2: Thermodynamics Review

Special Cases

Adiabatic: q = 0

Steady:

No body forces: P.E. = 0

No work done except that of expansion: = 0

 

If all of the above are true,

 

 

so

 

is a constant.

Stagnation enthalpy is constant along a streamline in steady adiabatic flow, where body forces are negligible and the only work is that of expansion.

 


 

Energy Equation for Steady One-Dimensional Flow

 

Consider an engine represented by a control volume as shown below. Fluid enters from the left at the rate of per unit time, and leaves from the right boundary. Work is extracted from the fluid per unit mass flow rate, and heat is added to the fluid per unit mass flow rate.

 

 

Neglect changes in potential energy of the fluid. Assume that steady-state conditions exist, so that time derivatives are zero in the frame of reference moving with the control volume. Ignore variations across the streamlines, so that integrals such as can be replaced by .Thus, the energy equation reduces to

 

or

 

 

Note:

Stagnation enthalpy increases when heat is added, and decreases when work is taken out.


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