basic fluid dynamic - vicphysics基本的流体动力vicphysics

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1、6NagleCollegeU2PhysicsBasicFluiddynamicDraftThisisanoteforsomegiftedstudentswhowantmorechallengeofthetopic.1.Laminar(steady)flowAcceleratingforce(inertiaforce)Retardingforce(viscousforce)·Afluidisshearedwhenitflowspastasurface.Theoppositionsetupbythefluidtosheariscalle

2、dviscosity.·Viscosityisakindofinternalfrictionexhibitedtosomedegreebyallfluid.Itarisesinliquidsbecausetheforcedmovementofamoleculerelativetoitsneighboursisopposedbytheintermolecularforcesbetweenthem.·Viscousforcesactassoonasfluidflowstarts.Iftheexternalforcescausingthe

3、flowareconstant,therateofflowbecomesconstant–steadyflow,retardingforce(viscousforce)=appliedforce(acceleratingforce,inertiaforce).Theviscousforcestopstheflowwhentheappliedforceisremoved.·Newtonianfluid;Tangentialstressαvelocitygradientwhentemperature=const.2.Coefficien

4、tofviscosityη·η=(tangentialstress/velocitygradient)=shearstress/velocitygradientAccelerationforceη=(F/A)/(δv/δh)RetardingforceAV+δvVδh3.Bernoulli’sequationP1+½ρV12+ρgh1=P2+½ρV22+ρgh2=kP1+½ρV12+ρgh1=k=totalpressurecreatedbythefluidinasystem.P1isthestaticpressure,apressu

5、recomponent,whichisnormal(90o)tothevelocityoftheflowingfluid.6½ρV12isthedynamicpressure,apressurecomponent,whichcreatedbythevelocityoftheflowingfluid.ρgh1isthefluidpressure.P1+½ρV12=k=totalpressurecreatedbythemovingfluid(V1)inasystem.whenh1=0m.P1=staticpressure(theonly

6、realpressure),½ρV12=dynamicpressure.Pressure(P1)fallswhenvelocityV1risesandviceversa.1.UnderSteadyFlow·Poiseuille’sFormulaeQ=(πΔpr4)/(8ηL)eg.weepP+ΔpL2r·Thisformulaewillnotworkwhentheflowbecomesunsteady(turbulent)orwithnonNewtonianfluid(compressibleandviscous),eg.blood

7、flowinvessel.2.TurbulentFlow·Afluidmotioninwhichvelocity,pressure,andotherflowquantitiesfluctuatesirregularlyintimeandspace,Eddiescurrentexisted.Itiscalledturbulentornonlaminarflow.3.Reynold’sNumber.ReRe=Inertiaforce/ViscousforceRe=(ρvL)/ηρ=densityofafluidv=velocityoft

8、hefluidL=Lengthofflowordiameterofthepipeη=coefficientofviscosityofthefluid·Itplayacentralroleindeterminethestateofflu