Fluid mechanics

901 Pages·2008·8.56 MB·English

by  Kundu P.K.

Fluid Mechanics, Fourth 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
Fourth Edition
Pijush K. Kundu
OceanographicCenter
NovaSoutheasternUniversity
Dania,Florida
Ira M. Cohen
DepartmentofMechanicalEngineeringand
AppliedMechanics
UniversityofPennsylvania
Philadelphia,Pennsylvania
withcontributionsbyP.S.AyyaswamyandH.H.Hu
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Library of Congress Cataloging-in-Publication Data
Kundu, Pijush K.
Fluid mechanics / Pijush K. Kundu, Ira M. Cohen. – 4th ed.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-12-373735-9 (alk. paper) /
1. Fluid mechanics. I. Cohen, Ira M. II. Title.
QA901.K86 2008
620.1’06–dc22 2007042765
Reprinted January 2010 – ISBN: 978-0-12-381399-2

British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.

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Printed in the United States
10 11 12 13 14 10 9 8 7 6 5 4 3 2 1
The fourth edition is dedicated to the memory of Pijush K. Kundu and also to my
wifeLindaanddaughtersSusanandNancywhohavegreatlyenrichedmylife.
“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-
dentatPennStateUniversity.WithDr.John
L.Lumleyashisadvisor,hestudiedinstabili-
tiesofviscoelasticfluids,receivinghisdoctor-
atein1972.Hebeganhislifelonginterestin
oceanographysoonafterhisgraduation,workingasResearchAssociateinOceano-
graphy at Oregon State University from 1968 until 1972. After spending a year at
theUniversitydeOrienteinVenezuela,hejoinedthefacultyoftheOceanographic
CenterofNovaSoutheasternUniversity,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
New in This Book ......................................... xvi
Preface................................................... xvii
PrefacetoThirdEdition.................................... xix
PrefacetoSecondEdition .................................. xxi
PrefacetoFirstEdition .................................... xxiii
Author’sNotes............................................ xxvii
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 ...................... 18
Exercises........................................................ 22
LiteratureCited.................................................. 24
SupplementalReading............................................ 24
Chapter 2
Cartesian Tensors
1. ScalarsandVectors............................................... 25
2. RotationofAxes:FormalDefinitionofaVector..................... 26
3. MultiplicationofMatrices ........................................ 29
4. Second-OrderTensor............................................. 30
5. ContractionandMultiplication .................................... 32
vii
viii Contents
6. ForceonaSurface ............................................... 33
7. KroneckerDeltaandAlternatingTensor............................ 36
8. DotProduct ..................................................... 37
9. CrossProduct.................................................... 38
10. Operator∇:Gradient,Divergence,andCurl ........................ 38
11. SymmetricandAntisymmetricTensors............................. 40
12. EigenvaluesandEigenvectorsofaSymmetricTensor ................ 41
13. Gauss’Theorem ................................................. 44
14. Stokes’Theorem................................................. 47
15. CommaNotation................................................. 49
16. BoldfacevsIndicialNotation...................................... 49
Exercises........................................................ 50
LiteratureCited.................................................. 51
SupplementalReading............................................ 51
Chapter 3
Kinematics
1. Introduction ..................................................... 53
2. LagrangianandEulerianSpecifications............................. 54
3. EulerianandLagrangianDescriptions:TheParticleDerivative........ 55
4. Streamline,PathLine,andStreakLine ............................. 57
5. ReferenceFrameandStreamlinePattern............................ 59
6. LinearStrainRate................................................ 60
7. ShearStrainRate ................................................ 61
8. VorticityandCirculation.......................................... 62
9. RelativeMotionnearaPoint:PrincipalAxes........................ 64
10. KinematicConsiderationsofParallelShearFlows ................... 67
11. KinematicConsiderationsofVortexFlows.......................... 68
12. One-,Two-,andThree-DimensionalFlows ......................... 71
13. TheStreamfunction .............................................. 73
14. PolarCoordinates ................................................ 75
Exercises........................................................ 77
SupplementalReading............................................ 79
Chapter 4
Conservation Laws
1. Introduction ..................................................... 82
2. TimeDerivativesofVolumeIntegrals .............................. 82
3. ConservationofMass ............................................ 84
4. Streamfunctions:RevisitedandGeneralized ........................ 87
5. OriginofForcesinFluid.......................................... 88
6. StressataPoint.................................................. 90
Contents ix
7. ConservationofMomentum....................................... 92
8. MomentumPrincipleforaFixedVolume........................... 93
9. AngularMomentumPrincipleforaFixedVolume................... 98
10. ConstitutiveEquationforNewtonianFluid.......................... 100
11. Navier–StokesEquation .......................................... 104
12. RotatingFrame .................................................. 105
13. MechanicalEnergyEquation...................................... 111
14. FirstLawofThermodynamics:ThermalEnergyEquation ............ 115
15. SecondLawofThermodynamics:EntropyProduction ............... 116
16. BernoulliEquation ............................................... 118
17. ApplicationsofBernoulli’sEquation............................... 122
18. BoussinesqApproximation........................................ 124
19. BoundaryConditions............................................. 129
Exercises........................................................ 134
LiteratureCited.................................................. 136
SupplementalReading............................................ 137
Chapter 5
Vorticity Dynamics
1. Introduction ..................................................... 139
2. VortexLinesandVortexTubes .................................... 140
3. RoleofViscosityinRotationalandIrrotationalVortices.............. 141
4. Kelvin’sCirculationTheorem ..................................... 144
5. VorticityEquationinaNonrotatingFrame.......................... 149
6. VelocityInducedbyaVortexFilament:LawofBiotandSavart ....... 151
7. VorticityEquationinaRotatingFrame ............................. 152
8. InteractionofVortices ............................................ 157
9. VortexSheet..................................................... 161
Exercises........................................................ 161
LiteratureCited.................................................. 163
SupplementalReading............................................ 163
Chapter 6
Irrotational Flow
1. RelevanceofIrrotationalFlowTheory.............................. 165
2. VelocityPotential:LaplaceEquation ............................... 167
3. ApplicationofComplexVariables ................................. 169
4. FlowataWallAngle ............................................. 171
5. SourcesandSinks................................................ 173
6. IrrotationalVortex................................................ 174
7. Doublet ......................................................... 174
8. FlowpastaHalf-Body............................................ 175