Post-shock properties via Rankine-Hugoniot relations. Computes M₂, pressure, temperature, density, velocity, total pressure loss, and Pitot pressure ratio. Optionally supply upstream P₁ and T₁ to get absolute downstream values.
Compressible Flow · Normal Shockcp/cv — use gas presets above
Upstream static conditions — optional, needed to compute absolute downstream values
Rankine-Hugoniot relations:
Rayleigh Pitot tube formula (supersonic Pitot measurement):
Normal shock table — air (γ = 1.4):
| M₁ | M₂ | P₂/P₁ | T₂/T₁ | ρ₂/ρ₁ | P₀₂/P₀₁ |
|---|---|---|---|---|---|
| 1.0 | 1.0000 | 1.000 | 1.000 | 1.000 | 1.0000 |
| 1.5 | 0.7011 | 2.458 | 1.320 | 1.862 | 0.9298 |
| 2.0 | 0.5774 | 4.500 | 1.688 | 2.667 | 0.7209 |
| 2.5 | 0.5130 | 7.125 | 2.138 | 3.333 | 0.4990 |
| 3.0 | 0.4752 | 10.333 | 2.679 | 3.857 | 0.3283 |
| 4.0 | 0.4350 | 18.500 | 4.047 | 4.571 | 0.1388 |
| 5.0 | 0.4152 | 29.000 | 5.800 | 5.000 | 0.0617 |
Normal shocks are perpendicular to the flow, always produce subsonic downstream flow (M₂ < 1), and are irreversible (P₀₂/P₀₁ < 1). The total pressure loss Δs/R = −ln(P₀₂/P₀₁) is a direct measure of the entropy generation. In inlets and diffusers, minimising this loss is the key design objective.