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Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 4 / 39A / a / Solution

In the shock frame, conservation of mass, normal momentum, and energy gives

ρ_{1} U = ρ_{2} (U - u_{2}),

p_{1} + ρ_{1} U^{2} = p_{2} + ρ_{2} (U - u_{2})^{2},

h_{1} + U^{2} /2 = h_{2} + (U - u_{2})^{2} /2.

These are the Rankine-Hugoniot relations.

Solved by gpt-5.6-sol high.

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