Suppose a particular compressor has a compression ratio P$3/$P$2=25$; the incoming air temperature is $300$ K and its pressure is $1\mathrm{.}2$ atm. $20$ kgm per sec$.$ of air flows through the compressor.

$($a$)$ If the adiabatic efficiency is $90\%,$ what is the final temperature?

$($b$)$ What is the power required?

$($c$)$ What is the minimum number of stages $($pairs of rotor and stator sections$)$ required to protect against separation due to adverse pressure gradients?

$5.$ Do a preliminary design on a ramjet engine which produces $50001$bf of thrust. Size constraints limit the intake cross$-$sectional capture area to $0\mathrm{.}80$ square feet. The engine is intended to cruise at a Mach number of $2\mathrm{.}5.$ Assume ambient air conditions are one atmosphere of pressure and $500$R$.$ Indicate your choices of inlet type, fuel, temperature at entrance to nozzle, and extent of expansion in nozzle. All choices must be rational and defensible, of course. Indicate mass flows of air and fuel, mixture ratio$($s$),$ thrust specific fuel consumption, exhaust velocity, stagnation pressure ratios across each component, throat area, nozzle exit area, and nozzle exit pressure.