# Find the nozzle’s exit temperature and density if its exit pressure is \(1\,atm\).

The reservoir of a supersonic wind-tunnel has a total temperature and total pressure of \(600\,K\) and \(11\,atm\). If the flow is isentropic through the nozzle of this wind tunnel, find the nozzle’s exit temperature and density if its exit pressure is \(1\,atm\).

In an isentropic flow total pressure is constant.

For an isentropic flow,\[\left ( \frac{p_{0}}{p} \right )=\left ( \frac{T_{0}}{T} \right )^{\frac{\gamma }{\gamma -1}}\]\[\Rightarrow T= T_{0}\left ( \frac{p}{p_{0}} \right )^{\frac{\gamma-1 }{\gamma}}\]\[\Rightarrow T= 600\left ( \frac{1}{11} \right )^{\frac{0.4}{1.4}}=302.42\,K\]Also,\[p=\rho RT\]\[\Rightarrow \rho =\frac{p}{RT}=\frac{1.01\times 10^{5}}{\left ( 287 \right )\left ( 302.42 \right )}=1.164\,kg/m^{3}\]