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\begin{equation}\nonumber
M_{2N}^2 = M_{1N}^2(\frac{(\gamma -1)M_{1N}+2}{2\gamma M_{1N}-(\gamma -1)})
\end{equation}
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\begin{equation}\nonumber
M_2 =\frac{M_{2N}}{sin(\beta-\theta)}
\end{equation}
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\begin{equation}\nonumber
\frac{p2p_2}{p1p_1} = \frac{2\gamma M_{1N}^2 - (\gamma - 1)}{\gamma + 1}
\end{equation}
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\begin{equation}\nonumber
\frac{T_2}{T_1} = \frac{(2\gamma M_{1N}^2 - (\gamma - 1))((\gamma -1)M_{1N}^2 +2)}{(\gamma +1)^2 M_{1N}^2}
\end{equation}
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