls(rapidchangesincross-section)OverfallsChangesinchannelslopefrommildtosteepUsedforflowmeasurements___________________________________________UniquerelationshipbetweendepthanddischargeDifficulttomeasuredepthBroad-crestedWeirHPycECdcorrectsforusingHratherthanE.Broad-crestedweirEmeasuredfromtopofweirHardtomeasureycBroad-crestedWeir:ExampleCalculatetheflowandthedepthupstream.Thechannelis3mwide.IsHapproximatelyequaltoE?0.5ycEBroad-crestedweiryc=0.3mSolutionHowdoyoufindflow?____________________HowdoyoufindH?______________________CriticalflowrelationEnergyequationHydraulicJumpUsedforenergydissipationOccurswhenflowtransitionsfromsupercriticaltosubcriticalbaseofspillwayWewouldliketoknowdepthofwaterdownstreamfromjumpaswellasthelocationofthejumpWhichequation,EnergyorMomentum?HydraulicJump!HydraulicJumpy1y2LEGLhLConservationofMomentumHydraulicJump:

ConjugateDepthsMuchalgebraForarectangularchannelmakethefollowingsubstitutionsFroudenumbervalidforslopes<0.02HydraulicJump:

EnergyLossandLengthNogeneraltheoreticalsolutionExperimentsshowLengthofjumpEnergyLosssignificantenergyloss(toturbulence)injumpalgebraforGraduallyVariedFlowEnergyequationfornon-uniform,steadyflowPATdyyGraduallyVariedFlowChangeinKEChangeinPEWeareholdingQconstant!GraduallyVariedFlowGoverningequationforgraduallyvariedflowGiveschangeofwaterdepthwithdistancealongchannelNoteSoandSfarepositivewhenslopingdownindirectionofflowyismeasuredfromchannelbottomdy/dx=0meanswaterdepthisconstantyniswhenSurfaceProfilesMildslope(yn>yc)inalongchannelsubcriticalflowwilloccurSteepslope(yn<yc)inalongchannelsupercriticalflowwilloccurCriticalslope(yn=yc)inalongchannelunstableflowwilloccurHorizontalslope(So=0)ynundefinedAdverseslope(So<0)ynundefinedNote:Theseslopesaref(Q)!NormaldepthSteepslope(S2)HydraulicJumpSluicegateSteepslopeObstructionSurfaceProfiles S0-Sf 1-Fr2

dy/dx + + + - + - - - +ynycMoreSurfaceProfiles S0-Sf 1-Fr2

dy/dx1 + + +2 + - -3 - - +ynycDirectStepMethodenergyequationsolveforDxrectangularchannelprismaticchannelDirectStepMethod

FrictionSlopeManningDarcy-WeisbachSIunitsEnglishunitsDirectStepLimitation:channelmustbe_________(sothatvelocityisafunctionofdepthonlyandnotafunctionofx)Methodidentifytypeofprofile(determineswhetherDyis+or-)chooseDyandthusyn+1calculatehydraulicradiusandvelocityatynandyn+1calculatefrictionslopeynandyn+1

calculateaveragefrictionslopecalculate

DxprismaticDirectStepMethod=(G16-G15)/((F15+F16)/2-So)ABCDEFGHIJKLMyAPRhVSfEDxxTFrbottomsurface0.9001.7994.2230.4260.1390.000040.90103.7990.0650.0000.9000.8701.6874.0890.4120.1480.000050.8710.4980.53.6790.0700.0300.900=y*b+y^2*z=2*y*(1+z^2)^0.5+b=A/P=Q/A=(n*V)^2/Rh^(4/3)=y+(V^2)/(2*g)StandardStepGivenadepthatonelocation,determinethedepthatasecondlocationStepsize(x)mustbesmallenoughsothatchangesinwaterdeptharen’tverylarge.OtherwiseestimatesofthefrictionslopeandthevelocityheadareinaccurateCansolveinupstreamordownstreamdirectionupstreamforsubcriticaldownstreamforsupercriticalFindadepththatsatisfiestheenergyequationWhatcurvesareavailable?S1S3Isthereacurvebetweenycandynthatdecreasesindepthintheupstreamdirection?WaveCelerityF1y+yV+VVVwunsteadyflowyyy+yV+V-VwV-VwsteadyflowV+V-VwV-VwF2WaveCelerity:

MomentumConservationyy+yV+V-VwV-VwsteadyflowPerunitwidthWaveCelerityMassconservationyy+yV+V-VwV-VwsteadyflowMomentumWavePropagationSupercriticalflowc<Vwavesonlypropagatedownstreamwaterdoesn’t“know”whatishappeningdownstream_________controlCriticalflowc=VSubcriticalflowc>VwavespropagatebothupstreamanddownstreamupstreamMostEfficientHydraulicSectionsAsectionthatgivesmaximumdischargeforaspecifiedflowareaMinimumperimeterperareaNofrictionallossesonthefreesurfaceAnalogytopipeflowBestshapesbestbestwith2sidesbestwith3sidesWhyisn’tthemostefficienthydraulicsectionthebestdesign?Minimumarea=leastexcavationonlyiftopofchannelisatgradeCostoflinerComplexityofformworkErosionconstraint-stabilityofsidewallsOpenChannelFlowDischargeMeasurementsDischargeWeirbroadcrestedsharpcrestedtriangularVenturiFlumeSpillwaysSluicegatesVelocity-Area-IntegrationDischargeMeasurementsSharp-CrestedWeirTriangularWeirBroad-CrestedWeirSluiceGateExp