Mechanics of Liquids and Gases (eBook)

Front Cover 1
Mechanics of Liquids 
4 
Copyright Page 5
Table of Contents 6
Foreword to the Second Edition 12
Introduction 14
1. The Mechanics of Fluids as a Subject. The Fundamental Properties of Liquid and Gaseous Media 14
2. The Basic Methods of the Mechanics of Fluids, the Fields of 
18 
3. A Brief Survey of the Development of the Mechanics of Fluids. 
20 
4. The Period of Euler and Bernoulli. Hydromechanics in the 
23 
5. The Development of the Mechanics of Fluids in the First Half 
33 
CHAPTER 1. 
43 
6. Consideration of the Motion of a Continuous Medium. Velocity Field. Streamlines and Particle Paths. Stream Tubes and Particle Streams 43
7. The Velocity Field of a Continuous Medium in the Neighbourhood 
50 
8. Vortex Lines and Tubes. Second Theorem of Helmholtz. Strength 
53 
9. Rate of Strain Tensor 61
10. The Acceleration of a Fluid Particle. Kelvin's Theorem 67
11. Some Points on Tensor Calculus 70
CHAPTER 2. General Equations and Theorems of Motion of a Continuous Medium 84
12. Distribution of Mass in a Continuous Medium. The Stress Tensor and Its Symmetry 84
13. The Continuity Equation. Momentum Equations 92
14. The Law of Conservation of Energy and the Energy Equation 97
15. Particular Applications of the General Theorems on the Dynamics 
101 
16. General Equations of Hydrostatic Equilibrium. Atmospheric Equilibrium. Approximate Barometric Formulae 107
17. Equilibrium of an Incompressible Fluid. 
115 
18. Pressure of a Heavy Incompressible Liquid on the Surface of the Body. Force and Moment Acting on the Body 120
CHAPTER 3. 
125 
19. An Ideal Fluid. Fundamental Equations of Motion 125
20. Bernoulli's Theorem 129
21. The Equation of Energy in the Adiabatic Motion of a Perfect 
135 
22. The Velocity of Propagation of Small Disturbances in an Ideal Gas 140
23. The Subsonic and Supersonic Flow of a Gas. The Numbers M and .. Isentropic Formulae 146
CHAPTER 4. 
154 
24. One-dimensional Steady Motion of a Gas in a Tube of Varying 
154 
25. The Flow of Gas through a Nozzle 159
26. An Example of Non-adiabatic Motion of a Gas 165
27. One-dimensional Flow of Gas in a Tube with Frictional 
168 
28. Plane Shock Waves (Compression Discontinuities) 171
29. The Change of Speed and Thermodynamic Variables of a Gas 
178 
30. The Speed of Propagation of a Shock Wave and of the Accompanying 
185 
31. The Effect of a Shock Wave on the Pressure in the Chamber of a Jet Engine. Velocity Measurements of Speeds in Supersonic Flow 188
32. Unsteady One-dimensional Flow of an Ideal Gas. Propagation 
194 
33. Elementary Theory of the Shock Tube 204
CHAPTER 5. 
208 
34. The Theorems of Kelvin and Lagrange: Conditions for the 
208 
35. The Velocity Potential and its Definition for a Given 
210 
36. The Lagrange-Cauchy Integral. Some General Properties of Irrotational Flow of an Ideal Incompressible Fluid in a Simplyconnected Domain 216
37. Plane Irrotational Flow of an Incompressible Fluid. The Application 
221 
38. Examples ef Plane Flows 229
39. Flow past a Circular Cylinder without Circulation 237
40. Flow past a Circular Cylinder with Circulation 243
41. The External Flow past a Wing Profile 247
42. The Zhukovskii-Chaplygin Hypothesis the Formula for the Circulation
43. Examples of the Application of the Method of Conformal Mapping. Flow past an Ellipse and a Flat Plate 254
44. The Theoretical Wing Profiles of Zhukovskii and Chaplygin 261
45. The Calculation of Flow past a Wing Profile of Arbitrary Shape 267
46. Zhukovskii's Theorem on the Lift of a Wing the Formula
272 
47. Chaplygin's Formulae for the Resultant Vector and the Resultant 
280 
48. Lift and Moment Coefficients of Theoretical Wing Profiles 286
49. The Flow past a Slightly Curved Arc of Arbitrary Shape (The 
293 
50. Zhukovskii's Theorem on the Lift of Aerofoils in Cascades 300
51. The Flow past a Cascade of Flat Plates 304
52. Discontinuous Flows 315
53. Applications of the Method of Conformal Mapping to Discontinuous Flows 324
CHAPTER 6. 
334 
54. The Basic Equations of Motion and Their Linearization 334
55. Subsonic Flow past a Thin Aerofoil 337
56. Supersonic Flow past a Thin Aerofoil 341
57. The Symmetric Supersonic Flow past a Wedge. Oblique Shock Waves 349
58. Supersonic Flow past a Convex Corner 359
59. The Equations of Gas Dynamics in the Hodograph Plane 364
60. The Effect of Compressibility on Pressure Distribution in Subsonic Flow 368
61. The Transcritical Flow past a Wing Profile 380
62. Zhukovskii's Theorem on the Lift of Aerofoils in Cascades in Subcritical Flow 384
63. The General Properties of the Characteristics 387
CHAPTER 7. Three-dimensional Irrotational Flow of Liquids and Gases 394
64. Differential Operators in Orthogonal Curvilinear Coordinates 394
65. The Velocity Potentials of Some Simple Three-dimensional Flows 400
66. The Velocity Field round a Vortex System the Biot-Savart Formula
67. The Potential of the Velocity Field of a Closed Vortex Line 410
68. The Stream Function in Three-dimensional Flows 412
69. The Flow past a Sphere. D'Alembert's Paradox 416
70. The Equations of Axially Symmetric Motion. The Flow in a Duct 423
71. Axi -symmetric Flow past Bodies of Revolution 430
72. Transverse Flow past Bodies of Revolution 436
73. Axial and Transverse Flow past Slender Bodies of Revolution 441
74. Application of the Method of Singularities to the Calculation of Axial and Transverse Flow past Bodies of Revolution 444
75. Elements of the Theory of Wings of Finite Span 449
76. The Elliptic Wing. General Formula of the Wing Theory 458
77. Effects of Compressibility on Three-dimensional Subsonic Flow 463
78. Supersonic Flow past Slender Bodies of Revolution 472
79. General Motion of a Rigid Body in an Incompressible Ideal Fluid 480
80. Virtual Masses 485
CHAPTER 8. 
493 
81. Internal Friction and Thermal Conductivity in Liquids and 
493 
82. Generalization of Newton's Law 497
83. Stokes's Equations of Motion of a Viscous Fluid 501
84. Hydrodynamical Similarity 504
85. Laminar Flow of a Viscous Fluid in a Cylindrical Pipe 509
86. Oscillatory Laminar Motion of a Viscous Fluid in a Cylindrical Tube of Circular Cross-section 518

522 
88. The Hydrodynamic Theory of Cylindrical Bearings 529
89. The Diffusion of a Vortex Filament in a Viscous Fluid 539
90. The Dissipation of Mechanical Energy in the Motion of a Viscous Fluid Helmholtz's Principle
91. The Fundamental Equations of the Theory of the Plane Laminar 
548 
92. The Laminar Boundary Layer on a Flat Plate Parallel to a 
557 
93. The Laminar Boundary Layer with a Power-Law Velocity Distribution in the External Stream 564
94. The Laminar Submerged Jet the Laminar Wake
95. The Momentum Integral Equation and its Application in Approximate Methods of the Laminar Boundary Layer Theory 581
96. Determination of the Function F(f) an Approximate Method of Calculating the Laminar Boundary Layer
97. The Laminar Boundary Layer on a Slender Body of Revolution in Axisymmetric Flow 596
98. The Spreading of a Laminar Axially-symmetric Jet without Swirl 601
99. The Spreading of a Laminar Swirling Jet 606
CHAPTER 9. Turbulent Flows 614
100. Transition from Laminar to Turbulent Flow 614
101. The Drag Crisis of Bluff Bodies 625
102. The Reynolds Equations of Mean Turbulent Motion 631
103. Turbulent Mixing Prandtl's Formula for Turbulent Skin Friction
104. Application of Prandtl's Formula to the Analysis of the 
641 
105. The Axisymmetric Turbulent Jet the Turbulent Wake
106. Turbulent Flow Past an Infinite Solid Wall 656
107. Kármán's Formula for the Mixing Length and its Application to the Analysis of Turbulent Flow in a Channel 663
108. Logarithmic and Power-law Formulae for the Velocity Profiles and the Resistance of Smooth Pipes 669
109. Turbulent Flow in Rough Pipes 674
110. The Turbulent Boundary Layer on Smooth and Rough Flat Plates 679
111. The Turbulent Boundary Layer with an External Pressure Gradient 692
112. Effects of the Boundary Layer on the External Stream 701
113. Approximate Formulae for the Profile Drag 707
114. Some Remarks on the Internal Structure of Turbulent Flows 715
115. Homogeneous and Isotropic Turbulence 725
CHAPTER 10. Dynamics of a Viscous Gas 734
116. Basic Equations of Motion of a Viscous Gas 734
117. Conditions for the Similarity of Two Flows of a Viscous Gas 739
118. Application of the Dynamics of a Viscous Gas to the Theory 
743 
119. An Example of Isothermal Viscous Gas Flow: a Sphere Suspended 
750 
120. The Laminar Boundary Layer in High-Speed Gas Flows 759
121. Low-Speed Laminar Boundary Layer on a Flat Plate with 
765 
122. The Laminar Boundary Layer on a Flat Plate at High Speeds 772
123. The Laminar Boundary Layer in High-Speed Flow with External 
786 
124. Transition from Laminar to Turbulent Flow at High Speeds 796
125. The Turbulent Boundary Layer in High-Speed Gas Flows 799
Index 808