Solve this problem by showing all the steps taken. Solutions are below to check your work. Air expands from a storage tank through a converging$-$diverging nozzle $($see Figure$).$ Under certain conditions, it is found that a

normal shock exists in the diverging section of the nozzle at an area

equal to twice the throat area, with the exit area of the nozzle equal

to four times the throat area. Assuming isentropic flow except for

shock waves, that the air behaves as a perfect gas with constant gamma

$=1\mathrm{.}4,$ and that the storage tank pressure and temperature are $200$

kPa and $300$ K $,$ determine the following:

$($a$)$ A$*$ for flow from inlet to shock $(50$cm$^2)$

$($b$)$ A$*$ for flow from shock to exit $(80$cm$^2)$

$($c$)$ Mach number at nozzle exit plane $($M$=0\mathrm{.}238)$

$($d$)$ Stagnation pressure at nozzle exit plane $($Po$=125\mathrm{.}6$kpa$)$

$($e$)$ Exit plane static pressure $($P$=120\mathrm{.}4$kpa$)$

$($f$)$ Exit plane velocity $(82\mathrm{.}4$m$/$s$)$