where W is the weight of gas passing A or B per second. As in the case of an incompressible fluid, the work of the pressures on the ends of the mass AB is
p1ω1v1t − p2ω2v2t,
= (p1/G1 − p2/G2) Wt.
The work done by expansion of Wt ℔ of fluid between A and B is ∫v2v1 The change of kinetic energy as before is (W/2g) (v22 − v12) t. Hence, equating work to change of kinetic energy,
W (z1 − z2) t + (p1/G1 − p2/G2)Wt + Wt ∫v2v1 p dv = (W/2g) (v22 − v12) t;
∴ z1 + p1/G1 + v12/2g = z2 + p2/G2 + v22/2g − ∫v2v1 p dv.
(1)
Now the work of expansion per pound of fluid has already been given. If the temperature is constant, we get (eq. 1a, § 61)
Z1 + P1/G1 + v12/2g = z2 + p2/G2 + v22/2g − (p1/G1) logε (G1/G2).
But at constant temperature p1/G1 = p2/G2;