1. Introduction to Fluid Mechanics
Chapter 12
Introduction to Compressible Flow

2. Main Topics Review of Thermodynamics Propagation of Sound Waves
Reference State: Local Isentropic Stagnation Conditions
Critical Conditions
Basic Equations for One-Dimensional Compressible Flow
Isentropic Flow of an Ideal Gas: Area Variation
Normal Shocks
Supersonic Channel Flow with Shocks
Flow in a Constant-Area Duct with Friction
Frictionless Flow in a Constant-Area Duct with Heat Exchange
Oblique Shocks and Expansion Waves

3. Review of Thermodynamics
Ideal Gas

4. Review of Thermodynamics
Specific Heat Formulas

5. Review of Thermodynamics
Internal Energy and Enthalpy

6. Review of Thermodynamics
Entropy

7. Review of Thermodynamics
The Second Law of Thermodynamics

8. Review of Thermodynamics
Isentropic (Reversible Adiabatic) Processes

9. Propagation of Sound Waves

10. Propagation of Sound Waves
Speed of Sound
Solids and Liquids:
Ideal Gas:

11. Propagation of Sound Waves
Types of Flow – The Mach Cone

12. Propagation of Sound Waves
Types of Flow – The Mach Cone (Continued)
Mach Angle:

13. Reference State: Local Isentropic Stagnation Conditions

14. Reference State: Local Isentropic Stagnation Conditions
Computing Equations

15. Critical Conditions
A useful reference value for velocity is the critical speed —the speed V we attain when a flow is either accelerated or decelerated (actually or conceptually) isentropically until we reach M=1.

16. Basic Equations for One-Dimensional Compressible Flow
Control Volume
Steady flow.
One-dimensional flow.

17. Basic Equations for One-Dimensional Compressible Flow
Continuity
Momentum
Assumption: FBx =0

18. Basic Equations for One-Dimensional Compressible Flow
First Law of Thermodynamics
Ws =0
Wshear =Wother =0
Effects of gravity are negligible
Second Law of Thermodynamics

19. Basic Equations for One-Dimensional Compressible Flow
Equation of State
Property Relations

20. Isentropic Flow of an Ideal Gas: Area Variation
Basic Equations for Isentropic Flow

21. Isentropic Flow of an Ideal Gas: Area Variation

22. Isentropic Flow of an Ideal Gas: Area Variation
Subsonic, Supersonic, and Sonic Flows

23. Isentropic Flow of an Ideal Gas: Area Variation
Reference Stagnation and Critical Conditions for Isentropic Flow

24. Isentropic Flow of an Ideal Gas: Area Variation
Property Relations

25. Isentropic Flow of an Ideal Gas: Area Variation
A/A*

26. Isentropic Flow of an Ideal Gas: Area Variation
Isentropic Flow in a Converging Nozzle

27. Isentropic Flow of an Ideal Gas: Area Variation
Isentropic Flow in a Converging Nozzle

28. Isentropic Flow of an Ideal Gas: Area Variation
Isentropic Flow in a Converging-Diverging Nozzle

29. Isentropic Flow of an Ideal Gas: Area Variation
Isentropic Flow in a Converging-Diverging Nozzle

30. Normal Shocks
Control Volume

31. Normal Shocks
Basic Equations for a Normal Shock

32. Normal Shocks
Normal Shock Relations

33. Normal Shocks
Normal Shock Relations (Continued)

34. Supersonic Channel Flow with Shocks
Flow in a Converging-Diverging Nozzle

35. Flow in a Constant-Area Duct with Friction
Control Volume

36. Flow in a Constant-Area Duct with Friction
Basic Equations for Adiabatic Flow

37. Flow in a Constant-Area Duct with Friction
Adiabatic Flow: The Fanno Line

38. Flow in a Constant-Area Duct with Friction
Fanno-Line Flow Functions for One-Dimensional Flow of an Ideal Gas

39. Flow in a Constant-Area Duct with Friction
Fanno-Line Relations

40. Flow in a Constant-Area Duct with Friction
Fanno-Line Relations (Continued)

41. Frictionless Flow in a Constant-Area Duct with Heat Exchange
Control Volume

42. Frictionless Flow in a Constant-Area Duct with Heat Exchange
Basic Equations for Flow with Heat Exchange

43. Frictionless Flow in a Constant-Area Duct with Heat Exchange
Heat Exchange: The Rayleigh Line

44. Frictionless Flow in a Constant-Area Duct with Heat Exchange
Rayleigh-Line Relations

45. Normal Shocks
Fanno and Rayleigh Interpretation

46. Oblique Shocks and Expansion Waves
Mach Angle and Oblique Shock Angle

47. Oblique Shocks and Expansion Waves
Oblique Shock: Control Volume

48. Oblique Shocks and Expansion Waves
Oblique Shock: Useful Formulas
Steady flow
Negligible body forces
Adiabatic flow
No work terms
Negligible gravitational effect

49. Oblique Shocks and Expansion Waves
Oblique Shock Relations

50. Oblique Shocks and Expansion Waves
Oblique Shock Relations (Continued)

51. Oblique Shocks and Expansion Waves
Oblique Shock: Deflection Angle

52. Oblique Shocks and Expansion Waves
Oblique Shock: Deflection Angle

53. Oblique Shocks and Expansion Waves
Expansion and Compression Waves

54. Oblique Shocks and Expansion Waves
Expansion Wave: Control Volume

55. Oblique Shocks and Expansion Waves
Expansion Wave: Prandtl-Meyer Expansion Function

56. Oblique Shocks and Expansion Waves
Expansion Wave: Isentropic Relations