Problem $3$: Air, with $P_{0,1}=1\mathrm{.}0$MPa and $T_{0,1}=125C,$ flows steadily and adiabatically from a large tank through a converging nozzle connected to an insulated constant$-$area duct. The nozzle may be considered frictionless. The pressure at the nozzle exit $($i$.$e$.$ duct inlet$)$ is $784$ kPa $.$

Calculate the pressure at the end of the duct, where the static temperature is $65C,$ and the entropy change of the air $(\frac{J}{k}gK).$ Confirm that the flow is not choked and calculate the percent reduction in pressure required for $P_2=P^{**}.$

Sketch a Fanno line on the $Ts$ diagram for the process and label all states.