Normal shock relations

$$\frac{\rho_2}{\rho_1} = \frac{u_1}{u_2} = \frac{ (\gamma + 1)M_1^2}{2 + (\gamma - 1) M_1^2}$$

$$\frac{p_2}{p_1} = 1 + \left( \frac{2\gamma}{\gamma + 1} \right) (M_1^2 - 1)$$

$$\frac{T_2}{T_1} = \frac{p_2}{p_1} \frac{\rho_1}{\rho_2}$$

$$M_2^2 = \frac{ 1 + \left( \frac{\gamma-1}{2} \right) M_1^2 }{ \gamma M_1^2 - \left( \frac{\gamma-1}{2} \right) }$$

Hugoniot relation

$$e_2 - e_1 = \left(\frac{p_1 + p_2}{2}\right) (v_1 - v_2)$$