$(25$ points$)$ We consider the two dimensional supersonic air$-$intake illustrated here. The upstream part of the air intake is constituted by a simple wedge of angle $$ The configuration is such that: The air intake is adapted for an upstream Mach number $M_o=2\mathrm{.}0$ The critical regime is established and the Mach number $M_1$ in front of the terminal shock is equal to $1\mathrm{.}4.$ Diffuser terminal section area $A_2=0\mathrm{.}8m^2,$ flow Mach number is $M_2=0\mathrm{.}4$ and the diffuser pressure recovery coefficient is $0\mathrm{.}97($subsonic part$).$

Figure $3$

$($a$)$ Determine wedge and shock angles: $,.$

$($b$)$ Compute the pressure jump through the leading oblique shock wave.

$($c$)$ Compute the total efficiency of the air intake, $P_r.$