= Pressure-density Hugoniot relation for a perfect gas
Let $P=p_2/p_1$ and $D=\rho_2/\rho_1$ be the <pressure> and <mass density> ratios across a <normal shock wave> in a <perfect gas> with <specific-heat ratio> $\gamma$. Eliminating the velocities from the <Rankine-Hugoniot conditions for a perfect gas> gives
$$
\frac{\gamma}{\gamma-1}(p_2/\rho_2-p_1/\rho_1)
=\frac12(p_2-p_1)(1/\rho_1+1/\rho_2),
\qquad
D=\frac{(\gamma+1)P+\gamma-1}{(\gamma-1)P+\gamma+1}.
$$
As $P\to\infty$, the ratio tends to the <shock compression ratio> $(\gamma+1)/(\gamma-1)$.
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