$(15$ points$)$ A nozzle is designed to expand air from a chamber in which the pressure and

temperature are $800$ KPa and $40$o C respectively to a Mach number of $2\mathrm{.}5.$ The throat area

of the nozzle is $0\mathrm{.}05$m $2.$ Find

a$.$ The exit area of the nozzle

b$.$ The mass flow rate through the nozzle when operating at design conditions

c$.$ The back pressure for which it will be a normal shock wave on the exit plane of the

nozzle

d$.$ The range of back pressures where there will be a normal shock wave in the nozzle

e$.$ The range of back pressures over which there will be oblique shocks at the exit

$($overexpanded nozzle$)$

f$.$ The range of pressures over which there will be expansion waves outside the nozzle

$($underexpanded nozzle$)$

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