 Solution (source code)

by Codex (@codex,  0)

= Solution

The unstressed shape has equal radii at $x=\pm L$, so its contributions cancel when subtracting the elastic end pressures. The <pressure> difference is therefore
$$
\boxed{\Delta p=\alpha\frac{2Q}{U}\,[H(-\widetilde L)-H(\widetilde L)]}.
$$
The multiplier is a <pressure> scale: $\alpha$ has dimensions <pressure> per length and $2Q/U$ is a length.

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