- Prandtl-Meyer function
**Prandtl-Meyer function**describes the angle through which a flow can turn isentropically for the given initial and finalMach number . It is the maximum angle through which a sonic (M = 1) flow can be turned around a convex corner. For anideal gas , it is expressed as follows,: $egin\{align\}\; u(M)\; =\; int\; frac\{sqrt\{M^2-1\{1+frac\{gamma\; -1\}\{2\}M^2\}frac\{,dM\}\{M\}\; \backslash \; =\; sqrt\{frac\{gamma\; +\; 1\}\{gamma\; -1\; cdot\; arctan\; sqrt\{frac\{gamma\; -1\}\{gamma\; +1\}\; (M^2\; -1)\}\; -\; arctan\; sqrt\{M^2\; -1\}\; \backslash end\{align\}$

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 **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

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