Viscous Fluid Flow Frank M White Third Edition

 

VIS

O US FLU I D F LO LOW W Third Edition

Fra nk M . W hit hi t e University of Rhode sland

Me Graw Hill

Higher

ducation

Boston Bur Burrr Ridge IL Du buq ue IIA A M adiso n Wl New Yo Yorrk San Franci San Francisco sco St. Louis Louis Bangkok Bogota Caracas Kuala Lumpur Lisbon Lis bon London M adrid Mex ico City City Milan Montreal New Delhi Santiago Seoul Singapore Sydney Taipei Toronto

 

CONTENTS

Preface List  o f  Sy m b ols 1

P reli relim m in inary ary Conc ep ts  

xiii xvii

1

1-1 1-2 1-3 1-3

Historical Ou tline Some Ex am ples of Viscous-Flow P henom ena P roperties of a Fluid

1 4 15

1-4

Boundar Boundaryy Cond itions itions for Visc ous-Flow P robl em s

45

Summary Problems

54 55

2 Funda Fundam m ent ental al Equations Equations of Com p ress re ss ible Viscous Flo Flow w

59

22-11 2-2 2-2 22-33

Introduction Classifi Classificati cation on of The Fund am ental Equations Cons ervation of   M a s s :  The Equation of Continuity

59 59 60

2-4

Conser Conservati vation on of Mom entum : The Nav ier-Stokes Equations

62

2-5 2-6

The Ener Energy gy Equation First L aw of Therm odynam ics) Boundar Boundaryy Conditions for Viscous Heat-Cond ucting Flow

69 74

2-7 2-8

Orthogona Orthogonall Coo rdinate Sy stem s Mathem ati atical cal Charac ter of The Bas ic Equations

75 77

2-9

Dim ensio ensionless nless Param ete eters rs in Viscous Flow

81

2-10 2-10 Vor Vorti ticit cityy Considerati Considerations ons in Incom pres sib le Viscous Flow 22-11 11 Two-Dim ensional Con siderations : The Stream Func tion

84 86

22-12 12 Noninert Noninertial ial Coo rdinate Sy stem s 22-13 13 Contro Control-Volum l-Volum e Form ulations

88 89

Summary Problems

92 92

ix

 

X

CONTENTS

Solutions   o f  The Newtonian Viscous-Flow Equations 

96

3-1

Introduction and Class ificati ification on of Solu tions

96

3-2 3-2 3-3 3-3 3-4 3-4 3-5 3-5 3-6 3-6

Couette Flows Du e to Mov ing Surfaces Po iseuille Flow thro through ugh Duc ts Unsteady Duc t Flows Unsteady Flows with Mo ving Boun daries Asy m ptotic Suction Flows

98 106 125 129 135

3-7 3-7 3-8 3-8 3-9 3-9

Wind-Dr Wind-Driven iven Flow s: The Ekm an Dri Drift ft Sim ilar ilarit ityy Solutions Low Reynolds Num ber: L ineari inearized zed Creeping Motion

141 144 165

3-10 3-10

Com putat putationa ionall Fluid Dy nam ics

183

Summary

205

Problems

205

L a m i n a r B o u n d a r y L a y e r s 

215

4-1 4-2 4-3

Intr Introduction oduction L am inar Boundary -Lay er Equations Sim ilar ilarity ity Solutions for Steady Two-D im ensional Flow

215 225 ..230 ..230

4-4 4-5 4-6

FreeFree-Shear Shear Flows Other Analytic Two-Dim ensional Soluti Solutions ons App roxim ate ate Int Integra egrall Methods

3

4

4-7 DigitalDigital-Com Com puter Solutions 4-8 Thermal-Boundary-Layer Calculati Calculations ons 4-9 Flow in the Inlet of Duc ts 4-10 Rota Rotati tionall onallyy Sym m etri etricc Boundar Boundaryy L ayers 4-11 Asym ptot ptotic ic Exp ansions and and Tri Triple-Deck ple-Deck Theor Theoryy 4-12 Three Three-Dim -Dim ensiona ensionall L am inar Boundary L ayers 4-13 Unsteady Boundary L ayers : Separati Separation on Anxiety 4-14 FreeFree-Conv Conv ection Boundary L ayers

251 257 261 271 278 287 290 300 307 318 321

Summary Problems

328 328

T h e Stability  o f L a m i n a r F l o w s 

33 3377

5-1 5-2 5-2

Intr Introduc oduc tion: The Con cep t of Sm all-Disturbanc e Stabilit Stabilityy L inea ineariz rized ed Stabili Stability ty of P arallel Viscous Flows

337 344

5-3 5-3 5-4

P arametric Effe Effects cts in the L inea inearr Stabilit Stabilityy Theory Transiti Transition on to Turbulenc e

357 370

5-5

Engineering P rediction of Transition Summary

378 394

Problems

394

5 

 

CONTENTS

XI

I n c o m p r e s s i b l e T u r b u l e n t M e a n F l o w 

398

6-1

Phy sical and Mathem atical Des cription of Turbu lence

398

6-2

The Reynolds Equations of Turbulent Motion

406

66-33

The Two-Dim ensional Turb ulent-Boundary-L ayer Equations

41 1

6-4

Vel Veloci ocity ty P rofi rofiles: les: The Inne Inner, r, Outer, and Ov erlap L ayers

41 4

6-5 6-6 6-6

Turbule Turbulent nt Flow in P ipes and Channels The Turbulent Boundary L ayer on a Flat P late

425 43 3

6-7 6-7

Turbulen Turbulence ce M odeling

44 0

6-8

Analysis of Turbulent Boundary L ayers with a P ress ure Gradient

454

6-9

Fr Free ee Turbulence: Jets, Wakes, and M ixing L ayers

473

6-10 6-10

Turbulent Conv ective Heat Transfer

48 5

Summary

498

Problems

498

C o m p r e s s i b l e - B o u n ddaa r y - L a y e r F l o w  

505

7-1

Int Introduct roduction ion:: The Com press ible-Boundary-Lay er Equati Equations ons

505

7-2

Simila Similari rity ty Solut Solutions ions for Com pressib le L am inar Flow

511

7-3

Solut Solution ionss for L am inar Flat-Plate and Stagnation-Point Flow

51 4

7-4

Com pressible L am inar Boundar Boundaryy L ayers under Arbitr Arbitrary ary Condit Conditions ions

525

7-5

Specia Speciall Topics in Com press ible L am inar Flow Flow

539

7-6

The Com pressible-Turbulentpressible-Turbulent-Boundary-Lay Boundary-Lay er Equati Equations ons

544

7-7

Wal Walll and and Wake L aws for Turbulent Com pres sib le Flow

547

7.8 7.8

Com pressible Turbulent Flow P ast a Flat P late

7-9

Com press ible-Turbulent-Boundary-L ayer Calc ulation with a P ressu re Gradient

561

Summary

566

Problems

566

6

7

A p p e n d i c e s 

.... ....553 553

571

A

Tra Transport nsport P roperties of Vari Various ous New tonia toniann Fluids

571

B

Equat Equation ionss of Motion of Incom p ressib le New tonian Fluids in Cylindrical Cylindri cal and Sp herical P olar Coordinates

58 1

A Runge-Kutta Sub rout routine ine for for   N  Sim ultaneous Differe Differenti ntial al Equations

585

C

Bibliography  

590

Index  

xxx