Analytical Solutions of the Groundwater Flow Equation

The differential groundwater flow equation derived in Chap.2can besolved analytically in various geometries, provided that certain hypotheses are satis-fied. In this chapter, a polar coordinate system with radial geometry, describing theradial groundwater flow towards a well, is considered. The hypotheses underlying theanalytical solutions concern the aquifer’s geometry (constant thickness, homogene-ity and isotropy, unlimited horizontal extension, initially horizontal potentiometricsurface) and the pumping well (fully penetrating, infinitesimal radius, negligiblestorage, laminar flow and constant pumping rate). Steady state and transient analyt-ical solutions, respectively describing the drawdown as a function of the distancefrom the well (r), or of r and time, are provided for confined, leaky and unconfinedaquifers. Theis’ (and Cooper and Jacob’s approximation) and Thiem’s equationsdescribe, respectively, the transient and steady state solutions of the groundwaterflow equation for confined aquifers. Hantush and Jacob, instead, derived the tran-sient analytical solution for leaky aquifers, while De Glee formalized the steady statesolution. In the case of unconfined aquifers, the steady state solution formally coin-cides, except for an adjustment to the drawdown, to Thiem’s solution. The transientsolution was, instead, derived by Neuman, under specific simplifying hypotheses,given that a fully rigorous description of flow in unconfined aquifers would entail theuse of a nonlinear and nonhomogeneous differential equation due to the inclinationof the water table with pumping and the generation of a vertical component of flowvelocity.