工程流体力学英文版第三章pdf_.pdf
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工程流体力学英文版第三章pdf_.pdf
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Chapter3ConceptsandBasicEquationofFluidsinmotion(onedimension,idealfluids)?
Contents1.MethodstoStudyFluidsinMotion2.FlowClassification3.Pathline(?
)andStreamline(?
)4.Streamtube(?
)andDischarge(?
)5.ContinuityEquationforSteadyFlowinaConduit6.MotionDifferentialEquationforIdeal1-DFlow&TheBernoulliEquationAlongaStreamlineContents7.DifferentialEquationforIdealFlowalongNormalLine8.TheBernoulliEquationfor1-Dpipeflow9.ApplicationofTheBernoulliEquation10.TheLinear-Momentum(?
)EquationandMoment-of-Momentum(?
)EquationforIdealFlow?
3.1MethodstoStudyFluidsinMotion1.LagrangianApproach(?
)2.EulerianApproach(?
)3.SystemandControlVolume4.EulerianAccelerationAABBviewpoints:
aindividualfluidparticlebcertainpointinspaceLagrangianDescriptionofMotionisthedescriptionthateveryfluidpartideinflowfieldisobservedasafunctionoftime.Spacecoordinates?
=),(),(),(tcbazztcbayytcbaxx1.LagrangianApproachAABBEulerApproachisthedescriptionthatthemotionfactorsofeveryspacepointinflowfieldareobservedasafunctionoftime.flowfielddescription.Flowfieldmotionfactorsarethecontinuousfunctionsoftimeandspace?
x,y,z?
EulerianDescriptionisutilizedwidelyinengineering.2.EulerianApproach(x,y,z)-EulerianVariables()()(),xyztppxyztVVxyzt?
=?
=?
=?
3.System(?
andControlVolume?
DefinitionofaSystemAsystemreferstoaspecificmassoffluidwithintheboundariesdefinedbyaclosedsurface.ShapemaychangemassnochangeAcontrolvolumereferstoafixedregioninspace,whichdoesnotmoveorchangeshape.Thesurfacesurroundingthecontrolvolumeiscalledcontrolsurface3.System(?
andControlVolume?
ShapenochangemassmaychangeDefinitionofaControlVolume1?
1?
2?
2?
.Euleriancceleration(),Vxyzt?
t:
position:
?
x,y,z?
tt+:
position:
velocity:
(),xxyyzz+(),tVxxyyzzt+?
velocity:
y?
x?
z?
0?
t?
(x,y,z)?
()()()()000,lim1lim,limxtttuxxyyzzttuxyztatuuuuuxyztxyztuxyzttxyztutuxuyuzttxtytzt+=?
=+?
=+?
000lim,lim,limtttyxzuvwttt=y?
x?
z?
0?
t?
(x,y,z)?
so?
ddxuuuuuauvwttxyz=+and?
ddddddxyzuuuuuauvwttxyzvvvvvauvwttxyzwwwwwauvwttxyz?
=+?
=+?
=+?
or:
()VaVVt=+?
ijkxyz=+?
Similarly?
Accelerationofparticlesiscomposedoftwoparts?
1?
LocalAccelerationthechangeofvelocityateverypointwithtime.?
2?
ConvectiveAccelerationthechangeofvelocitywithpositionddpppppuvwttxyz=+dduvwttxyz=+Fordensityandpressure:
Generalform:
ddVtt=+?
.TheTotalDerivativeexample3.1velocityis:
2232Vxyiyjzk=+?
(m/s),Whatistheaccelerationofpoint(3,1,2).solution:
2220
(2)(3)027xuuuuauvwxyxyyxmstxyz=+=+=22200(3)(3)209yvvvvauvwxyyzmstxyz=+=+=22200(3)02464zwwwwauvwxyyzzmstxyz=+=+=So,theaccelerationofpoint(3,1,2):
27964aijk=+?
3.2ClassificationofFluidFlowClassificationofFluidFlowBasedontheCharacteristicofFluidBasedontheStateofFlowBasedontheNumberofSpaceVariables1.BasedontheCharacteristicsofFluidIdealflowandViscousflow0or=Incompressibleflowandcompressiblefloworconst=2.BasedontheStateofFlowSteadyflowandunsteadyflow0ort=Rotational(?
)flowandirrotational(?
)flowLaminarflow(?
)andturbulentflow(?
)Subsonicflow(?
)?
Transonicflow(?
)andsupersonicflow(?
)Uniformflowandnon-uniformflow0Vors=?
3.BasedontheNumberofSpaceVariablesOnedimensionalflow(?
)Twodimensionalflow(?
)Threedimensionalflow(?
)4.Steadyflowandunsteadyflowistheflowwhosemotionfactorsdontchangewithtime.Thatis:
SteadyFlow(),VVxyz=?
0Vt=?
H=C?
Unsteadyflowistheflowthatatleastoneofitsmotionfactorschangeswithtime.ThatisunsteadyFlow(),VVxyzt=?
0Vt?
H?
H?
H?
51-D,2-Dand3-DFlowOne-dimensionalFlow:
(2)cross-sectionalaveragevaluesSfluidmotionfactorsarefunctionofaspacecoordinate.
(1)Idealflow.(3)motionfactorsarefunctionsofcurvedcoordinatess.(,)xt=(,)xt=(,)st=(,)st=Two-dimensionalFlow:
fluidmotionfactorsarefunctionoftwospacecoordinates.(Notonlylimitedtorectangularcoordinates).Fluidflowsmotionfactorsarefunctionsofthreespacecoordinates.Forexample:
Waterflowinanaturalriverwhosecrosssectionshapeandmagnitudechangealongthedirectionofflow;waterflowsaroundtheship.Three-dimensionalFlow:
Apathlineisthetraceafterasingleparticletravelsinafieldofflowoveraperiodoftime.
(1).DefinitionKinescope1Kinescope2?
3.3Pathline(?
)andStreamline(?
)1.Pathline
(2)?
EquationofPathlineu?
v?
warefunctionsofbothtimetandspace(x?
y?
z).Heretisanindependentvariabledydxdzuvwdt=AStreamlineisacurvethatshowthedirectionofanumberofparticlesattheatthesameinstantoftime.Thecurveindicatesthevelocityvectorsofanypointsoccupyingonthestreamline.Kinescope2.Streamline1.DefinitionaV?
bV?
cV?
dV?
eV?
2?
EquationofStreamlineSelectpointAinstreamline,dsisadifferentialarclength,uisthevelocityatpointAdsdxidyjdzk=+?
dsuAVuivjwk=+?
Directionalcosinebetweenvelocityvectorandcoordinatescos(,)vVyV=?
cos(,)uVxV=?
cos(,)wVzV=?
Directionalcosinebetweendsandcoordi
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