Calculate Prandtl-Meyer expansion angles and final Mach numbers for supersonic flow. This essential tool helps analyze expansion waves and deflection angles in gas dynamics accurately, ideal for aerospace engineering and fluid mechanics applications.
Formula:
The Prandtl-Meyer function, ν(M), describes the angle through which a supersonic flow must turn to reach a Mach number M from M=1. The calculator uses this function to find the final Mach number M2 given an initial Mach number M1 and a deflection angle θ.
The Prandtl-Meyer function is defined as:
ν(M) = √ ( γ+1 ) / ( γ-1 ) ⋅ arctan &left;( √ ( γ-1 ) / ( γ+1 ) ⋅ ( M² - 1 ) &right;) - arctan &left;( √ M² - 1 &right;)
Where:
- M: Mach Number (dimensionless)
- γ: Ratio of Specific Heats (dimensionless, e.g., 1.4 for air, 1.66 for monatomic gases)
- ν(M): Prandtl-Meyer angle in radians (or degrees, depending on context).
For an expansion from M1 with a deflection angle θ, the final Prandtl-Meyer function value ν(M2) is given by:
ν(M2) = ν(M1) + θ
The calculator finds M2 by iteratively solving this equation.