12.15 Air passes through a normal shock in a supersonic wind tunnel. Upstream conditions are M1 =1 8, T1 =270 K, and p1 =

10 0 kPa absolute. Downstream conditions are M2 =0 6165,T2 =

413 6 K, and p2 =36 13 kPa absolute. (Four significant figures are given to minimize roundoff errors.) Evaluate local isentropic stagnation conditions

(a) upstream from, and

(b) downstream from, the normal shock. Calculate the change in specific entropy across the shock. Plot static and stagnation state points on a Ts diagram.