Air enters a frictionless, constant area duct with \(\mathrm{Ma}=2.5\) \(T_{0}=20^{\circ} \mathrm{C},\) and \(p_{0}=101 \mathrm{kPa}(\mathrm{abs}) .\) The gas is decelerated by heating until a normal shock occurs where the local Mach number is \(1.3 .\) Downstream of the shock, the subsonic fow is accelerated with heating until it exits with a Mach number of \(0.9 .\) Determine the static temperature and pressure, the stagnation temperature and pressure, and the fluid velocity at the duct entrance, just upstream and downstream of the normal shock, and at the duct exit. Sketch the temperature- entropy diagram for this flow.

Static temperature and pressure at the entrance are 293.15K and 101000Pa. The same before the shock, however, after the shock the static temperature and pressure reduce to 225.6K and 12000Pa. At the duct exit, they are 210K and 8000Pa respectively. Stagnation temperature and pressure start at 293.15K and 101000Pa. They increase after the shock to become 905 K and 850000Pa. Then they reduce at the exit of the duct to 293.15K and 101000Pa respectively. Fluid velocity at the entrance is 867.4m/s, which reduce to 321.4m/s after the shock, and further decrease to 299m/s at the duct exit. The temperature-entropy diagram should reflect these increases and decreases during different stages of air flow through the duct.