introduction to fluid mechanics chapter 13 compressible...

© Fox, Pritchard, & McDonald

Introduction to Fluid Mechanics

Chapter 13

Compressible Flow


Main Topics

�Basic Equations for One-Dimensional Compressible Flow

� Isentropic Flow of an Ideal Gas – Area Variation

�Flow in a Constant Area Duct with Friction

�Frictionless Flow in a Constant-Area Duct with Heat Exchange

�Normal Shocks

�Supersonic Channel Flow with Shocks

�Oblique Shocks and Expansion Waves


Basic Equations for

One-Dimensional Compressible Flow

�Control Volume


Basic Equations for


�Continuity

�Momentum


Basic Equations for


�Second Law of Thermodynamics

�First Law of Thermodynamics


Basic Equations for


�Property Relations

�Equation of State


Isentropic Flow of an Ideal Gas

– Area Variation

�Basic Equations for Isentropic Flow



– Area Variation

�Isentropic Flow



– Area Variation

�Subsonic, Supersonic, and Sonic Flows



– Area Variation

�Reference Stagnation and Critical Conditions for Isentropic Flow



– Area Variation

�Property Relations



– Area Variation

�Isentropic Flow in a Converging Nozzle



– Area Variation

�Isentropic Flow in a Converging-Diverging Nozzle


Flow in a Constant-Area Duct

with Friction

�Control Volume



with Friction �Basic Equations for Adiabatic Flow



with Friction

�Adiabatic Flow: The Fanno Line



with Friction �Fanno-Line Flow Functions for One-Dimensional Flow of an Ideal Gas



with Friction �Fanno-Line Relations



with Friction

�Fanno-Line Relations (Continued)


Frictionless Flow in a Constant-

Area Duct with Heat Exchange

�Control Volume




�Basic Equations for Flow with Heat Exchange




�Heat Exchange: The Rayleigh Line



Area Duct with Heat Exchange �Rayleigh-Line Relations


Normal Shocks

�Control Volume


Normal Shocks

�Basic Equations for a Normal Shock


Normal Shocks

� Intersection of Fanno & Rayleigh Lines


Normal Shocks

�Normal Shock Relations


Normal Shocks

�Normal Shock Relations (Continued)


Supersonic Channel Flow

with Shocks

�Flow in a Converging-Diverging Nozzle


Oblique Shocks and

Expansion Waves

�Typical Application


Oblique Shocks and

Expansion Waves

�Mach Angle and Oblique Shock Angle


Oblique Shocks and

Expansion Waves

�Oblique Shock: Control Volume


Oblique Shocks and

Expansion Waves

�Oblique Shock: Useful Formulas


Oblique Shocks and

Expansion Waves

�Oblique Shock Relations


Oblique Shocks and

Expansion Waves

�Oblique Shock Relations (Continued)


Oblique Shocks and

Expansion Waves

�Oblique Shock: Deflection Angle


Oblique Shocks and

Expansion Waves

�Expansion and Compression Waves


Oblique Shocks and

Expansion Waves

�Expansion Wave: Control Volume


Oblique Shocks and

Expansion Waves

�Expansion Wave: Prandtl-Meyer Expansion Function


Oblique Shocks and

Expansion Waves

�Expansion Wave: Isentropic Relations

introduction to fluid mechanics chapter 13 compressible...

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