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.

\[\overrightarrow{\mathbf{v}}=-\frac{k}{\mu} \vec{abla} P \quad \text { Darcy's Law }\]

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

\[v_{x}=-\frac{k}{\mu}\left(\frac{\partial P}{\partial x}\right) \quad v_{y}=-\frac{k}{\mu}\left(\frac{\partial P}{\partial y}\right) \quad v_{z}=-\frac{k}{\mu}\left(\frac{\partial P}{\partial z}\right)\]

Show that if the fluid is incompressible, the pressure must obey Laplace's Equation $\left(abla^{2} P=0\right)$.