Prandtl-Meyer function

Prandtl-Meyer function describes the angle through which a flow can turn isentropically for the given initial and final Mach number. It is the maximum angle through which a sonic (M = 1) flow can be turned around a convex corner. For an ideal gas, it is expressed as follows,

:

where, $u\; ,$ 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 $u(1)\; =\; 0.\; ,$

As Mach number varies from 1 to $infty$, $u\; ,$ takes values from 0 to $u\_\{max\}\; ,$, where

:

where, $heta$ 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

* cite book
last = Liepmann | first = Hans W. | coauthors = Roshko, A.
title = Elements of Gasdynamics | origyear = 1957
publisher = Dover Publications | year = 2001
id = ISBN 0-486-41963-0