In 1856, H. Darcy published a paper where he described experiments showing that the flow of fluid through a porous medium was linearly related to the pressure drop across the medium. where k is the...

In 1856, H. Darcy published a paper where he described experiments showing that the flow of fluid through a porous medium was linearly related to the pressure drop across the medium.

where k is the permeability of the porous medium. In three dimensions Darcy’s Law can be written as:

Show that if the fluid is incompressible, the pressure must obey Laplace’s Equation (∇²P = 0).