Ratio of flow velocity to local speed of sound. Determines compressibility regime from incompressible to hypersonic.
Compressible FlowAir at moderate T: γ = 1.4 · High-T air: γ → 1.3
R = Ru / Mmol · Air: 287 J/(kg·K)
Speed of sound and Mach number:
Stagnation (total) temperature:
T₀ is the temperature a fluid parcel would reach if brought isentropically to rest.
Flow regime classification:
| Regime | Mach range | Notes |
|---|---|---|
| Incompressible | M < 0.3 | ρ change < 5%, incompressible eqs. valid |
| Subsonic | 0.3 – 0.8 | Compressibility significant, no shocks |
| Transonic | 0.8 – 1.2 | Mixed sub/supersonic regions, shocks form |
| Supersonic | 1.2 – 5 | Oblique shocks, Mach cone |
| Hypersonic | M > 5 | Aero-heating, real-gas effects |
Common gas properties (at moderate temperature):
| Gas | γ | R (J/kg·K) |
|---|---|---|
| Air | 1.400 | 287 |
| Helium | 1.667 | 2077 |
| Argon | 1.667 | 208 |
| Hydrogen | 1.405 | 4124 |
| CO₂ | 1.289 | 189 |
| Methane | 1.320 | 518 |
Where: