Gas Dynamics and Propulsion / BY Dr.G.KUMARESAN, / PROFESSOR, / ANNA UNIVERSITY
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Isothermal flow with friction GDJP Anna University Introduction The Fanno flow of an ideal gas through a constant area duct under adiabatic condition is achievable in practice when the duct is not very long. Avoiding heat transfer to the environment is not convenient when a gas line is taken over long lengths. The supply of natural or by-product gases over long pipe lines from an industrial area to a consuming city. The pipe is exposed to the atmosphere and heat transfer through the pipe wall is a reality. The pipe gas attains the environment temperature by heat exchange. The study of isothermal flow of an ideal gas through a constant area pipe is applicable to long pipe lines. Friction is accounted for. PDF created with pdfFactory trial version www.pdffactory.com
Transcript
Isothermal flow with friction
GDJP Anna University
IntroductionØ The Fanno flow of an ideal gas through a constant area duct
under adiabatic condition is achievable in practice when theduct is not very long.
Ø Avoiding heat transfer to the environment is not convenientwhen a gas line is taken over long lengths.
Ø The supply of natural or by-product gases over long pipelines from an industrial area to a consuming city.
The pipe is exposed to the atmosphere and heattransfer through the pipe wall is a reality. The pipe gasattains the environment temperature by heat exchange.
Ø The study of isothermal flow of an ideal gas through aconstant area pipe is applicable to long pipe lines. Friction isaccounted for.
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where, G - mass velocity or mass flow densityD - duct diameterμ - viscosity of the fluid
For a constant temperature the viscosity of the flowingfluid μ is a constant. Since G is constant, the Reynoldsnumber is constant at all points in the flow.
Friction coefficient for a given pipe surface is a functionof the Reynolds number alone, it follows that in isothermalflow friction coefficient is invariant along the pipe.
µµρ GDVD
==Re
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Choking velocityØ As the gas flows along the pipe, its static pressure
decreases. Eventually a limiting condition is reached wherethe pipe cannot be increased in length without altering theupstream conditions; that is the flow has become choked.
Ø Hence the limiting or choking velocity for the isothermalflow of a perfect gas in a constant-area duct in thepresence of wall friction alone is
LT1T 1 L 1
1
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=
Qγγ
γ
aorLaCLaLc
LM
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Air flows in a long pipe (diameter=0.150 m) under isothermal conditions. At the pipe inlet, the static temperature and pressure are 300 K and 3.5 bar, respectively, and the velocity is 175 m/s. The friction coefficient is 0.005
Calculate (a) the length of pipe required to choke the flow, (b) the limiting velocity and pressure, and (c) the length of pipe at the station where the Mach number is 0.60
Solution:(a) The inlet speed of sound and Mach number are
50.02.347
175
111
sec/ 2.3473002874.11*
1
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acM
mRTaaa γ
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