The foundations of our modern understanding of groundwater movement began in the mid-nineteenth century with the work of the French scientist-engineer Henri Darcy. One of the experiments Darcy carried out showed that the velocity of groundwater flow is proportional to the slope of the water table: The steeper the slope, the faster the water moves (because the steeper the slope, the greater the pressure difference between two points). The water table slope is known as the hydraulic gradient and can be expressed as follows:
where h1 is the elevation of one point on the water table, h2 is the elevation of a second point, and d is the horizontal distance between the two points (Figure 1). Darcy also experimented with different materials, such as coarse sand and fine sand, by measuring the rate of flow through sediment-filled tubes that were tilted at varying angles.
He found that flow velocity varied with the permeability of the sediment: Groundwater flows more rapidly through sediments having greater permeability than through materials having lower permeability. This factor is known as hydraulic conductivity and is a coefficient that takes into account the permeability of the aquifer and the viscosity of the fluid. To determine discharge (Q)—that is, the actual volume of water that flows through an aquifer in a specified time—the following equation is used:
where is the hydraulic gradient, K is the coefficient that represents hydraulic conductivity, and A is the cross-sectional area of the aquifer. This expression has come to be called Darcy’s law, in honour of the pioneering French scientist-engineer. Using this equation, if you know an aquifer’s hydraulic gradient, conductivity, and cross-sectional area, you can calculate its discharge.
Different Scales of Movement The geographic extent of groundwater flow systems varies from a few square kilometres or less to tens of thousands of square kilometres. The length of flow paths ranges from a few meters to tens and sometimes hundreds of kilometres. Figure 2 is a cross-section of a hypothetical region in which a deep groundwater flow system is overlain by and connected to several, more shallow local flow systems. The subsurface geology exhibits a complicated arrangement of high-hydraulic-conductivity aquifer units and low hydraulic- conductivity aquitard units.
Starting near the top of Figure 2, the blue arrows represent water movement in several local groundwater systems that occur in the upper water-table aquifer. The groundwater systems are separated by groundwater divides at the center of the hills, and they discharge into the nearest surface water body. Beneath these most shallow systems, red arrows show water movement in a somewhat deeper system in which groundwater does not discharge into the nearest surface water body but into a more distant one. Finally, the black arrows show groundwater movement in a deep regional system that lies beneath the more shallow ones and is connected to them. The horizontal scale of the figure could range from tens to hundreds of kilometres.