An introduction to fluid dynamics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2009
|
| Ausgabe: | 1. Cambridge Math. Library ed., 11th print. |
| Schriftenreihe: | Cambridge mathematical library
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 615 S. Ill., graph. Darst. |
| ISBN: | 9780521663960 |
Internformat
MARC
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| 245 | 1 | 0 | |a An introduction to fluid dynamics |c by G. K. Batchelor |
| 250 | |a 1. Cambridge Math. Library ed., 11th print. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2009 | |
| 300 | |a XVIII, 615 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804143073810186240 |
|---|---|
| adam_text | CONTENTS
Preface
page
xiii
Conventions and Notation
xviii
Chapter
1.
The Physical Properties of Fluids
t.i Solids, liquids and gases
ι
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
isotropie
media at rest,
3г
Molecular transport of momentum in a fluid,
36
1.7
The distinctive properties of gases
37
Λ
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
r
.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 How Field
г. і
Specification of the flow field
71
Differentiation following the motion of the fluid,
73
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
vi
Contents
2.4 Expression
for the velocity distribution with specified rate page
84
of expansion and vorticity
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
99
vorticity
Conditions for V0 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 V<j> to be determined uniquely,
112
2.9
Three-dimensional flow fields extending to infinity
114
Asymptotic expressions for u, and
u„, 114
The behaviour of
φ
at large distances,
117
Conditions for
νφ
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
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
deviatone
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-
156
conducting fluid
Special forms of Bernoulli s theorem,
161
Constancy of
Η
across a transition region in one-dimensional steady flow,
163
3.6
The complete set of equations governing fluid flow
164
Isentropic flow,
163
Conditions for the velocity distribution to be approximately solenoidal,
167
3.7
Concluding remarks to chapters i,
2
and
3 171
Contents
vii
Chapter
4.
Flow of a Uniform Incompressible Viscous Fluid
4.1
Introduction page
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,
18г
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
Piane
boundary moved suddenly in a fluid at rest,
189
One rigid boundary moved suddenly and one held stationary,
ідо
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
240
bodies at small Reynolds number
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
255
1
to about
100
viii Contents
Chapter
5.
Flow at Large Reynolds Number: Effects of Viscosity
5.1
Introduction page
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
273
fluid
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
282
prevented by convection from diffusing far away from it
(а) Flow along plane and circular walla with suction through the wall,
28г
(б)
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
294
channel
Purely convergent flow,
297
Purely divergent flow,
298
Solutions showing both outflow and inflow,
30t
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
314
stream
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, 33a
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,
338
Applications of the theory of steady streaming,
36t
Contents ix
5.14
Flow systems with a free surface Pa§e
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,
37г
The effect of a sudden enlargement of a pipe,
373
Chapter
6.
Irrotational Flow Theory and its Applications
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,
38г
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
386
momentum theorem
Efflux from a circular orifice in an open vessel,
387
Flow over a weir,
391
Jet of liquid impinging on a plane wall,
39г
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
409
dimensions
Flow fields obtained by special choice of the function
10(2), 410
Conformai
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,
42г
6.6
Two-dimensional irrotational flow due to a moving cylinder
423
with circulation
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, 43s
The generation of circulation round an aerofoil and the basis for
Joukowski e hypothesis,
438
Aerofoils obtained by transformation of a circle,
441
Joukowski aerofoilt,
444
x
Contents
6.8 Axisymmetric irrotational
flow due to moving bodies page
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
4^3
Slender bodies of revolution,
463
Slender bodies in two dimensions,
466
Thin aerofoils in two dimensions,
467
6.10
Impulsive motion of a fluid
47
l
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
aß1
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,
s
02
Chapter
7.
Flow of Effectively Invlsdd Fluid with Vorticity
7.1
Introduction
507
The self-induced movement of a line vortex,
509
The instability of a sheet vortex,
511
η.
г
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,
53г
74
Steady two-dimensional flow with vorticity throughout the fluid
5 36
Uniform vorticity in a region bounded externally,
538
Fluid in rigid rotation at infinity,
539
Fluid in simple shearing motion at infinity,
541
Contents xi
7.5
Steady axisymmetric flow with swirl page
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
1
Measured values of some physical properties of common fluids
594
(а) Dry air at a pressure of one atmosphere,
594
(б)
The Standard Atmosphere,
595
{¿) Pure water,
595
(d) Difmsivities for momentum and heat at
15 °С
and
1
atm,
597
(e) Surface tension between two fluids,
597
2
Expressions for some common vector differential quantities in
598
orthogonal curvilinear co-ordinate systems
Publications referred to in the text
604
Subject Index
609
Plates
1
to
24
are between pages
364
and
365
|
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| indexdate | 2024-07-09T22:41:52Z |
| institution | BVB |
| isbn | 9780521663960 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020429751 |
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| spelling | Batchelor, G. K. 1920-2000 Verfasser (DE-588)13314299X aut An introduction to fluid dynamics by G. K. Batchelor 1. Cambridge Math. Library ed., 11th print. Cambridge [u.a.] Cambridge Univ. Press 2009 XVIII, 615 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge mathematical library Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Strömungsmechanik (DE-588)4077970-1 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020429751&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Batchelor, G. K. 1920-2000 An introduction to fluid dynamics Strömungsmechanik (DE-588)4077970-1 gnd |
| subject_GND | (DE-588)4077970-1 (DE-588)4151278-9 |
| title | An introduction to fluid dynamics |
| title_auth | An introduction to fluid dynamics |
| title_exact_search | An introduction to fluid dynamics |
| title_full | An introduction to fluid dynamics by G. K. Batchelor |
| title_fullStr | An introduction to fluid dynamics by G. K. Batchelor |
| title_full_unstemmed | An introduction to fluid dynamics by G. K. Batchelor |
| title_short | An introduction to fluid dynamics |
| title_sort | an introduction to fluid dynamics |
| topic | Strömungsmechanik (DE-588)4077970-1 gnd |
| topic_facet | Strömungsmechanik Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020429751&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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