流体力学6-粘性流体

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1、06ViscousFlowinDucts06-2ObjectivesHaveadeeperunderstandingoflaminarandturbulentflowinpipesandtheanalysisoffullydevelopedflow.Calculatethemajorandminorlossesassociatedwithpipeflowinpipingnetworksanddeterminethepumpingpowerrequirements.06-3Recall-becauseoftheno-slipcondition,thev

2、elocityisnotuniform,andatthewallsofaductflowiszero.IncompressibleFlow:VelocityandMassFlowRateWeareofteninterestedonlyinVavg,whichweusuallycalljustV(dropthesubscriptforconvenience).Keepinmindthattheno-slipconditioncausesshearstressandfrictionalongthepipewalls.Forpipesofconstantd

3、iameterandincompressibleflow,V(average)staysthesamesinceQ1=Q2.VV21Forpipeswithvariablediameter,misstillthesameduetoconservationofmass,butV1≠V2..d221V1d1m.m.V206-4LaminarandTurbulentFlowsCanbesteadyorunsteady.Alwaysunsteady.Therearealwaysrandom,swirlingmotionsinaturbulentflow.Ca

4、nbeone-,two,three-dimensional.Alwaysthree-dimensional.However,itcanbe1-Dor2-Dinthemean.Hasregular,predictablebehavior.Hasirregularorchaoticbehavior.Cannotpredictexactlythereissomerandomnessassociatedwithit.Analyticalsolutionpossible.Noanalyticalsolutionexitssofar!It’stoocompli

5、cated.OccursatlowReynoldsnumbers.OccursathighReynoldsnumbers.LaminarFlowTurbulentFlowFlow06-5LaminarandTurbulentFlows:ReynoldsNumberDefinitionForcircularpipes/ducts,PhysicalSignificanceForcircularpipes/ducts,Thesevaluesareapproximate,differentbooksmaygiveslightlydifferentvalues

6、.Foragivenapplication,thesevaluesdependsuponPiperoughnessVibrationsUpstreamfluctuations,disturbances(valves,elbows,etc.thatmaydisturbtheflow),...CriticalReynoldsNumberForcircularpipes/ducts,thecriticalReynoldsnumberistheReynoldsnumberatwhichtransitionfromlaminaflowstarts,06-6Th

7、eEntranceRegionEntranceLengthAboundarylayerisalayeroffluidintheimmediatevicinityofaboundingsurface,overwhichthevelocitygradientisnotequaltozero.BoundaryLayerTheprofiledevelopsdownstreamoverseveraldiameterscalledtheentrylengthLe.Le/disafunctionofRe.Consideraroundpipeofdiameterd.

8、06-7EntranceLengthofCircularPipesLaminarflowTurbulentf