Indeed. In fact, the problem was with a reversible compressor; the process was polytropic, and after performing the mass and energy balance, when calculating the compressor's specific work, the professor established w = ∫ vdP
And he said that for flow machines, the work took that expression...
I have this little doubt because in class, the professor said the work is equal to the integrate of vdP, but i don't know how to prove it, why it isn't PdV like those exercises in a cylinder-piston