The Groundwater Flow Equation

Abstract

In this chapter, the differential groundwater flow equation that governs the distribution of the flow directions and rates in an aquifer is derived. The problem is examined at a macroscopic scale, neglecting an analysis of detailed solid–liquid interface distribution, which would entail excessive analytical and computational complexity, without contributing useful information from an operational standpoint. The equation is thus determined as a combination of the equations that express the law of mass conservation (whose terms are described for a representative elementary volume), Darcy’s law, and the storage variation due to changes in hydraulic head. Unsteady state groundwater flow in each aquifer type is described by a different equation, each defining the Laplacian of the hydraulic head as a function of the aquifer’s storage and transport capacity, and of the hydraulic head’s partial derivative with respect to time. In particular, in the case of confined aquifers, flow is a function of specific yield and transmissivity, as is the case even for leaky aquifers, whose hydrodynamic behavior is, however, also affected by the leakage between aquifers (quantified by the leakage factor). A rigorous description of flow in unconfined aquifers would require a nonlinear and nonhomogeneous differential equation due to the inclination of the water table with flow; however, under simplifying conditions an approximate description, analogous to the confined aquifer equation, can be defined as a function of specific yield and transmissivity.