Fluid Mechanics

784 Pages·2004·6.38 MB·English

by  Ira M. Cohen

Fluid Mechanics, Third Edition
Founders of Modern Fluid Dynamics
LudwigPrandtl G.I.Taylor
(1875–1953) (1886–1975)
(BiographicalsketchesofPrandtlandTayloraregiveninAppendixC.)
PhotographofLudwigPrandtlisreprintedwithpermissionfromtheAnnualReviewofFluid
Mechanics,Vol.19,Copyright1987byAnnualReviewswww.AnnualReviews.org.
PhotographofGeoffreyIngramTayloratage69inhislaboratoryreprintedwithpermission
fromtheAIPEmilioSegre`VisualArchieves.Copyright,AmericanInstituteofPhysics,2000.
Fluid Mechanics
Third Edition
Pijush K. Kundu
OceanographicCenter
NovaUniversity
Dania,Florida
Ira M. Cohen
DepartmentofMechanicalEngineeringand
AppliedMechanics
UniversityofPennsylvania
Philadelphia,Pennsylvania
withachapteronComputationalFluidDynamicsbyHowardH.Hu
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PrintedintheUnitedStatesofAmerica
04 05 06 07 08 9 8 7 6 5 4 3 2 1
ThethirdeditionisdedicatedtothememoryofPijushK.Kunduandalsotomywife
LindaanddaughtersSusanandNancywhohavegreatlyenrichedmylife.
“Everythingshouldbemadeassimpleaspossible,
butnotsimpler.”
—AlbertEinstein
“Ifnaturewerenotbeautiful,itwouldnotbeworthstudyingit.
Andlifewouldnotbeworthliving.”
—HenryPoincare´
In memory of Pijush Kundu
Pijush Kanti Kundu was born in Calcutta,
India, on October 31, 1941. He received a
B.S. degree in Mechanical Engineering in
1963 from Shibpur Engineering College of
Calcutta University, earned an M.S. degree
in Engineering from Roorkee University in
1965,andwasalecturerinMechanicalEngi-
neeringattheIndianInstituteofTechnology
in Delhi from 1965 to 1968. Pijush came to
the United States in 1968, as a doctoral stu-
dent at Penn State University.With Dr. John
L.Lumleyashisadvisor,hestudiedinstabili-
tiesofviscoelasticfluids,receivinghisdoctor-
atein1972.Hebeganhislifelonginterestin
oceanographysoonafterhisgraduation,workingasResearchAssociateinOceanog-
raphyatOregonStateUniversityfrom1968until1972.Afterspendingayearatthe
UniversitydeOrienteinVenezuela,hejoinedthefacultyoftheOceanographicCenter
ofNovaSoutheasternUniversity,whereheremaineduntilhisdeathin1994.
Duringhiscareer,Pijushcontributedtoanumberofsub-disciplinesinphysical
oceanography,mostnotablyinthefieldsofcoastaldynamics,mixed-layerphysics,
internal waves, and Indian-Ocean dynamics. He was a skilled data analyst, and, in
thisregard,oneofhisaccomplishmentswastointroducethe“empiricalorthogonal
eigenfunction”statisticaltechniquetotheoceanographiccommunity.
IarrivedatNovaSoutheasternUniversityshortlyafterPijush,andheandIworked
closelytogetherthereafter.Iwasimmediatelyimpressedwiththeclarityofhisscien-
tificthinkingandhisthoroughness.Hismostimpressiveandobviousquality,though,
was his love of science, which pervaded all his activities. Some time after we met,
Pijush opened a drawer in a desk in his home office, showing me drafts of several
chapters to a book he had always wanted to write.A decade later, this manuscript
becamethefirsteditionof“FluidMechanics,”theculminationofhislifelongdream;
which he dedicated to the memory of his mother, and to his wife Shikha, daughter
Tonushree,andsonJoydip.
JulianP.McCreary,Jr.,
UniversityofHawaii
Contents
Preface ................................................... xvii
PrefacetoSecondEdition ................................. xviii
PrefacetoFirstEdition ..................................... xx
Author’sNotes ........................................... xxiii
Chapter 1
Introduction
1. FluidMechanics.............................................. 1
2. UnitsofMeasurement......................................... 2
3. Solids,Liquids,andGases..................................... 3
4. ContinuumHypothesis........................................ 4
5. TransportPhenomena......................................... 5
6. SurfaceTension .............................................. 8
7. FluidStatics ................................................. 9
8. ClassicalThermodynamics .................................... 12
9. PerfectGas .................................................. 16
10. StaticEquilibriumofaCompressibleMedium................... 17
Exercises .................................................... 22
LiteratureCited .............................................. 23
SupplementalReading ........................................ 23
Chapter 2
Cartesian Tensors
1. ScalarsandVectors ........................................... 24
2. RotationofAxes:FormalDefinitionofaVector.................. 25
vii
viii Contents
3. MultiplicationofMatrices..................................... 28
4. Second-OrderTensor ......................................... 29
5. ContractionandMultiplication................................. 31
6. ForceonaSurface............................................ 32
7. KroneckerDeltaandAlternatingTensor......................... 35
8. DotProduct.................................................. 36
9. CrossProduct ................................................ 36
10. Operator :Gradient,Divergence,andCurl..................... 37
∇
11. SymmetricandAntisymmetricTensors ......................... 38
12. EigenvaluesandEigenvectorsofaSymmetricTensor............. 40
13. Gauss’Theorem.............................................. 42
14. Stokes’Theorem.............................................. 45
15. CommaNotation ............................................. 46
16. BoldfacevsIndicialNotation .................................. 47
Exercises .................................................... 47
LiteratureCited .............................................. 49
SupplementalReading ........................................ 49
Chapter 3
Kinematics
1. Introduction.................................................. 50
2. LagrangianandEulerianSpecifications ......................... 51
3. EulerianandLagrangianDescriptions:TheParticleDerivative .... 53
4. Streamline,PathLine,andStreakLine.......................... 54
5. ReferenceFrameandStreamlinePattern ........................ 56
6. LinearStrainRate ............................................ 57
7. ShearStrainRate............................................. 58
8. VorticityandCirculation ...................................... 59
9. RelativeMotionnearaPoint:PrincipalAxes .................... 61
10. KinematicConsiderationsofParallelShearFlows................ 64
11. KinematicConsiderationsofVortexFlows ...................... 65
12. One-,Two-,andThree-DimensionalFlows...................... 68
13. TheStreamfunction........................................... 69
14. PolarCoordinates............................................. 72
Exercises .................................................... 73
SupplementalReading ........................................ 75
Contents ix
Chapter 4
Conservation Laws
1. Introduction.................................................. 77
2. TimeDerivativesofVolumeIntegrals........................... 77
3. ConservationofMass......................................... 79
4. Streamfunctions:RevisitedandGeneralized..................... 81
5. OriginofForcesinFluid ...................................... 82
6. StressataPoint .............................................. 84
7. ConservationofMomentum ................................... 86
8. MomentumPrincipleforaFixedVolume........................ 88
9. AngularMomentumPrincipleforaFixedVolume................ 92
10. ConstitutiveEquationforNewtonianFluid ...................... 94
11. Navier–StokesEquation....................................... 97
12. RotatingFrame............................................... 99
13. MechanicalEnergyEquation .................................. 104
14. FirstLawofThermodynamics:ThermalEnergyEquation......... 108
15. SecondLawofThermodynamics:EntropyProduction............ 109
16. BernoulliEquation............................................ 110
17. ApplicationsofBernoulli’sEquation............................ 114
18. BoussinesqApproximation .................................... 117
19. BoundaryConditions ......................................... 121
Exercises .................................................... 126
LiteratureCited .............................................. 128
SupplementalReading ........................................ 128
Chapter 5
Vorticity Dynamics
1. Introduction.................................................. 129
2. VortexLinesandVortexTubes ................................. 130
3. RoleofViscosityinRotationalandIrrotationalVortices .......... 130
4. Kelvin’sCirculationTheorem.................................. 134
5. VorticityEquationinaNonrotatingFrame....................... 138
6. VelocityInducedbyaVortexFilament:LawofBiotandSavart. ... 140
7. VorticityEquationinaRotatingFrame.......................... 141
8. InteractionofVortices......................................... 146
9. VortexSheet ................................................. 149
Exercises .................................................... 150