[Book] Fluid Mechanics, Vol. 6

This book deals with the theory of the motion of liquids and gases. All matters of physical interest are fully discussed giving a clear picture of the phenomena and their interrelations.

Prefaces to the English editions ix
E. M. Lifshitz xi
Notation xiii
Ideal Fluids
The equation of continuity 1(1)
Euler's equation 2(3)
Hydrostatics 5(2)
The condition that convection be absent 7(1)
Bernoulli's equation 8(1)
The energy flux 9(2)
The momentum flux 11(1)
The conservation of circulation 12(2)
Potential flow 14(3)
Incompressible fluids 17(9)
The drag force in potential flow past a body 26(5)
Gravity waves 31(6)
Internal waves in an incompressible fluid 37(3)
Waves in a rotating fluid 40(4)
Viscous Fluids
The equations of motion of a viscous fluid 44(6)
Energy dissipation in an incompressible fluid 50(1)
Flow in a pipe 51(4)
Flow between rotating cylinders 55(1)
The law of similarity 56(2)
Flow with small Reynolds numbers 58(9)
The laminar wake 67(6)
The viscosity of suspensions 73(2)
Exact solutions of the equations of motion for a viscous fluid 75(8)
Oscillatory motion in a viscous fluid 83(9)
Damping of gravity waves 92(3)
Turbulence
Stability of steady flow 95(4)
Stability of rotary flow 99(4)
Stability of flow in a pipe 103(3)
Instability of tangential discontinuities 106(2)
Quasi-periodic flow and frequency locking 108(5)
Strange attractors 113(5)
Transition to turbulence by period doubling 118(11)
Fully developed turbulence 129(6)
The velocity correlation functions 135(11)
The turbulent region and the phenomenon of separation 146(1)
The turbulent jet 147(5)
The turbulent wake 152(1)
Zhukovskii's theorem 153(4)
Boundary Layers
The laminar boundary layer 157(6)
Flow near the line of separation 163(4)
Stability of flow in the laminar boundary layer 167(5)
The logarithmic velocity profile 172(4)
Turbulent flow in pipes 176(2)
The turbulent boundary layer 178(2)
The drag crisis 180(3)
Flow past streamlined bodies 183(2)
Induced drag 185(4)
The lift of a thin wing 189(3)
Thermal Conduction in Fluids
The general equation of heat transfer 192(4)
Thermal conduction in an incompressible fluid 196(4)
Thermal conduction in an infinite medium 200(3)
Thermal conduction in a finite medium 203(5)
The similarity law for heat transfer 208(2)
Heat transfer in a boundary layer 210(4)
Heating of a body in a moving fluid 214(3)
Free convection 217(4)
Convective instability of a fluid at rest 221(6)
Diffusion
The equations of fluid dynamics for a mixture of fluids 227(3)
Coefficients of mass transfer and thermal diffusion 230(5)
Diffusion of particles suspended in a fluid 235(3)
Surface Phenomena
Laplace's formula 238(6)
Capillary waves 244(4)
The effect of adsorbed films on the motion of a liquid 248(3)
Sound
Sound waves 251(4)
The energy and momentum of sound waves 255(4)
Reflection and refraction of sound waves 259(1)
Geometrical acoustics 260(3)
Propagation of sound in a moving medium 263(3)
Characteristic vibrations 266(3)
Spherical waves 269(2)
Cylindrical waves 271(2)
The general solution of the wave equation 273(3)
The lateral wave 276(5)
The emission of sound 281(8)
Sound excitation by turbulence 289(3)
The reciprocity principle 292(2)
Propagation of sound in a tube 294(3)
Scattering of sound 297(3)
Absorption of sound 300(5)
Acoustic streaming 305(3)
Second viscosity 308(5)
Shock Waves
Propagation of disturbances in a moving gas 313(3)
Steady flow of a gas 316(4)
Surfaces of discontinuity 320(4)
The shock adiabatic 324(3)
Weak shock waves 327(2)
The direction of variation of quantities in a shock wave 329(2)
Evolutionary shock waves 331(2)
Shock waves in a polytropic gas 333(3)
Corrugation instability of shock waves 336(7)
Shock wave propagation in a pipe 343(2)
Oblique shock waves 345(5)
The thickness of shock waves 350(5)
Shock waves in a relaxing medium 355(1)
The isothermal discontinuity 356(2)
Weak discontinuities 358(3)
One-Dimensional Gas Flow
Flow of gas through a nozzle 361(3)
Flow of a viscous gas in a pipe 364(2)
One-dimensional similarity flow 366(7)
Discontinuities in the initial conditions 373(5)
One-dimensional travelling waves 378(7)
Formation of discontinuities in a sound wave 385(6)
Characteristics 391(3)
Riemann invariants 394(3)
Arbitrary one-dimensional gas flow 397(6)
A strong explosion 403(3)
An imploding spherical shock wave 406(5)
Shallow-water theory 411(3)
The Intersection of Surfaces of Discontinuity
Rarefaction waves 414(5)
Classification of intersections of surfaces of discontinuity 419(6)
The intersection of shock waves with a solid surface 425(2)
Supersonic flow round an angle 427(5)
Flow past a conical obstacle 432(3)
Two-Dimensional Gas Flow
Potential flow of a gas 435(3)
Steady simple waves 438(4)
Chaplygin's equation: the general problem of steady two-dimensional gas flow 442(3)
Characteristics in steady two-dimensional flow 445(2)
The Euler--Tricomi equation. Transonic flow 447(5)
Solutions of the Euler--Tricomi equation near non-singular points of the sonic surface 452(4)
Flow at the velocity of sound 456(5)
The reflection of a weak discontinuity from the sonic line 461(6)
Flow Past Finite Bodies
The formation of shock waves in supersonic flow past bodies 467(3)
Supersonic flow past a pointed body 470(4)
Subsonic flow past a thin wing 474(2)
Supersonic flow past a wing 476(3)
The law of transonic similarity 479(2)
The law of hypersonic similarity 481(3)
Fluid Dynamics of Combustion
Slow combustion 484(5)
Detonation 489(5)
The propagation of a detonation wave 494(6)
The relation between the different modes of combustion 500(3)
Condensation discontinuities 503(2)
Relativistic Fluid Dynamics
The energy-momentum tensor 505(1)
The equations of relativistic fluid dynamics 506(4)
Shock waves in relativistic fluid dynamics 510(2)
Relativistic equations for flow with viscosity and thermal conduction 512(3)
Dynamics of Superfluids
Principal properties of superfluids 515(2)
The thermo-mechanical effect 517(1)
The equations of superfluid dynamics 518(5)
Dissipative processes in superfluids 523(3)
The propagation of sound in superfluids 526(7)
Index 533