Problem $10$: Incompressible air flows steadily under isentropic conditions through a horizontal nozzle. The inlet pressure, temperature, and velocity of the air is $1200$kPa,$600K,$ and $7\frac{m}{s},$ respectively, and the exit temperature $T_2=410K.$ Complete the following:

$($a$)$ Draw the relevant schematic showing inlet and exit flow conditions and the selected control volume;

$($b$)$ Calculate the density of the air;

$($c$)$ Calculate the static pressure at the exit, $P_2(kPa)$;

$($d$)$ Calculate the stagnation pressure, $P_0(kPa)$;

$($e$)$ Calculate the exit velocity, $A{A}_2(\frac{m}{s})$;

$($f$)$ Calculate the percent change in static pressure $(P)$ and velocity $(darr)$ from State $1$ to State $2$;

$($g$)$ Confirm, using calculations, that the flow is isentropic;