# Mechanics of Liquids and Gases

## 2nd Edition

### International Series of Monographs in Aeronautics and Astronautics: Division II: Aerodynamics

**Author:**L. G. Loitsyanskii

**Editors:**R. T. Jones W. P. Jones

**eBook ISBN:**9781483184968

**Imprint:**Pergamon

**Published Date:**1st January 1966

**Page Count:**816

## Description

Mechanics of Liquids and Gases, Second Edition is a 10-chapter text that covers significant revisions concerning the dynamics of an ideal gas, a viscous liquid and a viscous gas.

After an expanded introduction to the fundamental properties and methods of the mechanics of fluids, this edition goes on dealing with the kinetics and general questions of dynamics. The next chapters describe the one-dimensional pipe flow of a gas with friction, the elementary theory of the shock tube; Riemann's theory of the wave propagation of finite intensity, and the theory of plane subsonic and supersonic flows. Other chapters consider the elements of the theory of three-dimensional subsonic and supersonic flows past bodies; the fluctuating laminar flow in a uniform pipe of circular cross-section; the hydrodynamic theory of lubrication; the variational principle of Helmholtz; and the theory of plane and axisymmetric laminar jets. The remaining chapters look into the semi-empirical theories of turbulence and their application in the analysis of axisymmetric jets, with and without swirl, and in the calculation of the resistance of rough plates. These chapters also discuss the dynamics of a viscous gas and the elements of the theory of laminar and turbulent boundary layers at high speeds.

This book will be of value to mechanical engineers, physicists, and researchers.

## Table of Contents

Foreword to the Second Edition

Introduction

1. The Mechanics of Fluids as a Subject. The Fundamental Properties of Liquid and Gaseous Media

2. The Basic Methods of the Mechanics of Fluids, the Fields of Application and the Principal Problems

3. A Brief Survey of the Development of the Mechanics of Fluids. From the Hydromechanics of the Ancients to the Newtonian Period

4. The Period of Euler and Bernoulli. Hydromechanics in the Nineteenth Century

5. The Development of the Mechanics of Fluids in the First Half of the Twentieth Century

Chapter 1 Kinematics of a Continuous Medium

6. Consideration of the Motion of a Continuous Medium. Velocity Field. Streamlines and Particle Paths. Stream Tubes and Particle Streams

7. The Velocity Field of a Continuous Medium in the Neighborhood of a Point. The First Theorem of Helmholtz

8. Vortex Lines and Tubes. Second Theorem of Helmholtz. Strength of the Vortex Tube and its Connection with the Circulation

9. Rate of Strain Tensor

10. The Acceleration of a Fluid Particle. Kelvin's Theorem

11. Some Points on Tensor Calculus

Chapter 2 General Equations and Theorems of Motion of a Continuous Medium

12. Distribution of Mass in a Continuous Medium. The Stress Tensor and Its Symmetry

13. The Continuity Equation. Momentum Equations

14. The Law of Conservation of Energy and the Energy Equation

15. Particular Applications of the General Theorems on the Dynamics of a System to a Continuous Medium

16. General Equations of Hydrostatic Equilibrium. Atmospheric Equilibrium. Approximate Barometric Formulae

17. Equilibrium of an Incompressible Fluid. Equilibrium of a Rotating Fluid

18. Pressure of a Heavy Incompressible Liquid on the Surface of a Body. Force and Moment Acting on the Body

Chapter 3 Fundamental Equations and Theorems of the Dynamics of an Ideal Liquid and Gas

19. An Ideal Fluid. Fundamental Equations of Motion

20. Bernoulli's Theorem

21. The Equation of Energy in the Adiabatic Motion of a Perfect Ideal Gas

22. The Velocity of Propagation of Small Disturbances in an Ideal Gas

23. The Subsonic and Supersonic Flow of a Gas. The Numbers M and λ. Isentropic Formulae

Chapter 4 One-Dimensional Flow of an Ideal Gas

24. One-dimensional Steady Motion of a Gas in a Tube of Varying Cross-section

25. The Flow of Gas through a Nozzle

26. An Example of Non-adiabatic Motion of a Gas

27. One-dimensional Flow of a Gas in a Tube with Frictional Resistance

28. Plane Shock Waves (Compression Discontinuities)

29. The Change of Speed and Thermodynamic Variables of a Gas Passing through a Normal Shock

30. The Speed of Propagation of a Shock Wave and of the Accompanying Flow behind it

31. The Effect of a Shock Wave on the Pressure in the Chamber of a Jet Engine. Velocity Measurements in Supersonic Flow

32. Unsteady One-dimensional Flow of an Ideal Gas. Propagation of Disturbances of Finite Intensity

33. Elementary Theory of the Shock Tube

Chapter 5 Plane Irrotational Flow of an Ideal Incompressible Fluid

34. The Theorems of Kelvin and Lagrange: Conditions for the Existence of Irrotational Flow

35. The Velocity Potential and its Definition for a Given Velocity Field

36. The Lagrange-Cauchy Integral. Some General Properties of Irrotational Flow of an Ideal Incompressible Fluid in a Simply-connected Domain

37. Plane Irrotational Flow of an Incompressible Fluid. The Application of Functions of a Complex Variable

38. Examples of Plane Flows

39. Flow past a Circular Cylinder without Circulation

40. Flow past a Circular Cylinder with Circulation

41. The External Flow past a Wing Profile

42. The Zhukovskii—Chaplygin Hypothesis; the Formula for the Circulation

43. Examples of the Application of the Method of Conformai Mapping. Flow past an Ellipse and a Flat Plate

44. The Theoretical Wing Profiles of Zhukovskii and Chaplygin

45. The Calculation of Flow past a Wing Profile of Arbitrary Shape

46. Zhukovskii's Theorem on the Lift of a Wing; the Formula for the Coefficient of Lift

47. Chaplygin's Formulae for the Resultant Vector and the Resultant Moment of the Pressure Forces on an Aerofoil

48. Lift and Moment Coefficients of Theoretical Wing Profiles

49. The Flow past a Slightly Curved Arc of Arbitrary Shape (The Thin Aerofoil Theory)

50. Zhukovskii's Theorem on the Lift of Aerofoils in Cascades

51. The Flow past a Cascade of Flat Plates

52. Discontinuous Flows

53. Applications of the Method of Conformai Mapping to Discontinuous Flows

Chapter 6 Plane Irrotational Flow of an Ideal Gas

54. The Basic Equations of Motion and Their Linearization

55. Subsonic Flow past a Thin Aerofoil

56. Supersonic Flow past a Thin Aerofoil

57. The Symmetric Supersonic Flow past a Wedge. Oblique Shock Waves

58. Supersonic Flow past a Convex Corner

59. The Equations of Gas Dynamics in the Hodograph Plane

60. The Effect of Compressibility on Pressure Distribution in Subsonic Flow

61. The Transcritical Flow past a Wing Profile

62. Zhukovskii's Theorem on the Lift of Aerofoils in Cascades in Subcritical Flow

63. The General Properties of the Characteristics

Chapter 7 Three-Dimensional Irrotational Flow of Liquids and Gases

64. Differential Operators in Orthogonal Curvilinear Coordinates

65. The Velocity Potentials of Some Simple Three-dimensional Flows

66. The Velocity Field round a Vortex System; the Biot-Savart Formula

67. The Potential of the Velocity Field of a Closed Vortex Line

68. The Stream Function in Three-dimensional Flows

69. The Flow past a Sphere. D'Alembert's Paradox

70. The Equations of Axially Symmetric Motion. The Flow in a Duct

71. Axi-symmetric Flow past Bodies of Revolution

72. Transverse Flow past Bodies of Revolution

73. Axial and Transverse Flow past Slender Bodies of Revolution

74. Application of the Method of Singularities to the Calculation of Axial and Transverse Flow past Bodies of Revolution

75. Elements of the Theory of Wings of Finite Span

76. The Elliptic Wing. General Formula of the Wing Theory

77. Effects of Compressibility on Three-dimensional Subsonic Flow

78. Supersonic Flow past Slender Bodies of Revolution

79. General Motion of a Rigid Body in an Incompressible Ideal Fluid

80. Virtual Masses

Chapter 8 Dynamics of an Incompressible Viscous Fluid

81. Internal Friction and Thermal Conductivity in Liquids and Gases

82. Generalization of Newton's Law

83. Stokes's Equations of Motion of a Viscous Fluid

84. Hydrodynamical Similarity

85. Laminar Flow of a Viscous Fluid in a Cylindrical Pipe

86. Oscillatory Laminar Motion of a Viscous Fluid in a Cylindrical Tube of Circular Cross-section

87. The Flow past a Sphere at Low Values of the Reynolds Number; Stokes's Formula

88. The Hydrodynamic Theory of Cylindrical Bearings

89. The Diffusion of a Vortex Filament in a Viscous Fluid

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 Boundary Layer

92. The Laminar Boundary Layer on a Flat Plate Parallel to a Uniform Stream

93. The Laminar Boundary Layer with a Power-Law Velocity Distribution in the External Stream

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

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

98. The Spreading of a Laminar Axially-symmetric Jet without Swirl

99. The Spreading of a Laminar Swirling Jet

Chapter 9 Turbulent Flow

100. Transition from Laminar to Turbulent Flow

101. The Drag Crisis of Bluff Bodies

102. The Reynolds Equations of Mean Turbulent Motion

103. Turbulent Mixing; Prandtl's Formula for Turbulent Skin Friction

104. Application of PrandtPs Formula to the Analysis of the Plane Mixing Region

105. The Axisymmetric Turbulent Jet; the Turbulent Wake

106. Turbulent Flow Past an Infinite Solid Wall

107. Kármán's Formula for the Mixing Length and its Application to the Analysis of Turbulent Flow in a Channel

108. Logarithmic and Power-law Formulae for the Velocity Profiles and the Resistance of Smooth Pipes

109. Turbulent Flow in Rough Pipes

110. The Turbulent Boundary Layer on Smooth and Rough Flat Plates

111. The Turbulent Boundary Layer with an External Pressure Gradient

112. Effects of the Boundary Layer on the External Stream

113. Approximate Formulae for the Profile Drag

114. Some Remarks on the Internal Structure of Turbulent Flows

115. Homogeneous and Isotropie Turbulence

Chapter 10 Dynamics of a Viscous Gas

116. Basic Equations of Motion of a Viscous Gas

117. Conditions for the Similarity of Two Flows of a Viscous Gas

118. Application of the Dynamics of a Viscous Gas to the Theory of Normal Shock Waves

119. An Example of Isothermal Viscous Gas Flow: a Sphere Suspended by Air in a Spherical Cup

120. The Laminar Boundary Layer in High-Speed Gas Flows

121. The Low-Speed Laminar Boundary Layer on a Flat Plate with Heat Transfer

122. The Laminar Boundary Layer on a Flat Plate at High Speeds

123. The Laminar Boundary Layer in High-Speed Flow with External Pressure Gradients

124. Transition from Laminar to Turbulent Flow at High Speeds

125. The Turbulent Boundary Layer in High-Speed Gas Flows

Index

Other Titles in the Series

## Details

- No. of pages:
- 816

- Language:
- English

- Copyright:
- © Pergamon 1966

- Published:
- 1st January 1966

- Imprint:
- Pergamon

- eBook ISBN:
- 9781483184968