Prandtl–Meyer Function

In aerodynamics, the Prandtl–Meyer function describes the angle through which a flow turns isentropically from sonic velocity (M=1) to a Mach (M) number greater than 1. The maximum angle through which a sonic ( ''M'' = 1) flow can be turned around a convex corner is calculated for M = $\infty$. For an ideal gas, it is expressed as follows,

: \begin \nu(M)
& = \int \frac\frac \\ pt& = \sqrt \cdot \arctan \sqrt - \arctan \sqrt
\end

where $\nu \,$ is the Prandtl–Meyer function, $M$ is the Mach number of the flow and $\gamma$ is the ratio of the specific heat capacities.

By convention, the constant of integration is selected such that $\nu(1) = 0. \,$

As Mach number varies from 1 to $\infty$, $\nu \,$ takes values from 0 to $\nu_\text \,$, where

: $\nu_\text = \frac \bigg( \sqrt -1 \bigg)$

where, $\theta$ is the absolute value of the angle through which the flow turns, $M$ is the flow Mach number and the suffixes "1" and "2" denote the initial and final conditions respectively.

See also

* Gas dynamics
* Prandtl–Meyer expansion fan

References

*

Aerodynamics
Fluid dynamics

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