Introduction to Basic Ground-Water Flow
 
By the earthDr!
 
Describing Ground-Water Flow using Equipotentials
 
Looking at the figure below, it is evident that ground-water flow is in the direction of the red arrows which follow the steepest grade at the surface of the water table.  These arrows are at right angles to the ground-water contour lines (equipotential lines).  The construction of contour lines is not limited to just
depicting changes in grade at the surface of the earth. Contour lines can also be drawn to depict the elevation change at the water table. Just as water flowing down a slope during a rain storm is at a right angle to the constructed contour line in a topographic relief map, the flow of ground water is at a right angle to the equipotential line (or normal to the equipotential surface - both equipotential line and equipotential surface to be better defined later).  At any given point, the steepest slope is always at a right angle to the unique contour line that could be constructed to intersect that point. In other words: if a point is at an elevation of 4 1/2 feet, then, the steepest slope, starting at that point, is always at a right angle to the 4 1/2 foot contour line joining this point with contiguous and nearby points of equal elevation.

A 3-dimensional view of the water table is depicted in this figure using equipotential lines (equipotential lines are often referred to as water table contour lines when they are depicted at the surface of the water table).  In a 3-dimensional view such as this, it is possible to display equipotential lines in both a cross-sectional view (side view) and in a plan view (downward view from overhead) for all water table elevations.   Notice that the cross-sectional equipotential line of 88 foot also shares this contour line with the plan-view equipotential line of 88 foot.  All of the cross-sectional equipotential lines are paired in like manner with one, and only one, plan-view equipotential line of similar magnitude.  These paired equipotential lines when turned about their origin describe a plane (flat surface), unless these equipotential lines are describing some boundary of a curved equipotential surface. Equipotential surfaces assist in visualization of water-table flow, but from a 3-dimensional perspective.  Remember: just as surface runoff flows as sheet flow over hilly terrain, at a right angle to imaginary contours of the surface grade, so too does ground water flow at a right angle to equipotential lines and normal to the equipotential surface.
This sectional view of the water table is a 3-dimensional view.  A 3-dimensional view is not a typical way to present ground-water flow.

Typically ground-water flow is presented in 2 dimensions.  A 2-dimensional plot of ground-water flow can be displayed in cross-section (side view) or more commonly in plan view (as if looking down from above the water table) as depicted in this second figure. A 3-dimensional view may be sleeker, but it is not easily represented on a piece of paper or on a computer monitor.  It is especially hard to represent laminae (similar to the layering of onion leaves in an onion bulb) of curved equipotential surfaces (what this means will be discussed later) on either a piece of paper or on a computer monitor. The flow of ground water (arrows) always follows the steepest slope (in general - but only when isotropic conditions prevail - to be explained later), which is always at a right angle to the (properly) constructed contour line or normal to the constructed equipotential surface. Ground-water flow in this plan view is again at a right angle to the constructed contour. This second figure displays only the side view of the first figure.


The presentation of a cross-sectional view (this last figure) of equipotential lines is not as common as a plan view presentation of equipotential lines.
Development of cross-sectional equipotential lines requires
construction of pieziometers or wells at discrete depths. As well depths increase so too does the cost to define vertical flow components. However, construction of equipotential maps in both plan view and cross-section provide the means by which you can conceptualize a fairly complex 3-dimensional ground-water flow system. Try to keep in mind that that there are equipotential surfaces and that if we could slice a 3-dimensional ground-water system along any orientation, then, from that perspective we could only see the cut-surface expression of the equipotential surface expressed as an equipotential line.
 
 
 
 
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