2.1 Introduction
One of the fundamental equations that govern groundwater flow is called Darcy’s law as shown by Equation (2).1
| [latex]Q = - K\ A\ \frac{dh}{dl}[/latex] | (2) |
|---|
where (parameter dimensions are dark green font with mass as M, length as L, time as T):
| [latex]Q[/latex] | = | discharge (L3T-1) |
|---|---|---|
| [latex]K[/latex] | = | hydraulic conductivity (LT-1) |
| [latex]A[/latex] | = | cross sectional area perpendicular to flow (L2) |
| [latex]\frac{dh}{dl}[/latex] | = | hydraulic gradient, change in hydraulic head h over a distance [latex]l[/latex] (:) |
In plain words, this equation states that discharge (i.e., volumetric flow) through a cross‑sectional area of a porous medium is directly and linearly proportional to the hydraulic gradient, and the constant of proportionality that relates discharge to the hydraulic gradient is a quantity called the hydraulic conductivity. The negative sign indicates that flow is in the opposite direction of the gradient.
We get into the details of the equation in other sections of this book, but for now, let us focus on the lowercase h in the hydraulic gradient term—that is, hydraulic head.
1 Units for all equation variables in this book are expressed in general terms of length (L), mass (M), and time (T); for example, units of volumes are expressed as L3, velocity as LT-1, and so on.