DIVISION ONEFUNDAMENTAL PRINCIPLES

Chapter 1Parameters in Compressible Flow００3

1.1Velocity of Sound and Mach Number００3

1.2Viscosity, Reynolds Number００4

1.3Heat Conduction, Prandtl Number００5

1.4Property of Gas, Ratio of Specific Heat００6

1.5Similarity of Flows００6

Chapter 2Steady One�睤imensional Motion of a Perfect Compressible Fluid００8

2.1Thermodynamic Relations, and Energy Equation００8

2.2Perfect Gas Relations０10

2.3Flow Area, Conditions at the Throat０13

2.4Flow Through a De Laval Nozzle０15

2.5Pressure and Velocity Relations in Isentropic Flow０15
Chapter 3Shock Wave０19

3.1Relation of Quantities in front and behind the Shock０19

3.2Thickness of Shock０23

3.3Creation of Shock from Finite Compression Disturbances０25

3.4Oblique Shock０29

3.5Flow over a Wedge０33

3.6Pitot Tube０34

AppendixThe Concept of Entropy and the Second Law of Thermodynamics０36
Chapter 4Basic Equations of Motion of a Compressible, Inviscid and
Non�睭eat Conducting Fluid０38

4.1General Equations０38

4.2Kelvin Theorem０42

4.3Helmholtz Theorem０44

4.4Steady Two�睤imensional Rotational Flow Detached Shock０46

4.5Non�瞫teady Irrotational Flow０50

4.6Method of Approximate Solution of Irrotational Subsonic Isentropic Flow０51

AppendixVector Differentiation０53

DIVISION TWOTWO�睤IMENSIONAL FLOWS

Chapter 5RayleighJanzen Method０59

5.1General Equations０59

5.2Solution by means of Complex Variables０61

5.3Flow around a Circular Cylinder０64

5.4Pressure Coefficient as a Series of Ma02０68

5.5Higher Order of Approximation for the Circular Cylinder０69

Bibliography０70
Chapter 6PrandtlGlauert Method０72

6.1Basic Equations for Iteration０72

6.2First Approximation PrandtlGlauert Rule０76

6.3First Approximation, Using Velocity Potential０78

6.4Higher Approximations０80

Bibliography０81
Chapter 7Hodograph Method and K�騬m�騨Tsien Approximation０83

7.1Basic Equations in Hodograph Variables０84

7.2Formulation of Problem in Hodograph Plane０89

7.3K�騬m�騨Tsien Approximation０90

7.4Velocity and Pressure Correction Formulae０93

7.5Coordinate Correction０96

7.6Application to the Flow around an Elliptic Cylinder０98

7.7Further Development of K�騬m�騨Tsien Approximation102

Bibliography102
Chapter 8
Velocity and Pressure Correction Formulae104

8.1Correction for Boundary Effects in Subsonic Flow104

8.2Limitations of the Correction Formulae107

8.3The Recommended Correction Formulae110

Bibliography113
Chapter 9Exact Solution of Isentropic Irrotational Flow114

9.1Flow with 180 Turn114

9.2Limiting Line119

9.3Breakdown of Potential Flow121

9.4General Exact Solutions123

Bibliography125
Chapter 10
Two�睤imensional Supersonic Flows127

10.1The Lost Solution127

10.2PrandtlMeyer Flow130

10.3Flow over an Airfoil131

10.4Ackeret�餾 Formulae134

10.5Further Remarks136

Bibliography136
Chapter 11
Transonic and Hypersonic Similarity Laws138

11.1Transonic Flow Equation138

11.2Transonic Similarity Law142

11.3Slightly Supersonic Flow143

11.4Hypersonic Flows and Similarity Laws148

Bibliography152
Chapter 12Linearized Theory of Flow over a Slender Body of Revolution153

12.1Subsonic Flows with Axial Symmetry153

12.2Linearized Subsonic Flow154

12.3Subsonic Flow over a Slender Ellipsoid of Revolution157

12.4Supersonic Flow over a Slender Body of Revolution159

12.5Pressure Distribution163

12.6Wave Drag165

12.7Origin of Wave Drag Transfer of Momentum167

12.8Body of Minimum Wave Drag168

12.9Lift of a Body of Revolution171

Bibliography174

Appendix175
CHAPTER 13
Non�睱inear Theory of Axially Symmetric Flows176

13.1Transonic Similarity Law176

13.2Hypersonic Similarity Law179

13.3Lost Solution of the Exact Equation181

13.4Exact Solution for Flow over a Cone182

Bibliography184
Chapter 14
Similarity Laws for
Wings of Finite Span186

14.1Similarity Law in Subsonic Flow186

14.2Similarity Law in Transonic Flow190

14.3Similarity Laws in Supersonic Flow193

14.4Similarity Laws in Hypersonic Flow194
Chapter 15
Rectangular Wing in Supersonic Flow197

15.1Source and Doublet Distribution197

15.2General Relation Between Source Distribution and Thickness Distribution of the
Wing201

15.3Rectangular Wing at Zero Angle of Attack Drag Problem203

15.4Drag of Rectangular Wing at Very Small Aspect Ratio 207

15.5Lift Problem of a Rectangular Flat Plate208

15.6General Relation Between the Doublet Distribution and the Lift
Distribution214

15.7Aerodynamic Characteristics of a Rectangular Wing215

Appendix218
Chapter 16
Linearized Supersonic Wing Theory219

16.1Swept Wings of Infinite Span219

16.2Triangular Source Distribution221

16.3Arrowhead Wings224

16.4Reverse Flow Theorems228

16.5Conditions of the Edges of a Wing230

16.6Flow behind the Wing232

Bibliography233
Chapter 17Flow of a Viscous Compressible Fluid237

17.1Stresses and their Equations of Transformation237

17.2Rates of Strain and their Equations of Transformation239

17.3Relation between Stress and Rate of Strain241

17.4Justification of the Stress�睸train Relation244

17.5NavierStokes Equations246

17.6Energy Equation248
Chapter 18Boundary Layer251

18.1Boundary Layer Equations251

18.2Steady Flow in Boundary Layer and TemperatureVelocity Relation254

18.3Boundary Layer without Pressure Gradient257

18.4Approximate Solution of Boundary Layer over a Flat Plate259

18.5Cooling by Radiation262

18.6Steady Boundary Layer over a Body of Revolution263

18.7Integral Theorems267

18.8Stability of Laminar Boundary Layer and Turbulent Boundary Layer 270

Bibliography271
Chapter 19
Interaction of Boundary Layer and Shock273

19.1The λShock and the Simple Shock273

19.2Applications of the Concept of Softening of Shock275

Bibliography276
Appendix AProblems277
Appendix BExam283