Prandtl-Meyer function

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,

: egin{align} u(M) & = int frac{sqrt{M^2-1{1+frac{gamma -1}{2}M^2}frac{,dM}{M} \& = sqrt{frac{gamma + 1}{gamma -1 cdot arctan sqrt{frac{gamma -1}{gamma +1} (M^2 -1)} - arctan sqrt{M^2 -1} \end{align}

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

: u_{max} = frac{pi}{2} igg( sqrt{frac{gamma+1}{gamma-1 -1 igg)

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


* 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

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