Prandtl–Meyer expansion fan - first Mach line angle


A supersonic expansion fan, technically known as Prandtl–Meyer expansion fan, is a centred expansion process that occurs when a supersonic flow turns around a convex corner. The fan consists of an infinite number of Mach waves, diverging from a sharp corner. When a flow turns around a smooth and circular corner, these waves can be extended backwards to meet at a point.

Each wave in the expansion fan turns the flow gradually (in small steps). It is physically impossible for the flow to turn through a single “shock” wave because this would violate the second law of thermodynamics.

The expansion fan consists of infinite number of expansion waves or Mach lines.The first Mach line is at an angle calculated by the shown formula.

Related formulas


μ1angle of first Mach line with respect to the flow direction (radian)
M1first line Mach number (dimensionless)