4) This question concerns choked flow through a converging nozzle. Consider a reservoir with stagnation properties Po and To. A converging nozzle is attached to the reservoir, allowing gas to flow out of the tank. The nozzle throat area is A, and the background pressure is Pb. b) Derive an expression for the mass flow rate through the nozzle (assuming the flow is not choked). The expression should only be a function of Pb/Po, stagnation properties, A1, y, and Rgas. c) Develop an expression for the mass flow rate (as a function of Pb/Po, stagnation properties, Ai, y, and Rgas) if the gas is assumed to be incompressible. (Hint: Start with Bernoulli's equation) d) On the same graph, plot the non-dimensional mass flux (m /^, max ) versus Pb/P, for both cases in part (b) and (c). Find the value Pb/P, where the flow becomes choked. e) At what Mach number does the percent error between the incompressible and compressible mass flow become greater than 5%