# Find the combustion chamber pressure of a rocket engine.

Find the combustion chamber pressure of a rocket engine using hydrogen and oxygen as propellants, whose mass flow in combustion chamber is $$300\,kg/s$$. The temperature of the combustion chamber is $$3500\,K$$. Gas flowing into the engine has a ratio of specific heats of $$1.2$$ and a molecular weight of $$16$$. The rocket nozzle throat area is $$0.25\,m^{2}$$.

Mass flow rate at the throat which is at sonic condition is $\dot{m}=\rho ^{*}A^{*}V^{*}$Specific gas constant $R=\frac{8314}{16}=519.6\,J/\left ( kg\,K \right )$At sonic condition, $\frac{\rho ^{*}}{\rho _{0}}=\left ( \frac{2}{\gamma +1} \right )^{\frac{1}{\gamma -1}} =\left ( \frac{2}{1.2+1} \right )^{\left ( \frac{1}{1.2-1} \right )}=0.621$$\rho ^{*}=\left ( \frac{\rho ^{*}}{\rho _{0}} \right )\rho _{0}=0.621\rho _{0}=0.621\left ( \frac{p_{0}}{RT_{0}} \right ) =0.621\left ( \frac{p_{0}}{519.6\times 3500K} \right )=3.415\times 10^{-7}p_{0}$At sonic condition,
$\left ( \frac{T^{*}}{T_{0}} \right )=\left ( \frac{2}{\gamma +1} \right )=\left ( \frac{2}{1.2 +1} \right )=0.9091$$T^{*}=\left ( \frac{T^{*}}{T_{0}} \right )T_{0}=0.9091\times 3500=3181.85\,K$Also, at throat$V^{*}=a^{*}=\sqrt{\gamma RT^{*}}=\sqrt{\left ( 1.2 \right )\left ( 519.6 \right )\left ( 3500 \right )}=1477.27\,m/s$Since, $$\dot{m}=\rho ^{*}A^{*}V^{*}$$$\Rightarrow 300=\left ( 3.415\times 10^{-7} p_{0}\right )\times \left ( 0.25 \right )\times 1477.27$$\Rightarrow p_{0}=2.3787\times 10^{6}\,N/m^{2}$