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