A test thrust$-$stand for determining the thrust of a liquid$-$fuel rocket is shown below. The propellant enters section $1$ at a mass flow rate of $15k\frac{g}{s},$ a velocity of $30\frac{m}{s},$ and pressure of $0\mathrm{.}7$ MPa $.$ The inlet pipe for the propellants is very flexible, and the force it exerts on the rocket is negligible. At the nozzle exit, section $2,$ the area is $0\mathrm{.}064m^2,$ and pressure is $110$ kPa $.$ The force read by the scales is $2700$ N $,$ atmospheric pressure is $82\mathrm{.}7$ kPa $,$ and the flow is steady. Determine the exhaust velocity at section $2,$ assuming one$-$dimensional flow exists. Consider mechanical frictional effects are negligible.

$2$

Propellant