The Speed of groundwater flows
Water enters and leaves the saturated zone through recharge and discharge. Recharge is the infiltration of water into any subsurface formation, often by infiltration of rain or snow meltwater from the surface. Recharge also may take place through the bottom of a stream where the stream channel lies at an elevation above that of the water table (Figure 11.2). Streams that recharge groundwater in this way are called influent streams, and they are most characteristic of arid regions, where the water table is deep. Discharge is the opposite of recharge: the exit if groundwater to the surface.
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When a stream channel intersects the water table, water discharges from the groundwater to the stream. Such an effluent stream is typical of humid areas. Effluent streams continue to flow long after runoff has stopped because they are fed by groundwater. Thus, the reservoir of groundwater may be increased by influent streams and depleted by effluent streams.
The balance between discharge and recharge is strongly affected by the speeds at which water moves in the ground. Most groundwaters move slowly, a fact of nature responsible for our groundwater supplies.
If groundwater moved as rapidly as rivers do, aquifers would run dry after a period of time without rain, just as many small streams run dry. The slow-moving groundwater flow also makes rapid recharge impossible of groundwater levels are lowered by excessive pumping.
Figure 11.2 The depth of the water table fluctuates in response to the balance between water added from precipitation (recharge) and water lost by evaporation plus discharge from wells, springs, and streams. Streams become influent mainly in arid climates but also may do so after prolonged dry periods in temperate climates.
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Although all groundwaters flow through aquifers slowly, some flow more slowly than others. In the middle of the nineteenth century, Henri Darcy, town engineer of Dijon, France, proposed an explanation for the difference in flows. While studying the town’s water supply, Darcy measured the elevations of water in various wells and mapped the varying heights of the water table in the district. He calculated the distances the water traveled from well to well and measured the permeability of the aquifers. (Remember that permeability is the ease with which water passes through the pore space of the aquifer.) Here are his findings.
For given aquifer and distance of travel, the rate at which water flows from one point to another is directly proportional to the drop in elevation of the water table between the two points. As the difference in elevation increases, the rate of flow increases.
The rate of flow for a given aquifer and given difference in elevation is inversely proportional to the flow distance the water travels. As the distance increases, the rate decreases. The ratio between the elevation difference and the flow distance is known as the hydraulic gradient. Just as a ball runs faster down a steeper slope than a gentler one, groundwater flows more quickly down a steeper hydraulic gradient. Groundwater in general does not run down the slope of the groundwater table but follows the hydraulic gradient of the flow, which may travel various paths below the water table.
Darcy reasoned that the relationship between flow and hydraulic gradient should hold whether the water is moving through a porous sandstone aquifer or an open pipe. You might guess (correctly) that the water should move more quickly through a pipe that through the tortuous turns of pore spaces in an aquifer. Darcy recognized this factor and included a measure of permeability in his final equation, so that, other things being equal, the greater the permeability and thus the greater the ease of flow, the aster the flow.
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Darcy’s law, as this discovery is called, can be expressed in a simple relationship (Figure 11.3): the volume of water flowing in a certain time (Q) is proportional to the vertical drop (h) divided by the flow distance (l). The two remaining symbols are A, the cross-sectional area through which the water flows, and K, the hydraulic conductivity (a measure of permeability). (K also depends on the properties of the fluid, especially density and viscosity, which are important in dealing with fluids other than water.)
Velocities calculated by Darcy’s law have been confirmed experimentally by measuring how long it takes a harmless dye introduced into one well to reach another. In most aquifers, groundwater moves at a rate of a few centimeters per day. In very permeable gravel beds near the surface, groundwater may travel as much as 15 cm per day. This is still much slower than the speeds of 20 to 50 cm per second typical of river flow.
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Figure 11.3 Darcy’s law describes the rate of groundwater flow down a slope between two points, P1 and P2. The rate of flow is proportional to the difference in height between the high and low points of the slope (here is shown as the drop in the elevation of the water table between the two points), divided by the flow distance between them (the hydraulic gradient) and K, a constant proportional to the permeability of the aquifer.