## Fundamental Equations Of Groundwater Flow

The flow of water through a body of soil is a complex phenomenon. A body of soil constitutes, as described in Section 9.1, a solid matrix and pores. For simplicity, assume that all pores are interconnected and the soil body has a uniform distribution of phases throughout. To find the law governing groundwater flow, the phenomenon is described in terms of average velocities, average flow paths, average flow discharge, and pressure distribution across a given area of soil.

The theory of groundwater flow originates with Henry Darcy who published the results of his experimental work in 1856. He performed a series of experiments of the type shown in Figure 9.2.1. He found that the total discharge Q was proportional to cross-sectional area A, inversely proportional to the length As, and proportional to the head difference — as expressed mathematically in the form

where K is the proportionality constant representing hydraulic conductivity. This equation is known as Darcy's equation. The quantity Q/A is called specific discharge q. If <j)1 — <j)2 = Afi and As ® 0, Equation 9.2(1) becomes q = -K

This equation states that the specific discharge is directly proportional to the derivative of the head in the direction of flow (hydraulic gradient). The specific discharge is also known as Darcy's velocity. Note that q is not the actual flow velocity (seepage velocity) because the flow is limited to pore space only. The seepage velocity v is then FIG. 9.2.1 Darcy's experiment.