Fluid Mechanics

Fluid Mechanics, Second Edition deals with fluid mechanics, that is, the theory of the motion of liquids and gases. Topics covered range from ideal fluids and viscous fluids to turbulence, boundary layers, thermal conduction, and diffusion. Surface phenomena, sound, and shock waves are also discussed, along with gas flow, combustion, superfluids, and relativistic fluid dynamics. This book is comprised of 16 chapters and begins with an overview of the fundamental equations of fluid dynamics, including Euler's equation and Bernoulli's equation. The reader is then introduced to the equations of motion of a viscous fluid; energy dissipation in an incompressible fluid; damping of gravity waves; and the mechanism whereby turbulence occurs. The following chapters explore the laminar boundary layer; thermal conduction in fluids; dynamics of diffusion of a mixture of fluids; and the phenomena that occur near the surface separating two continuous media. The energy and momentum of sound waves; the direction of variation of quantities in a shock wave; one- and two-dimensional gas flow; and the intersection of surfaces of discontinuity are also also considered. This monograph will be of interest to theoretical physicists.

1;Front Cover;1 2;Fluid Mechanics;6 3;Copyright Page;7 4;Table of Contents;8 5;Prefaces to the English editions;12 6;E. M. Lifshitz;14 7;Notation;16 8;CHAPTER I. IDEAL FLUIDS;18 8.1;1. The equation of continuity;18 8.2;2. Euler's equation;19 8.3;3. Hydrostatics;22 8.4;4. The condition that convection be absent;24 8.5;5. Bernoulli's equation;25 8.6;6. The energy flux;26 8.7;7. The momentum flux;28 8.8;8. The conservation of circulation;29 8.9;9. Potential flow;31 8.10;10. Incompressible fluids;34 8.11;11. The drag force in potential flow past a body;43 8.12;12. Gravity waves;48 8.13;13. Internal waves in an incompressible fluid;54 8.14;14. Waves in a rotating fluid;57 9;CHAPTER II. VISCOUS FLUIDS;61 9.1;15. The equations of motion of a viscous fluid;61 9.2;16. Energy dissipation in an incompressible fluid;67 9.3;17. Flow in a pipe;68 9.4;18. Flow between rotating cylinders;72 9.5;19. The law of similarity;73 9.6;20. Flow with small Reynolds numbers;75 9.7;21. The laminar wake;84 9.8;22. The viscosity of suspensions;90 9.9;23. Exact solutions of the equations of motion for a viscous fluid;92 9.10;24. Oscillatory motion in a viscous fluid;100 9.11;25. Damping of gravity waves;109 10;CHAPTER III. TURBULENCE;112 10.1;26. Stability of steady flow;112 10.2;27. Stability of rotary flow;116 10.3;28. Stability of flow in a pipe;120 10.4;29. Instability of tangential discontinuities;123 10.5;30. Quasi-periodic flow and frequency locking;125 10.6;31. Strange attractors;130 10.7;32. Transition to turbulence by period doubling;135 10.8;33. Fully developed turbulence;146 10.9;34. The velocity correlation functions;152 10.10;35. The turbulent region and the phenomenon of separation;163 10.11;36. The turbulent jet;164 10.12;37. The turbulent wake;169 10.13;38. Zhukovskii's theorem;170 11;CHAPTER IV. BOUNDARY LAYERS;174 11.1;39. The laminar boundary layer;174 11.2;40. Flow near the line of separation;180 11.3;41. Stability of flow in the laminar boundary layer;184 11.4;42. The logari
thmic velocity profile;189 11.5;43. Turbulent flow in pipes;193 11.6;44. The turbulent boundary layer;195 11.7;45. The drag crisis;197 11.8;46. Flow past streamlined bodies;200 11.9;47. Induced drag;202 11.10;48. The lift of a thin wing;206 12;CHAPTER V. THERMAL CONDUCTION IN FLUIDS;209 12.1;49. The general equation of heat transfer;209 12.2;50. Thermal conduction in an incompressible fluid;213 12.3;51. Thermal conduction in an infinite medium;217 12.4;52. Thermal conduction in a finite medium;220 12.5;53. The similarity law for heat transfer;225 12.6;54. Heat transfer in a boundary layer;227 12.7;55. Heating of a body in a moving fluid;231 12.8;56. Free convection;234 12.9;57. Convective instability of a fluid at rest;238 13;CHAPTER VI. DIFFUSION;244 13.1;58. The equations of fluid dynamics for a mixture of fluids;244 13.2;59. Coefficients of mass transfer and thermal diffusion;247 13.3;60. Diffusion of particles suspended in a fluid;252 14;CHAPTER VII. SURFACE PHENOMENA;255 14.1;61. Laplace's formula;255 14.2;62. Capillary waves;261 14.3;63. The effect of adsorbed films on the motion of a liquid;265 15;CHAPTER VIII. SOUND;268 15.1;64. Sound waves;268 15.2;65. The energy and momentum of sound waves;272 15.3;66. Reflection and refraction of sound waves;276 15.4;67. Geometrical acoustics;277 15.5;68. Propagation of sound in a moving medium;280 15.6;69. Characteristic vibrations;283 15.7;70. Spherical waves;286 15.8;71. Cylindrical waves;288 15.9;72. The general solution of the wave equation;290 15.10;73. The lateral wave;293 15.11;74. The emission of sound;298 15.12;75. Sound excitation by turbulence;306 15.13;76. The reciprocity principle;309 15.14;77. Propagation of sound in a tube;311 15.15;78. Scattering of sound;314 15.16;79. Absorption of sound;317 15.17;80. Acoustic streaming;322 15.18;81. Second viscosity;325 16;CHAPTER IX. SHOCK WAVES;330 16.1;82. Propagation of disturbances in a moving gas;330 16.2;83. Steady flow of a gas;333 16.3;84. Surfaces of discontin
uity;337 16.4;85. The shock adiabatic;341 16.5;86. Weak shock waves;344 16.6;87. The direction of variation of quantities in a shock wave;346 16.7;88. Evolutionary shock waves;348 16.8;89. Shock waves in a polytropic gas;350 16.9;90. Corrugation instability of shock waves;353 16.10;91. Shock wave propagation in a pipe;360 16.11;92. Oblique shock waves;362 16.12;93. The thickness of shock waves;367 16.13;94. Shock waves in a relaxing medium;372 16.14;95. The isothermal discontinuity;373 16.15;96. Weak discontinuities;375 17;CHAPTER X. ONE-DIMENSIONAL GAS FLOW;378 17.1;97. Flow of gas through a nozzle;378 17.2;98. Flow of a viscous gas in a pipe;381 17.3;99. One-dimensional similarity flow;383 17.4;100. Discontinuities in the initial conditions;390 17.5;101. One-dimensional travelling waves;395 17.6;102. Formation of discontinuities in a sound wave;402 17.7;103. Characteristics;408 17.8;104. Riemann invariants;411 17.9;105. Arbitrary one-dimensional gas flow;414 17.10;106. A strong explosion;420 17.11;107. An imploding spherical shock wave;423 17.12;108. Shallow-water theory;428 18;CHAPTER XI. THE INTERSECTION OF SURFACES OF DISCONTINUITY;431 18.1;109. Rarefaction waves;431 18.2;110. Classification of intersections of surfaces of discontinuity;436 18.3;111. The intersection of shock waves with a solid surface;442 18.4;112. Supersonic flow round an angle;444 18.5;113. Flow past a conical obstacle;449 19;CHAPTER XII. TWO-DIMENSIONAL GAS FLOW;452 19.1;114. Potential flow of a gas;452 19.2;115. Steady simple waves;455 19.3;116. Chaplygin's equation: the general problem of steady two-dimensional gas flow;459 19.4;117. Characteristics in steady two-dimensional flow;462 19.5;118. The EulerTricomi equation. Transonic flow;464 19.6;119. Solutions of the EulerTricomi equation near non-singular points of the sonic surface;469 19.7;120. Flow at the velocity of sound;473 19.8;121. The reflection of a weak discontinuity from the sonic line;478 20;CHAPTER XIII. FLOW PAST FINITE BODI
ES;484 20.1;122. The formation of shock waves in supersonic flow past bodies;484 20.2;123. Supersonic flow past a pointed body;487 20.3;124. Subsonic flow past a thin wing;491 20.4;125. Supersonic flow past a wing;493 20.5;126. The law of transonic similarity;496 20.6;127. The law of hypersonic similarity;498 21;CHAPTER XIV. FLUID DYNAMICS OF COMBUSTION;501 21.1;128. Slow combustion;501 21.2;129. Detonation;506 21.3;130. The propagation of a detonation wave;511 21.4;131. The relation between the different modes of combustion;517 21.5;132. Condensation discontinuities;520 22;CHAPTER XV. RELATIVISTIC FLUID DYNAMICS;522 22.1;133. The energy-momentum tensor;522 22.2;134. The equations of relativistic fluid dynamics;523 22.3;135. Shock waves in relativistic fluid dynamics;527 22.4;136. Relativistic equations for flow with viscosity and thermal conduction;529 23;CHAPTER XVI. DYNAMICS OF SUPERFLUIDS;532 23.1;137. Principal properties of superfluids;532 23.2;138. The thermo-mechanical effect;534 23.3;139. The equations of superfluid dynamics;535 23.4;140. Dissipative processes in superfluids;540 23.5;141. The propagation of sound in superfluids;543 24;Index;550