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Introduction to Fluid Mechanics

Chapter 13

Compressible Flow

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Main TopicsBasic Equations for

One-Dimensional Compressible Flow Isentropic Flow of an Ideal Gas

– Area VariationFlow in a Constant Area Duct with FrictionFrictionless Flow in a Constant-Area Duct with

Heat ExchangeNormal ShocksSupersonic Channel Flow with ShocksOblique Shocks and Expansion Waves

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Basic Equations forOne-Dimensional Compressible Flow

Control Volume

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Basic Equations forOne-Dimensional Compressible Flow

Continuity

Momentum

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Basic Equations forOne-Dimensional Compressible Flow

Second Law of Thermodynamics

First Law of Thermodynamics

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Basic Equations forOne-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 aConverging-Diverging Nozzle

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Isentropic Flow of an Ideal Gas– Area Variation

Isentropic Flow in aConverging-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 forOne-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 ShocksBasic 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 Flowwith Shocks

Flow in a Converging-Diverging Nozzle

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Oblique Shocks andExpansion Waves

Typical Application

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Oblique Shocks andExpansion Waves

Mach Angle and Oblique Shock Angle

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Oblique Shocks andExpansion Waves

Oblique Shock: Control Volume

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Oblique Shocks andExpansion Waves

Oblique Shock: Useful Formulas

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Oblique Shocks andExpansion Waves

Oblique Shock Relations

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Oblique Shocks andExpansion Waves

Oblique Shock Relations (Continued)

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Oblique Shocks andExpansion Waves

Oblique Shock: Deflection Angle

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Oblique Shocks andExpansion Waves

Oblique Shock: Deflection Angle

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Oblique Shocks andExpansion Waves

Expansion and Compression Waves

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Oblique Shocks andExpansion Waves

Expansion Wave: Control Volume

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Oblique Shocks andExpansion Waves

Expansion Wave:Prandtl-Meyer Expansion Function

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Oblique Shocks andExpansion Waves

Expansion Wave: Isentropic Relations