Sonic velocity
\(\alpha=\sqrt{\gamma RT}=\sqrt{\gamma (p/\rho)}=\sqrt{1.4\times30\times10^3/0.45}=305.5\,m/s\)
Speed of plane
V = 2000 km/hr = \(\frac{2000\times10^3}{3600}=555.56\,m/s\)
Mach number M \(=\frac{V}{\alpha}=\frac{555.56}{305.5}=1.818\)
From characteristic gas equation, \(\frac{P}{\rho}=RT\)
Temperature \(T=\frac{P}{\rho\,R}=\frac{30\times 10^ 3}{0.45\times287}=233.3\,K\)
Stagnation pressure,
\(P_0=P\left(1+\frac{\gamma -1}{2}M^ 2\right)^{\frac{\gamma}{\gamma -1}}\)
\(=30\left(1+\frac{1.4-1}{2}\times 1.818^2\right)^{\frac{1.4}{1.4-1}}=177.19\,KN/m^ 2\)
Stagnation temperature,
\(T_0=T\left[1+\frac{\gamma -1}{2}M^ 2\right]=233.3\left[1+\frac{1.4-1}{2}\times1.818^2\right]=387.5\,K\)
Stagnation density,
\(\rho _0 =\frac{p_0}{RT_0}=\frac{177.19\times 10^3}{287\times 387.5}=1.583\,Kg/m^3\)
