# Isentropic Mach number

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The isentropic Mach number is the Mach number you would have without any losses in the flow. This property is often used to investigate the ideal surface Mach number you would have without losses and walls without any friction (slip conditions). The isentropic Mach number is for example often plotted on turbomachinery blades. The isentropic Mach number can be computed from the isentropic flow relations using the following formula:

$\frac{p_0^{freestream}}{p}=(1+\frac{\gamma-1}{2}M^2)^{\frac{\gamma}{\gamma-1}}$

This gives the following formula for the isentropic Mach number:

$M^{isentropic} = \sqrt{ \left( \left( \frac{p_0^{freestream}}{p} \right) ^{\frac{\gamma - 1}{\gamma}} - 1 \right) \cdot \frac{2}{\gamma - 1}}$

Where:

$p_0^{freestream}$ is the Total pressure in the freestream outside of the boundary layers. Usually the inlet total pressure is used.
$p$ is the local Static pressure.
$\gamma$ is the ratio of specific heats, for air $\gamma = 1.4$.