Problem 4.7.1

Air is stored in a tank at 100 psi and 70 degrees Fahrenheit. If one allows the air to release, what is the maximum flow per unit area under isentropic conditions? What is the mass velocity at the exit of a nozzle where pressure is 14.7 psi? Gas constant = 53.3 ft pound-force per pound-mass per degree Fahrenheit.

Solution:

Density of air under reservoir conditions is p₀ over RT₀. and is equal to 0.51 pounds per cubic foot. Temperature under critical (sonic) conditions is 0.833 time T₀ or 441.7 degrees Rankine. Sonic velocity is 1030 foot per second. Critical (sonic) density is 0.634 rho₀ or 0.323 pounds per cubic foot. Mass velocity under sonic conditions is rho_star time velocity_star. Mass velocity is 0.323 time 1030 or 332.6 pounds per second per square foot.

At a point where pressure is 14.7 psi, p₁ over p₀ is 0.147. This corresponds to Mach number, M₁, of 1.909. We can calculate A₁ as 1.567 A_star.

Mass velocity, G1, is 332.6 over 1.567 or 212.2 pounds per second per square foot.