Consider an air$-$breathing jet engine which is flying at a velocity of $600$ feet per second. For

every $lb\frac{m}{second}$ of air mass flow, a $0\mathrm{.}030lb\frac{m}{sec}$ mass flow of fuel is injected into the engine.

The thrust force is $5000$ lbf $.$; the entrance pressure equals the ambient pressure at the altitude $(0\mathrm{.}5$

atm $)$ and the exhaust pressure is $0\mathrm{.}75$ times the ambient atmospheric pressure. The incoming air

temperature is $525R.$ The entrance area and exhaust areas are both ten square feet. Determine:

$($a$)$ exhaust velocity

$($b$)$ specific fuel consumption