$4\mathrm{.}23$Helium gas flows through a well$-$insulated nozzle at steady state. The temperature and velocity at the inlet are

$550R$ 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.

$4\mathrm{.}24-$Nitrogen, modeled as an ideal gas, flows at a rate of $3k\frac{g}{s}$ through a well$-$insulated horizontal nozzle operating