Isentropic Flow Calculator (Mach Number, Static and Stagnation Properties)

What this tool does

At low speed a gas barely changes density, but near and above Mach 0.3 the compression is no longer negligible, and the stagnation (total) pressure and temperature, the values the gas would reach if brought to rest without losses, are the reference for everything else. At Mach 1 the static temperature has dropped to about 83 % of the stagnation value for air, and the pressure to about 53 %. The area ratio shows why a nozzle must narrow and then widen to go supersonic: for any area there is a subsonic and a supersonic Mach number, and the throat is where the flow reaches Mach 1.

Formula

T₀ ÷ T = 1 + (γ−1)/2 · M² · p₀ ÷ p = (T₀ ÷ T)^(γ/(γ−1)) · v = M √(γ R T) · A ÷ A* = (1/M) [ (2/(γ+1)) (1 + (γ−1)/2 · M²) ]^((γ+1)/(2(γ−1)))

Variables

Worked example

Limitations

• The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
• Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.