One way of cleaning up environmentally polluted underground water is to pump it out of the ground, treat it with some equipment (by catalytic or photochemical oxidation, for example), and then pump it back into the ground. This is referred to as the pump-and-treat process in the EPA jargon.

Here we address a part of the design calculations, namely the problem of the pressuredrop calculation. In particular, the problem we wish to solve is that of determining an estimate of the pressure drop between the point of pumping and the point of discharge The system is modeled as a line source (along a vertical line) at a point A (the pump location) and a line sink at a point B (the location of the discharge point). Also the pressure variation in the vertical direction is ignored. This makes the problem \(2 \mathrm{D}\), and the theory for potential flow developed in this chapter can be used. Note that once the 2D case has been solved corrections can be applied for the pressure variation in the vertical direction. Your goal is to use some Laplace solver and simulate pressure profiles in this medium. The corresponding velocity profiles can then be computed by applying Darcy's law.