Recently I used the Rankine-Hugoniot equation to reason that the limit of the speed of shock waves for extremely strong shocks is $\bigl(\frac{6P}{5r_0}\bigr)^{1/2}$ where $P$ is the pressure of the shock and $r_0$ the regular density of the air. But, in contrast, I used the mathematical form of the similarity solution to deduce that the speed of the shock is $\frac{2}{5}\bigl(\frac{P}{r_0}\bigr)^{0.5}$. Why the inconsistency? And what is the real value of the constant?
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