If the volume discharged is measured at the pressure p1 and absolute temperature τ1 in the vessel from which the air flows, let Q1 be that volume; then
p1Q1γ = p2Q2γ;
Q1 = (p2/p1)1/γ Q2;
Q1 = cω √ [ {2gγp1 / (γ − 1) G1} {(p2/p1)2/γ − (p2/p1)(γ+1)/γ}].
Let
(p2/p1)2/γ − (p2/p1)(γ−1)/γ = (p2/p1)1.41 − (p2/p1)1.7 = ψ; then
Q1 = cω √ [2gγp1ψ / (γ − 1) G1]
= 108.7cω √ (τ1ψ).
(4)
The weight of air at pressure p1 and temperature τ1 is