# 12.4: The Maximum Turning Angle

- Page ID
- 857

*Fig. 12.25 Expansion of Prandtl-Meyer function when it exceeds the maximum angle.*

The maximum turning angle is obtained when the starting Mach number is 1 and the end Mach number approaches infinity. In this case, Prandtl–Meyer function becomes

Maximum Turning Angle

\[
\label{pm:eq:MaxTurning}

\nu_{\infty} = \dfrac{\pi }{ 2} \left[

\sqrt{\dfrac{k+1 }{ k -1 }} - 1 \right]

\]

The maximum of the deflection point and the maximum turning point are only a function of the specific heat ratios. However, the maximum turning angle is much larger than the maximum deflection point because the process is isentropic. What happens when the deflection angel exceeds the maximum angle? The flow in this case behaves as if there is almost a maximum angle and in that region beyond the flow will became vortex street see Figure 12.25

## Contributors and Attributions

Dr. Genick Bar-Meir. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or later or Potto license.