流体力学英文版复习课件

Chapter1.FLUIDPROPERTIES

第一章流体性质Chapter1.FLUIDPROPERTIES

Inphysics,afluidisasubstancethatcontinuallydeformsunderanappliedshearstress,nomatterhowsmallitis.

流体是一种一受到切力作用（不论多么小）就会连续变形的物体。

Definitionofafluid2023/9/26Inphysics,afluidisa2(1)Density（密度）Densityistheratioofthemassoffluidtoitsvolume.

(1.12)

Specificvolume

(比容):volumeoccupiedbyunitmass.

(1.13)

Thespecificvolumeisthereciprocal(倒数)ofdensity.

(kg/m3

)(m3/kg)2023/9/26(1)Density（密度）Densityisthe3(2)SpecificWeight（重度）It’stheweightperunitvolume

(1.14)

inwhich

isthespecificweightoffluid,N/m3;Gistheweightoffluid,N.

(1.14a)

Ortheproductofdensity

andaccelerationofgravityg.

2023/9/26(2)SpecificWeight（重度）It’s4(3)Relativedensityandspecificgravity

Therelativedensity

(相对密度)RDofafluidistheratioofitsdensitytothedensityofagivenreferencematerial.

Thereferencematerialiswaterat4Ci.e.,

ref=

water.=1000kg/m3dimensionlessquantity无量纲

Thespecificgravity

(比重)

SGofafluidis

theratioofitsweighttotheweightofanequalvolumeofwaterat

standardconditions(标准状态).

dimensionlessquantity无量纲

2023/9/26(3)Relativedensityandspeci5(4)Compressibility（压缩性）

Thevolumeoffluidchangesunderdifferentpressure.Asthetemperatureisconstant,themagnitudeofcompressibilityisexpressedbycoefficientofvolumecompressibility

(体积压缩系数)

p

,

arelativevariationrate（相对变化率）

ofvolumeperunitpressure.

(1.15)

Thebulkmodulusofelasticity

(体积弹性模量)Kisthereciprocalofcoefficientofvolumecompressibility

p.(1.16)

（Pa）（Pa

1）2023/9/26(4)Compressibility（压缩性）6Amineraloilincylinderhasavolumeof1000cm3

at0.1MN/m2

andavolumeof998cm3at3.1MN/m2.Whatisitsbulkmodulusofelasticity?Example1.1Solution:2023/9/26Amineraloilincylinde7PredominantCause:

Cohesionisthecauseofviscosityofliquid.Transferof

molecularmomentum

isthecause

ofviscosityofgas.(5)Viscosity

Viscosity

isaninternalpropertyofafluidthatoffersresistancetosheardeformation.Itdescribesafluid'sinternalresistancetoflowandmaybethoughtasameasureoffluidfriction.

Theresistanceofafluidtosheardependsuponitscohesion(内聚力)anditsrateoftransferofmolecularmomentum(分子动量交换).2023/9/26PredominantCause:(5)Viscosi8Newton’slawofviscosityFigure1.5Deformationresultingfromapplicationofconstantshearforce

InFig.1.5,asubstanceisfilledtothespacebetweentwocloselyspacedparallelplates（平行板）.Thelowerplateisfixed,theupperplatewithareaA

movewithaconstantvelocityV,aforceFisappliedtotheupperplate.

2023/9/26Newton’slawofviscosityFigur9ExperimentshowsthatFisdirectlyproportionaltoAandtoVandisinverselyproportional

（反比）tothicknessh.

(1.18)

Iftheshearstressis

=F/A,itcanbeexpressedasTheratioV/histheangularvelocityoflineab,oritistherateofangulardeformationofthefluid.2023/9/26ExperimentshowsthatFis10(1.19)

Theangularvelocitymayalsobewrittenasdu/dz,soNewton’slawofviscosityis

Theproportionalityfactor(比例因子）

iscalledthe

viscositycoefficient（黏性系数，黏度）.

FluidsmaybeclassifiedasNewtonianornon-Newtonian.

Newtonianfluid:

isconstant.(gasesandthinliquids稀液)Non-Newtonianfluid:

isnotconstant.(thick稠的,long-chainedhydrocarbons长链碳氢化合物)

2023/9/26(1.19)Theangularvelo11DynamicviscosityandKinematicviscosityThedynamicviscosity（动力黏度）isalsocalledabsoluteviscosity（绝对黏度）.From（1.19）SIunit：kg/(m

s)orN

s/m2

U.S.customaryunit：dyne

s/cm2（达因

秒/厘米2）cgsunit：

Poise(P,泊).

1P=100cP(厘泊)1P=0.1Pa

s(帕秒)

Thekinematicviscosity

（运动黏度）istheratioofdynamicviscositytodensity.

SI

unit：m2/s

U.S.customary

unit：ft2/s（英尺2/秒）

cgsunit：stokes(St,斯).1cm2/s=1St1mm2/s=1cSt(厘斯)2023/9/26DynamicviscosityandKinemat12Chapter2.FLUIDSTATICS

第二章流体静力学Chapter2.FLUIDSTATICS

第二章BasicequationofhydrostaticsundergravityGravityG(G=mg)istheonlymassforceactingontheliquid

fx=0，fy=0，fz=

gFigure2.4Avesselcontainingliquidatrest

rewritingFrom(2.5)cistheconstantofintegration(积分常数)determinedbytheboundarycondition.integrating(2.7)2023/9/26Basicequationofhydrosta14Forthetwopoints1and2inthestaticfluid

Forthetwopoints0and1

Figure2.4Avesselcontainingliquidatrest

Thepressureatapointinliquidatrestconsistsoftwoparts:the

surfacepressure,andthe

pressurecausedbytheweightofcolumnofliquid.2023/9/26Forthetwopoints1and2For15Physicalmeaning

z——thepositionpotentialenergyperunitweightoffluidtothebaselevel；

p/

g——thepressurepotentialenergy

(压强势能)perunitweightoffluid.Geometricalmeaning

z——thepositionheightorelevationhead(位置水头)

p/

g——thepressurehead(压力水头)perunitweightoffluid

Sumofthepositionhead(位置水头)andpressureheadiscalledthehydrostatichead(静水头),alsoknownasthepiezometrichead(测压管水头).

Theenergyperunitweightoffluidcanbealsoexpressedintermsofthelengthofcolumnofliquid(液柱),andcalledthehead(水头).2023/9/26Physicalmeaningz——th16

localatmosphericpressure(当地大气压)pa

absolutepressure(绝对压强)pabs

gaugepressure(表压,计示压强)=relativepressure

vacuumpressure

(真空压强,真空度)pv

,orsuctionpressure(吸入压强),also

callednegativepressure(负压强)

relativepressure(相对压强)

p

Itisusuallymeasuredintheheightofliquidcolumn,suchasmillimetersofmercury

(mmHg,毫米水银柱),denotedbyhv.RelatedPressures2023/9/26localatmosphericpressure(当17Localatmosphericpressure

p=paCompletevacuumpabs=0AbsolutepressureVacuumpressureGaugepressure

Figure2.6absolutepressure,gaugepressureandvacuumpressure

p

Absolutepressure2

p<pa

1p>pa

O

RelationshipGraph2023/9/26LocalatmosphericpressureCo18

Toavoidanyconfusion,theconventionisadoptedthroughoutthistextthatapressureisingaugepressureunlessspecificallymarked‘abs’,withtheexceptionofagas,whichisabsolutepressureunit.

Attention:

2023/9/26Toavoidanyconfusion,th19Differentialmanometer[mə’nɔmitə](差压计)

usedtomeasurethedifferencesinpressurefortwocontainersortwopointsinacontainer.

Structure：Measurementprinciple：

Figure2.10Differentialmanometer2

AApA1

>

A,

B

hh1

B

BpBh2ρA=ρB=ρ1Fortwosameair,

ρA=ρB=02023/9/26Differentialmanometer[mə’n20EXAMPLE2.1

ApressuremeasurementapparatuswithoutleakageandfrictionbetweenpistonandcylinderwallisshowninFig.2.11.Thepistondiameterisd=35mm,therelativedensityofoilisRDoil=0.92,therelativedensityofmercuryisRDHg=13.6,andtheheightis

h=700mm.Ifthepistonhasaweightof15N,calculatethevalueofheightdifferenceofliquidΔhinthedifferentialmanometer.11pa

hRDoil=0.92RDHg=13.6dhFigure2.11Pressuremeasurementapparatuspistonpa2023/9/26EXAMPLE2.1Apressure21

Thepressureonthepistonundertheweight

Fromtheisobaricsurface1-1theequilibriumequationissolvingfor

h

Solution:

2023/9/26Thepressureonthepis22Chapter3.FLUIDFLOWCONCEPTS&BASICEQUATIONS

第三章

流体流动概念和基本方程组

Chapter3.FLUIDFLOWCONCEPTS

Thespacepervaded(弥漫,充满)theflowingfluidiscalledflowfield(流场).

velocityu,

accelerationa,density

,pressurep,

temperature

T,

viscosityforce

Fv,andsoon.

Motionparameters:2023/9/26Thespacepervaded(弥漫24Steadyflowandunsteadyflow

For

steadyflow

(定常流),motionparametersindependentoftime.

u=u(x,y,z)p=p(x,y,z)

Steadyflowmaybeexpressedas

Themotionparametersaredependentontime,theflowisunsteadyflow

(非定常流).u=u(x,y,z,t)p=p(x,y,z,t)2023/9/26Steadyflowandunsteadyf25

Apathline(迹线,轨迹线)isthetrajectoryofanindividual

fluidparticleinflowfieldduringaperiodoftime.

Streamline(流线)isacontinuousline(manydifferentfluidparticles)drawnwithinfluidflied

atacertaininstant,thedirectionofthevelocityvectorateachpointiscoincidedwith（与…一致）

thedirectionoftangentatthatpointinthe

line.PathlineandstreamlinepathlineStreamline2023/9/26Apathline(迹线,轨迹线)i26Crosssection,flowrateandaveragevelocity1.Flowsection(通流面)Theflowsectionisasectionthateveryareaelementinthesectionisnormaltomini-streamtubeorstreamline.Theflowsectionisacurvedsurface（曲面）.Iftheflowsectionisaplanearea,itiscalledacrosssection(横截面).1122IIIu1u2dA1dA2Figure3.5Flowsection2023/9/26Crosssection,flowratea27Theamountoffluidpassingthroughacrosssectioninunitintervaliscalledflowrateordischarge.weightflowratevolumetricflowratemassflowrate

(3.7)Foratotalflow

2.Flowrate(流量)

2023/9/26weightflowratevolumetricflo28

3.Averagevelocity(平均速度)umaxVFigure3.6DistributionofvelocityovercrosssectionThevelocityutakesthemaximumumaxonthepipeaxleandthezeroontheboundaryasshowninFig.3.6.TheaveragevelocityVaccordingtotheequivalencyofflowrateiscalledthesectionaveragevelocity(截面平均速度).Accordingtotheequivalencyofflowrate,VA=∫AudA=Q,therewith,2023/9/263.Averagevelocity(平均速度)uma293.3.2Controlvolume

Controlvolume(cv,控制体)isdefinedasaninvariablyhollowvolumeorframefixedinspaceormovingwithconstantvelocitythroughwhichthefluidflows.

Theboundaryofcontrolvolumeiscalledcontrolsurface

(cs,控制面).

Foracv:1)itsshape,volumeanditscscannotchangewithtime.

2)itisstationaryinthecoordinatesystem.(inthisbook)3)theremaybetheexchangeofmassandenergyonthecs.

2023/9/263.3.2Controlvolume30Systemvs

ControlVolume2023/9/26SystemvsControlVolume2023/8313.4.1Steadyflowcontinuityequationof1DministreamtubedA1u1dA2u2A1A2Figure3.8

One-dimensionalstreamtubeThenetmassinflow

dM=(

lu1dA1

2u2dA2)dtForcompressiblesteadyflowdM=0

lu1dA1=

2u2dA2Ifincompressible,ρl=ρ2=ρ

u1dA1=u2dA2Theformulaisthecontinuityequationforincompressiblefluid,steadyflowalongwithmini-streamtube.(3.23)2023/9/263.4.1Steadyflowcontinu323.4.2Totalflowcontinuityequationfor1Dsteadyflow

lmV1A1=2mV2A2

(3.24)Forincompressiblefluidflow,ρisaconstant.

Q1=Q2

orV1A1=V2A2dA1u1dA2u2A1A2Figure3.8One-dimensionalstreamtubeMakingintegralsatbothsidesofEq.(3.23)IntegratingitaveragedensityaveragevelocityThetotalflowcontinuityequationfortheincompressiblefluidinsteadyflow.2023/9/263.4.2Totalflowcontinui333.5.2Bernoulli’sequation

Eq.(3.8)isusedforidealfluidflowsalongastreamlineinsteady.Bernoulli’sequation

canbeobtainedwith

anintegralalongastreamline:(m2/s2)(3.29)

Thisisanenergyequationperunitmass.Ithasthedimensions(L/T)2becausem

N/kg=(m

kg

m/s2)/kg=m2/s2.

Themeanings

u2/2——thekineticenergyperunitmass(mu2/2)/m.

p/

——thepressureenergyperunitmass.gz——thepotentialenergyperunitmass.Eq.(3.29)showsthatthetotalmechanicalenergyperunitmassoffluidremainsconstantatanypositionalongtheflowpath.2023/9/263.5.2Bernoulli’sequati34

TheBernoulli’sequationperunitvolumeis(N/m2)(3.30)

Becausethedimensionof

u2/2isthesameasthatofpressure,itiscalleddynamicpressure(动压强).

TheBernoulli’sequationperunitweightis(m

N/N,or,m)(3.31)

Forarbitrarytwopoints1and2alongastreamline,

(3.32)

2023/9/26TheBernoulli’sequation35

Themechanicalenergyperunitweightoverthesectioningraduallyvariedflowis

Lethwbetheenergylossesperunitweightoffluidfrom1-1to2-2,theBernoulli’sequationforatotalflowis

Leths

betheshaftworkperunitweightoffluid,theBernoulli’sequationforarealsystemis

(3.45)(3.44)

3.7.2TheBernoulli’sequationforthereal-fluidtotalflow2023/9/26Themechanicalenergype36011dhe0Figure3.20Pumpingwater

Acentrifugalwaterpump(离心式水泵)withasuctionpipe(吸水管)isshowninFig.3.20.PumpoutputisQ=0.03m3/s,thediameterofsuctionpiped=150mm,vacuumpressurethatthepumpcanreachispv/(

g)=6.8mH2O,andallheadlossesinthesuctionpipe

hw=1mH2O.Determinetheutmostelevation(最大提升)hefromthepumpshafttothewatersurfaceonthepond.EXAMPLE3.62023/9/26011dhe0Figure3.20Pumpingwat37Solution

1)twocrosssectionsandthedatumplaneareselected.

Thesectionsshouldbeonthegraduallyvariedflow,thetwocrosssectionshereare:1)thewatersurface0-0onthepond,2)thesection1-1ontheinletofpump.Meanwhile,thesection0-0istakenasthedatumplane,

z0=0.2023/9/26Solution1)twocrosssec382)theparametersintheequationaredetermined.

Thepressurep0andp1areexpressedinrelativepressure(gaugepressure).，andSo,V0=0.Let=1

hw0-1=1mH2O

，and，and2023/9/262)theparametersintheequat393)calculationfortheunknownparameteriscarriedout.

BysubstitutingV0=0，p0=0，z0=0，p1=

pv，z1=he，α1=1andV1=1.7intotheBernoulli’sequation,i.e.,

Thevaluesofpv/(

g)

and

V1

aresubstitutedintoaboveformulaanditgivesnamely,2023/9/263)calculationfortheunknown40Intheactualflowthevelocityoveraplanecrosssection(横截平面)isnotuniformorIftheun-uniforminvelocityoverthesectionistakenintoaccount,Eq.(3.48)mayberewrittenas

is

momentumcorrectionfactor

(动量修正系数).

=4/3inlaminarflowforastraightroundtube.

=

1.02~1.05inturbulentflow

anditcouldbetakenas1.

oror

(3.49)

(3.50)

3.8THELINEAR-MOMENTUMEQUATION

2023/9/26Intheactualflowthevelocit41Chapter4.FLUID

RESISTANCE

4.流体阻力Chapter4.FLUIDRESISTANCE

4hw

—headlosses(水头损失)

comprisesoffrictionlossesandminorlosses.1.Frictionloss(沿程损失,摩擦水头损失)hl

Intheflowthroughastraighttubewithconstantcrosssection,theenergylossincreaseslinearlyinthedirectionofflowandthelossiscalledfrictionloss.

2.Minorloss(次要损失)orLocalloss(局部损失)hmWhentheshapeofflowpathchanges,suchassectionenlargementandsoon,itwillgiverisetoachangeinthedistributionofvelocityfortheflow.Thechangeresultsinenergyloss,whichiscalledminorlossorlocalloss.4.1REYNOLDSNUMBER2023/9/26hw—headlosses(水头损失)compris43Reynoldsnumber

Reisusedtodescribethecharacteristicofflow.2023/9/26ReynoldsnumberReisusedto44Thedischarge（流量）passingthroughafixedcrosssectionis4.2LAMINARBETWEENPARALLELPLATES

2023/9/26Thedischarge（流量）passingth45Itcanbewrittenas

Supposethediameterofcirculartubeisd.Substitutingknownconditionsabovetothedischargeequation,thedischargeofcirculartubeisHagen-Poiseuille(哈根-泊肃叶)equation.

Sotheaveragevelocityoflaminarflowinthecirculartubeis4.3LAMINARFLOWTHROUGHCIRCULARTUBE2023/9/26ItcanbewrittenasSu46

Fluidflowsina3-mm-IDhorizontaltube.Findthepressuredroppermeter.μ=60cP,RD=0.83,atRe=200.

Example4.2Solution:2023/9/26Fluidflowsina3-mm-ID47IntheFig.4.7,

pisfrictionlossoflaminarflowinthetubebetweensections1-1and2-2.Letthecoefficientoffrictionloss(沿程摩擦系数，沿程损失系数)obtainsDarcy-Weisbch(达西-韦斯巴赫)Equation4.3.3Frictionallossforlaminarflowinhorizontalcirculartube

Itisusedtocalculatethefrictionalpressuredropforlaminarfloworturbulentflowinhorizontalcirculartube.Fortheconvenienceofapplication,itcanbewrittenfrictionloss:2023/9/26IntheFig.4.7,pisfrictio48

Thelossesjustoccurlocally,whichcalledasminorenergylosses(局部能量损失)or

minorpressurelosses,denotedby

pm.Itusuallyisexpressedasthefollowingequation.4.6.5Minorresistance

:theminorlosscoefficientorlocallosscoefficient,V:thevelocityoverthecrosssection,

:themassdensity2023/9/26Thelossesjustoccurl49

Itisthatthefrictionlossistheonlyfactorforenergylossesinfluidflow.Inthesimplepipeproblem,assumingthatthefluidisincompressible,itinvolvessixparameters,Q,L,D,hw,

,

.Ingeneral,thelengthofpipe,L,kinematicviscosityoffluid,

,andabsoluteroughnessofpipe,

,maybedeterminedalready.

So,simplepipeproblemcanbeclassifiedintothreetypes:(1)solutionforpressuredrophw

withQ,L,D;(2)solutionfordischargeQwithL,D,hw;(3)solutionfordiameterDwithQ,L,hw.Table4.5Simplepipeproblem“Simplepipeproblem”2023/9/26Itisthatthefriction50m

isthenumberofthefrictionalresistance,nisthenumberoftheminorresistance,thesubscriptsiand

jexpresstheithandthejthsegmentofpipeline.ThemajorworkinsimplepipeproblemistosolvehW.2023/9/26misthenumberofthefrictio51EXAMPLE4.6AhorizontalpipelineisusedtosupplylandwithwaterasshowninFig.4.22.Thecomponentpartsofpipelineareasfollowing:threepipesoflength30m,12m,and60m;twostandardelbowsAandB;andaglobevalve(fullyopen)C.IftheelevationisH=10mandtheinsidediameterofcleancastironpipeis150mm,determine:1)thedischargeinthepipe;2)theheadlosswhenQ=60L/s.Figure4.22Horizontalpipelineusedtoirrigateacropland2023/9/26EXAMPLE4.6Ahoriz52SolutionTheentrancelosscoefficientis0.5,losscoefficientofelbow0.9,andlosscoefficientoftheglobevalve10.Bernoulli’sequationisappliedbetweensection1-1andsection2-2,includingallthelosses,2023/9/26SolutionTheentrancel53Chapter5.APPLICATIONSOFFLUIDMECHANICS

第五章流体力学应用Chapter5.APPLICATIONSOFFLU5.1Orifices

5.1孔口2023/9/265.1Orifices

5.1孔口2023/8/155Orificedischargeisthehydraulicphenomenonthatfluidflowsthroughanorificeinwalloftank.orificeedge(l/d)

thin-walledorificethick-walledorificeccldFigure5.1Thin-walledorificeccldFigure5.2Thick-walledorificeOrificeclassification(孔口分类)(l/d<0.5)(2<l/d<4)2023/9/26Orificedischargeisthe56Orificedischargeisthehydraulicphenomenonthatfluidflowsthroughanorificeinwalloftank.dischargeconditionOrificeclassification(孔口分类)freedischarge:fluidflowsintoairdirectlysubmergeddischarge:fluidisdischargedintoanother