Problem $4$: $[10$ points$]$

A graduate of this class decides to design the diffuser at the outlet of the compressor in

$2($a$).$ At compressor outlet, the velocity is $300\frac{m}{s}.$ What are the static pressure and static

temperature at compressor outlet? The stagnation pressure drop in the diffuser is $2\%$ and

the velocity at diffuser outlet is $210\frac{m}{s}.$ What are the static pressure and temperature at

diffuser outlet?

FOR RERFERENCE $(2)(a)$ :

For this problem The environment is at $101\mathrm{.}30$ kPa and $288\mathrm{.}15$ K $.$

$($a$)$ Model air as a perfect gas with specific heat capacity at constan$($Ctrl$),$Cros$=1,030$

$\frac{J}{k}\frac{g}{K},$ and gas specific constant $R=286\mathrm{.}96\frac{J}{k}\frac{g}{K}.$ The outlet of a small industrial

compressor is at stagnation conditions $485\mathrm{.}00$ kPa and $492\mathrm{.}45$ K $.$ What is the isentropic

stagnation$-$to$-$stagnation efficiency?

What is the polytropic stagnation$-$to$-$stagnation efficiency? Which of these two efficiencies

is bigger?