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Chapter 1 Introduction1

1.Fluid Mechanics1

2.Units of Measurement2

3.Solids，Liquids，and Gases3

4.Continuum Hypothesis4

5.Transport Phenomena5

6.Surface Tension8

7.Fluid Statics9

8.Classical Thermodynamics12

9.Perfect Gas16

10.Static Equilibrium of a Compressible Medium18

Exercises22

Literature Cited24

Supplemental Reading24

Chapter 2 Cartesian Tensors25

1.Scalars and Vectors25

2.Rotation of Axes：Formal Definition of a Vector26

3.Multiplication of Matrices29

4.Second-Order Tensor30

5.Contraction and Multiplication32

6.Force on a Surface33

7.Kronecker Delta and Alternating Tensor36

8.Dot Product37

9.Cross Product38

10.Operator ？：Gradient，Divergence，and Curl38

11.Symmetric and Antisymmetric Tensors40

12.Eigenvalues and Eigenvectors of a Symmetric Tensor41

13.Gauss’ Theorem44

14.Stokes’ Theorem47

15.Comma Notation49

16.Boldface vsIndicial Notation49

Exercises50

Literature Cited51

Supplemental Reading51

Chapter 3 Kinematics53

1.Introduction53

2.Lagrangian and Eulerian Specifications54

3.Eulerian and Lagrangian Descriptions：The Particle Derivative55

4.Streamline，Path Line，and Streak Line57

5.Reference Frame and Streamline Pattern59

6.Linear Strain Rate60

7.Shear Strain Rate61

8.Vorticity and Circulation62

9.Relative Motion near a Point：Principal Axes64

10.Kinematic Considerations of Parallel Shear Flows67

11.Kinematic Considerations of Vortex Flows68

12.One-，Two-，and Three-Dimensional Flows71

13.The Streamfunction73

14.Polar Coordinates75

Exercises77

Supplemental Reading79

Chapter 4 Conservation Laws82

1.Introduction82

2.Time Derivatives of Volume Integrals82

3.Conservation of Mass84

4.Streamfunctions：Revisited and Generalized87

5.Origin of Forces in Fluid88

6.Stress at a Point90

7.Conservation of Momentum92

8.Momentum Principle for a Fixed Volume93

9.Angular Momentum Principle for a Fixed Volume98

10.Constitutive Equation for Newtonian Fluid100

11.Navier—Stokes Equation104

12.Rotating Frame105

13.Mechanical Energy Equation111

14.First Law of Thermodynamics：Thermal Energy Equation115

15.Second Law of Thermodynamics：Entropy Production116

16.Bernoulli Equation118

17.Applications of Bernoulli’s Equation122

18.Boussinesq Approximation124

19.Boundary Conditions129

Exercises134

Literature Cited136

Supplemental Reading137

Chapter 5 Vorticity Dynamics139

1.Introduction139

2.Vortex Lines and Vortex Tubes140

3.Role of Viscosity in Rotational and Irrotational Vortices141

4.Kelvin’s Circulation Theorem144

5.Vorticity Equation in a Nonrotating Frame149

6.Velocity Induced by a Vortex Filament：Law of Biot and Savart151

7.Vorticity Equation in a Rotating Frame152

8.Interaction of Vortices157

9.Vortex Sheet161

Exercises161

Literature Cited163

Supplemental Reading163

Chapter 6 Irrotational Flow165

1.Relevance of Irrotational Flow Theory165

2.Velocity Potential：Laplace Equation167

3.Application of Complex Variables169

4.Flow at a Wall Angle171

5.Sources and Sinks173

6.Irrotational Vortex174

7.Doublet174

8.Flow pasta Half-Body175

9.Flow past a Circular Cylinder without Circulation178

10.Flow past a Circular Cylinder with Circulation180

11.Forces on a Two-Dimensional Body184

12.Source near a Wall：Method of Images189

13.Conformal Mapping190

14.Flow around an Elliptic Cylinder with Circulation192

15.Uniqueness of Irrotational Flows194

16.Numerical Solution of Plane Irrotational Flow195

17.Axisymmetric Irrotational Flow201

18.Streamfunction and Velocity Potential for Axisymmetric Flow203

19.Simple Examples of Axisymmetric Flows205

20.Flow around a Streamlined Body of Revolution206

21.Flow around an Arbitrary Body of Revolution208

22.Concluding Remarks209

Exercises209

Literature Cited212

Supplemental Reading212

Chapter 7 Gravity Waves214

1.Introduction214

2.The Wave Equation214

3.Wave Parameters216

4.Surface Gravity Waves219

5.Some Features of Surface Gravity Waves223

6.Approximations for Deep and Shallow Water229

7.Influence of Surface Tension234

8.Standing Waves237

9.Group Velocity and Energy Flux238

10.Group Velocity and Wave Dispersion242

11.Nonlinear Steepening in a Nondispersive Medium246

12.Hydraulic Jump248

13.Finite Amplitude Waves of Unchanging Form in a Dispersive Medium250

14.Stokes’ Drift253

15.Waves at a Density Interface between Infinitely Deep Fluids255

16.Waves in a Finite Layer Overlying an Infinitely Deep Fluid259

17.Shallow Layer Overlying an Infinitely Deep Fluid262

18.Equations of Motion for a Continuously Stratified Fluid263

19.Internal Waves in a Continuously Stratified Fluid267

20.Dispersion of Internal Waves in a Stratified Fluid270

21.Energy Considerations of Internal Waves in a Stratified Fluid272

Exercises276

Literature Cited277

Chapter 8 Dynamic Similarity279

1.Introduction279

2.Nondimensional Parameters Determined from Differential Equations280

3.Dimensional Matrix284

4.Buckingham’s Pi Theorem285

5.Nondimensional Parameters and Dynamic Similarity287

6.Comments on Model Testing290

7.Significance of Common Nondimensional Parameters292

Exercises294

Literature Cited294

Supplemental Reading294

Chapter 9 Laminar Flow295

1.Introduction295

2.Analogy between Heat and Vorticity Diffusion297

3.Pressure Change Due to Dynamic Effects297

4.Steady Flow between Parallel Plates298

5.Steady Flow in a Pipe302

6.Steady Flow between Concentric Cylinders303

7.Impulsively Started Plate：Similarity Solutions306

8.Diffusion of a Vortex Sheet313

9.Decay of a Line Vortex315

10.Flow Due to an Oscillating Plate317

11.High and Low Reynolds Number Flows320

12.Creeping Flow around a Sphere322

13.Nonuniformity of Stokes’ Solution and Oseen’s Improvement327

14.Hele-Shaw Flow332

15.Final Remarks334

Exercises335

Literature Cited337

Supplemental Reading337

Chapter 10 Boundary Layers and Related Topics340

1.Introduction340

2.Boundary Layer Approximation340

3.Different Measures of Boundary Layer Thickness346

4.Boundary Layer on a Flat Plate with a Sink at the Leading Edge：Closed Form Solution348

5.Boundary Layer on a Flat Plate：Blasius Solution352

6.von Karman Momentum Integral362

7.Effect of Pressure Gradient364

8.Separation366

9.Description of Flow past a Circular Cylinder368

10.Description of Flow past a Sphere375

11.Dynamics of Sports Balls376

12.Two-Dimensional Jets381

13.Secondary Flows388

14.Perturbation Techniques389

15.An Example of a Regular Perturbation Problem394

16.An Example of a Singular Perturbation Problem396

17.Decay of a Laminar Shear Layer401

Exercises407

Literature Cited409

Supplemental Reading410

Chapter 11 Computational Fluid Dynamics411

1.Introduction411

2.Finite Difference Method413

3.Finite Element Method418

4.Incompressible Viscous Fluid Flow426

5.Three Examples440

6.Concluding Remarks461

Exercises463

Literature Cited464

Chapter 12 Instability467

1.Introduction467

2.Method of Normal Modes469

3.Thermal Instability：The Benard Problem470

4.Double-Diffusive Instability482

5.Centrifugal Instability：Taylor Problem486

6.Kelvin—Helmholtz Instability493

7.Instability of Continuously Stratified Parallel Flows500

8.Squire’s Theorem and Orr—Sommerfeld Equation507

9.Inviscid Stability of Parallel Flows510

10.Some Results of Parallel Viscous Flows514

11.Experimental Verification of Boundary Layer Instability520

12.Comments on Nonlinear Effects522

13.Transition523

14.Deterministic Chaos525

Exercises533

Literature Cited535

Chapter 13 Turbulence537

1.Introduction537

2.Historical Notes539

3.Averages541

4.Correlations and Spectra543

5.Averaged Equations of Motion547

6.Kinetic Energy Budget of Mean Flow554

7.Kinetic Energy Budget of Turbulent Flow556

8.Turbulence Production and Cascade559

9.Spectrum of Turbulence in Inertial Subrange562

10.Wall-Free Shear Flow564

11.Wall-Bounded Shear Flow570

12.Eddy Viscosity and Mixing Length580

13.Coherent Structures in a Wall Layer584

14.Turbulence in a Stratified Medium586

15.Taylor’s Theory of Turbulent Dispersion591

16.Concluding Remarks598

Exercises598

Literature Cited600

Supplemental Reading601

Chapter 14 Geophysical Fluid Dynamics603

1.Introduction603

2.Vertical Variation of Density in Atmosphere and Ocean605

3.Equations of Motion607

4.Approximate Equations for a Thin Layer on a Rotating Sphere610

5.Geostrophic Flow613

6.Ekman Layer at a Free Surface617

7.Ekman Layer on a Rigid Surface622

8.Shallow-Water Equations625

9.Normal Modes in a Continuously Stratified Layer628

10.High- and Low-Frequency Regimes in Shallow-Water Equations634

11.Gravity Waves with Rotation636

12.Kelvin Wave639

13.Potential Vorticity Conservation in Shallow-Water Theory644

14.Internal Waves647

15.Rossby Wave657

16.Barotropic Instability663

17.Baroclinic Instability665

18.Geostrophic Turbulence673

Exercises676

Literature Cited677

Chapter 15 Aerodynamics679

1.Introduction679

2.The Aircraft and Its Controls680

3.Airfoil Geometry683

4.Forces on an Airfoil684

5.Kutta Condition684

6.Generation of Circulation687

7.Conformal Transformation for Generating Airfoil Shape688

8.Lift of Zhukhovsky Airfoil692

9.Wing of Finite Span695

10.Lifting Line Theory of Prandtl and Lanchester697

11.Results for Elliptic Circulation Distribution701

12.Lift and Drag Characteristics of Airfoils704

13.Propulsive Mechanisms of Fish and Birds706

14.Sailing against the Wind708

Exercises709

Literature Cited711

Supplemental Reading711

Chapter 16 Compressible Flow713

1.Introduction713

2.Speed of Sound717

3.Basic Equations for One-Dimensional Flow721

4.Stagnation and Sonic Properties724

5.Area—Velocity Relations in One-Dimensional Isentropic Flow729

6.Normal Shock Wave733

7.Operation of Nozzles at Different Back Pressures741

8.Effects of Friction and Heating in Constant-Area Ducts747

9.Mach Cone750

10.Oblique Shock Wave752

11.Expansion and Compression in Supersonic Flow756

12.Thin Airfoil Theory in Supersonic Flow758

Exercises761

Literature Cited763

Supplemental Reading763

Chapter 17 Introduction to Biofluid Mechanics765

1.Introduction765

2.The Circulatory System in the Human Body766

3.Modelling of Flow in Blood Vessels782

4.Introduction to the Fluid Mechanics of Plants831

Exercises837

Acknowledgment838

Literature Cited838

Appendix A Some Properties of Common Fluids841

A1.Useful Conversion Factors841

A2.Properties of Pure Water at Atmospheric Pressure842

A3.Properties of Dry Air at Atmospheric Pressure842

A4.Properties of Standard Atmosphere843

Appendix B Curvilinear Coordinates845

B1.Cylindrical Polar Coordinates845

B2.Plane Polar Coordinates847

B3.Spherical Polar Coordinates847

Appendix C Founders of Modern Fluid Dynamics851

Ludwig Prandtl（1875—1953）851

Geoffrey Ingram Taylor （1886—1975）852

Supplemental Reading853

Appendix D Visual Resources855

Index857