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by Robert D. Zucker and Oscar Biblarz

Edition: 2ND 02Copyright: 2002

Publisher: John Wiley & Sons, Inc.

Published: 2002

International: No

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The primary aspects of gas dynamics, meticulously covered and easy to understand

Fundamentals of Gas Dynamics provides the essential applications and problem-solving techniques used in gas dynamics. Written in an accessible but rigorous style, this book includes all the equations, tables, and charts necessary to approach the problems and exercises in each chapter. Temperature-entropy diagrams and the role of entropy are highlighted throughout to make this elusive property more understandable and useful.

New to this Second Edition is a chapter covering real gas behavior. The information in this chapter provides a valuable bridge between the conventional types of lower-temperature applications and propulsion applications, both covered elsewhere in this book. Included in this new chapter on real gas behavior is a simplified technique for solving problems where the ratio of the heat capacities varies appreciably, as well as discussions and examples comparing this technique to more exact methods.

Unique coverage also includes:

- Updated information on propulsion applications and new engine photographs
- Key parameter variations plotted as a function of Mach number
- Updated material and appendixes on conical shocks
- Appendixes containing information to treat air as a real gas
- Enhanced gas property tabular entries that are given in both English Engineering and SI units
- Alternatives to using tabular information in calculations

Fundamentals of Gas Dynamics, Second Edition is an indispensable book for students in mechanical, aerospace, and chemical engineering courses, as well as aerospace engineers.

**Zucker, Robert D. : Naval Postgraduate School in Monterey**

Robert D. Zucker, PhD, is Professor Emeritus of Aeronautics and Astronautics at the Naval Postgraduate School in Monterey, California.

**Biblarz, Oscar : Naval Postgraduate School in Monterey**

Oscar Biblarz, PhD, is Professor of Aeronautics and Astronautics at the Naval Postgraduate School in Monterey, California. He is coauthor (with George Sutton) of Rocket Propulsion Elements, published by Wiley.

PREFACE.

TO THE STUDENT.

1. REVIEW OF ELEMENTARY PRINCIPLES.

1.1 Introduction.

1.2 Units and Notation.

1.3 Some Mathematical Concepts.

1.4 Thermodynamic Concepts for Control Mass Analysis.

Review Questions.

Review Problems.

2. CONTROLVOLUME ANALYSIS-PART I.

2.1 Introduction.

2.2 Objectives.

2.3 Flow Dimensionality and Average Velocity.

2.4 Transformation of a Material Derivative to a Control Volume Approach.

2.5 Conservation of Mass.

2.6 Conservation of Energy.

2.7 Summary.

Problems.

Check Test.

3. CONTR OLVOLUME ANALYSIS-PART II.

3.1 Introduction.

3.2 Objectives.

3.3 Comments on Entropy.

3.4 Pressure-Energy Equation.

3.5 The Stagnation Concept.

3.6 Stagnation Pressure-Energy Equation.

3.7 Consequences of Constant Density.

3.8 Momentum Equation.

3.9 Summary.

Problems.

Check Test.

4. INTRODUCTIONTO COMPRESSIBLE FLOW.

4.1 Introduction.

4.2 Objectives.

4.3 Sonic Velocity and Mach Number.

4.4 Wave Propagation.

4.5 Equations for Perfect Gases in Terms of Mach Number.

4.6 h-s and T-s Diagrams.

4.7 Summary.

Problems.

Check Test.

5. VARYING-AREA ADIABATIC FLOW.

5.1 Introduction.

5.2 Objectives.

5.3 General Fluid-No Losses.

5.4 Perfect Gases with Losses.

5.5 The * Reference Concept.

5.6 Isentropic Table.

5.7 Nozzle Operation.

5.8 Nozzle Performance.

5.9 Diffuser Performance.

5.10 When ? Is Not Equal to 1.4.

5.11 (Optional) Beyond the Tables.

5.12 Summary.

Problems.

Check Test.

6. STANDING NORMAL SHOCKS.

6.1 Introduction.

6.2 Objectives.

6.3 Shock Analysis-General Fluid.

6.4 Working Equations for Perfect Gases.

6.5 Normal-Shock Table.

6.6 Shocks in Nozzles.

6.7 Supersonic Wind Tunnel Operation.

6.8 When ? Is Not Equal to 1.4.

6.9 (Optional) Beyond the Tables.

6.10 Summary.

Problems.

Check Test.

7. MOVING AND OBLIQUE SHOCKS.

7.1 Introduction.

7.2 Objectives.

7.3 Normal Velocity Superposition: Moving Normal Shocks.

7.4 Tangential Velocity Superposition: Oblique Shocks.

7.5 Oblique-Shock Analysis: Perfect Gas.

7.6 Oblique-Shock Table and Charts.

7.7 Boundary Condition of Flow Direction.

7.8 Boundary Condition of Pressure Equilibrium.

7.9 Conical Shocks.

7.10 (Optional) Beyond the Tables.

7.11 Summary.

Problems.

Check Test.

8 PRANDTL-MEYER FLOW.

8.1 Introduction.

8.2 Objectives.

8.3 Argument for Isentropic Turning Flow.

8.4 Analysis of Prandtl-Meyer Flow.

8.5 Prandtl-Meyer Function.

8.6 Overexpanded and Underexpanded Nozzles.

8.7 Supersonic Airfoils.

8.8 When ? Is Not Equal to 1.4.

8.9 (Optional) Beyond the Tables.

8.10 Summary.

Problems.

Check Test.

9. FANNO FLOW.

9.1 Introduction.

9.2 Objectives.

9.3 Analysis for a General Fluid.

9.4 Working Equations for Perfect Gases.

9.5 Reference State and Fanno Table.

9.6 Applications.

9.7 Correlation with Shocks.

9.8 Friction Choking.

9.9 When ? Is Not Equal to 1.4.

9.10 (Optional) Beyond the Tables.

9.11 Summary.

Problems.

Check Test.

10. RAYLEIGH FLOW.

10.1 Introduction.

10.2 Objectives.

10.3 Analysis for a General Fluid.

10.4 Working Equations for Perfect Gases.

10.5 Reference State and the Rayleigh Table.

10.6 Applications.

10.7 Correlation with Shocks.

10.8 Thermal Choking due to Heating.

10.9 When ? Is Not Equal to 1.4.

10.10 (Optional) Beyond the Tables.

10.11 Summary.

Problems.

Check Test.

11. REAL GAS EFFECTS.

11.1 Introduction.

11.2 Objectives.

11.3 What's Really Going On.

11.4 Semiperfect Gas Behavior, Development of the Gas Table.

11.5 Real Gas Behavior: Equations of State and Compressibility Factors.

11.6 Variable ?-Variable Area Flows.

11.7 Variable ?-Constant Area Flows.

11.8 Summary.

Problems.

Check Test.

12. PROPULSION SYSTEMS.

12.1 Introduction.

12.2 Objectives.

12.3 Brayton Cycle.

12.4 Propulsion Engines.

12.5 General Performance Parameters, Thrust, Power, and Efficiency.

12.6 Air-Breathing Propulsion Systems Performance Parameters.

12.7 Air-Breathing Propulsion Systems Incorporating Real Gas Effects.

12.8 Rocket Propulsion Systems Performance Parameters.

12.9 Supersonic Diffusers.

12.10 Summary.

Problems.

Check Test.

APPENDIXES.

A. Summary of the English Engineering (EE) System of Units.

B. Summary of the International System (SI) of Units.

C. Friction-Factor Chart.

D. Oblique-Shock Charts (? = 1.4) (Two-Dimensional).

E. Conical-Shock Charts (? = 1.4) (Three-Dimensional).

F. Generalized Compressibility Factor Chart.

G. Isentropic Flow Parameters (? = 1.4) (including Prandtl-Meyer Function).

H. Normal-Shock Parameters (? = 1.4).

I. Fanno Flow Parameters (? = 1.4).

J. Rayleigh Flow Parameters (? = 1.4).

K. Properties of Air at Low Pressures.

L. Specific Heats of Air at Low Pressures.

SELECTED REFERENCES.

ANSWERSTO PROBLEMS.

INDEX.

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Summary

The primary aspects of gas dynamics, meticulously covered and easy to understand

Fundamentals of Gas Dynamics provides the essential applications and problem-solving techniques used in gas dynamics. Written in an accessible but rigorous style, this book includes all the equations, tables, and charts necessary to approach the problems and exercises in each chapter. Temperature-entropy diagrams and the role of entropy are highlighted throughout to make this elusive property more understandable and useful.

New to this Second Edition is a chapter covering real gas behavior. The information in this chapter provides a valuable bridge between the conventional types of lower-temperature applications and propulsion applications, both covered elsewhere in this book. Included in this new chapter on real gas behavior is a simplified technique for solving problems where the ratio of the heat capacities varies appreciably, as well as discussions and examples comparing this technique to more exact methods.

Unique coverage also includes:

- Updated information on propulsion applications and new engine photographs
- Key parameter variations plotted as a function of Mach number
- Updated material and appendixes on conical shocks
- Appendixes containing information to treat air as a real gas
- Enhanced gas property tabular entries that are given in both English Engineering and SI units
- Alternatives to using tabular information in calculations

Fundamentals of Gas Dynamics, Second Edition is an indispensable book for students in mechanical, aerospace, and chemical engineering courses, as well as aerospace engineers.

Author Bio

**Zucker, Robert D. : Naval Postgraduate School in Monterey**

Robert D. Zucker, PhD, is Professor Emeritus of Aeronautics and Astronautics at the Naval Postgraduate School in Monterey, California.

**Biblarz, Oscar : Naval Postgraduate School in Monterey**

Oscar Biblarz, PhD, is Professor of Aeronautics and Astronautics at the Naval Postgraduate School in Monterey, California. He is coauthor (with George Sutton) of Rocket Propulsion Elements, published by Wiley.

Table of Contents

PREFACE.

TO THE STUDENT.

1. REVIEW OF ELEMENTARY PRINCIPLES.

1.1 Introduction.

1.2 Units and Notation.

1.3 Some Mathematical Concepts.

1.4 Thermodynamic Concepts for Control Mass Analysis.

Review Questions.

Review Problems.

2. CONTROLVOLUME ANALYSIS-PART I.

2.1 Introduction.

2.2 Objectives.

2.3 Flow Dimensionality and Average Velocity.

2.4 Transformation of a Material Derivative to a Control Volume Approach.

2.5 Conservation of Mass.

2.6 Conservation of Energy.

2.7 Summary.

Problems.

Check Test.

3. CONTR OLVOLUME ANALYSIS-PART II.

3.1 Introduction.

3.2 Objectives.

3.3 Comments on Entropy.

3.4 Pressure-Energy Equation.

3.5 The Stagnation Concept.

3.6 Stagnation Pressure-Energy Equation.

3.7 Consequences of Constant Density.

3.8 Momentum Equation.

3.9 Summary.

Problems.

Check Test.

4. INTRODUCTIONTO COMPRESSIBLE FLOW.

4.1 Introduction.

4.2 Objectives.

4.3 Sonic Velocity and Mach Number.

4.4 Wave Propagation.

4.5 Equations for Perfect Gases in Terms of Mach Number.

4.6 h-s and T-s Diagrams.

4.7 Summary.

Problems.

Check Test.

5. VARYING-AREA ADIABATIC FLOW.

5.1 Introduction.

5.2 Objectives.

5.3 General Fluid-No Losses.

5.4 Perfect Gases with Losses.

5.5 The * Reference Concept.

5.6 Isentropic Table.

5.7 Nozzle Operation.

5.8 Nozzle Performance.

5.9 Diffuser Performance.

5.10 When ? Is Not Equal to 1.4.

5.11 (Optional) Beyond the Tables.

5.12 Summary.

Problems.

Check Test.

6. STANDING NORMAL SHOCKS.

6.1 Introduction.

6.2 Objectives.

6.3 Shock Analysis-General Fluid.

6.4 Working Equations for Perfect Gases.

6.5 Normal-Shock Table.

6.6 Shocks in Nozzles.

6.7 Supersonic Wind Tunnel Operation.

6.8 When ? Is Not Equal to 1.4.

6.9 (Optional) Beyond the Tables.

6.10 Summary.

Problems.

Check Test.

7. MOVING AND OBLIQUE SHOCKS.

7.1 Introduction.

7.2 Objectives.

7.3 Normal Velocity Superposition: Moving Normal Shocks.

7.4 Tangential Velocity Superposition: Oblique Shocks.

7.5 Oblique-Shock Analysis: Perfect Gas.

7.6 Oblique-Shock Table and Charts.

7.7 Boundary Condition of Flow Direction.

7.8 Boundary Condition of Pressure Equilibrium.

7.9 Conical Shocks.

7.10 (Optional) Beyond the Tables.

7.11 Summary.

Problems.

Check Test.

8 PRANDTL-MEYER FLOW.

8.1 Introduction.

8.2 Objectives.

8.3 Argument for Isentropic Turning Flow.

8.4 Analysis of Prandtl-Meyer Flow.

8.5 Prandtl-Meyer Function.

8.6 Overexpanded and Underexpanded Nozzles.

8.7 Supersonic Airfoils.

8.8 When ? Is Not Equal to 1.4.

8.9 (Optional) Beyond the Tables.

8.10 Summary.

Problems.

Check Test.

9. FANNO FLOW.

9.1 Introduction.

9.2 Objectives.

9.3 Analysis for a General Fluid.

9.4 Working Equations for Perfect Gases.

9.5 Reference State and Fanno Table.

9.6 Applications.

9.7 Correlation with Shocks.

9.8 Friction Choking.

9.9 When ? Is Not Equal to 1.4.

9.10 (Optional) Beyond the Tables.

9.11 Summary.

Problems.

Check Test.

10. RAYLEIGH FLOW.

10.1 Introduction.

10.2 Objectives.

10.3 Analysis for a General Fluid.

10.4 Working Equations for Perfect Gases.

10.5 Reference State and the Rayleigh Table.

10.6 Applications.

10.7 Correlation with Shocks.

10.8 Thermal Choking due to Heating.

10.9 When ? Is Not Equal to 1.4.

10.10 (Optional) Beyond the Tables.

10.11 Summary.

Problems.

Check Test.

11. REAL GAS EFFECTS.

11.1 Introduction.

11.2 Objectives.

11.3 What's Really Going On.

11.4 Semiperfect Gas Behavior, Development of the Gas Table.

11.5 Real Gas Behavior: Equations of State and Compressibility Factors.

11.6 Variable ?-Variable Area Flows.

11.7 Variable ?-Constant Area Flows.

11.8 Summary.

Problems.

Check Test.

12. PROPULSION SYSTEMS.

12.1 Introduction.

12.2 Objectives.

12.3 Brayton Cycle.

12.4 Propulsion Engines.

12.5 General Performance Parameters, Thrust, Power, and Efficiency.

12.6 Air-Breathing Propulsion Systems Performance Parameters.

12.7 Air-Breathing Propulsion Systems Incorporating Real Gas Effects.

12.8 Rocket Propulsion Systems Performance Parameters.

12.9 Supersonic Diffusers.

12.10 Summary.

Problems.

Check Test.

APPENDIXES.

A. Summary of the English Engineering (EE) System of Units.

B. Summary of the International System (SI) of Units.

C. Friction-Factor Chart.

D. Oblique-Shock Charts (? = 1.4) (Two-Dimensional).

E. Conical-Shock Charts (? = 1.4) (Three-Dimensional).

F. Generalized Compressibility Factor Chart.

G. Isentropic Flow Parameters (? = 1.4) (including Prandtl-Meyer Function).

H. Normal-Shock Parameters (? = 1.4).

I. Fanno Flow Parameters (? = 1.4).

J. Rayleigh Flow Parameters (? = 1.4).

K. Properties of Air at Low Pressures.

L. Specific Heats of Air at Low Pressures.

SELECTED REFERENCES.

ANSWERSTO PROBLEMS.

INDEX.

Publisher Info

Publisher: John Wiley & Sons, Inc.

Published: 2002

International: No

Published: 2002

International: No

The primary aspects of gas dynamics, meticulously covered and easy to understand

Fundamentals of Gas Dynamics provides the essential applications and problem-solving techniques used in gas dynamics. Written in an accessible but rigorous style, this book includes all the equations, tables, and charts necessary to approach the problems and exercises in each chapter. Temperature-entropy diagrams and the role of entropy are highlighted throughout to make this elusive property more understandable and useful.

New to this Second Edition is a chapter covering real gas behavior. The information in this chapter provides a valuable bridge between the conventional types of lower-temperature applications and propulsion applications, both covered elsewhere in this book. Included in this new chapter on real gas behavior is a simplified technique for solving problems where the ratio of the heat capacities varies appreciably, as well as discussions and examples comparing this technique to more exact methods.

Unique coverage also includes:

- Updated information on propulsion applications and new engine photographs
- Key parameter variations plotted as a function of Mach number
- Updated material and appendixes on conical shocks
- Appendixes containing information to treat air as a real gas
- Enhanced gas property tabular entries that are given in both English Engineering and SI units
- Alternatives to using tabular information in calculations

Fundamentals of Gas Dynamics, Second Edition is an indispensable book for students in mechanical, aerospace, and chemical engineering courses, as well as aerospace engineers.

**Zucker, Robert D. : Naval Postgraduate School in Monterey**

Robert D. Zucker, PhD, is Professor Emeritus of Aeronautics and Astronautics at the Naval Postgraduate School in Monterey, California.

**Biblarz, Oscar : Naval Postgraduate School in Monterey**

Oscar Biblarz, PhD, is Professor of Aeronautics and Astronautics at the Naval Postgraduate School in Monterey, California. He is coauthor (with George Sutton) of Rocket Propulsion Elements, published by Wiley.

TO THE STUDENT.

1. REVIEW OF ELEMENTARY PRINCIPLES.

1.1 Introduction.

1.2 Units and Notation.

1.3 Some Mathematical Concepts.

1.4 Thermodynamic Concepts for Control Mass Analysis.

Review Questions.

Review Problems.

2. CONTROLVOLUME ANALYSIS-PART I.

2.1 Introduction.

2.2 Objectives.

2.3 Flow Dimensionality and Average Velocity.

2.4 Transformation of a Material Derivative to a Control Volume Approach.

2.5 Conservation of Mass.

2.6 Conservation of Energy.

2.7 Summary.

Problems.

Check Test.

3. CONTR OLVOLUME ANALYSIS-PART II.

3.1 Introduction.

3.2 Objectives.

3.3 Comments on Entropy.

3.4 Pressure-Energy Equation.

3.5 The Stagnation Concept.

3.6 Stagnation Pressure-Energy Equation.

3.7 Consequences of Constant Density.

3.8 Momentum Equation.

3.9 Summary.

Problems.

Check Test.

4. INTRODUCTIONTO COMPRESSIBLE FLOW.

4.1 Introduction.

4.2 Objectives.

4.3 Sonic Velocity and Mach Number.

4.4 Wave Propagation.

4.5 Equations for Perfect Gases in Terms of Mach Number.

4.6 h-s and T-s Diagrams.

4.7 Summary.

Problems.

Check Test.

5. VARYING-AREA ADIABATIC FLOW.

5.1 Introduction.

5.2 Objectives.

5.3 General Fluid-No Losses.

5.4 Perfect Gases with Losses.

5.5 The * Reference Concept.

5.6 Isentropic Table.

5.7 Nozzle Operation.

5.8 Nozzle Performance.

5.9 Diffuser Performance.

5.10 When ? Is Not Equal to 1.4.

5.11 (Optional) Beyond the Tables.

5.12 Summary.

Problems.

Check Test.

6. STANDING NORMAL SHOCKS.

6.1 Introduction.

6.2 Objectives.

6.3 Shock Analysis-General Fluid.

6.4 Working Equations for Perfect Gases.

6.5 Normal-Shock Table.

6.6 Shocks in Nozzles.

6.7 Supersonic Wind Tunnel Operation.

6.8 When ? Is Not Equal to 1.4.

6.9 (Optional) Beyond the Tables.

6.10 Summary.

Problems.

Check Test.

7. MOVING AND OBLIQUE SHOCKS.

7.1 Introduction.

7.2 Objectives.

7.3 Normal Velocity Superposition: Moving Normal Shocks.

7.4 Tangential Velocity Superposition: Oblique Shocks.

7.5 Oblique-Shock Analysis: Perfect Gas.

7.6 Oblique-Shock Table and Charts.

7.7 Boundary Condition of Flow Direction.

7.8 Boundary Condition of Pressure Equilibrium.

7.9 Conical Shocks.

7.10 (Optional) Beyond the Tables.

7.11 Summary.

Problems.

Check Test.

8 PRANDTL-MEYER FLOW.

8.1 Introduction.

8.2 Objectives.

8.3 Argument for Isentropic Turning Flow.

8.4 Analysis of Prandtl-Meyer Flow.

8.5 Prandtl-Meyer Function.

8.6 Overexpanded and Underexpanded Nozzles.

8.7 Supersonic Airfoils.

8.8 When ? Is Not Equal to 1.4.

8.9 (Optional) Beyond the Tables.

8.10 Summary.

Problems.

Check Test.

9. FANNO FLOW.

9.1 Introduction.

9.2 Objectives.

9.3 Analysis for a General Fluid.

9.4 Working Equations for Perfect Gases.

9.5 Reference State and Fanno Table.

9.6 Applications.

9.7 Correlation with Shocks.

9.8 Friction Choking.

9.9 When ? Is Not Equal to 1.4.

9.10 (Optional) Beyond the Tables.

9.11 Summary.

Problems.

Check Test.

10. RAYLEIGH FLOW.

10.1 Introduction.

10.2 Objectives.

10.3 Analysis for a General Fluid.

10.4 Working Equations for Perfect Gases.

10.5 Reference State and the Rayleigh Table.

10.6 Applications.

10.7 Correlation with Shocks.

10.8 Thermal Choking due to Heating.

10.9 When ? Is Not Equal to 1.4.

10.10 (Optional) Beyond the Tables.

10.11 Summary.

Problems.

Check Test.

11. REAL GAS EFFECTS.

11.1 Introduction.

11.2 Objectives.

11.3 What's Really Going On.

11.4 Semiperfect Gas Behavior, Development of the Gas Table.

11.5 Real Gas Behavior: Equations of State and Compressibility Factors.

11.6 Variable ?-Variable Area Flows.

11.7 Variable ?-Constant Area Flows.

11.8 Summary.

Problems.

Check Test.

12. PROPULSION SYSTEMS.

12.1 Introduction.

12.2 Objectives.

12.3 Brayton Cycle.

12.4 Propulsion Engines.

12.5 General Performance Parameters, Thrust, Power, and Efficiency.

12.6 Air-Breathing Propulsion Systems Performance Parameters.

12.7 Air-Breathing Propulsion Systems Incorporating Real Gas Effects.

12.8 Rocket Propulsion Systems Performance Parameters.

12.9 Supersonic Diffusers.

12.10 Summary.

Problems.

Check Test.

APPENDIXES.

A. Summary of the English Engineering (EE) System of Units.

B. Summary of the International System (SI) of Units.

C. Friction-Factor Chart.

D. Oblique-Shock Charts (? = 1.4) (Two-Dimensional).

E. Conical-Shock Charts (? = 1.4) (Three-Dimensional).

F. Generalized Compressibility Factor Chart.

G. Isentropic Flow Parameters (? = 1.4) (including Prandtl-Meyer Function).

H. Normal-Shock Parameters (? = 1.4).

I. Fanno Flow Parameters (? = 1.4).

J. Rayleigh Flow Parameters (? = 1.4).

K. Properties of Air at Low Pressures.

L. Specific Heats of Air at Low Pressures.

SELECTED REFERENCES.

ANSWERSTO PROBLEMS.

INDEX.