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Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo
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Page 1: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Mekanika Fluida II

Fluida Tekompresi

(Bahan Tambahan)

Haryo Tomo

Page 2: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Basic Equations for 1-D Compressible Flow

• Control Volume

Page 3: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Basic Equations for 1D Compressible Flow

• Continuity

Momentum

Page 4: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Basic Equations for 1D Compressible Flow

Second Law of Thermodynamics

• First Law of Thermodynamics

Page 5: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Property Relations

• Equation of State

Basic Equations for 1D Compressible Flow

Page 6: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Isentropic Flow of an Ideal Gas–Area Variation

• Basic Equations for Isentropic Flow

Page 7: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Isentropic Flow of an Ideal Gas – Area Variation

• Isentropic Flow

Page 8: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Isentropic Flow of an Ideal Gas – Area Variation

• Subsonic, Supersonic, and Sonic Flows

Page 9: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Isentropic Flow of an Ideal Gas – Area Variation

• Reference Stagnation and Critical Conditions for Isentropic Flow

Page 10: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Isentropic Flow of an Ideal Gas – Area Variation

• Property Relations

Page 11: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Isentropic Flow of an Ideal Gas – Area Variation

• Isentropic Flow in a Converging Nozzle

Page 12: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Isentropic Flow of an Ideal Gas – Area Variation

• Isentropic Flow in a Converging Nozzle

Page 13: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Isentropic Flow of an Ideal Gas – Area Variation

• Isentropic Flow in aConverging-Diverging Nozzle

Page 14: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Isentropic Flow of an Ideal Gas – Area Variation

• Isentropic Flow in aConverging-Diverging Nozzle

Page 15: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Flow in a Constant-Area Duct with Friction

• Control Volume

Page 16: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Flow in a Constant-Area Duct with Friction

• Basic Equations for Adiabatic Flow

Page 17: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Flow in a Constant-Area Duct with Friction

• Adiabatic Flow: The Fanno Line

Page 18: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Flow in a Constant-Area Duct with Friction

• Fanno-Line Flow Functions forOne-Dimensional Flow of an Ideal Gas

Page 19: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Flow in a Constant-Area Duct with Friction

• Fanno-Line Relations

Page 20: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Flow in a Constant-Area Duct with Friction

• Fanno-Line Relations (Continued)

Page 21: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Frictionless Flow in a Constant-Area Duct with Heat Exchange

• Control Volume

Page 22: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Frictionless Flow in a Constant-Area Duct with Heat Exchange

• Basic Equations for Flow with Heat Exchange

Page 23: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Frictionless Flow in a Constant-Area Duct with Heat Exchange

• Heat Exchange: The Rayleigh Line

Page 24: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Frictionless Flow in a Constant-Area Duct with Heat Exchange

• Rayleigh-Line Relations

Page 25: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Normal Shocks

• Control Volume

Page 26: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Normal Shocks

• Basic Equations for a Normal Shock

Page 27: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Normal Shocks

• Intersection of Fanno & Rayleigh Lines

Page 28: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Normal Shocks

• Normal Shock Relations

Page 29: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Normal Shocks

• Normal Shock Relations (Continued)

Page 30: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Supersonic Channel Flow with Shocks

• Flow in a Converging-Diverging Nozzle

Page 31: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Oblique Shocks and Expansion Waves

• Typical Application

Page 32: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Oblique Shocks and Expansion Waves

• Mach Angle and Oblique Shock Angle

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Oblique Shocks and Expansion Waves

• Oblique Shock: Control Volume

Page 34: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Oblique Shocks and Expansion Waves

• Oblique Shock: Useful Formulas

Page 35: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Oblique Shocks and Expansion Waves

• Oblique Shock Relations

Page 36: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Oblique Shocks and Expansion Waves

• Oblique Shock Relations (Continued)

Page 37: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Oblique Shocks and Expansion Waves

• Oblique Shock: Deflection Angle

Page 38: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Oblique Shocks and Expansion Waves

• Oblique Shock: Deflection Angle

Page 39: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Oblique Shocks and Expansion Waves

• Expansion and Compression Waves

Page 40: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Oblique Shocks and Expansion Waves

• Expansion Wave: Control Volume

Page 41: Mekanika Fluida II - Institut Teknologi Bandungkuliah.ftsl.itb.ac.id/wp-content/uploads/2010/08/Slide11a... · Mekanika Fluida II Fluida Tekompresi (Bahan Tambahan) Haryo Tomo. Basic

Oblique Shocks and Expansion Waves

• Expansion Wave:Prandtl-Meyer Expansion Function

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Oblique Shocks and Expansion Waves

• Expansion Wave: Isentropic Relations


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