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1.Introduction1

1.1.Fluid Mechanics2

1.2.Units of Measurement3

1.3.Solids，Liquids，and Gases3

1.4.Continuum Hypothesis5

1.5.Molecular Transport Phenomena5

1.6.Surface Tension8

1.7.Fluid Statics9

1.8.Classical Thermodynamics12

First Law of Thermodynamics13

Equations of State14

Specific Heats14

Second Law of Thermodynamics15

Property Relations16

Speed of Sound16

Thermal Expansion Coefficient16

1.9.Perfect Gas16

1.10.Stability of Stratified Fluid Media18

Potential Temperature and Density19

Scale Height of the Atmosphere21

1.11.Dimensional Analysis21

Step 1.Select Variables and Parameters22

Step 2.Create the Dimensional Matrix23

Step 3.Determine the Rank of the Dimensional Matrix23

Step 4.Determine the Number of Dimensionless Groups24

Step 5.Construct the Dimensionless Groups24

Step 6.State the Dimensionless Relationship26

Step 7.Use Physical Reasoning or Additional Knowledge to Simplify the Dimensionless Relationship26

Exercises30

Literature Cited36

Supplemental Reading37

2.Cartesian Tensors39

2.1.Scalars，Vectors，Tensors，Notation39

2.2.Rotation of Axes：Formal Definition of a Vector42

2.3.Multiplication of Matrices44

2.4.Second-Order Tensors45

2.5.Contraction and Multiplication47

2.6.Force on a Surface48

2.7.Kronecker Delta and Alternating Tensor50

2.8.Vector，Dot，and Cross Products51

2.9.Gradient，Divergence，and Curl52

2.10.Symmetric and Antisymmetric Tensors55

2.11.Eigenvalues and Eigenvectors of a Symmetric Tensor56

2.12.Gauss’ Theorem58

2.13.Stokes’ Theorem60

2.14.Comma Notation62

Exercises62

Literature Cited64

Supplemental Reading64

3.Kinematics65

3.1.Introduction and Coordinate Systems65

3.2.Particle and Field Descriptions of Fluid Motion67

3.3.Flow Lines，Fluid Acceleration，and Galilean Transformation71

3.4.Strain and Rotation Rates76

Summary81

3.5.Kinematics of Simple Plane Flows82

3.6.Reynolds Transport Theorem85

Exercises89

Literature Cited93

Supplemental Reading93

4.Conservation Laws95

4.1.Introduction96

4.2.Conservation of Mass96

4.3.Stream Functions99

4.4.Conservation of Momentum101

4.5.Constitutive Equation for a Newtonian Fluid111

4.6.Navier-Stokes Momentum Equation114

4.7.Noninertial Frame of Reference116

4.8.Conservation of Energy121

4.9.Special Forms of the Equations125

Angular Momentum Principle for a Stationary Control Volume125

Bernoulli Equations128

Neglect of Gravity in Constant Density Flows134

The Boussinesq Approximation135

Summary137

4.10.Boundary Conditions137

Moving and Deforming Boundaries139

Surface Tension Revisited139

4.11.Dimensionless Forms of the Equations and Dynamic Similarity143

Exercises151

Literature Cited168

Supplemental Reading168

5.Vorticity Dynamics171

5.1.Introduction171

5.2.Kelvin’s Circulation Theorem176

5.3.Helmholtz’s Vortex Theorems179

5.4.Vorticity Equation in a Nonrotating Frame180

5.5.Velocity Induced by a Vortex Filament：Law of Biot and Savart181

5.6.Vorticity Equation in a Rotating Frame183

5.7.Interaction of Vortices187

5.8.Vortex Sheet191

Exercises192

Literature Cited195

Supplemental Reading196

6.Ideal Flow197

6.1.Relevance of Irrotational Constant-DensityFlow Theory198

6.2.Two-Dimensional Stream Function and Velocity Potential200

6.3.Construction of Elementary Flows in Two Dimensions203

6.4.Complex Potential216

6.5.Forces on a Two-Dimensional Body219

Blasius Theorem219

Kutta-Zhukhovsky Lift Theorem221

6.6.Conformal Mapping222

6.7.Numerical Solution Techniques in Two Dimensions225

6.8.Axisymmetric Ideal Flow231

6.9.Three-Dimensional Potential Flow and Apparent Mass236

6.10.Concluding Remarks240

Exercises241

Literature Cited251

Supplemental Reading251

7.Gravity Waves253

7.1.Introduction254

7.2.Linear Liquid-Surface Gravity Waves256

Approximations for Deep and Shallow Water265

7.3.Influence of Surface Tension269

7.4.Standing Waves271

7.5.Group Velocity，Energy Flux，and Dispersion273

7.6.Nonlinear Waves in Shallow and Deep Water279

7.7.Waves on a Density Interface286

7.8.Internal Waves in a Continuously Stratified Fluid293

Internal Waves in a Stratified Fluid296

Dispersion of Internal Waves in a Stratified Fluid299

Energy Considerations for Internal Waves in a Stratified Fluid302

Exercises304

Literature Cited307

8.Laminar Flow309

8.1.Introduction309

8.2.Exact Solutions for Steady Incompressible Viscous Flow312

Steady Flow between Parallel Plates312

Steady Flow in a Round Tube315

Steady Flow between Concentric Rotating Cylinders316

8.3.Elementary Lubrication Theory318

8.4.Similarity Solutions for Unsteady Incompressible Viscous Flow326

8.5.Flow Due to an Oscillating Plate337

8.6.Low Reynolds Number Viscous Flow Past a Sphere338

8.7.Final Remarks347

Exercises347

Literature Cited359

Supplemental Reading359

9.Boundary Layers and Related Topics361

9.1.Introduction362

9.2.Boundary-Layer Thickness Definitions367

9.3.Boundary Layer on a Flat Plate：Blasius Solution369

9.4.Falkner Skan Similarity Solutions of the Laminar Boundary-Layer Equations373

9.5.Von Karman Momentum Integral Equation375

9.6.Thwaites’ Method377

9.7.Transition，Pressure Gradients，and Boundary-Layer Separation382

9.8.Flow Past a Circular Cylinder388

Low Reynolds Numbers389

Moderate Reynolds Numbers389

High Reynolds Numbers392

9.9.Flow Past a Sphere and the Dynamics of Sports Balls395

Cricket Ball Dynamics396

Tennis Ball Dynamics398

Baseball Dynamics399

9.10.Two-Dimensional Jets399

9.11.Secondary Flows407

Exercises408

Literature Cited418

Supplemental Reading419

10.Computational Fluid Dynamics&HOWARD H.HU421

10.1.Introduction421

10.2.Finite-Difference Method423

Approximation to Derivatives423

Discretization and Its Accuracy425

Convergence，Consistency，and Stability426

10.3.Finite-Element Method429

Weak or Variational Form of Partial Differential Equations429

Galerkin’s Approximation and Finite-Element Interpolations430

Matrix Equations，Comparison with Finite-Difference Method431

Element Point of View of the Finite- Element Method434

10.4.Incompressible Viscous Fluid Flow436

Convection-Dominated Problems437

Incompressibility Condition439

Explicit MacCormack Scheme440

MAC Scheme442

O-Scheme446

Mixed Finite-Element Formulation447

10.5.Three Examples449

Explicit MacCormack Scheme for Driven-Cavity Flow Problem449

Explicit MacCormack Scheme for Flow Over a Square Block453

Finite-Element Formulation for Flow Over a Cylinder Confined in a Channel459

10.6.Concluding Remarks470

Exercises470

Literature Cited471

Supplemental Reading472

11.Instability473

11.1.Introduction474

11.2.Method of Normal Modes475

11.3.Kelvin-Helmholtz Instability477

11.4.Thermal Instability：The Benard Problem484

11.5.Double-Diffusive Instability492

11.6.Centrifugal Instability：Taylor Problem496

11.7.Instability of Continuously Stratified Parallel Flows502

11.8.Squire’s Theorem and the Orr-Sommerfeld Equation508

11.9.Inviscid Stability of Parallel Flows511

11.10.Results for Parallel and Nearly Parallel Viscous Flows515

Two-Stream Shear Layer515

Plane Poiseuille Flow516

Plane Couette Flow517

Pipe Flow517

Boundary Layers with Pressure Gradients517

11.11.Experimental Verification of Boundary-Layer Instability520

11.12.Comments on Nonlinear Effects522

11.13.Transition523

11.14.Deterministic Chaos524

Closure531

Exercises532

Literature Cited539

12.Turbulence541

12.1.Introduction542

12.2.Historical Notes544

12.3.Nomenclature and Statistics for Turbulent Flow545

12.4.Correlations and Spectra549

12.5.Averaged Equations of Motion554

12.6.Homogeneous Isotropic Turbulence560

12.7.Turbulent Energy Cascade and Spectrum564

12.8.Free Turbulent Shear Flows571

12.9.Wall-Bounded Turbulent Shear Flows581

Inner Layer：Law of the Wall584

Outer Layer：Velocity Defect Law585

Overlap Layer：Logarithmic Law585

Rough Surfaces590

12.10.Turbulence Modeling591

A Mixing Length Model593

One-Equation Models595

Two-Equation Models595

12.11.Turbulence in a Stratified Medium596

The Richardson Numbers597

Monin-Obukhov Length598

Spectrum of Temperature Fluctuations600

12.12.Taylor’s Theory of Turbulent Dispersion601

Rate of Dispersion of a Single Particle602

Random Walk605

Behavior of a Smoke Plume in the Wind606

Turbulent Diffusivity607

12.13.Concluding Remarks607

Exercises608

Literature Cited618

Supplemental Reading620

13.Geophysical Fluid Dynamics621

13.1.Introduction622

13.2.Vertical Variation of Density in the Atmosphere and Ocean623

13.3.Equations of Motion625

13.4.Approximate Equations for a Thin Layer on a Rotating Sphere628

f-Plane Model630

β-Plane Model630

13.5.Geostrophic Flow630

Thermal Wind632

Taylor-Proudman Theorem632

13.6.Ekman Layer at a Free Surface633

Explanation in Terms of Vortex Tilting637

13.7.Ekman Layer on a Rigid Surface639

13.8.Shallow-Water Equations642

13.9.Normal Modes in a Continuously Stratified Layer644

Boundary Conditions on ？n646

Vertical Mode Solution for Uniform N646

Summary649

13.10.High-and Low-Frequency Regimes in Shallow-Water Equations649

13.11.Gravity Waves with Rotation651

Particle Orbit652

Inertial Motion653

13.12.Kelvin Wave654

13.13.Potential Vorticity Conservation in Shallow-Water Theory658

13.14.Internal Waves662

WKB Solution664

Particle Orbit666

Discussion of the Dispersion Relation668

Lee Wave670

13.15.Rossby Wave671

Quasi-Geostrophic Vorticity Equation671

Dispersion Relation673

13.16.Barotropic Instability676

13.17.Baroclinic Instability678

Perturbation Vorticity Equation679

Wave Solution681

Instability Criterion682

Energetics684

13.18.Geostrophic Turbulence685

Exercises688

Literature Cited690

Supplemental Reading690

14.Aerodynamics691

14.1.Introduction692

14.2.Aircraft Terminology692

Control Surfaces693

14.3.Characteristics of Airfoil Sections696

Historical Notes701

14.4.Conformal Transformation for Generating Airfoil Shapes702

14.5.Lift of a Zhukhovsky Airfoil706

14.6.Elementary Lifting Line Theory for Wings of Finite Span708

Lanchester Versus Prandtl716

14.7.Lift and Drag Characteristics of Airfoils717

14.8.Propulsive Mechanisms of Fish and Birds719

14.9.Sailing against the Wind721

Exercises722

Literature Cited728

Supplemental Reading728

15.Compressible Flow729

15.1.Introduction730

Perfect Gas Thermodynamic Relations731

15.2.Acoustics732

15.3.Basic Equations for One-Dimensional Flow736

15.4.Reference Properties in Compressible Flow738

15.5.Area-Velocity Relationship in One-Dimensional Isentropic Flow740

15.6.Normal Shock Waves748

Stationary Normal Shock Wave in a Moving Medium748

Moving Normal Shock Wave in a Stationary Medium752

Normal Shock Structure753

15.7.Operation of Nozzles at Different Back Pressures755

Convergent Nozzle755

Convergent-Divergent Nozzle757

15.8.Effects of Friction and Heating in Constant-Area Ducts761

Effect of Friction763

Effect of Heat Transfer764

15.9.Pressure Waves in Planar Compressible Flow765

15.10.Thin Airfoil Theory in Supersonic Flow773

Exercises775

Literature Cited778

Supplemental Reading778

16.Introduction to Biofluid Mechanics&PORTONOVO S.AYYASWAMY779

16.1.Introduction779

16.2.The Circulatory System in the Human Body780

The Heart as a Pump785

Nature of Blood788

Nature of Blood Vessels793

16.3.Modeling of Flow in Blood Vessels796

Steady Blood Flow Theory797

Pulsatile Blood Flow Theory805

Blood Vessel Bifurcation：An Application of Poiseuille’s Formula and Murray’s Law820

Flow in a Rigid-Walled Curved Tube825

Flow in Collapsible Tubes831

Laminar Flow of a Casson Fluid in a Rigid-Walled Tube839

Pulmonary Circulation841

The Pressure Pulse Curve in the Right Ventricle842

Effect of Pulmonary Arterial Pressure on Pulmonary Resistance843

16.4.Introduction to the Fluid Mechanics of Plants844

Exercises849

Acknowledgment850

Literature Cited851

Supplemental Reading852

Appendix A853

Appendix B857

Appendix C869

Appendix D873

Index875