Isentropic Flow Relations
Isentropic relations connect static and stagnation quantities for a calorically perfect gas under adiabatic, reversible flow.
Governing Relations
For Mach number \(M\) and ratio of specific heats \(\gamma\):
\[
\frac{T}{T_0} = \left(1 + \frac{\gamma - 1}{2}M^2\right)^{-1}
\]
\[
\frac{p}{p_0} = \left(\frac{T}{T_0}\right)^{\gamma/(\gamma-1)}
\]
\[
\frac{\rho}{\rho_0} = \left(\frac{T}{T_0}\right)^{1/(\gamma-1)}
\]
\[
\frac{A}{A^*} = \frac{1}{M}\left[\frac{2}{\gamma+1}\left(1+\frac{\gamma-1}{2}M^2\right)\right]^{\frac{\gamma+1}{2(\gamma-1)}}
\]
References
Anderson, J. D. (2003). Modern Compressible Flow: With Historical Perspective, 3rd ed. McGraw-Hill, Chapter 3.