Prandtl-Meyer Expansion Calculator

Your details

Choose which quantity to solve for. The other two become the known inputs.
The ratio of specific heats for the gas. Air at standard conditions is 1.40.
The Mach number of the flow approaching the expansion corner. Must be greater than 1 (supersonic).
The angle of the convex wall turn that causes the expansion. Must be positive and less than the maximum Prandtl-Meyer angle.
deg
Optional. Enter the upstream static pressure to compute the absolute downstream pressure.
Pa
Optional. Enter the upstream static temperature to compute the absolute downstream temperature.
K
Downstream Mach number (M2)Supersonic
2.5984

Mach number after the expansion fan

Deflection angle (theta)15deg
Upstream Mach number (M1)2
Prandtl-Meyer angle (nu1)26.3798deg
Prandtl-Meyer angle (nu2)41.3798deg
Upstream Mach angle (mu1)30deg
Downstream Mach angle (mu2)22.6341deg
Pressure ratio (P2/P1)0.393068
Temperature ratio (T2/T1)0.765832
Density ratio (rho2/rho1)0.513256
Downstream pressure (P2)39,827.59Pa
Downstream temperature (T2)220.67K
P2/P10.393068
T2/T10.765832
rho2/rho10.513256

Isentropic expansion to M2 = 2.5984

  • The flow accelerates from Mach 2.000 to Mach 2.598 through the 15.00-degree expansion fan.
  • Static pressure drops by 60.69% (P2/P1 = 0.3931), consistent with isentropic expansion.
  • Static temperature falls by 23.42% (T2/T1 = 0.7658). Total temperature is conserved because the process is isentropic.
  • Total (stagnation) pressure is preserved across an expansion fan, unlike across a shock wave.

Next stepTo find oblique shock properties for compression, use a companion oblique shock calculator. Expansion and shock solutions bracket the full two-dimensional supersonic corner problem.

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