How this calculator works
These relations describe a calorically perfect gas in reversible adiabatic flow. Stagnation properties describe bringing that local stream to rest isentropically; sonic reference properties occur at Mach one. The same area ratio above one admits both subsonic and supersonic states, so the inverse modes choose a branch. Shock waves, friction and heat transfer invalidate the constant-entropy model. In velocity mode, entered static temperature determines stagnation temperature; the separate stagnation-temperature entry is ignored.
Formula
T/T0 = [1 + (gamma - 1)M²/2]^-1; p/p0 = (T/T0)^[gamma/(gamma - 1)]; rho/rho0 = (T/T0)^[1/(gamma - 1)]; A/A* = [(2/(gamma+1))(1+(gamma-1)M²/2)]^[(gamma+1)/(2(gamma-1))]/M; mdot = rho A M sqrt(gamma Rs T).
Worked example
For gamma = 1.4 and M = 1, T/T0 = 0.8333333333, p/p0 = 0.5282817877 and A/A* = 1. At M = 2, T/T0 = 0.5555555556, p/p0 = 0.1278045255 and A/A* = 1.6875.
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Frequently asked questions
Why choose an area-ratio branch?
A converging-diverging nozzle can have a subsonic or supersonic local state for the same A/A*; boundary conditions determine which occurs.
Is a Mach angle defined below Mach one?
No. The result appears only at sonic or supersonic speed.
What happens at Mach zero?
Mass flow and equivalent throat area are zero. The unbounded area ratio and undefined Mach angle are omitted.