# 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 $$1\,atm$$.

Asked on 15th April 2021 in
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}$