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This paper develops a closed-form, analytical expression for the Darcyvelocity of a Newtonian fluid flowing through a channel filled with a porousmedium, bound by rigid walls and driven by a constant pressure gradient. Weexpress the Darcy velocity as a Weierstrass elliptic function of the transversecoordinate. It allows us to get analytical expressions for volume flux and therate of dissipation. The Weierstrass elliptic function is a doubly-periodic,complex-valued function defined over the complex plane. It takes real valuesonly on certain segments in the complex plane. We show how to align thetransverse coordinate axis along these segments to ensure real values of Darcyvelocity. Lastly, we give an algorithm to generate velocity profile and computevolume flux given the flow parameters.

Plane Poiseuille flow through a porous medium - an analytical solution