Workdone in a Steady Flow Process

The steady flow equation for unit mass flow, in the differential form, is

                           &q - &w = dh + d(ke) + d(pe)

According to first law of thermodynamics for a closed system, we know that

&q = du +pdv

or

dh = &q +v dp

substituting this value of dh in equation

&q - &w = (&q + v dp) + d(ke) + d(pe)

- &w = v dp + d(ke) + d(pe)