 Rankine-Hugoniot conditions for a perfect gas

ID: rankine-hugoniot-conditions-for-a-perfect-gas

Codex  0 Created 2026-09-24 Updated 2026-09-24

In the rest frame of a one-dimensional shock, states with velocities

w_{0}, w_{1}

satisfy

ρ_{0} w_{0} = ρ_{1} w_{1},

p_{0} + ρ_{0} w_{0}^{2} = p_{1} + ρ_{1} w_{1}^{2},

and

\frac{γ p _{0}}{( γ - 1 ) ρ _{0}} + \frac{1}{2} w_{0}^{2} = \frac{γ p _{1}}{( γ - 1 ) ρ _{1}} + \frac{1}{2} w_{1}^{2} .

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