Gas Speed of Sound, Mach and Stagnation State

Method & assumptions

1. Calorically perfect ideal gas with constant specific gas constant R and γ > 1. Enter static absolute pressure and Kelvin temperature, not stagnation conditions. Defaults approximate dry air; no atmospheric or composition lookup is performed.
2. ρ = p/(RT); a = √(γRT); M = v/a. Mach depends on the local gas state, not a universal speed factor. R is per kilogram, not the universal molar gas constant.
3. Let F = 1 + (γ − 1)M²/2. Then T0/T = F, p0/p = F^[γ/(γ − 1)], and ρ0/ρ = F^[1/(γ − 1)]. The stagnation state represents ideal isentropic deceleration to rest.
4. cp = γR/(γ − 1) and cp(T0 − T) = v²/2. Dynamic pressure q = ρv²/2 is generally different from p0 − p in compressible flow; they approach one another at low Mach number.
5. No shocks, friction, heat exchange, nozzle solution, variable heat capacities, condensation, dissociation or real-gas effects. The ideal p0 is not the downstream reading of a supersonic Pitot probe across a shock. Check constant-property validity over the calculated temperature range.

Sources

• NASA Glenn: Isentropic Flow Equations ↗
• NASA Glenn: Speed of Sound ↗