A small, solid$-$fuel rocket motor is tested on a horizontal thrust stand at atmospheric conditions $(100$ kPa $).$ The chamber $($essentially a large tank$)$ absolute pressure and temperature are maintained at $4\mathrm{.}0$ MPa $($abs$)$ and $3000$ oC $,$ respectively. The rocket's converging$-$diverging nozzle is designed to expand the exhaust gas isentropically to an absolute pressure of $75$ kPa $.$ The nozzle exit area is $0\mathrm{.}056m^2.$ The gas may be treated as perfect gas with a specific heat ratio of $1\mathrm{.}2$ and an ideal gas constant of $300\frac{J}{k}g.K.$

$K=1\mathrm{.}2,R=\mathrm{.}3\frac{5}{54}$

By considering reasonable assumptions, determine the following:

$($a$).$ The static temperature, static pressure, static density, velocity, and the mass flow rate of propellant gas at the exit for design conditions. Is the flow subsonic or supersonic at the exit?

$($b$).$ The static temperature, static pressure, static density, velocity, area, and the mass flow rate of propellant gas at the throat for design conditions.

use prose to is throut contitas

$($c$).$ The exit pressure for which normal shock wave stands in the divergent section at an area $50\%$ larger than the throat area.

b$.>5000$

$($d$).$ The exit nressure for which a normal shock wave stands at the exit plane of the divergent nozzle.

$($e$).$ The maximum exit pressure for the flow to be subsonic at the exit. What is the mass flow rate at this exit pressure? Is it lower, higher, or the same as above?

$P_b=4000,000$

maximum exit pres

$($f$).$ The maximum exit pressure for the flow to be incompressible at the exit. What is the mass flow rate at this exit pressure?

Note: Choose the length of the rockite for nozzte appropriate for half angle is about $30$ degrees, focket nozzle approprith the above conditions. The Convergent