AN INTRODUCTION TO FLUID DYNAMICSPDF电子书下载

Chapter 1. The Physical Properties of Fluids 1

1.1 Solids， liquids and gases 1

1.2 The continuum hypothesis 4

1.3 Volume forces and surface forces acting on a fluid 7

Representation of surface forces by the stress tensor 9

The stress tensor in a fluid at rest 12

1.4 Mechanical equilibrium of a fluid 14

A body ‘floating’ in fluid at rest 16

Fluid at rest under gravity 18

1.5 Classical thermodynamics 20

1.6 Transport phenomena 28

The linear relation between flux and the gradient of a scalar intensity 30

The equations for diffusion and heat conduction in isotropic media at rest 32

Molecular transport of momentum in a fluid 36

1.7 The distinctive properties of gases 37

A perfect gas in equilibrium 38

Departures from the perfect-gas laws 45

Transport coefficients in a perfect gas 47

Other manifestations of departure from equilibrium of a perfect gas 50

1.8 The distinctive properties of liquids 53

Equilibrium properties 55

Transport coefficients 57

1.9 Conditions at a boundary between two media 60

Surface tension 60

Equilibrium shape of a boundary between two stationary fluids 63

Transition relations at a material boundary 68

Chapter 2. Kinematics of the Flow Field 71

2.1 Specification of the flow field 71

Differentiation following the motion of the fluid 72

2.2 Conservation of mass 73

Use of a stream function to satisfy the mass-conservation equation 75

2.3 Analysis of the relative motion near a point 79

Simple shearing motion 83

2.4 Expression for the velocity distribution with specified rate of expansion and vorticity 84

2.5 Singularities in the rate of expansion. Sources and sinks 88

2.6 The vorticity distribution 92

Line vortices 93

Sheet vortices 96

2.7 Velocity distributions with zero rate of expansion and zero vorticity 99

Conditions for ▽φ to be determined uniquely 102

Irrotational solenoidal flow near a stagnation point 105

The complex potential for irrotational solenoidal flow in two dimensions 106

2.8 Irrotational solenoidal flow in doubly-connected regions of space 108

Conditions for ▽φ to be determined uniquely 112

2.9 Three-dimensional flow fields extending to infinity 114

Asymptotic expressions for uoand uv 114

The behaviour of φ at large distances 117

Conditions for ▽φ to be determined uniquely 119

The expression of φ as a power series 120

Irrotational solenoidal flow due to a rigid body in translational motion 122

2.10 Two-dimensional flow fields extending to infinity 124

Irrotational solenoidal flow due to a rigid body in translational motion 128

Chapter 3. Equations Governing the Motion of a Fluid 131

3.1 Material integrals in a moving fluid 131

Rates of change of material integrals 133

Conservation laws for a fluid in motion 135

3.2 The equation of motion 137

Use of the momentum equation in integral form 138

Equation of motion relative to moving axes 139

3.3 The expression for the stress tensor 141

Mechanical definition of pressure in a moving fluid 141

The relation between deviatoric stress and rate-of-strain for a Newtonian fluid 142

The Navier-Stokes equation 147

Conditions on the velocity and stress at a material boundary 148

3.4 Changes in the internal energy of a fluid in motion 151

3.5 Bernoulli’s theorem for steady flow of a frictionless non-conducting fluid 156

Special forms of Bernoulli’s theorem 161

Constancy of H across a transition region in one-dimensional steady flow 163

3.6 The complete set of equations governing fluid flow 164

Isentropic flow 165

Conditions for the velocity distribution to be approximately solenoidal 167

3.7 Concluding remarks to chapters 1，2 and 3 171

Chapter 4. Flow of a Uniform Incompressible Viscous Fluid 174

4.1 Introduction 174

Modification of the pressure to allow for the effect of the body force 176

4.2 Steady unidirectional flow 179

Poiseuille flow 180

Tubes of non-circular cross-section 182

Two-dimensional flow 182

A model of a paint-brush 183

A remark on stability 185

4.3 Unsteady unidirectional flow 186

The smoothing-out of a discontinuity in velocity at a plane 187

Plane boundary moved suddenly in a fluid at rest 189

One rigid boundary moved suddenly and one held stationary 190

Flow due to an oscillating plane boundary 191

Starting flow in a pipe 193

4.4 The Ekman layer at a boundary in a rotating fluid 195

The layer at a free surface 197

The layer at a rigid plane boundary 199

4.5 Flow with circular streamlines 201

4.6 The steady jet from a point source of momentum 205

4.7 Dynamical similarity and the Reynolds number 211

Other dimensionless parameters having dynamical significance 215

4.8 Flow fields in which inertia forces are negligible 216

Flow in slowly-varying channels 217

Lubrication theory 219

The Hele-Shaw cell 222

Percolation through porous media 223

Two-dimensional flow in a corner 224

Uniqueness and minimum dissipation theorems 227

4.9 Flow due to a moving body at small Reynolds number 229

A rigid sphere 230

A spherical drop of a different fluid 235

A body of arbitrary shape 238

4.10 Oseen’s improvement of the equation for flow due to moving bodies at small Reynolds number 240

A rigid sphere 241

A rigid circular cylinder 244

4.11 The viscosity of a dilute suspension of small particles 246

The flow due to a sphere embedded in a pure straining motion 248

The increased rate of dissipation in an incompressible suspension 250

The effective expansion viscosity of a liquid containing gas bubbles 253

4.12 Changes in the flow due to moving bodies as R increases from I to about Ioo 255

Chapter 5. Flow at Large Reynolds Number：Effects of Viscosity 264

5.1 Introduction 264

5.2 Vorticity dynamics 266

The intensification of vorticity by extension of vortex-lines 270

5.3 Kelvin’s circulation theorem and vorticity laws for an inviscid fluid 273

The persistence of irrotationality 276

5.4 The source of vorticity in motions generated from rest 277

5.5 Steady flows in which vorticity generated at a solid surface is prevented by convection from diffusing far away from it 282

（a） Flow along plane and circular walls with suction through the wall 282

（b） Flow toward a ‘stagnation point’ at a rigid boundary 285

（c） Centrifugal flow due to a rotating disk 290

5.6 Steady two-dimensional flow in a converging or diverging channel 294

Purely convergent flow 297

Purely divergent flow 298

Solutions showing both outflow and inflow 301

5.7 Boundary layers 302

5.8 The boundary layer on a flat plate 308

5.9 The effects of acceleration and deceleration of the external stream 314

The similarity solution for an external stream velocity proportional to xm 316

Calculation of the steady boundary layer on a body moving through fluid 318

Growth of the boundary layer in initially irrotational flow 321

5.10 Separation of the boundary layer 325

5.11 The flow due to bodies moving steadily through fluid 331

Flow without separation 332

Flow with separation 337

5.12 Jets， free shear layers and wakes 343

Narrow jets 343

Free shear layers 346

Wakes 348

5.13 Oscillatory boundary layers 353

The damping force on an oscillating body 355

Steady streaming due to an oscillatory boundary layer 358

Applications of the theory of steady streaming 361

5.14 Flow systems with a free surface 364

The boundary layer at a free surface 364

The drag on a spherical gas bubble rising steadily through liquid 367

The attenuation of gravity waves 370

5.15 Examples of use of the momentum theorem 372

The force on a regular array of bodies in a stream 372

The effect of a sudden enlargement of a pipe 373

Chapter 6. Irrotational Flow Theory and its Applications 378

6.1 The role of the theory of flow of an inviscid fluid 378

6.2 General properties of irrotational flow 380

Integration of the equation of motion 382

Expressions for the kinetic energy in terms of surface integrals 383

Kelvin’s minimum energy theorem 384

Positions of a maximum of q and a minimum of P 384

Local variation of the velocity magnitude 386

6.3 Steady flow： some applications of Bernoulli’s theorem and the momentum theorem 386

Efflux from a circular orifice in an open vessel 387

Flow over a weir 391

Jet of liquid impinging on a plane wall 392

Irrotational flow which may be made steady by choice of rotating axes 396

6.4 General features of irrotational flow due to a moving rigid body 398

The velocity at large distances from the body 399

The kinetic energy of the fluid 402

The force on a body in translational motion 404

The acceleration reaction 407

The force on a body in accelerating fluid 409

6.5 Use of the complex potential for irrotational flow in two dimensions 409

Flow fields obtained by special choice of the function w（x） 410

Conformal transformation of the plane of flow 413

Transformation of a boundary into an infinite straight line 418

Transformation of a closed boundary into a circle 420

The circle theorem 422

6.6 Two-dimensional irrotational flow due to a moving cylinder with circulation 423

A circular cylinder 424

An elliptic cylinder in translational motion 427

The force and moment on a cylinder in steady translational motion 433

6.7 Two-dimensional aerofoils 435

The practical requirements of aerofoils 435

The generation of circulation round an serofoil and the basis for Joukowski’s hypothesis 438

Aerofoils obtained by transformation of a circle 441

Joukowaki aerofoils 444

6.8 Axisymmetric irrotational flow due to moving bodies 449

Generalities 449

A moving sphere 452

Ellipsoids of revolution 455

Body shapes obtained from source singularities on the axis of symmetry 458

Semi-infinite bodies 460

6.9 Approximate results for slender bodies 463

Slender bodies of revolution 463

Slender bodies in two dimensions 466

Thin aerofoils in two dimensions 467

6.10 Impulsive motion of a fluid 471

Impact of a body on a free surface of liquid 473

6.11 Large gas bubbles in liquid 474

A spherical-cap bubble rising through liquid under gravity 475

A bubble rising in a vertical tube 477

A spherical expanding bubble 479

6.12 Cavitation in a liquid 481

Examples of cavity formation in steady flow 482

Examples of cavity formation in unsteady flow 485

Collapse of a transient cavity 486

Steady-state cavities 491

6.13 Free-streamline theory， and steady jets and cavities 493

Jet emerging from an orifice in two dimensions 495

Two-dimensional flow past a flat plate with a cavity at ambient pressure 497

Steady-state cavities attached to bodies held in a stream of liquid 502

Chapter 7. Flow of Effectively Inviscid Fluid with Vorticity 507

7.1 Introduction 507

The self-induced movement of a line vortex 509

The instability of a sheet vortex 511

7.2 Flow in unbounded fluid at rest at infinity 517

The resultant force impulse required to generate the motion 518

The total kinetic energy of the fluid 520

Flow with circular vortex-lines 521

Vortex rings 522

7.3 Two-dimensional flow in unbounded fluid at rest at infinity 527

Integral invariants of the vorticity distribution 528

Motion of a group of point vortices 530

Steady motions 532

7.4 Steady two-dimensional flow with vorticity throughout the fluid 536

Uniform vorticity in a region bounded externally 538

Fluid in rigid rotation at infinity 539

Fluid in simple shearing motion at infinity 541

7.5 Steady axisymmetric flow with swirl 543

The effect of a change of cross-section of a tube on a stream of rotating fluid 546

The effect of a change of external velocity on an isolated vortex 550

7.6 Flow systems rotating as a whole 555

The restoring effect of Coriolis forces 555

Steady flow at small Rossby number 557

Propagation of waves in a rotating fluid 559

Flow due to a body moving along the axis of rotation 564

7.7 Motion in a thin layer on a rotating sphere 567

Geostrophic flow 571

Flow over uneven ground 573

Planetary waves 577

7.8 The vortex system of a wing 580

General features of the flow past lifting bodies in three dimensions 580

Wings of large aspect ratio， and ‘lifting-line’ theory 583

The trailing vortex system far downstream 589

Highly swept wings 591

Appendices 594

1 Measured values of some physical properties of common fluids 594

（a） Dry air at a pressure of one atmosphere 594

（b） The Standard Atmosphere 595

（c） Pure water 595

（d） Diffusivities for momentum and heat at 15 ℃ and I atm 597

（e） Surface tension between two fluids 597

2 Expressions for some common vector differential quantities in orthogonal curvilinear co-ordinate systems 598

Publications referred to in the text 604

Subject Index 609