Viscous Fluid Flow Frank m White Third Edition

8/18/2019 Viscous Fluid Flow Frank m White Third Edition

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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

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Viscous Fluid Flow Frank m White Third Edition