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Reversible Adiabatic Work In Steady Flow System







In the differential form, the steady flow energy equation per unit mass is given by 

dQ = dh + VDV + gdZ + dWx                                   (1)

For a reversible process, dQ = Tds

Tds = dh + VdV + gdZ + dWx                                    (2)

Using the property relation, 

Tds = dh - vdp                                                              (3)

From (2) and (3) ,

-vdp = VdV + gdZ + dWx                                            (4)

On Integration 

- Integral vdp = delta  (V^2 / 2)  + g (Delta Z)  +  Wx      (5)

If the changes in K.E and P.E are neglected, (5) reduces to 

Wx = - Integral (vdp)                                                          (6)

If dQ = 0, implying ds = 0, the property relation gives 

dh = vdp                                                                             

or 

h2-h1 = Integral vdp                                                             (7)

From Equation (6) and (7) 

Wx = h2 - h1 = - Integral vdp                                               (8)

The equation (8) holds good for a steady flow work producing machine like an engine or turbine as well as for a work absorbing machine like a pump or a compressor, when the fluid undergoes reversible adiabatic expansion or compression.


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