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wordword/wordChapter1Fluidstatics流体静力学连续介质假定(Continuumassumption):Therealfluidisconsideredasno-gapcontinuousmedia,calledthebasicassumptionofcontinuityoffluid,orthecontinuumhypothesisoffluid.流体是由连续分布的流体质点(fluidparticle)所组成,彼此间无间隙。它是流体力学中最根本的假定,1755年由欧拉提出。在连续性假设之下,表征流体状态的宏观物理量在空间和时间上都是连续分布的,都可以作为空间和时间的函数。流体质点〔Fluidparticle〕:AfluidelementthatissmallenoughwithenoughmolestomakesurethatthemacroscopicmeandensityhasdefinitevalueisdefinedasaFluidParticle.宏观上足够小,微观上足够大。流体的粘性〔Viscosity〕:isaninternalpropertyofafluidthatoffersresistancetosheardeformation.Itdescribesafluid'sinternalresistancetoflowandmaybethoughtasameasureoffluidfriction.流体在运动状态下抵抗剪切变形的性质,称为黏性或粘滞性。它表示流体的内部流动阻力,也可当做一个流体摩擦力量。Theviscosityofagasincreaseswithtemperature,theviscosityofaliquiddecreaseswithtemperature.牛顿内摩擦定律〔Newton’slawofviscosity〕:Thedynamicviscosity〔动力黏度〕isalsocalledabsoluteviscosity〔绝对黏度〕.Thekinematicviscosity〔运动黏度〕istheratioofdynamicviscositytodensity.pressibility〔压缩性〕:Asthetemperatureisconstant,themagnitudeofpressibilityisexpressedbycoefficientofvolumepressibility(体积压缩系数)к,arelativevariationrate〔相对变化率〕ofvolumeperunitpressure.Thebulkmodulusofelasticity(体积弹性模量)Eisthereciprocalofcoefficientofvolumepressibilityк.流体的膨胀性(expansibility;dilatability):Thecoefficientofcubicalexpansion(体积热膨胀系数)αtistherelativevariationrateofvolumeperunittemperaturechange.外表X力Surfacetension:Apropertyresultingfromtheattractiveforcesbetweenmolecules.单位长度所受拉力外表力Surfaceforce——istheforceexertedonthecontactsurfacebythecontactedfluidorotherbody.Itsvalueisproportionaltocontactarea.作用在所研究流体外外表上与外表积大小成正比的力。Stress〔应力〕isthesurfaceforceonperunitarea.质量力Massforce——Theforceactingoneveryfluidmassparticlewithinthecontrolbody.Itsvalueisproportionaltoitsmass.Massforceisalsoknownasbodyforce.作用在流体的每一个流体质点上,其大小与流体所具有的质量成正比。EulerEquilibriumEquations欧拉平衡微分方程〔分量式〕1775年PhysicalMeaning:Forthefluidinequilibrium,surfaceforceponentspermassfluidareequaltomassforceponentspermassfluid.Pressurevariationrateinaxesdirectionsareequaltomassforceponentsperunitvolumeinaxesdirectionsrespectivelyconstant-pressureSurface(等压面)——asurfacethatthepressureofeverypointinliquidisequal.monconstant-pressuresurfacesarefreeliquidsurfaceandinterfaceoftwounmixedfluidsinequilibrium.平衡流体中压强相等的点所组成的平面或曲面。PressureDistributionintheStaticFluid重力场中流体的平衡Conclusions:1.Pressureatapointinastaticfluidundergravityincreaseslinearlywithdepth.2.Pressureatapointinastaticfluidundergravityisequaltothesumofthepressureatthefreesurfaceandthefluidspecificweighttimingdepth.3.constant-pressuresurfaceinastaticfluidundergravityisahorizontalplane.4.Extended:whilethepressureatapointandthedepthdifferencebetweentwopointsareknown,thepressureatanotherpointcanbecalculated.Absolutepressure(绝对压力),Gagepressure(相对压力,又称“表压力〞),andVacuum(真空度):表压力=绝对压力-大气压力;真空度=大气压力-绝对压力FluidinRelativeEquilibrium(相对静止流体)Equationofconstant-pressuresurface(等压面方程):UniformLinearAcceleration等加速度直线运动流体:UniformRotationaboutaVerticalAxis等角速度旋转流体:Chapter2basicequationsoffluidmechanics迹线pathline:thetraceafterasingleparticletravelsinafieldofflowoveraperiodoftime.流体质点的运动轨迹曲线流线streamline:acurvethatshowthedirectionofanumberofparticlesatthesameinstantoftime.某一时刻处处与速度矢量相切的空间曲线--瞬时性。Stream-tube(流管)——Consideraclosedcurve(notstreamline)intheflowfield,thendrawstreamlinesthrougheverypointonit,soastoformatube-shapingspacewhosewallsarestreamlines.Thistubeiscalledthestream-tube.在流场中任取一个有流体从中通过的封闭曲线,在曲线上的每一个质点都可以引出一条流线,这些流线簇围成的管状曲面称为流管。Tube-flow流束——Fluidfullingthestreamtubeiscalledthetube-flowandthelimitofatube-flowisastreamline.流管内的全部流体称为流束。Ministream-tube微小流束——Thestreamtubewithaninfinitesimalsectionissaidtobemini-streamtube.Streamlineistheextremecaseofmini-streamtube.截面无穷小的流束。Totalflow总流——Totalofcountlessmini-streamtubesiscalledtotalflow.包含流动中所有的微小流束。Crosssection(过水断面)Thesectionisperpendiculartothedirectionoffluidflow.(suchaspipeflowandchannelflow)与流束或总流流线成正交的断面。Discharge(流量)Amountoffluidpassthroughacrosssectionperunittime(suchasthesectioninthechannelorpipe).单位时间内通过某一过水断面的流体体积称为体积流量,简称流量。Meanvelocity断面平均流速Thevelocitiesofpointsonthesamecrosssectioninthetotalflowaredifferent,sousuallyanaveragevelocityisusedinsteadoftherealvelocityoverthecrosssection,thisaveragevelocityiscalledthemeanvelocity.Uniformflow均匀流:isdefinedasuniformflowwhenintheflowfieldthevelocityandotherhydrodynamicparametersdonotchangefrompointtopointatanyinstantoftime(inwhichthecrosssectionofeachstreamtuberemainsunchanged.流场中每一空间点的各运动参数〔速度,压力〕不随空间位置而变化。Nonuniformflow非均匀流:Flowsuchthatthevelocityvariesfromplacetoplaceatanyinstant.Steadyflow恒定流:theflowwhosemotionfactorsdon’tchangewithtime.流场中所有的运动要素不随时间变化.Unsteadyflow非恒定流:theflowthatatleastoneofitsmotionfactorschangeswithtime.流场中至少有一个运动要素随时间变化.Onedimensionalflow(一元流动)--allmainvariablesintheflowfieldcanbepletelyspecifiedbyasinglecoordinateifthevariationofflowparameterstransversetothemainstreamdirectioncanbeneglected.流动参数只与一个坐标变量有关。Twodimensionalflow(二元流动)-fluidmotionfactorsarefunctionoftwospacecoordinates.流动参数与两个坐标变量有关。Three-dimensionalFlow(三元流动):Fluidflow’smotionfactorsarefunctionsofthreespacecoordinates.流动参数与三个坐标变量有关。System〔系统〕——isasetofdefinitefluidparticlesselectedintheinterestofresearcher.由确定的流体质点组成的流体团或流体体积V(t)。系统边界面S(t)在流体的运动过程中不断发生变化。反映了拉格朗日观点Controlvolume(控制体CV)——isdefinedasaninvariablyhollowvolumeorframefixedinspaceormovingwithconstantvelocitythroughwhichthefluidflows.相对于坐标系固定不变的空间体积V。是为了研究问题方便而取定的。反映了欧拉观点ForaCV:1)itsshape,volumeanditscscannotchangewithtime.2)itisstationaryinthecoordinatesystem.(inthisbook)3)theremaybetheexchangeofmassandenergyonthecs.Controlsurface控制面:thesurfaceareapletelyenclosestheCV.边界面S称为控制面。differentialformofcontinuityequation微分形式的连续性方程ForinpressiblefluidFor2-DinpressibleflowPhysicalmeaning:Thenetmassdischargeenteringthecontrolvolumeisequaltothemassincreasedinunittimeduetothechangeindensity.Fitfor:Steadyflow,unsteadyflow,pressibleandinpressiblefluid,idealfluidandrealfluid.Integralformofcontinuityequation积分形式的连续方程Physicalmeaning:在单位时间内,由于控制体内密度变化引起的质量变化量〔增加量或减少量〕与通过控制体外表的质量净流出量〔流出与流入的质量差〕之和等于零。Steadyflow定常流动inpressiblefluid不可压缩流体MotionDifferentialEquation运动微分方程ForIDEALFLOWforViscousFlowBernoulliEquation伯努利方程〔1〕steadyflow定常流动〔2〕inpressibleflow不可压缩〔3〕integrationalongastreamline沿流线积分〔4〕massforceisapotentialforce质量力有势ForstreamlineForpressibleflowingravityfieldForpressibleflowwithfluidmachineryingravityfieldz(m)——theelevationheightabovedatumsurfaceo-o,calledtheelevationhead(位置水头).p/(g)——risingheightoffluidwithunitweightundertheactionofpressureP,calledthepressurehead(压力水头).u2/(2g)——risingheightoffluidwithunitweightundertheactionofvelocityV,calledthevelocityhead(速度水头),denotedashu——thelostmechanicalenergyfrom1to2pointsperunitweightfluid——Theeffectiveenergyobtainedaftertheunitweightoftheliquidflowsthroughthepump.单位重量液体流经泵后获得的有效能量。Headofdelivery扬程Thesumofthemiscalledthetotalhead(总水头),denotedasH.Pumppower泵功率:Fortheideal-fluidtotalflow理想流体总流的伯努利方程forthereal-fluidtotalflow实际流体总流的伯努利方程momentumintegralequation动量积分方程ForCV——sumofthefluidmomentumchangeinCVandthenetoutflowmomentuminCS,isequaltotheresultantforce.Steadyflow:Moment-of-momentumintegralequation动量矩积分方程Forsteadyflow:[流出动量矩]CS–[流入动量矩]CS=[合外力矩]CV+CSForcesonbend(弯头〕fluidjetsondeflector(导流板〕Sprinkler(喷水器〕角速度:固定所需力矩Chapter3PipeFlowandBoundaryLayerTheory(管流和边界层概述)Laminarflow(层流):Inthefluidflowthefluidparticlesmovealongsmoothpathinlayerswithouttransversevelocityinthedirectionofmainflow,onelayerglidessmoothlyoveranadjacentlayer.Turbulentflow(紊流,湍流)orTurbulence:Ifthefluidparticleshaveatransversevelocitynormaltothemainflowdirection,thatleadstoparticlesmixingupeachother,withaviolenttransverseinterchangeofmomentum.Thisisturbulentflow(紊流,湍流)orturbulence.Reynoldsnumber雷诺数:isusedtodescribethecharacteristicofflow.Wettedperimeter(湿润长度):Thelengthofwallcontactedwithliquid.thehydraulicdiameter(水力直径)DH:Thecharacteristicdimensionofnoncirculartube.HeadLoses〔能头损失,或水头损失):thetotalenergylossesperunitweight〔单位重量流体所损失的机械能为能头损失(水头)〕,whichduetotheresistancebetweentwosectionsofgraduallyvariedflow.〔流体流动,克制粘性内摩擦力,消耗机械能为热能.〕FrictionLoss沿程水头损失(hλ):Intheflowthroughastraighttubewithconstantcrosssection,theenergylossincreaseslinearlyinthedirectionofflowandthelossiscalledfrictionloss.(原因:粘性内摩擦力,以与与管壁的摩擦阻力)Darcy-Weisbch(达西-韦斯巴赫)Equation:λ:thecoefficientoffrictionloss沿程阻力系数,与流态和壁面有关Locallosses局部水头损失(hξ):Whentheshapeofflowpathchanges,suchassectionenlargementandsoon,itwillgiverisetoachangeinthedistributionofvelocityfortheflow.Thechangeresultsinenergyloss,whichiscalledminorlossorlocalloss.原因:流速急剧变化,流体质点剧烈撞击和摩擦.ζ:minorlosscoefficientorlocallosscoefficient为局部阻力系数,与障碍物形式有关Headlosses总能量损失(hf=hλ+hξ)LAMINARFLOWTHROUGHCIRCULARTUBE圆管中的层流VelocitydistributionincrosssectionDischarge—Hagen-Poiseuille(哈根-泊肃叶)equation.Distributionofshearstress切应力分布:壁面剪切力Headlossalongthepath沿程能量(阻力)损失pressuredrop压强损失Headloss水头损失:thecoefficientoffrictionloss:Powerloss(功率损失):PulsationPhenomenon〔脉动现象〕:Thephenomenonthatthephysicalparameterfluctuatesaroundacertainaveragevalueiscalledpulsationphenomenon〔脉动现象〕.u=ū+u'where:ūistime-averagevelocity(时均速度);u'-theponentofrandomfluctuatingvelocity(脉动速度).hydraulicsmooth(水力光滑):Ifviscoussublayermorethanabsoluteroughness(ie.>),theeffectofforthecoreofturbulentflowisverylittle,namely,theinfluenceofintheenergylossisverylittle.hydraulicrough(水力粗糙):Ifviscoussublayerlessthanabsoluteroughness(ie.<),thefluidparticleswithcertainvelocityimpactorcrashtheroughnessprojectionsofpipewall,sothevelocityoftheseparticleschangesradically.Itcauseseddy(涡流)orvortex(漩涡)locally.Meantimetheinfluenceistransferredtothecoreofturbulentflow.Soplaysanimportantroleintheenergyloss.Parallellines并联管路——Byafewsimplelinesortandemlinewhichinletsideandoutletpipingconnectedrespectively.Pipelineinseries/tandemlines(串联管路〕:——Byacoupleofdifferentdiameterordifferentroughnesspipeline.BoundaryLayer边界层:Thefluidparticlesonasolidboundarymustadhereto(粘着,附着)thesolidwallinspiteof(不论)theReynoldsnumberReintheflow.Thevelocityoffluidneartheboundaryvariesrapidlyinasteep(陡的)velocitygradient(速度梯度)outwardnormaltothewallwherethefluidhasazerovelocity.Thevelocitygradientsetsup(产生)shearforceneartheboundaryandforthisreasontheeffectofviscositycannotbeneglectedintheregion.ThisregioncalledBoundarylayer.ThelargertheReynoldsnumberis,thethinnertheboundarylayeris.Chapter4OrificeOutflowandgapflow(孔口出流与缝隙流动)Thin-walledorifice(薄壁孔口):,theedgethicknessslightlyeffectsthejetflow,andonlyminorlosswasconsidered,thecontractedsectionlocatedatd/2afterthehole.Thick-walledorifice(厚壁孔口):,alsonamedlongorifice(长孔口)/nozzle(管嘴).Theedgethicknessdistinctlyeffectsthejetflow,andtheflowwasfirstcontractedandthendiffuseduntilcontactingthewall.Bothfrictionallossandminorlossshouldbeconsidered.bigorifice〔大孔口〕:H/d<=10,thehead,pressure,velocityonthesectionwillbechangedwiththeheight.smallorifice〔小孔口〕:H/d>10,thehead,pressure,velocityonthesectionwillNOTbechangedwiththeheight.free

outflow〔自由出流〕:thejetflowsintoatmospheredirectly,thepressureonthecontractedsectionwasBAR,pc=pa.submerged

outflow〔淹没出流〕:thejetflowsdowntothewater.Contractedsection收缩断面:thestreamlineswerecontractedafterthehole,andthesectionreachedtheminimumatd/2,whichwasthecontractedsectionC—C.contractioncoefficient收缩系数:theratiobetweenthecontractedsectionareaandtheholearea,labeledasCc:Thedischargecalculationofsteadyfreeflowinorifice孔口恒定自由出流流量计算Cvisthevelocitycoefficient流速系数dischargecoefficient流量系数gapflowbetweenstationary固定平板间的缝隙流动velocitydistributiondischargeaveragevelocitypressurelossgapflowbetweenrelativelymovedparallelplates具有相对运动的两平行平板间的流动velocitydischarge压差与平板运动方向一样取正号;方向相反取负号gapflowbetweenconcentriccylinders同心圆环间的缝隙流动dischargeChap.5SimilitudeandDimensionalAnalysis相似理论和量纲分析ThethreesimilaritiesareessentialconditionsofDynamicSimilitudeofFluidMotion(流动相似),inwhich,atanytime,alltheparametersofthemodelandprototypeareinthesameratiothroughouttheentireflowfield.DynamicSimilitudeofFluidMotion(流动相似)includesGeometricsimilarity几何相似,Kinematicsimilarity运动相似,andDynamicsimilarity动力相似;Geometricsimilarity几何相似isthebasicandthemostobviousrequirement;Kinematicsimilarity运动相似istheresult;Dynamicsimilarity动力相似istheconditions.dynamicsimilarityincludeskinematicsimilarity,whilekinematicsimilarityincludesgeometricsimilarity.Hence,ratiosofforce,timeandlengtharesameunderdynamicsimilarity,andotherquantitiesarealsoequal.动力相似包括运动相似,而运动相似又包括几何相似。所以动力相似包括力、时间和长度三个根本物理量相似。两系统的其它物理量由它们决定,也必然相似。Theinitialconditions(初始条件)andboundaryconditions(边界条件)alsomustbecoincidentfordyn

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