= Spherical Darcy injection
{title2=$q_r=\Pi a\Delta p/(\mu r^2)$}
For a sphere of radius $a$ injecting an <incompressible flow> into an infinite homogeneous isotropic <porous medium>, <Darcy's law> and <conservation of mass> give $r^2q_r=C$. Integrating $p_r=-\mu C/(\Pi r^2)$ with $p(a)-p(\infty)=\Delta p$ gives $C=\Pi a\Delta p/\mu$. The <hydraulic resistance> is $\Delta p/Q=\mu/(4\pi\Pi a)$. A common background <hydrostatic pressure> cancels <gravity> if the imposed excess <pressure> is measured relative to that background.
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