Problem 4.22: The governing equation for an unconfined aquifer with flow in the radial dir...

Problem 4.22: The governing equation for an unconfined aquifer with flow in the radial direction is given by the differential equation

where is the coefficient of permeability, the recharge, and the piezometric head. Pumping is considered to be a negative recharge. Consider the following problem. A well penetrates an aquifer and pumping is performed at at a rate Q = 150 m2/h. The permeability of the aquifer is = 25 m3/h. A constant head = 50 m exists at a radial distance L = 200 m. Determine the piezometric head at radial distances of 0, 10, 20, 40, 80, and 140 m (see Fig. P4.22). You are required to set up the finite element equations for the unknowns using a nonuniform mesh of six linear elements.