(20 pts) Consider air escaping from a tank under choked flow conditions. a) Plot P/P0 vs t/ for both isothermal and adiabatic conditions on the same graph. Real tanks are rarely 100% isothermal or 100% adiabatic, and so the curve for a real tank would likely lie in between the two you've plotted. b) For both isothermal and adiabatic conditions, at what non-dimensional time t/ will we expect pressure to have dropped by 50% ? c) Consider a tank with an initial pressure of P0=85.3 psig in a place where atmospheric pressure is 14.7 psi. A pressure relief valve in this tank is opened until absolute pressure within the tank has fallen by 50%. Is it valid to assume choked flow conditions for the entirety of the time the valve is open? Demonstrate why or why not. d) The tank in part c has a volume of 40ft3. The valve opens a circular orifice with a diameter of 1in, and its discharge coefficient under choked flow conditions has been measured as 0.9. The temperature of the tank when the valve is opened is 70F. For both isothermal and adiabatic conditions, find the time required for absolute tank pressure to drop by 50%