Introduction to Basic Ground-Water Flow
 
By the earthDr!
 
Equipotential Maps Describing Pumping Conditions
 
Not surprisingly, when a well is pumped, the water level in the soil drops the most in those soils closest to the well and drops the least in the more distant soils. The soils closest to the well would completely dry out if it were not for water being supplied from drainage of these more distant soils to the soils closest to the well. Both plan view and cross-sectional equipotential maps, under non-pumping conditions, were illustrated on an earlier page (remember: should you need to click on this link or any link to refresh your memory - use the back button on your browser to return to this page or go to the Table of Contents page
to relocate yourself).

The figure to the left illustrates a plan view of the surface of the water table when water is pumped from a well. Notice that this equipotential map of the water table is quite different than the earlier plan view equipotential map depicting non-pumping conditions. These equipotential lines are bent, with respect to the straight line illustration of the earlier page, due to the removal of ground water by pumping at the recovery well. The ground-water flowpaths are not illustrated because they, together with the equipotential lines, would make the figure too cluttered and, therefore too confusing to glean the pertinent information. Further, an equipotential map is a more powerful tool than is a map of ground
water flowpaths. Equipotential maps may at first appear to be an unnatural way to represent flow, but with use they will become more readily understandable.

We have already shown how an equipotential map is constructed. Ground-water flowpaths can only be defined from the construction of equipotential maps. All we need is to remember is that ground-water flowpaths are still perpendicular to the constructed equipotential map, even if the equipotential line is a curve as will be the case during pumping conditions (curved equipotential lines are often the case even during non-pumping conditions). For any curved equipotential line, the flowpath can easily be constructed by first drawing a tangent to the point on the equipotential line in question and then, drawing the flowpath normal (perpendicular) to the tangent line.

The capture zone is displayed by a parabolic-like shape. Using the information that all ground-water flowpaths are perpendicular to the constructed equipotential line, then it is easy to imagine that all ground-water flowpaths within the capture zone are flowing to the recovery well. The ground-water flowpaths immediately outside the capture zone are influenced, but not captured by the recovery well. These flowpaths following along the outside perimeter of the capture zone will be shown to be an important phenomenon on future pages. Although they are not illustrated by this figure, the more distance flowpaths are not even influenced at such distances from the recovery well. At these greater distances from the recovery well, the equipotential map under pumping conditions remains unchanged from the non-pumping condition.

Remember, the earlier pages discussing topography and contouring have contour lines more closely spaced on those landscapes with the steepest slopes. Similarly, in the case of ground water, the more closely spaced equipotentials indicate that the elevation of the water table is changing more in these areas. Notice that one result of pumpage is that most of the equipotential lines, nearby the pumping well, are now more closely spaced. Just as rainfall runoff flows faster on a steeper landscape, so too does ground-water flow faster upon a steeper gradient of the water table.Therefore, the ground water is now flowing faster through these areas under pumping conditions.
To the right of the stagnation point, the spacing between the 87 and 86 equipotential lines is greater indicating that ground-water is flowing at a slower rate through this area.

Looking at the first figure on this page, it is evident that all water pumped from the well comes from the upgradient direction: the area with the greatest total head: in this example, the highest water table elevation. That point on the water table that is upgradient from the recovery well where there is no measurable drawdown of the water table due to pumpage of ground water is known as the line source. The line source can be better identified in the second figure. All equipotential lines or surfaces that are upgradient of the line source remain unchanged. (The line source is not displayed for the plan view equipotential map, because I wanted to enlarge this first figure to better depict other details). The line source identifies that area of the water table where all water supplied to the pumping well originates.

Please note the point named the stagnation point in this second figure. This is the most-downgradient point on the capture zone boundary. This point is best illustrated in a cross-sectional view of a pumping well. The stagnation point is the lowest elevation of any point on the capture zone boundary. The stagnation point has a higher water table elevation than those points just to the left or right of it (relative to the perspective of this figure). The ground water to the right of the stagnation flows away from the pumping well avoiding capture while the ground water to the left of the stagnation point is captured by the recovery well. The stagnation point is a maximum point along this segment of the drawdown curve. To the left of recovery well, no maximum point exists, nor could it be constructed since a downward sloping water table to the pumping well prohibits its devolution. The steeper the slope of the water table, the faster ground water and the contaminant load move. Therefore, upgradient of the line source, ground-water flow rate is unaffected. Downgradient of the line source, ground-water flow rate and contaminant transport is accelerated by the pumpage at the well. Typically, water tables do not have such steep slopes as illustrated. In the cross-section presentation, the slope is exaggerated in order to more easily display both the line source and the stagnation point. Both of these figures are water table depression maps (water table depression maps due to pumpage of ground water).
 
 
 
 
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