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compressible vs incompressible flow

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Old   March 15, 2017, 08:58
Default compressible vs incompressible flow
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Hey guys,

I have two fundamental questions in fluid mechanics which I'm hoping to resolve here. Let's say we have a pipe in which the flow is fully developed and adiabatic. If I write the energy equation for the control volume that sits within the pipe and touches the inner surface, I end up with hinlet=houtlet. where h is the enthalpy. Now if I assume incompressibility, then since p is dropping and v is constant u(internal energy) should go up. This means that temperature would increase, right? However, if I assume compressible flow then hinlet =houtlet yields cpTinlet=CpToutlet. Therefore temperature wouldn't change! I wonder what really happens, say if we have fully-developed gas flow thru a pipe?

My second question is, in many textbooks in Engineering heat transfer they use h=cpT for incompressible flow. But isn't this incorrect? I mean with incompressible flow in a piper the pressure drops so how could this equation apply? As in the previous example applying this would result in constant temeprature for the incompressible flow whereas with water flow in a pipe I'd expect a slight temeprature rise.
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Old   March 15, 2017, 11:29
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Concerning the incompressible flow case (you have the exact solution), pressure has no thermodynamic meaning. If you would use the state equation you would have simply p=constant.

As concern to the compressible case, you could use the results of quasi one-dimensional flows with presence of friction (Fanno flow).
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