Shockwave — Rankine-Hugoniot Conditions

Mach number M₁3.0 Upstream T₁ (K)300 Upstream ρ₁ (kg/m³)1.225 γ (heat capacity ratio)1.40

Mach M₂—

Density ratio ρ₂/ρ₁—

Pressure ratio p₂/p₁—

Temperature ratio T₂/T₁—

Entropy rise ΔS/R—

Shock speed (km/s)—

The Rankine-Hugoniot conditions express conservation of mass, momentum, and energy across a shock:

ρ₁u₁ = ρ₂u₂
p₁+ρ₁u₁² = p₂+ρ₂u₂²
h₁+u₁²/2 = h₂+u₂²/2

For a normal shock, entropy always increases (2nd law). At M→∞, ρ₂/ρ₁→(γ+1)/(γ−1) ≈ 6 for air.