Normal Shock Relations
Normal shock relations describe a discontinuity normal to the flow direction in a supersonic stream.
Governing Relations
For upstream Mach number \(M_1\) and ratio of specific heats \(\gamma\):
\[
\frac{p_2}{p_1} = 1 + \frac{2\gamma}{\gamma+1}(M_1^2-1)
\]
\[
\frac{\rho_2}{\rho_1} = \frac{(\gamma+1)M_1^2}{(\gamma-1)M_1^2+2}
\]
\[
\frac{T_2}{T_1} = \frac{(p_2/p_1)}{(\rho_2/\rho_1)}
\]
\[
M_2^2 = \frac{1+\frac{\gamma-1}{2}M_1^2}{\gamma M_1^2-\frac{\gamma-1}{2}}
\]
References
Anderson, J. D. (2003). Modern Compressible Flow: With Historical Perspective, 3rd ed. McGraw-Hill, Chapter 4.