Solution
= Solution
Steady <mass conservation> makes $\alpha u=Q$. For uniform area, $u=U=Q/\alpha_0$ is constant and the <pressure-area law of a collapsible tube> gives $p_x=p'_e(x)$. The acceleration vanishes, so momentum balance requires
$$
\boxed{p'_e(x)=-R(\alpha_0)\frac{Q}{\alpha_0}.}
$$
The external <pressure> must therefore decrease linearly along a positive-flow tube. Its additive constant is free; the constant transmural <pressure> is $\widetilde P(\alpha_0)$.