A converging$-$diverging nozzle with a rectangular cross$-$section and exit area ratio $\frac{A_e}{A_t}=5\mathrm{.}5$

operates in an under$-$expanded condition as shown below. The working gas is air, the back pressure

away from the nozzle exit is $p_a=8$kPa, and the stagnation pressure upstream of the nozzle is

$p_0=800$kPa. The exit pressure is greater than the back pressure $p_e>p_a,$ so expansion waves

form outside the exit. For the given conditions, determine:

$($a$)$ the Mach number on the downstream side of the first set of expansion waves

$($b$)$ the flow turning angle

In this problem, you must use the flow tables and charts $($plus algebraic formulas$).$ You will

likely need to use interpolation. You may only use the online calculator to check your numbers,

but this is not required.