Question A supersonic wind finnel is designed with two ocmwergest$-$divergent nocziles as shown in Fig. B$3.$ The flow $($ sir, y $=14,R=\frac{2871}{k}g-K)$ peters the leat section supersonically, goes through a satoronacy bermal shock in the test seetiom and exits supersonically through the secoral noczele. You ame given:

The cross$-$secticenal area of the upvitream throat ia ${}_{Hi}=10c{m}^3$

The test$-$section cross$-$sectional area is $A=20c{m}^2.$

The crass$-$sectional erea at the exit of the secoed eoazie is $A=20c{m}^3$

Ail losses, except thase due bo the shock, are negligithle.

When the wind tunnel is operated at its design back peessure of $P_b=100kPs,$ the flow exits supersontically and the static tempermure, messured afler the fest$-$soction shock, is $280$ K $.$

a$)$ Determine the Mach number directly upstream and slownsteam of the levi$-$soction shock as well as the fotal $($stagnation$)$ tertinerature.

b$)$ What is the cross$-$sectional thront ares, AT$1,$ of the second nowale? Fint: the mass flow rate is constant througiout the wind unnul.

c$)$ What is the ait tempernture and spees at the exit of the wind runnel?

d$)$ Deiertuine the needod total $($stagnation$)$ pressure to drive the flow,