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Introduction to Fluid Mechanics
Chapter 13
Compressible Flow
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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
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Basic Equations for
One-Dimensional Compressible Flow
�Control Volume
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Basic Equations for
One-Dimensional Compressible Flow
�Continuity
�Momentum
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Basic Equations for
One-Dimensional Compressible Flow
�Second Law of Thermodynamics
�First Law of Thermodynamics
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Basic Equations for
One-Dimensional Compressible Flow
�Property Relations
�Equation of State
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Isentropic Flow of an Ideal Gas
– Area Variation
�Basic Equations for Isentropic Flow
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Isentropic Flow of an Ideal Gas
– Area Variation
�Isentropic Flow
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Isentropic Flow of an Ideal Gas
– Area Variation
�Subsonic, Supersonic, and Sonic Flows
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Isentropic Flow of an Ideal Gas
– Area Variation
�Reference Stagnation and Critical Conditions for Isentropic Flow
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Isentropic Flow of an Ideal Gas
– Area Variation
�Property Relations
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Isentropic Flow of an Ideal Gas
– Area Variation
�Isentropic Flow in a Converging Nozzle
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Isentropic Flow of an Ideal Gas
– Area Variation
�Isentropic Flow in a Converging Nozzle
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Isentropic Flow of an Ideal Gas
– Area Variation
�Isentropic Flow in a Converging-Diverging Nozzle
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Isentropic Flow of an Ideal Gas
– Area Variation
�Isentropic Flow in a Converging-Diverging Nozzle
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Flow in a Constant-Area Duct
with Friction
�Control Volume
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Flow in a Constant-Area Duct
with Friction �Basic Equations for Adiabatic Flow
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Flow in a Constant-Area Duct
with Friction
�Adiabatic Flow: The Fanno Line
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Flow in a Constant-Area Duct
with Friction �Fanno-Line Flow Functions for One-Dimensional Flow of an Ideal Gas
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Flow in a Constant-Area Duct
with Friction �Fanno-Line Relations
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Flow in a Constant-Area Duct
with Friction
�Fanno-Line Relations (Continued)
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Frictionless Flow in a Constant-
Area Duct with Heat Exchange
�Control Volume
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Frictionless Flow in a Constant-
Area Duct with Heat Exchange
�Basic Equations for Flow with Heat Exchange
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Frictionless Flow in a Constant-
Area Duct with Heat Exchange
�Heat Exchange: The Rayleigh Line
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Frictionless Flow in a Constant-
Area Duct with Heat Exchange �Rayleigh-Line Relations
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Normal Shocks
�Control Volume
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Normal Shocks
�Basic Equations for a Normal Shock
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Normal Shocks
� Intersection of Fanno & Rayleigh Lines
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Normal Shocks
�Normal Shock Relations
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Normal Shocks
�Normal Shock Relations (Continued)
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Supersonic Channel Flow
with Shocks
�Flow in a Converging-Diverging Nozzle
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Oblique Shocks and
Expansion Waves
�Typical Application
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Oblique Shocks and
Expansion Waves
�Mach Angle and Oblique Shock Angle
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Oblique Shocks and
Expansion Waves
�Oblique Shock: Control Volume
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Oblique Shocks and
Expansion Waves
�Oblique Shock: Useful Formulas
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Oblique Shocks and
Expansion Waves
�Oblique Shock Relations
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Oblique Shocks and
Expansion Waves
�Oblique Shock Relations (Continued)
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Oblique Shocks and
Expansion Waves
�Oblique Shock: Deflection Angle
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Oblique Shocks and
Expansion Waves
�Oblique Shock: Deflection Angle
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Oblique Shocks and
Expansion Waves
�Expansion and Compression Waves
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Oblique Shocks and
Expansion Waves
�Expansion Wave: Control Volume
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Oblique Shocks and
Expansion Waves
�Expansion Wave: Prandtl-Meyer Expansion Function
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Oblique Shocks and
Expansion Waves
�Expansion Wave: Isentropic Relations