ABSTRACT
In general, the steady-state flow of an incompressible, homogeneous fluid in a three-dimensional, isotropic, homogeneous aquifer is governed by the Laplace equation
∂ φ ∂ +
∂ φ ∂ +
∂ φ ∂
≡ φ = x y z
0 2
where ϕ represents the piezometric head (or level) at any point in the flow field. Of particular interest to us is the case when ϕ does not depend on one of the spatial coordinates, say z, where z-direction is taken vertically upward. In such a case, the piezometric head (or level) becomes a function of two independent variables, that is, ϕ = ϕ(x, y), and the Laplace equation reduces to a two-dimensional case:
∂ φ ∂ +
∂ φ ∂
≡ φ = x y
x y( , ) 0 2
Now, consider an aquifer bounded by two horizontal confining layers, some finite distance H apart (Figure 4.1). When H is much smaller than the areal extent, the aquifer is called a horizontal, shallow, confined aquifer. If we assume that the areal extent is infinite, (−∞ < x < + ∞) and (−∞ < y < + ∞), and there is no source or sink in the finite plane, then the following two inferences can be drawn:
1. At a given (fixed) value of z, on any two verticals, say at (x1,y1) and (x2,y2), the specific discharge vectors q must be identical. Borrowing the terminology from fluid mechanics, the velocity profiles at the two
verticals must be identical. This inference follows from our a priori intuition that both verticals can be considered as the centroidal axis for the infinite horizontal, confined aquifer.
