If the tank volume Vtank is 8 ft^3, the tank temperature Ttank is atmospheric 23°C, the compressor flowrate mcompr is 0.01 kg/s, the throat area A* is 4.03x10^-5 m^2, and the initial pressure in the tank Ptank,initial is 100 psia, use Equations (5)-(6) to determine how long it would take for the nozzle inlet pressure P0 = Ptank to reach 20 psia. Be careful with your unit conversions.
Equation 5:
Ptank(t) = Ptank,initial * exp[-at] + b * a * [1 - exp(-at)]
Equation 6:
a = 0.6847 * (A * (RTtank)^(1/2)) / Vtank
b = mcompr * (RTtank) / Ptank