Question $7-$ Supersonic Wind Tunnel $(15$ points$)$: A blow down supersonic wind tunnel has a test

section area of $0\mathrm{.}2m^2$ and a design Mach number of $2\mathrm{.}5.$ The pressure and temperature in the high

pressure air tank is $50$MPa and $400K.$ Ignore all losses between the high pressure tank and the test

section.

a$)$ Estimate the throat area of the nozzle.

b$)$ Estimate the static pressure and static temperature in the test section.

c$)$ Estimate the required gas temperature in the high pressure tank to achieve $298K$

temperature in the test section.