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 = ∞ {displaystyle infty } . For an ideal gas, it is expressed as follows, 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 = ∞ {displaystyle infty } . For an ideal gas, it is expressed as follows, where ν {displaystyle u ,} is the Prandtl–Meyer function, M {displaystyle M} is the Mach number of the flow and γ {displaystyle gamma } is the ratio of the specific heat capacities. By convention, the constant of integration is selected such that ν ( 1 ) = 0. {displaystyle u (1)=0.,} As Mach number varies from 1 to ∞ {displaystyle infty } , ν {displaystyle u ,} takes values from 0 to ν max {displaystyle u _{ ext{max}},} , where where, θ {displaystyle heta } is the absolute value of the angle through which the flow turns, M {displaystyle M} is the flow Mach number and the suffixes '1' and '2' denote the initial and final conditions respectively.