The Shock Jump — AE 302 Module 2

A normal shock is nature's rudest speed bump: in a distance thinner than a hair, the flow slams from supersonic to subsonic, and pressure, temperature & density all JUMP. Slide M₁ and watch the molecules — then press 🌡️ Pitot challenge to do what real engineers do: infer the Mach number from a single pressure reading.

🚀 Upstream Mach M₁ 2.00

M₂ (after)

—

p₂/p₁ pressure

T₂/T₁ temperature

ρ₂/ρ₁ density

p₀₂/p₀₁ — what you KEEP

Pitot would read p₀₂/p₁ = —

The normal-shock relations (γ = 1.4), Anderson §8.6:
M₂² = (1 + ½(γ−1)M₁²)/(γM₁² − ½(γ−1)) — always subsonic after.
p₂/p₁ = 1 + 2γ/(γ+1)·(M₁²−1) · ρ₂/ρ₁ = (γ+1)M₁²/(2+(γ−1)M₁²) · T₂/T₁ = (p₂/p₁)/(ρ₂/ρ₁)
Entropy rises, so total pressure falls: p₀₂/p₀₁ < 1 — the shock's "tax" that engineers fight to minimize.
Supersonic Pitot (Rayleigh): the probe creates its own bow shock, so it reads p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁²−2(γ−1))]^{γ/(γ−1)} · (1−γ+2γM₁²)/(γ+1) — invert it and one gauge tells you the Mach number.

Molecules go in fast & sparse (blue) — come out slow, dense & hot (red).

Module 2 · The Shock Jump