Consider a converging-diverging nozzle feeding air from a reservoir at \(p_{1}\) and \(T_{1}\). The exit area is \(A_{e}=4 A_{2}\), where \(A_{2}\) is the area at the throat. The back pressure \(p_{\text {rec }}\) is steadily reduced from an initial \(p_{\text {rec }}=p_{1}\).

(a) Determine the receiver pressures (in terms of \(p_{1}\) ) that would cause this nozzle to operate at first, second, and third critical points.

(b) Explain how the nozzle would be operating at the following back pressures: (i) \(p_{\text {rec }}=p_{1}\); (ii) \(p_{\text {rec }}=0.990 p_{1}\); (iii) \(p_{\text {rec }}=0.53 p_{1}\); (iv) \(p_{\text {rec }}=0.03 p_{1}\).