Consider a large tank of volume 27 m3 containing air at 300 K which is discharged into the atmosphere (atmosphere pressure is 101.325 KPa) through a convergent-divergent nozzle. The radius of the nozzle at the inlet and exit is 0.3m while at the throat it is 0.25m. (a) What is the minimum pressure the tank has to be pumped up to reach sonic flow somewhere in the nozzle? (b) At what location would this sonic flow occur? (c) What is the pressure the tank has to be pumped up to obtain supersonic flow at the nozzle exit without any shocks or expansions in the nozzle? (d) The tank is pumped up to the pressure as in (c) above and then the pump is turned off. How long (in seconds) would it take for the tank to reach the condition in (a) above. Assume that the temperature of the air in the tank remains unchanged. Assume that no shocks appear during this process.