A converging-diverging nozzle has an area ratio of 3.0. The stagnation pressure at the inlet is 8.0 bar and the receiver pressure is 3.5 bar. Assume that γ = 1.4. 

(a) Compute the critical operating pressure ratios for the nozzle and show that a shock is located within the diverging section.  

(b) Compute the Mach number at the outlet.  

(c) Compute the shock location (area) and the Mach number before the shock.