Supersonic airflow enters an adiabatic, constant area (inside diameter \(=1 \mathrm{ft}\) ) 30-ft-long pipe with \(\mathrm{Ma}_{1}=3.0\). The pipe friction factor is estimated to be 0.02 . What ratio of pipe exit pressure to pipe inlet stagnation pressure would result in a normal shock wave standing at

(a) \(x=5 \mathrm{ft}\), or

(b) \(x=10 \mathrm{ft}\), where \(x\) is the distance downstream from the pipe entrance? Determine also the duct exit Mach number and sketch the temperature-entropy diagram for each situation