工程流体力学(英文版)第二章资料下载.pdf资料下载.pdf
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工程流体力学(英文版)第二章资料下载.pdf资料下载.pdf
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Thereisonlycompressivestress(orpressure)inafluidatrest,andthedirectionofpressureisthesameasthedirectionofinwardnormallineofactingpoint.Fluidatrestcannotbearpullingforcebecauseofthetrendstoflow.xyznpppp=
(1)SelectatriangularprismelementOABC,dx,dy,dzpx,py,pz,pnarepressureintensityactedontherespectivesurface.Thesurfacepressure:
1dd2xpyz1dd2ypxz1dd2zpxydnpA,nisnormaldirectionofinclinedsurfaceABC.y?
x?
z?
0?
pz?
py?
px?
pn?
dy?
dx?
dz?
C?
A?
B?
Considerforcecomponentsinxdirection:
Surfaceforces:
Massforces?
(2)Forceanalysis:
?
OAC:
OAB:
OBC:
ABC:
1dd2xpyz1dd2ypxz1dd2zpxydnpA1ddd6xfxyz1ddd6yfxyz1ddd6zfxyz,(3)Equationoffluidinequilibrium0F=?
11cos(,)026xnxpdydzpdAnxfdxdydz+=y?
Similarly?
Whentheelementshrinkstoapointo,dx0?
thusTheresultsshowthatthepressuresareindependentofdirectionbecauseisarbitrary.Hencethepressureatapointonastaticfluidisthesameinalldirections.n?
n?
And:
1dcos(,)dd2Anxyz=So:
111ddddddd0226xnxpyzpyzfxyz+=1d03xnxppfx+=y?
xnpp=xyznpppp=(),ppxyz=11cos(,)026xnxpdydzpdAnxfdxdydz+=1DifferentialEquationsofaFluidinEquilibrium-EulerEquilibriumEquations2PressureDifferenceEquation3ForcePotentialFunction2SurfaceofEqualPressure2.2DifferentialEquationofFluidEquilibrium2.2.1DifferentialEquationsofaFluidinEquilibrium-EulerEquilibriumEquations2.2DifferentialEquationsofaFluidinEquilibriumConsiderthesixsurfacesofinfinitesimalelementinequilibriumfluid.Itssidesaredx,dy,dz.Assumethepressureatthecenteroftheelementisp(x,y,z)=p.2.2DifferentialEquationofFluidEquilibriumy?
2.2DifferentialEquationsofaFluidinEquilibriumConsiderforcecomponentsinydirection?
y?
d2Bpyppy=d2Cpyppy=+d()dd2pypxzyd()dd2pypxzy+left:
right:
dddyfxyzThereis?
Fy=0inydirectionbecausetheelementisinequilibrium:
dd()dd()ddddd022ypypypxzpxzfxyzyy+=()200()()()()2fxfxxfxfxxx+=+DifferentialEquationsofaFluidinEquilibrium?
EulerEquilibriumEquations?
condition:
or?
2.2DifferentialEquationsofaFluidinEquilibriumdd()dd()ddddd022ypypypxzpxzfxyzyy+=10ypfy=101010xyzpfxpfypfz?
=?
1grad0fp=?
EquilibriumandrelativeequilibriumCompressibleandincompressibleflowPhysicalMeaning:
Forthefluidinequilibrium,surfaceforcecomponentspermassfluidareequaltomassforcecomponentspermassfluid.Pressurevariationrateinaxesdirections?
)areequaltomassforcecomponentsperunitvolumeinaxesdirections?
fx,fy,fz)respectively.zpypxp,?
2.2DifferentialEquationsofaFluidinEquilibrium101010xyzpfxpfypfz?
2.2.2PressureDifferenceEquation(GeneralDifferentialEquationsofaFluidinEquilibrium)101010xyzpfxpfypfz?
ddddppppxyzxyz=+1ddd(ddd)xyzpppfxfyfzxyzxyz+=+?
p=p(x,y,z)Multiplyeveryequationinequationgroup
(1)withdx,dy,dzrespectively,thenaddthem:
thetotaldifferentialofpressureis:
2.2DifferentialEquationsofaFluidinEquilibriumd(ddd)xyzpfxfyfz=+2.2.3ForcePotentialFunction()xyzdpfdxfdyfdz=+Ifthedensityisaconstant:
Defineaforcepotentialfunction:
p=()xyzdpfdxfdyfdz=+()pdddxdydzxyy?
xyzfxfyfz?
2.2.4EquipressureSurfaceEquipressureSurfaceisasurfacethatthepressureofeverypointinliquidisequal.Commonequipressuresurfacesarefreeliquidsurfaceandinterfaceoftwounmixedfluidsinequilibrium.massforceofanypointontheequipressuresurfaceinequilibriumfluidisperpendiculartotheequipressuresurface.KinescopeCartoon2.2DifferentialEquationsofaFluidinEquilibriumd0p=ddd0xyzfxfyfz+=0fdr=?
Importantcharacterofequipressuresurface:
xyxffifjfkdrdxidyjdzk?
=+?
()xyzdpfdxfdyfdz=+Proving?
ConsiderafluidparticleMontheequipressuresurface,drisadifferentialdistanceontheequipressuresurface.Assumetheunitmassforceoftheparticleis?
Attheequipressuresurfaceinequilibriumfluid:
drdxidyjdzk=+?
()0xyzdpfdxfdyfdz=+=Massforce
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