流體靜力學方程和應用

1Chapter1

FluidFlow2345

Inindustry,eithertherawmaterialortheproductsarefluids.Thebehavioroffluidsisimportanttoprocessengineeringgenerallyandconstitutesoneofthefoundationsforthestudyofunitoperations.Thechaptersofthissectiondealwiththoseareasoffluidmechanicsthatareimportanttounitoperations.6Fluidstatics(流體靜力學):

fluidatrestwhichtreatsfluidsintheequilibriumstateofnoshearstress.Fluiddynamics(流體動力學):fluidinmotionwhichtreatsfluidswhenportionsofthefluidareinmotionrelativetootherparts.Twobranchesoffluidmechanics7CHAP1.1FluidStaticsandItsApplications流體靜力學及其應用Content1.1.1NATUREOFFLUIDS1.1.2HYDROSTATICEQUILIBRIUM1.1.3.APPLICATIONSOFFLUIDSTATICS81.1.1NATUREOFFLUIDS

1.Flowability(流動性)2.Density3.Pressure9OneshapeAnothershapeFluidlayerslideoveroneanothershearstressesandviscosityexist.1.Flowability(流動性)

Afluidisasubstancethatdoesnotpermanentlyresistdistortion.10２.DensityUnitofdensity:SIunit:kg/m3cgsunit:g/cm3fpsunit:lb/ft311Usuallyρsolid>ρliquid>ρgasThedensityofallfluidsdependsonthetemperatureandpressureρ=f(T,P)Forliquid:Forgases:12incompressible

fluid不可壓縮流體pressible

fluid可壓縮流體

thechangesindensitywithtemperatureandpressurearesignificant.13ρofidealgases:

IfT=273K,P=1atm:14Sourceofdensitydata：handbook,Appendix6Densityofmixture:liquidmixtureWhereai----massfractionofcomponentsinthemixture15GasmixtureWhereψi----molefractionorvolumefractionofcomponentsinthemixtureNote:

thedifferenceofdensityandspecificgravity163.PressureThepressureinastaticfluidisasurfaceforceexertedbythefluidagainstaunitareaofthewallsofitscontainer.scalarquantity

sameinalldirections.17Unitofpressure:

SIunit:Pa(N/m2)others:atm,mmHg,mH2O,kgf/cm2,bar,at,psi(lbf/in2)1at:一工程大氣壓，俗稱一公斤力18Threekindsofpressure:GaugepressureZeroabsolutepressureAtmosphericpressurevacuumAbsolutepressureFig.TherelationofthreekindsofpressureAbsolutepressureGaugepressureDegreeofvacuum(orvacuum)19Gaugepressure=absolutepressure–localatmosphericpressureVacuumpressure=atmosphericpressure–localabsolutepressureVacuumpressure

=–gaugepressurelocalatmospheritrcpressure=1atm??20表壓真空度動畫211.1.2HYDROSTATICEQUILIBRIUM

1.Equationofhydrostaticequilibrium2.Barometricequation3.Hydrostaticequilibriuminacentrifugalfield221.Equationofhydrostaticequilibrium23forincompressiblefluids----------Equationofhydrostaticequilibrium.UsingConditions

：static,continuous,homogeneousfluids.24(a).Itistheverticalheightthatdeterminethepressure,theshapeofthevesseldoesnotaffectthepressure.靜止的，連通的，同一液體內(nèi)，處于同一水平面上的各點壓強相等。----equipressuresurface等壓面(b).Ifaisthesurfaceofliquid,pamustbetheatmosphericpressure,pb=ρgΔZ(gauge)

Pressure=f(density,height)(c).Pressurecanbeexpressby‘headoffluid’.25262.BarometricequationForanidealgas(2.5)Replaceρinequation(2.2)27Or(2.6)(2.7)----------barometricequation

28☆3.HydrostaticequilibriuminacentrifugalfieldarotatingcentrifugealayerofliquidisillustratedinFig.2.2Fig.2.2Singleliquidincentrifugebowl

29ConsidertheringofliquidshowninFig.2.2andthevolumeelementofthicknessdrataradiusr:wheredF=centrifugalforcedm=massofliquidinelementω=angularvelocity,rad/s30Ifρisthedensityoftheliquidandbthebreadthofthering,31Assumingthedensityisconstantandintegratinggive(2.8)Equation(2.8)strictlyappliesonlywhenr1andr2arenotgreatlydifferent,butforpracticalsystemstheerrorissmall.

321.1.3APPLICATIONSOFFLUIDSTATICS1.Manometers(壓差計)2.Measurementofliquidlevel3.Liquidsealofequipment331.Manometers(液壓計)Figurebelowshowsthesimplestformofmanometer.Flowdirection34Equi-pressurelevel35Example2.1.AmanometerofthetypeshowninFig.1.33isusedtomeasurethepressuredropacrossanorifice(seeFig.8.18).LiquidAismercury(density13,590kg/m3)andfluidB,flowingthroughtheorificeandfillingthemanometerleads,isbrine(density1,260kg/m3).Whenthepressuresatthetapsareequal,thelevelofthemercuryinthemanometeris0.9mbelowtheorificetaps.Underoperatingconditions,thegaugepressure1attheupstreamtapis0.14bar;thepressureatthedownstreamtapis250mmHgbelowatmospheric.Whatisthereadingofthemanometerinmillimeters?36Fig.1.33Orificemeter37Solution:

38Othertypeofmanometers(absolutepressure)

(gauge)

（vacuum）

39404142Differentialmanometer

微差壓差計△RwhereIffluidBisagas43Iftheheightdifferenceofthereservoircanbeneglected.44Inclinedmanometer斜管壓差計(2.11)

45Seriesmanometer462.MeasurementofliquidlevelFlash1-05474849503.LiquidsealofequipmentFlash1-0451525354551.AU-tubemanometerisbeingusedtomeasuretheheightofoilinatankasshowninthefigure.Themanometerisfilledwithmercury(densityρA),andthedensityofoilisρ.OntherightsideofU-tubemanometer,oilisalsofilledabovethemercurywithheighth1.

56WhentheheightofoilinthetankisH1,themanometerreadsR.Calculate,whentheamountofoilinthetankisreduced,theheightofoilinthetankbecomes(H1-H),calculatethechangeofreadingR.572.Pressuredropbetweentwopointsinalinecontainingairis160Pa.TwokindsofU-tubemanometerisbeingusedtomeasurethispressuredrop.InthesimpleU-tubemanometer(asshowninfig.a),carbontetrachloridehavingadensityρA(1594kg/m3)is