Consider a supersonic nozzle with a Pitot tube mounted at the exit. The reservoir pressure and temperature are \(10 \mathrm{~atm}\) and \(500 \mathrm{~K}\), respectively. The pressure measured by the Pitot tube is \(0.6172 \mathrm{~atm}\). The throat area is \(0.3 \mathrm{~m}^{2}\). Calculate:

a. Exit Mach number \(M_{e}\)

b. Exit area \(A_{e}\)

c. Exit pressure and temperature \(p_{e}\) and \(T_{e}\)

d. Mass flow through the nozzle