= Choking by wall thickness in an elastic tube
{title2=$h_c/R=1+\lambda/4-5\lambda^{1/5}/4$}
For steady uniform-density inviscid flow with pressure law $p=p_0+k(r-R)$ and a prescribed thickness $h$, mass conservation and the <Bernoulli equation> give $h/R=1-s^{-1/2}+\lambda(1-s^2)/4$, where $s=u/V$ and $\lambda=2\rho V^2/(kR)$. The function has a unique maximum at $s=\lambda^{-2/5}$, producing the displayed choking bound. Below it there are two positive roots; continuity from the upstream state selects the lower-speed root for $\lambda<1$ and higher-speed root for $\lambda>1$. At $\lambda=1$, the maximum is zero and any positive prescribed thickness is incompatible with this model.
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