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Tables of Contents for Introduction to Fluid Dynamics
Chapter/Section Title
Page #
Page Count
Preface
xiii
Conventions and Notation
xviii
The Physical Properties of Fluids
Solids, liquids and gases
1
3
The continuum hypothesis
4
3
Volume forces and surface forces acting on a fluid
7
7
Representation of surface forces by the stress tensor
9
3
The stress tensor in a fluid at rest
12
2
Mechanical equilibrium of a fluid
14
6
A body `floating' in fluid at rest
16
2
Fluid at rest under gravity
18
2
Classical thermodynamics
20
8
Transport phenomena
28
9
The linear relation between flux and the gradient of a scalar intensity
30
2
The equations for diffusion and heat conduction in isotropic media at rest
32
4
Molecular transport of momentum in a fluid
36
1
The distinctive properties of gases
37
16
A perfect gas in equilibrium
38
7
Departures from the perfect-gas laws
45
2
Transport coefficients in a perfect gas
47
3
Other manifestations of departure from equilibrium of a perfect gas
50
3
The distinctive properties of liquids
53
7
Equilibrium properties
55
2
Transport coefficients
57
3
Conditions at a boundary between two media
60
11
Surface tension
60
3
Equilibrium shape of a boundary between two stationary fluids
63
5
Transition relations at a material boundary
68
3
Kinematics of the Flow Field
Specification of the flow field
71
2
Differentiation following the motion of the fluid
72
1
Conservation of mass
73
6
Use of a stream function to satisfy the mass-conservation equation
75
4
Analysis of the relative motion near a point
79
5
Simple shearing motion
83
1
Expression for the velocity distribution with specified rate of expansion and vorticity
84
4
Singularities in the rate of expansion. Sources and sinks
88
4
The vorticity distribution
92
7
Line vortices
93
3
Sheet vortices
96
3
Velocity distributions with zero rate of expansion and zero vorticity
99
9
Conditions for ∇ &phis; to be determined uniquely
102
3
Irrotational solenoidal flow near a stagnation point
105
1
The complex potential for irrotational solenoidal flow in two dimensions
106
2
Irrotational solenoidal flow in doubly-connected regions of space
108
6
Conditions for ∇ &phis; to be determined uniquely
112
2
Three-dimensional flow fields extending to infinity
114
10
Asymptotic expressions for ue and uv
114
3
The behaviour of &phis; at large distances
117
2
Conditions for ∇ &phis; to be determined uniquely
119
1
The expression of &phis; as a power series
120
2
Irrotational solenoidal flow due to a rigid body in translational motion
122
2
Two-dimensional flow fields extending to infinity
124
7
Irrotational solenoidal flow due to a rigid body in translational motion
128
3
Equations Governing the Motion of a Fluid
Material integrals in a moving fluid
131
6
Rates of change of material integrals
133
2
Conservation laws for a fluid in motion
135
2
The equation of motion
137
4
Use of the momentum equation in integral form
138
1
Equation of motion relative to moving axes
139
2
The expression for the stress tensor
141
10
Mechanical definition of pressure in a moving fluid
141
1
The relation between deviatoric stress and rate-of-strain for a Newtonian fluid
142
5
The Navier-Stokes equation
147
1
Conditions on the velocity and stress at a material boundary
148
3
Changes in the internal energy of a fluid in motion
151
5
Bernoulli's theorem for steady flow of a frictionless nonconducting fluid
156
8
Special forms of Bernoulli's theorem
161
2
Constancy of H across a transition region in one-dimensional steady flow
163
1
The complete set of equations governing fluid flow
164
7
Isentropic flow
165
2
Conditions for the velocity distribution to be approximately solenoidal
167
4
Concluding remarks to chapters I, 2 and 3
171
3
Flow of a Uniform Incompressible Viscous Fluid
Introduction
174
5
Modification of the pressure to allow for the effect of the body force
176
3
Steady unidirectional flow
179
7
Poiseuille flow
180
2
Tubes of non-circular cross-section
182
1
Two-dimensional flow
182
1
A model of a paint-brush
183
2
A remark on stability
185
1
Unsteady unidirectional flow
186
9
The smoothing-out of a discontinuity in velocity at a plane
187
2
Plane boundary moved suddenly in a fluid at rest
189
1
One rigid boundary moved suddenly and one held stationary
190
1
Flow due to an oscillating plane boundary
191
2
Starting flow in a pipe
193
2
The Ekman layer at a boundary in a rotating fluid
195
6
The layer at a free surface
197
2
The layer at a rigid plane boundary
199
2
Flow with circular streamlines
201
4
The steady jet from a point source of momentum
205
6
Dynamical similarity and the Reynolds number
211
5
Other dimensionless parameters having dynamical significance
215
1
Flow fields in which inertia forces are negligible
216
13
Flow in slowly-varying channels
217
2
Lubrication theory
219
3
The Hele-Shaw cell
222
1
Percolation through porous media
223
1
Two-dimensional flow in a corner
224
3
Uniqueness and minimum dissipation theorems
227
2
Flow due to a moving body at small Reynolds number
229
11
A rigid sphere
230
5
A spherical drop of a different fluid
235
3
A body of arbitrary shape
238
2
Oseen's improvement of the equation for flow due to moving bodies at small Reynolds number
240
6
A rigid sphere
241
3
A rigid circular cylinder
244
2
The viscosity of a dilute suspension of small particles
246
9
The flow due to a sphere embedded in a pure straining motion
248
2
The increased rate of dissipation in an incompressible suspension
250
3
The effective expansion viscosity of a liquid containing gas bubbles
253
2
Changes in the flow due to moving bodies as R increases from I to about 100
255
9
Flow at Large Reynolds Number: Effects of Viscosity
Introduction
264
2
Vorticity dynamics
266
7
The intensification of vorticity by extension of vortex-lines
270
3
Kelvin's circulation theorem and vorticity laws for an inviscid fluid
273
4
The persistence of irrotationality
276
1
The source of vorticity in motions generated from rest
277
5
Steady flows in which vorticity generated at a solid surface is prevented by convection from diffusing far away from it
282
12
Flow along plane and circular walls with suction through the wall
282
3
Flow toward a `stagnation point' at a rigid boundary
285
5
Centrifugal flow due to a rotating disk
290
4
Steady two-dimensional flow in a converging or diverging channel
294
8
Purely convergent flow
297
1
Purely divergent flow
298
3
Solutions showing both outflow and inflow
301
1
Boundary layers
302
6
The boundary layer on a flat plate
308
6
The effects of acceleration and deceleration of the external stream
314
11
The similarity solution for an external stream velocity proportional to xm
316
2
Calculation of the steady boundary layer on a body moving through fluid
318
3
Growth of the boundary layer in initially irrotational flow
321
4
Separation of the boundary layer
325
6
The flow due to bodies moving steadily through fluid
331
12
Flow without separation
332
5
Flow with separation
337
6
Jets, free shear layers and wakes
343
10
Narrow jets
343
3
Free shear layers
346
2
Wakes
348
5
Oscillatory boundary layers
353
11
The damping force on an oscillating body
355
3
Steady streaming due to an oscillatory boundary layer
358
3
Applications of the theory of steady streaming
361
3
Flow systems with a free surface
364
8
The boundary layer at a free surface
364
3
The drag on a spherical gas bubble rising steadily through liquid
367
3
The attenuation of gravity waves
370
2
Examples of use of the momentum theorem
372
6
The force on a regular array of bodies in a stream
372
1
The effect of a sudden enlargement of a pipe
373
5
Irrotational Flow Theory and its Applications
The role of the theory of flow of an inviscid fluid
378
2
General properties of irrotational flow
380
6
Integration of the equation of motion
382
1
Expressions for the kinetic energy in terms of surface integrals
383
1
Kelvin's minimum energy theorem
384
1
Positions of a maximum of q and a minimum of p
384
2
Local variation of the velocity magnitude
386
1
Steady flow: some applications of Bernoulli's theorem and the momentum theorem
386
12
Efflux from a circular orifice in an open vessel
387
4
Flow over a weir
391
1
Jet of liquid impinging on a plane wall
392
4
Irrotational flow which may be made steady by choice of rotating axes
396
2
General features of irrotational flow due to a moving rigid body
398
11
The velocity at large distances from the body
399
3
The kinetic energy of the fluid
402
2
The force on a body in translational motion
404
3
The acceleration reaction
407
2
The force on a body in accelerating fluid
409
1
Use of the complex potential for irrotational flow in two dimensions
409
14
Flow fields obtained by special choice of the function w(z)
410
3
Conformal transformation of the plane of flow
413
5
Transformation of a boundary into an infinite straight line
418
2
Transformation of a closed boundary into a circle
420
2
The circle theorem
422
1
Two-dimensional irrotational flow due to a moving cylinder with circulation
423
12
A circular cylinder
424
3
An elliptic cylinder in translational motion
427
6
The force and moment on a cylinder in steady translational motion
433
2
Two-dimensional aerofoils
435
14
The practical requirements of aerofoils
435
3
The generation of circulation round an aerofoil and the basis for Joukowski's hypothesis
438
3
Aerofoils obtained by transformation of a circle
441
3
Joukowski aerofoils
444
5
Axisymmetric irrotational flow due to moving bodies
449
14
Generalities
449
3
A moving sphere
452
3
Ellipsoids of revolution
455
3
Body shapes obtained from source singularities on the axis of symmetry
458
2
Semi-infinite bodies
460
3
Approximate results for slender bodies
463
8
Slender bodies of revolution
463
3
Slender bodies in two dimensions
466
1
Thin aerofoils in two dimensions
467
4
Impulsive motion of a fluid
471
3
Impact of a body on a free surface of liquid
473
1
Large gas bubbles in liquid
474
7
A spherical-cap bubble rising through liquid under gravity
475
2
A bubble rising in a vertical tube
477
2
A spherical expanding bubble
479
2
Cavitation in a liquid
481
12
Examples of cavity formation in steady flow
482
3
Examples of cavity formation in unsteady flow
485
1
Collapse of a transient cavity
486
5
Steady-state cavities
491
2
Free-streamline theory, and steady jets and cavities
493
14
Jet emerging from an orifice in two dimensions
495
2
Two-dimensional flow past a flat plate with a cavity at ambient pressure
497
5
Steady-state cavities attached to bodies held in a stream of liquid
502
5
Flow of Effectively Inviscid Fluid with Vorticity
Introduction
507
10
The self-induced movement of a line vortex
509
2
The instability of a sheet vortex
511
6
Flow in unbounded fluid at rest at infinity
517
10
The resultant force impulse required to generate the motion
518
2
The total kinetic energy of the fluid
520
1
Flow with circular vortex-lines
521
1
Vortex rings
522
5
Two-dimensional flow in unbounded fluid at rest at infinity
527
9
Integral invariants of the vorticity distribution
528
2
Motion of a group of point vortices
530
2
Steady motions
532
4
Steady two-dimensional flow with vorticity throughout the fluid
536
7
Uniform vorticity in a region bounded externally
538
1
Fluid in rigid rotation at infinity
539
2
Fluid in simple shearing motion at infinity
541
2
Steady axisymmetric flow with swirl
543
12
The effect of a change of cross-section of a tube on a stream of rotating fluid
546
4
The effect of a change of external velocity on an isolated vortex
550
5
Flow systems rotating as a whole
555
12
The restoring effect of Coriolis forces
555
2
Steady flow at small Rossby number
557
2
Propagation of waves in a rotating fluid
559
5
Flow due to a body moving along the axis of rotation
564
3
Motion in a thin layer on a rotating sphere
567
13
Geostrophic flow
571
2
Flow over uneven ground
573
4
Planetary waves
577
3
The vortex system of a wing
580
14
General features of the flow past lifting bodies in three dimensions
580
3
Wings of large aspect ratio, and `lifting-line' theory
583
6
The trailing vortex system far downstream
589
2
Highly swept wings
591
3
Appendices
1 Measured values of some physical properties of common fluids
594
4
(a) Dry air at a pressure of one atmosphere
594
1
(b) The Standard Atmosphere
595
1
(c) Pure water
595
2
(d) Diffusivities for momentum and heat at 15 °C and I atm
597
1
(e) Surface tension between two fluids
597
1
2 Expressions for some common vector differential quantities in orthogonal curvilinear co-ordinate systems
598
6
Publications referred to in the text
604
5
Subject Index
609