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 OneDimensional 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 NonHeat Conducting Fluid038 4.1General Equations038 4.2Kelvin Theorem042 4.3Helmholtz Theorem044 4.4Steady TwoDimensional Rotational Flow — Detached Shock046 4.5Nonsteady Irrotational Flow050 4.6Method of Approximate Solution of Irrotational Subsonic Isentropic Flow051 AppendixVector Differentiation053 DIVISION TWOTWODIMENSIONAL 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 KrmnTsien Approximation083 7.1Basic Equations in Hodograph Variables084 7.2Formulation of Problem in Hodograph Plane089 7.3KrmnTsien Approximation090 7.4Velocity and Pressure Correction Formulae093 7.5Coordinate Correction096 7.6Application to the Flow around an Elliptic Cylinder098 7.7Further Development of KrmnTsien 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 TwoDimensional Supersonic Flows127 10.1The Lost Solution127 10.2PrandtlMeyer Flow130 10.3Flow over an Airfoil131 10.4Ackerets 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 NonLinear Theory of Axially Symmetric Flows176 13.1Transonic Similarity Law176 13.2Hypersonic Similarity Law179 13.3“Lost 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 StressStrain 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