Problem $1$

Helium gas flows through a well$-$insulated nozzle at steady state. The temperature and velocity at the inlet are $560R$ and $150f\frac{t}{s},$ respectively. At the exit, the temperature is $400R$ and the pressure is $40lb\frac{f}{i}{n}^2$ The area of the exit is $0\mathrm{.}0085f{t}^2.$ Using the ideal gas model with $k=1\mathrm{.}67,$ and neglecting potential energy effects, determine the mass flow rate, in lb$/$s$,$ through the nozzle.