= Hydrostatic self-gravitating incompressible cylinder
{title2=$p(r)=p_{\rm ext}+\pi G\rho^2(R^2-r^2)$}
For an infinitely long circular cylinder of uniform <mass density> $\rho$, the gravitational <Poisson equation> and the <divergence theorem> give $d\Phi/dr=2\pi G\rho r$ internally. The <hydrostatic equilibrium> equation $dp/dr=-\rho\,d\Phi/dr$ and boundary value $p(R)=p_{\rm ext}$ then give the title formula. This model neglects rotation, <surface tension> and end effects.
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