# Fundamentals of Aerodynamics, 7th Edition PDF by John D Anderson and Christopher P Cadou

## Fundamentals of Aerodynamics, Seventh Edition

By John D. Anderson and Christopher P. Cadou

Contents:

Preface to the Seventh Edition XV

PART 1

Fundamental Principles 1

Chapter 1

Aerodynamics: Some Introductory

Thoughts 3

1.1 Importance of Aerodynamics: Historical Examples 5

1.2 Aerodynamics: Classification and Practical Objectives 11

1.3 Road Map for This Chapter 15

1.4 Some Fundamental Aerodynamic Variables 15

1.4.1 Units 18

1.5 Aerodynamic Forces and Moments 19

1.6 Center of Pressure 32

1.7 Dimensional Analysis: The Buckingham Pi Theorem 34

1.8 Flow Similarity 41

1.9 Fluid Statics: Buoyancy Force 52

1.10 Types of Flow 62

1.10.1 Continuum Versus Free Molecule Flow 62

1.10.2 Inviscid Versus Viscous Flow 62

1.10.3 Incompressible Versus Compressible Flows 64

1.10.4 Mach Number Regimes 64

1.11 Viscous Flow: Introduction to Boundary Layers 68

1.12 Applied Aerodynamics: The Aerodynamic

Coefficients—Their Magnitudes and Variations 75

1.13 Historical Note: The Illusive Center of Pressure 89

1.14 Historical Note: Aerodynamic Coefficients 93

1.15 Summary 97

1.16 Integrated Work Challenge: Forward-Facing

Axial Aerodynamic Force on an Airfoil—

Can It Happen and, If So, How? 98

1.17 Problems 101

Chapter 2

Aerodynamics: Some Fundamental Principles

and Equations 107

2.1 Introduction and Road Map 108

2.2 Review of Vector Relations 109

2.2.1 Some Vector Algebra 110

2.2.2 Typical Orthogonal Coordinate

Systems 111

2.2.3 Scalar and Vector Fields 114

2.2.4 Scalar and Vector Products 114

2.2.5 Gradient of a Scalar Field 115

2.2.6 Divergence of a Vector Field 117

2.2.7 Curl of a Vector Field 118

2.2.8 Line Integrals 118

2.2.9 Surface Integrals 119

2.2.10 Volume Integrals 120

2.2.11 Relations Between Line, Surface, and

Volume Integrals 121

2.2.12 Summary 121

2.3 Models of the Fluid: Control Volumes and

Fluid Elements 121

2.3.1 Finite Control Volume Approach 122

2.3.2 Infinitesimal Fluid Element

Approach 123

2.3.3 Molecular Approach 123

2.3.4 Physical Meaning of the Divergence of

Velocity 124

2.3.5 Specification of the Flow Field 125

2.4 Continuity Equation 129

2.5 Momentum Equation 134

2.6 An Application of the Momentum Equation:

Drag of a Two-Dimensional Body 139

2.6.1 Comment 148

2.7 Energy Equation 148

2.8 Interim Summary 153

2.9 Substantial Derivative 154

2.10 Fundamental Equations in Terms of the

Substantial Derivative 160

2.11 Pathlines, Streamlines, and Streaklines

of a Flow 162

2.12 Angular Velocity, Vorticity, and Strain 167

2.13 Circulation 178

2.14 Stream Function 181

2.15 Velocity Potential 185

2.16 Relationship Between the Stream Function

and Velocity Potential 188

2.17 How Do We Solve the Equations? 189

2.17.1 Theoretical (Analytical) Solutions 189

2.17.2 Numerical Solutions—Computational

Fluid Dynamics (CFD) 191

2.17.3 The Bigger Picture 198

2.18 Summary 198

2.19 Problems 202

PART 2

Inviscid, Incompressible Flow 207

Chapter 3

Fundamentals of Inviscid, Incompressible

Flow 209

3.1 Introduction and Road Map 210

3.2 Bernoulli’s Equation 213

3.3 Incompressible Flow in a Duct: The Venturi

and Low-Speed Wind Tunnel 217

3.4 Pitot Tube: Measurement of Airspeed 230

3.5 Pressure Coefficient 239

3.6 Condition on Velocity for Incompressible

Flow 241

3.7 Governing Equation for Irrotational,

Incompressible Flow: Laplace’s

Equation 242

3.7.1 Infinity Boundary Conditions 245

3.7.2 Wall Boundary Conditions 245

3.8 Interim Summary 246

3.9 Uniform Flow: Our First

Elementary Flow 247

3.10 Source Flow: Our Second

Elementary Flow 249

3.11 Combination of a Uniform Flow with a

Source and Sink 253

3.12 Doublet Flow: Our Third Elementary

Flow 257

3.13 Nonlifting Flow over a Circular

Cylinder 259

3.14 Vortex Flow: Our Fourth Elementary

Flow 268

3.15 Lifting Flow over a Cylinder 272

3.16 The Kutta-Joukowski Theorem and the

Generation of Lift 286

3.17 Nonlifting Flows over Arbitrary Bodies:

The Numerical Source Panel Method 288

3.18 Applied Aerodynamics: The Flow over a

Circular Cylinder—The Real Case 298

3.19 Historical Note: Bernoulli and Euler—The

Origins of Theoretical Fluid

Dynamics 306

3.20 Historical Note: d’Alembert and His

3.21 Summary 312

3.22 Integrated Work Challenge: Relation

Between Aerodynamic Drag and the Loss of

Total Pressure in the Flow field 315

3.23 Integrated Work Challenge: Conceptual

Design of a Subsonic Wind Tunnel 318

3.24 Problems 322

Chapter 4

Incompressible Flow over Airfoils 325

4.1 Introduction 327

4.2 Airfoil Nomenclature 330

4.3 Airfoil Characteristics 332

4.4 Philosophy of Theoretical Solutions for

Low-Speed Flow over Airfoils: The Vortex

Sheet 337

4.5 The Kutta Condition 342

4.5.1 Without Friction Could We Have

Lift? 346

4.6 Kelvin’s Circulation Theorem and the

Starting Vortex 346

4.7 Classical Thin Airfoil Theory: The

Symmetric Airfoil 350

4.8 The Cambered Airfoil 360

Considerations 369

4.10 Lifting Flows over Arbitrary Bodies: The

Vortex Panel Numerical Method 373

4.11 Modern Low-Speed Airfoils 379

4.12 Viscous Flow: Airfoil Drag 383

4.12.1 Estimating Skin-Friction Drag: Laminar

Flow 384

4.12.2 Estimating Skin-Friction Drag: Turbulent

Flow 386

4.12.3 Transition 388

4.12.4 Flow Separation 393

4.12.5 Comment 398

4.13 Applied Aerodynamics: The Flow over

an Airfoil—The Real Case 399

4.14 Historical Note: Early Airplane Design and

the Role of Airfoil Thickness 410

4.15 Historical Note: Kutta, Joukowski, and the

Circulation Theory of Lift 415

4.16 Summary 417

4.17 Integrated Work Challenge: Wall Effects on

Tunnels 419

4.18 Problems 423

Chapter 5

Incompressible Flow over Finite Wings 427

5.1 Introduction: Downwash and Induced

Drag 431

5.2 The Vortex Filament, the Biot-Savart Law,

and Helmholtz’s Theorems 436

5.3 Prandtl’s Classical Lifting-Line

Theory 440

5.3.1 Elliptical Lift Distribution 446

5.3.2 General Lift Distribution 451

5.3.3 Effect of Aspect Ratio 454

5.3.4 Physical Significance 460

5.4 A Numerical Nonlinear Lifting-Line

Method 469

5.5 The Lifting-Surface Theory and the Vortex

Lattice Numerical Method 473

5.6 Applied Aerodynamics: The Delta

Wing 480

5.7 Historical Note: Lanchester and

Prandtl—The Early Development of

Finite-Wing Theory 492

5.8 Historical Note: Prandtl—The Person 496

5.9 Summary 499

5.10 Problems 500

Chapter 6

Three-Dimensional Incompressible Flow 503

6.1 Introduction 503

6.2 Three-Dimensional Source 504

6.3 Three-Dimensional Doublet 506

6.4 Flow over a Sphere 508

6.4.1 Comment on the Three-Dimensional

Relieving Effect 511

6.5 General Three-Dimensional Flows: Panel

Techniques 511

6.6 Applied Aerodynamics: The Flow over a

Sphere—The Real Case 513

6.7 Applied Aerodynamics: Airplane Lift and

Drag 516

6.7.1 Airplane Lift 516

6.7.2 Airplane Drag 518

6.7.3 Application of Computational Fluid

Dynamics for the Calculation of Lift and

Drag 523

6.8 Summary 527

6.9 Problems 528

PART 3

Inviscid, Compressible Flow 529

Chapter 7

Compressible Flow: Some Preliminary

Aspects 531

7.1 Introduction 532

7.2 A Brief Review of Thermodynamics 534

7.2.1 Perfect Gas 534

7.2.2 Internal Energy and Enthalpy 534

7.2.3 First Law of Thermodynamics 539

7.2.4 Entropy and the Second Law of

Thermodynamics 540

7.2.5 Isentropic Relations 542

7.3 Definition of Compressibility 546

7.4 Governing Equations for Inviscid,

Compressible Flow 547

7.5 Definition of Total (Stagnation)

Conditions 549

7.6 Some Aspects of Supersonic Flow:

Shock Waves 556

7.7 Summary 560

7.8 Problems 562

Chapter 8

Normal Shock Waves and Related Topics 567

8.1 Introduction 568

8.2 The Basic Normal Shock Equations 569

8.3 Speed of Sound 573

8.4 Special Forms of the Energy Equation 582

8.5 When Is a Flow Compressible? 590

8.6 Calculation of Normal Shock-Wave

Properties 593

8.6.1 Comment on the Use of Tables to Solve

Compressible Flow Problems 608

8.7 Measurement of Velocity in a Compressible

Flow 609

8.7.1 Subsonic Compressible Flow 609

8.7.2 Supersonic Flow 610

8.8 Summary 614

8.9 Problems 617

Chapter 9

Oblique Shock and Expansion Waves 619

9.1 Introduction 620

9.2 Oblique Shock Relations 626

9.3 Supersonic Flow over Wedges and

Cones 640

9.3.1 A Comment on Supersonic Lift and Drag

Coefficients 643

9.4 Shock Interactions and Reflections 644

9.5 Detached Shock Wave in Front of a Blunt

Body 650

9.5.1 Comment on the Flow Field Behind a

and Vorticity 654

9.6 Prandtl-Meyer Expansion Waves 654

9.7 Shock-Expansion Theory: Applications to

Supersonic Airfoils 666

9.8 A Comment on Lift and Drag

Coefficients 670

9.9 The X-15 and Its Wedge Tail 670

9.10 VISCOUS FLOW: Shock-Wave/

Boundary-Layer Interaction 675

9.11 Historical Note: Ernst Mach—A

Biographical Sketch 677

9.12 Summary 680

9.13 Integrated Work Challenge: Relation

Between Supersonic Wave Drag and

Entropy Increase—Is There a Relation? 681

9.14 Integrated Work Challenge: The Sonic

Boom 684

9.15 Problems 687

Chapter 10

Compressible Flow Through Nozzles, Diffusers,

and Wind Tunnels 699

10.1 Introduction 700

10.2 Governing Equations for

Quasi-One-Dimensional Flow 702

10.3 Nozzle Flows 711

10.3.1 More on Mass Flow 725

10.4 Diffusers 726

10.5 Supersonic Wind Tunnels 728

10.6 Viscous Flow: Shock-Wave/

Boundary-Layer Interaction Inside

Nozzles 734

10.7 Summary 736

10.8 Integrated Work Challenge: Conceptual

Design of a Supersonic Wind Tunnel 737

10.9 Problems 746

Chapter 11

Subsonic Compressible Flow over Airfoils:

Linear Theory 751

11.1 Introduction 752

11.2 The Velocity Potential Equation 754

11.3 The Linearized Velocity Potential

Equation 757

11.4 Prandtl-Glauert Compressibility

Correction 762

11.5 Improved Compressibility

Corrections 767

11.6 Critical Mach Number 768

11.6.1 A Comment on the Location of Minimum

Pressure (Maximum Velocity) 777

11.7 Drag-Divergence Mach Number: The

Sound Barrier 777

11.8 The Area Rule 785

11.9 The Supercritical Airfoil 787

11.10 CFD Applications: Transonic Airfoils and

Wings 789

11.11 Applied Aerodynamics: The Blended

Wing Body 794

11.12 Historical Note: High-Speed

Airfoils—Early Research and

Development 800

11.13 Historical Note: The Origin of the

Swept-Wing Concept 804

11.14 Historical Note: Richard T.

Whitcomb—Architect of the Area Rule

and the Supercritical Wing 813

11.15 Summary 814

11.16 Integrated Work Challenge: Transonic

Testing by the Wing-Flow Method 816

11.17 Problems 820

Chapter 12

Linearized Supersonic Flow 823

12.1 Introduction 824

12.2 Derivation of the Linearized Supersonic

Pressure Coefficient Formula 824

12.3 Application to Supersonic Airfoils 828

12.4 Viscous Flow: Supersonic Airfoil

Drag 834

12.5 Summary 837

12.6 Problems 838

Chapter 13

Introduction to Numerical Techniques for

Nonlinear Supersonic Flow 841

13.1 Introduction: Philosophy of Computational

Fluid Dynamics 842

13.2 Elements of the Method of

Characteristics 844

13.2.1 Internal Points 850

13.2.2 Wall Points 851

13.3 Supersonic Nozzle Design 852

13.4 Elements of Finite-Difference

Methods 855

13.4.1 Predictor Step 861

13.4.2 Corrector Step 861

13.5 The Time-Dependent Technique:

Application to Supersonic Blunt

Bodies 862

13.5.1 Predictor Step 866

13.5.2 Corrector Step 866

13.6 Flow over Cones 870

13.6.1 Physical Aspects of Conical Flow 871

13.6.2 Quantitative Formulation 872

13.6.3 Numerical Procedure 877

13.6.4 Physical Aspects of Supersonic Flow over

Cones 878

13.7 Summary 881

13.8 Problem 882

Chapter 14

Elements of Hypersonic Flow 883

14.1 Introduction 884

14.2 Qualitative Aspects of Hypersonic

Flow 885

14.3 Newtonian Theory 889

14.4 The Lift and Drag of Wings at Hypersonic

Speeds: Newtonian Results for a Flat Plate

at Angle of Attack 893

14.4.1 Accuracy Considerations 900

14.5 Hypersonic Shock-Wave Relations and

Another Look at Newtonian Theory 904

14.6 Mach Number Independence 908

14.7 Hypersonics and Computational Fluid

Dynamics 910

14.8 Hypersonic Viscous Flow: Aerodynamic

Heating 913

14.8.1 Aerodynamic Heating and Hypersonic

Flow—The Connection 913

14.8.2 Blunt Versus Slender Bodies in

Hypersonic Flow 915

14.8.3 Aerodynamic Heating to a Blunt

Body 918

14.9 Applied Hypersonic Aerodynamics:

Hypersonic Waveriders 920

14.9.1 Viscous-Optimized Waveriders 926

14.10 Summary 933

14.11 Problems 934

PART 4

Viscous Flow 935

Chapter 15

Introduction to the Fundamental Principles

and Equations of Viscous Flow 937

15.1 Introduction 938

15.2 Qualitative Aspects of Viscous Flow 939

15.3 Viscosity and Thermal Conduction 947

15.4 The Navier-Stokes Equations 952

15.5 The Viscous Flow Energy Equation 956

15.6 Similarity Parameters 960

15.7 Solutions of Viscous Flows: A Preliminary

Discussion 964

15.8 Summary 967

15.9 Problems 969

Chapter 16

A Special Case: Couette Flow 971

16.1 Introduction 971

16.2 Couette Flow: General Discussion 972

16.3 Incompressible (Constant Property) Couette

Flow 976

16.3.1 Negligible Viscous Dissipation 982

16.3.2 Equal Wall Temperatures 983

Wall Temperature) 985

16.3.4 Recovery Factor 988

16.3.5 Reynolds Analogy 989

16.3.6 Interim Summary 990

16.4 Compressible Couette Flow 992

16.4.1 Shooting Method 994

16.4.2 Time-Dependent Finite-Difference

Method 996

16.4.3 Results for Compressible Couette

Flow 1000

16.4.4 Some Analytical Considerations 1002

16.5 Summary 1007

Chapter 17

Introduction to Boundary Layers 1009

17.1 Introduction 1010

17.2 Boundary-Layer Properties 1012

17.3 The Boundary-Layer Equations 1018

17.4 How Do We Solve the Boundary-Layer

Equations? 1021

17.5 Summary 1023

Chapter 18

Laminar Boundary Layers 1025

18.1 Introduction 1025

18.2 Incompressible Flow over a Flat Plate: The

Blasius Solution 1026

18.3 Compressible Flow over a Flat Plate 1033

18.3.1 A Comment on Drag Variation with

Velocity 1044

18.4 The Reference Temperature Method 1045

Reference Temperature Method 1048

18.5 Stagnation Point Aerodynamic

Heating 1049

18.6 Boundary Layers over Arbitrary Bodies:

Finite-Difference Solution 1055

18.6.1 Finite-Difference Method 1056

18.7 Summary 1061

18.8 Problems 1062

Chapter 19

Turbulent Boundary Layers 1063

19.1 Introduction 1064

19.2 Results for Turbulent Boundary Layers

on a Flat Plate 1064

19.2.1 Reference Temperature Method for

Turbulent Flow 1066

Temperature Method for Turbulent

Flow 1068

19.2.3 Prediction of Airfoil Drag 1069

19.3 Turbulence Modeling 1069

19.3.1 The Baldwin-Lomax Model 1070

19.5 Summary 1073

19.6 Problems 1074

Chapter 20

Navier-Stokes Solutions:

Some Examples 1075

20.1 Introduction 1076

20.2 The Approach 1076

20.3 Examples of Some Solutions 1077

20.3.1 Flow over a Rearward-Facing Step 1077

20.3.2 Flow over an Airfoil 1077

20.3.3 Flow over a Complete Airplane 1080

20.3.4 Shock-Wave/Boundary-Layer

Interaction 1081

20.3.5 Flow over an Airfoil with a

Protuberance 1082

20.4 The Issue of Accuracy for the Prediction of

Skin Friction Drag 1084

20.5 Summary 1089

Appendix A

Isentropic Flow Properties 1091

Appendix B

Normal Shock Properties 1097

Appendix C

Prandtl-Meyer Function and Mach

Angle 1101

Appendix D

Standard Atmosphere,

SI Units 1105

Appendix E

Standard Atmosphere, English Engineering

Units 1115

References 1123

Index 1129

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