中北 工程流体力学

2020/3/161第二章流体的性质2020/3/1622.1DistinctionsbetweenSolidsandFluids2.2ContinuumHypothesis2.3FluidsProperties2.4ForcesonFluidsOutlines2020/3/1631)Shape:asolidtendstoretainitsshape,andthisisnotthecaseforafluid.(固体有一定的形状，而流体没有)2)Deformation:underacertainforces,solidsproducelimiteddeformation,whilefluidsdeformcontinuously.(在一定的力的作用下，固体产生一定的变形，流体是连续变形)2020/3/1643)Distinctionbetweenagasandaliquidgasisverycompressiblegastendstoexpandindefinitely;aliquidhasafreesurfaceConclusion:Thesolidhasdefinitevolumeandshape;theliquidhasdefinitevolumebuthaveindefiniteshape,thegashasneitherindefinitevolumenorindefiniteshape.2020/3/165Elementalvolume（流体微团、流体质点）Largeenoughinmicroscope（微观）10-9mm3ofairatstandardconditionscontainsapproximately3×107molecules.Smallenoughinmacroscope（宏观）.Mostengineeringproblemsareconcernedwithphysicaldimensionsmuchlargerthanthislimitingvolume.2020/3/166Suchafluidiscalledacontinuum,whichsimplymeansthatitsvariationinpropertiesissosmooththatthedifferentialcalculuscanbeusedtoanalyzethesubstance.*Smallenoughinmacroscope（宏观）.微观无穷大宏观无穷小Sodensityisessentiallyapointfunctionandfluidpropertiescanbethoughtofasvaryingcontinuallyinspace.2.2ContinuumHypothesis(连续介质假设）2020/3/167Conclusion:Definitionofthemodel◦ThespaceofFluidsisfullofmoleculeswithoutanyclearance.Purpose◦Suchvariables(physicalquantity)asvolume,pressure,temperature,density,viscosity,velocity,accelerationandsooncanbedescribedbydifferentialequations.Appliedcondition◦Whenthecharacteristiclengthofanobjectisfargreaterthanthemeanfreedistanceofmolecules.2.2ContinuumHypothesis(连续介质假设）2020/3/168(1)Density(denotedbyρ):DensityofafluidisitsmassperunitvolumeDensity,specificweight,Viscosity,CompressibilityandExpansivitydvdmΔvΔm0ΔvlimρUnitofdensity:slug/ft3(slugspercubicfoot),kg/m3,lb.sec2/ft4,N.s2/m42020/3/169Specificweightrepresentstheforceexertedbygravityonaunitvolumeoffluid.Unitofspecificweight:lb/ft3(poundspercubicfoot),N/m3.dVdMΔVΔG0ΔVlimVGgg2020/3/1610orgg2020/3/1611Compressiblefluids:withvariabledensities.Incompressiblefluids:withconstantdensities.commonsenseThevolumeoffluidchangesunderdifferentpressure.Thepropertythatthevolumeofafluiddecreasesasthepressurerisesiscalledcompressibility2020/3/1612Liquidsareusuallybeconsideredasincompressiblefluids.Thegasescanalsobeconsideredasincompressiblefluids,whenthepressurevariationissmallcomparedwiththeabsolutepressure.2020/3/1613Inproblemsinvolvingwaterhammer(ashortquickstrikeindicateshighvelocityofflowing)Foragasorsteamflowingathighvelocity2020/3/1614dpvdvkvdvdpEvCompressionCoefficientAsthetemperatureisconstant,themagnitudeofcompressibilityisevaluatedbythecoefficientofvolumecompressibility,arelativevariationrateofvolumeperunitpressure.BulkModulusofElasticity(elasticmodulus)GuesstheunitThereciprocalunit2020/3/1615Forliquids,Evisafunctionoftemperatureandpressure.T一定时，p↑,则Ev↑p一定时，在120℉（50℃）水的Ev最大，即压缩性最小。2020/3/1616(4)ExpansibilitythermalexpansibilityThevolumeofliquidincreasesasthetemperaturerises.Themagnitudeofvolumeexpansionabilityisevaluatedby:VolumeexpansioncoefficientdTvdvv2020/3/1617Example1—1Calculatetherelativerateofchangeofwaterdensitywhenthewaterpressurewasincreasedfrom5atto10atundernormaltemperature.Solution:thisproblemistheapplicationofcompressioncoefficientequationofaliquidundernormaltemperature.Solution1：941then0.53810(105)9.81100.0264%ppddpddp2020/3/1618i)DefinitionandReasonDefinitionofviscosityThepropertyofshowinginteriorfrictionbetweentwoadjacentflowlayersforretardingtheirrelativemotions.Reasons◦thecohesion(astotheliquid)◦themomentuminterchange(astothegas).◦Slowingdownthefastflowlayer◦Speedinguptheslowflowlayer2020/3/1619y0ii)Newton’sLawofViscosityτ----Tangentstress,N/m2μ----Dynamicviscosity,Pa·spronounced/mu/(μ/ρ)----Kinematicviscosity,m2/sdenotedby,pronounced/nu/AhUF'FhFAdyduFUuYAUFdyduYUAF2020/3/1620Example1-2Inthefollowingfigure,alubricatedshaftrotatesinsideaconcentricsleevebearingat1200rpm.TheclearanceδissmallwithrespecttotheradiusRsoalinearvelocitydistributioninthelubricantmaybeassumed.Whatarethepowerrequirementstorotatetheshaft?R=2cm,L=6cm,δ=0.1mm,andμ=0.2Pa.s.2020/3/1621SolutionTheenergyloss,duetoviscousshear,perunittimeindicatesthepowerrequirements.)2(RLRAhUFNmRLRRFM758.0)2()(3.95WMrategenerationHeatPowerRLA22020/3/1622iii）InfluenceofTemperatureandPressureonViscosityTemperatureCistwhenTSTSMPapGasCistwhenttWater0023000200)273(273)1(0000221.00337.01：：GasLiquidTexchangeMomentumGasattractionsMolecule'LiquidfactorsMain2020/3/16232020/3/1624PressureForliquidμ0—whenp=1atmosphericpressure—Coefficient,Pa-1GasLiquidpppe0tconstan2020/3/1625iv）NewtonianFluidandNon-NewtonianFluidDA:NewtonianfluidCdydvxBτ0τoElasticsolidIdealfluidNewtonianfluid:μdoesnotchange(linear)non-Newtonianfluid:μvaries(nonlinear)2020/3/1626v）ViscousFluidandIdealFluidViscousfluid:PracticalfluidInarealfluid,tangentialorshearingforcesalwaysdevelopwheneverthereisarelativemotion,thuscreatingfluidfriction.2020