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Incompressible Flow, 2nd Edition

by: Ronald L. Panton (Univ. of Texas, Austin)

Incompressible Flow, 2nd Edition

by: Ronald L. Panton (Univ. of Texas, Austin)

ISBN 13:
9780471593584
ISBN 10:
0471593583
Edition: 2nd
Format: Hardcover
Copyright: 01/01/1996
Publisher: Wiley-Interscience
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Summary

The second edition is needed to update research, examples, and applications to industry. The presentation starts with basic principles followed with a patient development of the mathematics and physics leading to theories of fluids supported with examples and problem exercise.

Preface

(2)

Preface to the First Edition

vii

1. Continuum Mechanics

(17)

1.1 The Continuum Assumption

(1)

1.2 Fundamental Concepts, Definitions, and Laws

(2)

1.3 Space and Time

(2)

1.4 Density, Velocity, and Internal Energy

(4)

1.5 The Interface between Phases

(2)

1.6 Conclusion

(2)

Problems

(2)

2. Thermodynamics

(15)

2.1 Systems, Properties, and Processes

(1)

2.2 The Independent Variables

(1)

2.3 Temperature and Entropy

(2)

2.4 Fundamental Equations of Thermodynamics

(1)

2.5 Euler's Equation for Homogeneous Functions

(1)

2.6 The Gibbs-Duhem Equation

(1)

2.7 Intensive Forms of Basic Equations

(1)

2.8 Dimensions of Temperature and Entropy

(1)

2.9 Working Equations

(1)

2.10 The Ideal Gas

(3)

2.11 The Incompressible Substance

(1)

2.12 Conclusion

(1)

Problems

(2)

3. Vector Calculus and Index Notation

(30)

3.1 Index Notation Rules

(2)

3.2 Definition of Vectors and Tensors

(1)

3.3 Special Symbols and Isotropic Tensors

(2)

3.4 Direction Cosines and the Law of Cosines

(2)

3.5 Algebra with Vectors

(1)

3.6 Symmetric and Antisymmetric Tensors

(3)

3.7 Algebra with Tensors

(2)

3.8 Vector Cross-Product

(1)

*3.9 Alternative Definitions of Vectors and Tensors

(2)

*3.10 Principal Axes and Values

(2)

3.11 Derivative Operations on Vector Fields

(3)

3.12 Integral Formulas of Gauss and Stokes

(3)

3.13 Leibnitz's Theorem

(2)

3.14 Conclusion

(1)

Problems

(3)

4. Kinematics of Local Fluid Motion

(24)

4.1 Lagrangian Viewpoint

(4)

4.2 Eulerian Viewpoint

(2)

4.3 Substantial Derivative

(1)

4.4 Decomposition of Motion

(5)

4.5 Elementary Motions in a Linear Shear Flow

(2)

*4.6 Proof of Vorticity Characteristics

(2)

*4.7 Rate-of-Strain Characteristics

(2)

4.8 Rate of Expansion

(1)

*4.9 Streamline Coordinates

(2)

4.10 Conclusion

(1)

Problems

(3)

5. Basic Laws

(42)

5.1 Continuity Equation

(4)

5.2 Momentum Equation

(2)

5.3 Surface Forces

(1)

*5.4 Stress-Tensor Derivation

(2)

5.5 Interpretation of the Stress-Tensor Components

(1)

5.6 Pressure and Viscous Stress Tensor

(2)

5.7 Differential Momentum Equation

(6)

*5.8 Angular-Momentum Equation and Symmetry of T(ij)

105

(1)

5.9 Energy Equation

106

(4)

5.10 Mechanical- and Thermal-Energy Equations

110

(1)

5.11 Energy Equation with Temperature as Dependent Variable

111

(1)

*5.12 Second Law of Thermodynamics

112

(1)

5.13 Integral Form of the Continuity Equation

113

(2)

5.14 Integral Form of the Momentum Equation

115

(3)

*5.15 Momentum Equation for a Deformable Particle of Variable Mass

118

(4)

*5.16 Other Laws in Integral Form: Energy Equation

122

(1)

5.17 Jump Equations at Interfaces

123

(2)

5.18 Conclusion

125

(1)

Problems

125

(4)

6. Newtonian Fluids and the Navier-Stokes Equations

129

(19)

6.1 Newton's Viscosity Law

129

(4)

6.2 Molecular Model of Viscous Effects

133

(4)

6.3 Non-Newtonian Liquids

137

(3)

*6.4 The No-Slip Condition

140

(3)

6.5 Fourier's Heat-Conduction Law

143

(2)

6.6 Navier-Stokes Equations

145

(1)

6.7 Conclusion

146

(1)

Problems

146

(2)

7. Some Incompressible-Flow Patterns

148

(27)

7.1 Pressure-Driven Flow in a Slot

148

(6)

7.2 Mechanical Energy and Bernoulli Equations

154

(4)

7.3 Plane Couette Flow

158

(2)

7.4 Pressure-Driven Flow in a Slot with a Moving Wall

160

(1)

7.5 Double Falling Film on a Wall

161

(3)

7.6 Rotary Viscous Coupling; Outer Solution

164

(2)

7.7 The Rayleigh Problem

166

(6)

7.8 Conclusion

172

(1)

Problems

172

(3)

8. Dimensional Analysis

175

(37)

8.1 Measurement and Dimensions

175

(3)

8.2 Variables and Functions

178

(3)

8.3 The Pi Theorem

181

(4)

8.4 Pump or Blower Analysis

185

(4)

8.5 Number of Primary Dimensions

189

(3)

*8.6 Proof of Bridgman's Equation

192

(2)

*8.7 Proof of the Pi Theorem

194

(4)

8.8 Dynamic Similarity

198

(1)

8.9 Similarity with Geometric Distortion

199

(4)

8.10 Nondimensional Formulation of Physical Problems

203

(6)

8.11 Conclusion

209

(1)

Problems

209

(3)

9. Compressible Flow

212

(16)

9.1 Compressible Couette Flow: Adiabatic Wall

212

(4)

9.2 Flow with Power-Law Transport Properties

216

(2)

9.3 Compressible Waves

218

(8)

9.4 Conclusion

226

(1)

Problems

226

(2)

10. Incompressible Flow

228

(26)

10.1 Characterization

228

(2)

10.2 Incompressible Flow as a Low Mach Number Flow with Adiabatic Walls

230

(1)

10.3 Nondimensional Problem Statement

231

(5)

10.4 Characteristics of Incompressible Flow

236

(3)

10.5 Splitting the Pressure into Kinetic and Hydrostatic Parts

239

(3)

*10.6 Mathematical Aspects of the Limit Process M^2 --> 0

242

(1)

*10.7 Invariance of Incompressible-Flow Equations under Unsteady Motion

243

(3)

*10.8 Low-Mach-Number Flows with Constant-Temperature Walls

246

(4)

*10.9 The Energy-Equation Paradox

250

(2)

10.10 Conclusion

252

(1)

Problems

253

(1)

11. Some Solutions of the Navier-Stokes Equations

254

(49)

11.1 Pressure-Driven Flow in Tubes of Various Cross Sections: An Elliptical Tube

255

(3)

11.2 Flow in a Rectangular Tube

258

(3)

11.3 A Channel with Longitudinal Ribs

261

(2)

11.4 Stokes Oscillating Plate

263

(4)

11.5 Wall Under an Oscillating Free Stream

267

(3)

*11.6 Transient for Stokes Oscillating Plate

270

(2)

11.7 Flow in a Slot with an Oscillating Pressure Gradient

272

(5)

11.8 Decay of Line Vortices (Oseen Vortex)

277

(5)

11.9 Plane Stagnation-Point Flow (Hiemenz Flow)

282

(7)

11.10 Burgers Vortex

289

(2)

11.11 Complete Solution for the Rotary Coupling

291

(3)

11.12 von Karman Viscous "Pump"

294

(5)

11.13 Conclusion

299

(1)

Problems

299

(4)

12. Streamfunctions and the Velocity Potential

303

(21)

12.1 Streamlines

303

(3)

12.2 Streamfunction for Plane Flows

306

(4)

12.3 Flow in a Slot with Porous Walls

310

(2)

*12.4 Streamlines and Streamsurfaces for a Three-Dimensional Flow

312

(5)

12.5 Velocity Potential and Unsteady Bernoulli Equation

317

(2)

12.6 Flow Caused by a Sphere with Variable Radius

319

(2)

12.7 Conclusion

321

(1)

Problems

322

(2)

13. Vorticity Dynamics

324

(35)

13.1 Vorticity

324

(2)

13.2 Kinematic Results Concerning Vorticity

326

(2)

13.3 Vorticity Equation

328

(2)

13.4 Vorticity Diffusion

330

(1)

13.5 Vorticity Intensification by Straining Vortex Lines

331

(2)

13.6 Hill's Spherical Vortex

333

(2)

13.7 Production of Vorticity at a Stationary Wall

335

(3)

13.8 Production of Vorticity at a Translating Wall

338

(1)

13.9 Helmholtz's Laws for Inviscid Flow

339

(2)

13.10 Kelvin's Theorem

341

(1)

13.11 Inviscid Motion of Point Vortices

342

(2)

13.12 Reconnection of Vortex Lines

344

(2)

13.13 Development of Typical Vorticity Distributions

346

(6)

13.14 Vortex Breakdown

352

(4)

13.15 Conclusion

356

(1)

Problems

357

(2)

14. Flows at Moderate Reynolds Numbers

359

(43)

14.1 Some Unusual Flow Patterns

360

(3)

14.2 Entrance Flows

363

(1)

14.3 Entrance Flow into a Cascade of Plates: Computer Solution by the Streamfunction-Vorticity Method

364

(12)

14.4 Entrance Flow into a Cascade of Plates: Pressure Solution

376

(2)

14.5 Entrance Flow into a Cascade of Plates: Results

378

(6)

14.6 Flow Around a Circular Cylinder

384

(16)

14.7 Conclusion

400

(1)

Problems

400

(2)

15. Asymptotic Analysis Methods

402

(35)

15.1 Oscillation of a Gas Bubble in a Liquid

402

(3)

15.2 Order Symbols, Gauge Functions, and Asymptotic Expansions

405

(4)

15.3 Inviscid Flow over a Wavy Wall

409

(4)

*15.4 Nonuniform Expansions: Friedrich's Problem

413

(3)

*15.5 The Matching Process

416

(5)

15.6 Composite Expansions: Accuracy

421

(3)

15.7 Characteristics of Overlap Regions

424

(6)

15.8 Lagerstrom's Problems

430

(4)

15.9 Conclusion

434

(1)

Problems

435

(2)

16. Characteristics of High Reynolds Number Flow

437

(23)

16.1 Physical Motivation

437

(2)

16.2 Inviscid Main Flows: Euler Equations

439

(4)

16.3 Pressure Changes in Steady Flows: Bernoulli Equations

443

(4)

16.4 Boundary Layers

447

(11)

16.5 Conclusion

458

(1)

Problems

459

(1)

17. Kinematic Decomposition of Flow Fields

460

(11)

*17.1 General Approach

460

(1)

*17.2 Helmholtz's Decomposition

461

(2)

*17.3 Line Vortex and Vortex Sheet

463

(3)

*17.4 Complex-Lamellar Decomposition

466

(3)

*17.5 Conclusion

469

(1)

Problems

469

(2)

18. Ideal Flows in a Plane

471

(75)

18.1 Problem Formulation for Plane Ideal Flows

472

(4)

18.2 Simple Plane Flows

476

(3)

18.3 Line Source and Line Vortex

479

(3)

18.4 Flow over a Nose or a Cliff

482

(7)

18.5 Doublets

489

(3)

18.6 Cylinder in a Stream

492

(2)

18.7 Cylinder with Circulation in a Uniform Stream

494

(3)

18.8 Lift and Drag on Two-Dimensional Shapes

497

(3)

18.9 Magnus Effect

500

(2)

18.10 Conformal Transformations

502

(4)

18.11 Joukowski Transformation: Airfoil Geometry

506

(6)

18.12 Kutta Condition

512

(2)

18.13 Flow over a Joukowski Airfoil: Airfoil Lift

514

(8)

18.14 A Numerical Method for Airfoils

522

(3)

18.15 Actual Airfoils

525

(3)

*18.16 Schwarz-Christoffel Transformation

528

(2)

*18.17 Diffuser or Contraction Flow

530

(6)

*18.18 Gravity Waves in Liquids

536

(6)

18.19 Conclusion

542

(1)

Problems

542

(4)

19. Axisymmetric and Three-Dimensional Ideal Flows

546

(35)

19.1 General Equations and Characteristics of Three-Dimensional Ideal Flows

546

(2)

19.2 Swirling Flow Turned into an Annulus

548

(2)

19.3 Flow over a Weir

550

(2)

19.4 Point Source

552

(2)

19.5 Rankine Nose Shape

554

(2)

19.6 Experiments on the Nose Drag of Slender Shapes

556

(3)

19.7 Flow from a Doublet

559

(2)

19.8 Flow over a Sphere

561

(3)

19.9 Kinetic Energy

564

(1)

19.10 Wake Drag of Bodies

565

(2)

*19.11 Induced Drag: Drag Due to Lift

567

(5)

*19.12 Lifting-Line Theory

572

(1)

*19.13 Added Mass of Accelerating Bodies

573

(6)

19.14 Conclusion

579

(1)

Problems

579

(2)

20. Boundary Layers

581

(79)

20.1 Blasius Flow over a Flat Plate

581

(6)

20.2 Displacement Thickness

587

(2)

20.3 von Karman Momentum Integral

589

(2)

20.4 von Karman-Pohlhausen Approximate Method

591

(2)

20.5 Falkner-Skan Similarity Solutions

593

(6)

20.6 Arbitrary Two-Dimensional Layers: Crank-Nicolson Difference Method

599

(10)

*20.7 Vertical Velocity

609

(3)

20.8 Joukowski-Airfoil Boundary Layer

612

(4)

20.9 Boundary Layer on a Bridge Piling

616

(3)

20.10 Plane Boundary-Layer Separation

619

(3)

20.11 Axisymmetric Boundary Layers

622

(3)

20.12 Jets

625

(3)

20.13 Far Wake of Nonlifting Bodies

628

(4)

20.14 Free Shear Layers

632

(2)

20.15 Unsteady and Erupting Boundary Layers

634

(4)

*20.16 Entrance Flow into a Cascade

638

(3)

*20.17 Three-Dimensional Boundary Layers

641

(4)

*20.18 Boundary Layer with a Constant Transverse Pressure Gradient

645

(5)

*20.19 Howarth's Stagnation Point

650

(3)

*20.20 Three-Dimensional Separation

653

(4)

20.21 Conclusion

657

(1)

Problems

658

(2)

21. Low Reynolds Number Flows

660

(46)

21.1 General Relations for Re --> 0: Stokes Equations

661

(3)

21.2 Global Equations for Stokes Flow

664

(2)

21.3 Flow in Tubes and Channels with Varying Cross Sections

666

(3)

21.4 Reynolds Equations for Lubrication Theory

669

(3)

21.5 Slipper-Pad Bearing

672

(3)

*21.6 Squeeze Film Lubrication; Viscous Adhesion

675

(1)

21.7 Plane Corner Flows: Moffatt Vortices

676

(6)

21.8 Axisymmetric Flow: Cones, Orifices, and Tubes

682

(4)

21.9 Flow over a Sphere

686

(4)

*21.10 Nonuniformity of Stokes Flow on Infinite Domains

690

(1)

21.11 Asymptotic Analysis of Flow over a Sphere

691

(2)

21.12 Stokes Flow Near a Circular Cylinder

693

(2)

*21.13 Oseen's Equations

695

(1)

*21.14 Bubble or Droplet in an Infinite Fluid

696

(4)

*21.15 Stokes Flow over Particles of Arbitrary Shape

700

(2)

*21.16 Interference Effects

702

(1)

21.17 Conclusion

703

(1)

Problems

704

(2)

22. Introduction to Stability and Transition

706

(39)

22.1 Linear Stability and Normal Modes as Perturbations

707

(2)

22.2 Kelvin-Helmholtz Inviscid Shear-Layer Instability

709

(5)

22.3 Stability Problem for Nearly Parallel Viscous Flows

714

(3)

22.4 Orr-Sommerfeld Equation

717

(1)

22.5 Inviscid Stability of Nearly Parallel Flows

718

(2)

22.6 Viscous Stability of Nearly Parallel Flows

720

(3)

22.7 Experiments on Blasius Boundary Layers

723

(4)

22.8 Transition; Secondary Instability; Bypass

727

(3)

22.9 Spatially Developing Open Flows

730

(2)

22.10 Transition in Free Shear Flows

732

(1)

22.11 Poiseuille and Plane Couette Flows

732

(2)

22.12 Inviscid Instability of Flows with Curved Streamlines

734

(3)

22.13 Taylor Instability of Couette Flow

737

(2)

22.14 Stability of Regions of Concentrated Vorticity

739

(2)

22.15 Some Other Instabilities: Taylor; Curved Pipe; Capillary Jets; Gortler

741

(3)

22.16 Conclusion

744

(1)

23. Introduction to Turbulent Flows

745

(48)

23.1 Types of Turbulent Flows

745

(1)

23.2 Characteristics of Turbulent Flows

746

(3)

23.3 Reynolds Decomposition

749

(2)

23.4 Reynolds Stress

751

(3)

23.5 Free Turbulence: Plane Shear Layers

754

(5)

23.6 Free Turbulence: The Turbulent Jet

759

(3)

23.7 Bifurcating and Blooming Jets

762

(1)

*23.8 Correlations of Fluctuations

763

(2)

*23.9 Mean and Turbulent Kinetic Energy

765

(3)

23.10 Energy Cascade: Kolmogorov Scales; Taylor Microscale

768

(5)

23.11 Wall Turbulence; Channel Flow

773

(10)

23.12 Wall Layers; Experiments and Empirical Correlation

783

(5)

23.13 Turbulent Structures

788

(4)

23.14 Conclusion

792

(1)

Appendix A Properties of Fluids

793

(1)

Appendix B Differential Operations in Cylindrical and Spherical Coordinates

794

(5)

Appendix C Basic Equations in Rectangular, Cylindrical, and Spherical Coordinates

799

(6)

Appendix D Streamfunction Relations in Rectangular, Cylindrical, and Spherical Coordinates

805

(4)

Appendix E Computer Code for Runge-Kutta Integration

809

(3)

Appendix F Computer Code for Entrance Flow into a Cascade

812

(3)

Appendix G Computer Code for Boundary-Layer Analysis

815

(3)

Supplemental Reading List

818

(1)

References

819

(12)

Index

831

Amazon no longer offers textbook rentals. We do!

Incompressible Flow, 2nd Edition

Incompressible Flow, 2nd Edition

9780471593584

0471593583

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Incompressible Flow, 2nd Edition

Incompressible Flow, 2nd Edition

9780471593584

0471593583

Summary

Table of Contents

Supplemental Materials

Write a Review

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