Fluid Dynamics for Physicists

by T. E. Faber

• ISBN13: 9780521429696
• ISBN10: 0521429692
• Format: Paperback
• Copyright: 1995-08-25
• Publisher: Cambridge University Press

Summary

It is over three hundred and fifty years since Torricelli discovered the law obeyed by fountains, yet fluid dynamics remains an active and important branch of physics. This book provides an accessible and comprehensive account of the subject, emphasising throughout the fundamental physical principles, and stressing the connections with other branches of physics. Beginning with a gentle introduction, the book goes on to cover Bernouilli's theorem, compressible flow, potential flow, surface waves, viscosity, vorticity dynamics, thermal convection and instabilities, turbulence, non-Newtonian fluids and the propagation and attenuation of sound in gases. Undergraduate or graduate students in physics or engineering who are taking courses in fluid dynamics will find this book invaluable, but it will also be of great interest to anyone who wants to find out more about this fascinating subject.

Table of Contents

Preface	xv
Mathematical Conventions	xix
Symbols	xxiii
A bird's eye view
Introduction	1	(1)
What is a fluid?	2	(2)
Some facts about stress	4	(2)
Statement of the syringe problem: Mach and Reynolds Numbers	6	(2)
Dimensional analysis and dynamical similarity	8	(4)
Streaklines, streamlines, pathlines, and lines of flow	12	(2)
Bernoulli's theorem	14	(2)
When is compressibility negligible?	16	(2)
When are shear stresses negligible?	18	(3)
Potential flow	21	(2)
The no-slip boundary condition at fluid-solid interfaces	23	(2)
Boundary layers	25	(4)
Poiseuille's law	29	(2)
The syringe problem answered	31	(1)
Instabilities and turbulence	32	(2)
Summary	34	(3)
Further reading	36	(1)
The Euler fluid
The model	37	(1)
The continuity condition	37	(1)
Euler's equation	38	(1)
The operator D/Dt	38	(2)
Transverse pressure gradients in steady flow	40	(3)
Floating objects	43	(1)
The plug-hole vortex	44	(2)
Bernoulli's theorem revisited	46	(3)
Hydrostatic equilibrium and excess pressure	49	(1)
Devices for measuring rates of flow	49	(5)
Cavitation	54	(2)
Water jets, sheets and bells	56	(5)
Fans and windmills	61	(4)
Gravity waves on shallow water	65	(1)
When is surface tension negligible?	66	(1)
Bores and hydraulic jumps	67	(6)
The Coanda effect	73	(5)
Further reading	77	(1)
Gas dynamics
Introduction to compressible flow	78	(3)
Isothermal versus adiabatic flow	81	(5)
Bernoulli's theorem for compressible gas flow	86	(3)
The atmospheric lapse rate	89	(1)
Choked flow through a constriction	90	(3)
The development and decay of a shock front	93	(6)
Momentum transfer by sound waves	99	(2)
Normal shock fronts in gases	101	(4)
Shock fronts generated by explosions	105	(2)
Oblique shock fronts	107	(2)
Mach's construction	109	(2)
Supersonic flow past thin plates	111	(4)
Rockets	115	(4)
Further reading	118	(1)
Potential flow
The use of potentials to describe flow	119	(1)
Kelvin's circulation theorem	120	(2)
Bernoulli's theorem for unsteady potential flow	122	(1)
Sources and sinks	123	(4)
Magnetostatic analogies	127	(2)
Some analytical solutions of Laplace's equation	129	(4)
Potential flow round a sphere	133	(4)
The virtual mass of an accelerating solid body	137	(4)
The Rayleigh disc	141	(3)
Multi-valued potentials in electromagnetism	144	(1)
Vortex lines	145	(2)
The Magnus effect	147	(3)
Free vortex lines with cores	150	(5)
Behaviour of free vortex lines	155	(2)
Smoke rings	157	(5)
Further reading	161	(1)
Surface waves
The propagation of wave groups in one dimension	162	(4)
Boundary conditions	166	(4)
Gravity waves, 1 (|ζ|≪λ≪d,λ≫λ*)	170	(3)
Ripples (|ζ|≪λ≪d,λ≫λ*)	173	(1)
Waves on a liquid-fluid interface	174	(2)
Gravity waves, 2 (|ζ|≪λ≈d)	176	(1)
Gravity waves, 3 (|ζ|≈λ≪d)	177	(2)
Solitary waves (|ζ|≈λ≈d)	179	(3)
Ship waves in canals	182	(4)
Wave resistance	186	(2)
Ship waves on open water: the Kelvin wedge	188	(4)
Mach's construction revisited	192	(3)
Further reading	194	(1)
Viscosity
Shear stresses in Newtonian fluids	195	(3)
Stress and rate of deformation as tensors	198	(3)
Bulk viscosity	201	(1)
The Navier-Stokes equation	202	(2)
Viscous dissipation	204	(2)
Laminar viscous flow, 1 (planar laminae)	206	(8)
Hydrodynamic lubrication	214	(4)
Hele Shaw flow	218	(2)
Laminar viscous flow, 2 (cylindrical laminae)	220	(5)
The Ekman layer	225	(2)
Creeping flow past a sphere: Stokes's law	227	(5)
The viscosity of suspensions	232	(4)
Percolation	236	(4)
Further reading	238	(2)
Vorticity
Lines of vorticity	240	(3)
Boundary layers on plates	243	(9)
Boundary layer separation and eddy formation	252	(4)
Steady eddies behind cylinders and spheres	256	(3)
Eddy shedding by cylinders and spheres	259	(2)
Turbulent wakes behind cylinders and spheres	261	(2)
Submerged jets revisited	263	(1)
Drag forces	264	(4)
Techniques for drag reduction	268	(2)
Starting, stopping and trailing vortices	270	(3)
Wing theory	273	(6)
The Magnus effect revisited	279	(4)
Tealeaves and suchlike	283	(2)
Acoustic streaming	285	(4)
Further reading	288	(1)
Instabilities
Stability, instability and overstability	289	(4)
The Rayleigh--Taylor instability	293	(2)
The Rayleigh--Plateau instability	295	(2)
The Saffman--Taylor instability	297	(5)
Thermal convection - an introduction	302	(7)
Convection in an open vertical slot	309	(5)
The Rayleigh--Benard instability	314	(8)
Marangoni convection	322	(2)
Benard convection in binary fluids	324	(4)
The Taylor--Couette instability	328	(3)
The Kelvin--Helmholtz instability	331	(5)
Examples of the Kelvin--Helmholtz instability	336	(4)
The Tollmien--Schlichting instability	340	(1)
The Benjamin--Feir instability	341	(2)
Further reading	342	(1)
Turbulence
Introduction	343	(6)
Period doubling and intermittency in Benard convection	349	(2)
The transition to turbulence in pipe flow	351	(3)
The energy cascade in homogeneous turbulence	354	(4)
Eddy viscosity and the mixing length	358	(4)
A simple illustration of the scaling approach	362	(4)
Turbulent jets, wakes and mixing layers	366	(3)
Turbulent flow between parallel plates and in pipes	369	(6)
Turbulent boundary layers	375	(3)
Benard convection at large Rayleigh Numbers	378	(6)
Further reading	383	(1)
Non-Newtonian fluids
Introduction	384	(3)
Linear viscoelasticity	387	(3)
Viscosity in a uniaxial liquid	390	(4)
A theory of flow birefringence	394	(4)
Flow alignment: a general approach	398	(2)
Non-Newtonian effects in polymeric liquids	400	(7)
Non-Newtonian effects in suspensions	407	(2)
Flow phenomena in nematic liquid crystals	409	(4)
Plasmas in magnetic fields	413	(2)
Liquid helium	415	(9)
Further reading	422	(2)
Appendix One-dimensional sound waves in gases
A.1 Small-amplitude theory excluding attenuation	424	(1)
A.2 Riemann's treatment for arbitrary amplitudes	425	(3)
A.3 Attenuation due to thermal conduction	428	(3)
A.4 Attenuation due to viscosity	431	(1)
A.5 Additional attenuation mechanisms	432	(4)
Further reading	435	(1)
Index	436