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VIS OUS FLUID FLOW
Third Edition
Fra nk M . W hite
University of Rhode sland
M e
Graw
Hill
Higher ducation
Boston Burr Ridge IL Du buque IA Madison Wl New York
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CONTENTS
Preface xiii
Lis t
of
Sy m b ols xvii
1 P rel im inary Conc ep ts
1
1-1 Historical Ou tline 1
1-2 Some Ex am ples of Viscous-Flow P henom ena 4
1-3 P roperties of a Fluid 15
1-4 Boundary Cond itions for Visc ous-Flow P robl em s 45
Summary 54
Problems 55
2 Fundam ental Equations of Com p ress ible Viscous Flow 59
2-1 Introduction 59
2-2 Classification of The Fund am ental Equations 59
2-3 Cons ervation of Mass : The Equation of Continuity 60
2-4 Conservation of Mom entum : The Nav ier-Stokes Equations 62
2-5 The Energy Equation First L aw of Therm odynam ics) 69
2-6 Boundary Conditions for Viscous Heat-Cond ucting Flow 74
2-7 Orthogonal Coo rdinate Sy stem s 75
2-8 Mathem atical Charac ter of The Bas ic Equations 77
2-9 Dim ensionless Param eters in Viscous Flow 81
2-10 Vorticity Considerations in Incom pres sib le Viscous Flow 84
2-11 Two-Dim ensional Con siderations : The Stream Func tion 86
2-12 Noninertial Coo rdinate Sy stem s 88
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X CONTENTS
3 Solutions of The Newtonian Viscous-Flow Equations 96
3-1 Introduction and Class ification of Solu tions 96
3-2 Couette Flows Du e to Mov ing Surfaces 98
3-3 Po iseuille Flow through Duc ts 106
3-4 Unsteady Duc t Flows 125
3-5 Unsteady Flows with Mo ving Boun daries 129
3-6 Asy m ptotic Suction Flows 135
3-7 Wind-Driven Flow s: The Ekm an Drift 141
3-8 Sim ilarity Solutions 144
3-9 Low Reynolds Num ber: L inearized Creeping Motion 165
3-10 Com putational Fluid Dy nam ics 183
Summary 205
Problems 205
4 L am ina r B ounda ry L aye r s 215
4-1 Introduction 215
4-2 L am inar Boundary -Lay er Equations 225
4-3 Sim ilarity Solutions for Steady Two-D im ensional Flow ..230
4-4 Free-Shear Flows 251
4-5 Other Analytic Two-Dim ensional Solutions 257
4-6 App roxim ate Integral Methods 261
4-7 Digital-Com puter Solutions 271
4-8 Thermal-Boundary-Layer Calculations 278
4-9 Flow in the Inlet of Duc ts 287
4-10 Rotationally Sym m etric Boundary L ayers 290
4-11 Asym ptotic Exp ansions and Triple-Deck Theory 300
4-12 Three-Dim ensional L am inar Boundary L ayers 307
4-13 Unsteady Boundary L ayers : Separation Anxiety 318
4-14 Free-Conv ection Boundary L ayers 321
Summary 328
Problems 328
5 T h e Stabi l i ty o f L a m i n a r F l o w s 337
5-1 Introduc tion: The Con cep t of Sm all-Disturbanc e Stability 337
5-2 L inearized Stability of P arallel Viscous Flows 344
5-3 P arametric Effects in the L inear Stability Theory 357
5-4 Transition to Turbulenc e 370
5-5 Engineering P rediction of Transition 378
Summary 394
Problems 394
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CONTENTS XI
6 Incom p ress ib l e Turbu len t M ea n F lo w 398
6-1 Phy sical and Mathem atical Des cription of Turbu lence 398
6-2 The Reynolds Equations of Turbulent Motion 406
6-3 The Two-Dim ensional Turb ulent-Boundary-L ayer Equations 41 1
6-4 Velocity P rofiles: The Inner, Outer, and Ov erlap L ayers 41 4
6-5 Turbulent Flow in P ipes and Channels 425
6-6 The Turbulent Boundary L ayer on a Flat P late 43 3
6-7 Turbulence M odeling 44 0
6-8 Analysis of Turbulent Boundary L ayers with a P ress ure Gradient 454
6-9 Free Turbulence: Jets, Wakes, and M ixing L ayers 473
6-10 Turbulent Conv ective Heat Transfer 485
Summary 498
Problems 498
7 C o m p r e s s i b l e - B o u n da r y - L a y e r F l o w
505
7-1 Introduction: The Com press ible-Boundary-Lay er Equations 505
7-2 Similarity Solutions for Com pressib le L am inar Flow 511
7-3 Solutions for L am inar Flat-Plate and Stagnation-Point Flow 51 4
7-4 Com pressible L am inar Boundary L ayers under Arbitrary Conditions 525
7-5 Special Topics in Com press ible L am inar Flow 539
7-6 The Com pressible-Turbulent-Boundary-Lay er Equations 544
7-7 Wall and Wake L aws for Turbulent Com pres sib le Flow 547
7.8 Com pressible Turbulent Flow P ast a Flat P late ....553
7-9 Com press ible-Turbulent-Boundary-L ayer Calc ulation with a P ressu re Gradient 561
Summary 566
Problems 566
A p p e n d i c e s 571
A Transport P roperties of Various New tonian Fluids 571
B Equations of Motion of Incom p ressib le New tonian Fluids in
Cylindrical and Sp herical P olar Coordinates 58 1
C A Runge-Kutta Sub routine for
N
Sim ultaneous Differential Equations 585
Bibliography 590
Index
xxx