Isentropic Flow Calculator

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Choose the known quantity and enter its value below.
Flow speed divided by local speed of sound. M < 1 is subsonic, M > 1 is supersonic.
Ratio of specific heats Cp/Cv. Air at ambient temperature is 1.4.
Mach number (M)Supersonic
2

Flow speed relative to local speed of sound

Flow regimeSupersonic
Pressure ratio (P/P₀)0.127805
Temperature ratio (T/T₀)0.555556
Density ratio (ρ/ρ₀)0.230048
Area ratio (A/A*)1.6875
Critical pressure ratio (P*/P₀)0.528282
Critical temperature ratio (T*/T₀)0.833333
Critical density ratio (ρ*/ρ₀)0.633938
Mach angle (μ)30°
Prandtl-Meyer function (ν)26.38°
P/P₀ (Pressure ratio)0.127805
T/T₀ (Temperature ratio)0.555556
ρ/ρ₀ (Density ratio)0.230048
2 M
Subsonic<0.8High Subsonic0.8-1Supersonic1-3Hypersonic3+

Supersonic flow at M = 2.0000 with γ = 1.4

  • At M = 2.0000, the static pressure is 12.78% of the stagnation pressure, meaning the flow has converted 87.22% of its reservoir pressure into kinetic energy.
  • The static temperature is 55.56% of the stagnation temperature (T/T0 = 0.5556), and the density is 23.00% of the stagnation density.
  • A duct section at this Mach number requires an area ratio A/A* = 1.6875 relative to the sonic throat.
  • The Mach cone half-angle is 30.00 degrees. The Prandtl-Meyer expansion angle is 26.38 degrees, meaning the flow can turn up to 26.38 degrees isentropically from sonic conditions.

Next stepFor nozzle design, pair these results with a normal-shock calculator to determine the conditions downstream of a shock if one forms in the diverging section.

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