The value
of using contour maps and equipotential maps to define ground-water flow
has been illustrated. How is a contour map or equipotential map constructed?
First it is necessary to install a minimum of three wells. Perforated pipe
is used so that water can drain into the well from the surrounding saturated
soils. Three wells are needed for triangulation. Let's see just what is
triangulation. In this figure, three wells are depicted in a triangular
orientation. The perforated pipe or well screen for our example penetrates
approximatelty one foot into the water table. A survey is done to locate
the position of each well, both horizontally and vertically. The elevation
of the top of well, commonly known as the top of casing, is measured in
the survey. All future ground-water levels are measured from the top of
the well casing. Subtracting the measured depth to ground-water from the
surveyed elevation for the top of the well casing results in the establishment
of the water table elevation at that, and only that, well. The elevation
of the water table can be established in similar fashion for the position
of the water table at the remaining two wells. Now an imaginary line can
be constructed on the survey paper between the well with
the highest water level
elevation and the well with the lowest water elevation. In our example figure
to the left, monitoring well No. 1 has the highest ground-water level and
monitoring well No. 3 has the lowest ground-water level. The ground-water
level at monitoring well No. 1 is at an elevation of 90 feet and the ground-water
level at monitoring well No. 3 is at an elevation of 70 feet. The ground-water
level at monitoring well No. 2 is at an elevation of 80 feet. The 80 foot
elevation must be somewhere on this imaginary line joining monitoring well
numbers one and three. Obviously if the surface of the water table is a
plane, an 80-foot elevation must be halfway between the 90 foot elevation
at monitoring well No. 1 and the 70 foot elevation at monitoring well No.
3. We can now construct a line from the location of monitoring
well No. 2 to that point on the imaginary line that has an elevation equal
to 80 feet.The line produced by this construction, in this case, would be
called the 80-foot contour. Water elevations determined along this 80-foot
contour from any additional wells installed along this contour would also
have water table elevations of 80 feet. Please note that the 80-foot contour
would be at a right angle to an arrow arrow that could be drawn depicting
ground-water flow. Ground-water flow is at a right angle to the constructed
contour level. Contour levels are used to construct surface maps. Surface
maps utilizing contour levels are typically called topographic maps. The
contours from these maps indicate points of equal elevation. If contour
levels are closely placed, it indicates that surface elevation is changing
more over short distances than in other areas where they are not closely
spaced. If the ground-water level at monitoring well No. 2 had been 83 feet;
then, the 83-foot elevation would have been 13/20 along the imaginary line
joining monitoring well No. 1 and No. 3. Often times this is, at best, an
approximation. The change in the water level along this imaginary line,
joining the monitoring well with the highest water table elevation and the
monitoring well with the lowest water table elevation, normally is not changing
at a constant rate nor is the surface of the water table normally a plane.
In a 3-dimensional view such as this, it is possible to display the equipotential
lines in a plan view (downward view) and in a cross-sectional view (side
view). Notice that all of the plan view equipotential lines are paired in
like manner with cross-sectional equipotential lines of the same magnitude.
These paired equipotential lines describe a plane or a surface. Equipotential
surfaces assist in visualization of water-table flow, but from a 3-dimensional
perspective. Wells screened at a common equipotential surface have the same
static water level (total head - potential) even if the wells are constructed
to different depths (elevations).
Practically, it is not possible to complete a well so that the screened
interval only intersects one, and only one, equipotential surface. Therefore,
let's assume that all the wells have such infinitesimally small-screen lengths
so as to preclude them from intersecting any more than one equipotential
surface. In other words, all (short-screened) wells constructed with the
well screened across the same equipotential surface have the same measured
ground-water elevation in the well regardless of the final completion depth
of the wells. This figure depicts flat, but slightly, downwardly oriented
equipotential surfaces - like the pages in a book which is leaning to the
side in your bookcase. The 70 foot equipotential surface can be described
locating two other wells somewhere else on this surface, provided that at
least one of these wells intersect this surface at a different depth.
But how likely is it to locate the 70 foot equipotential surface that is
of itself an infinitesimally small cross-sectional area with an infinitesimally
small well screen? The answer to this is that the 70 foot equipotential
surface does not have to be intersected by even one well with an infinitesimally
small well screen. To simplify the solution to this problem: assume
that there are numerous wells situated to either side of the 70 foot equipotential
at various spatial locations.
Just as interpolation was used to define the equipotential lines for the
water table, interpolating between two wells with static water levels just
above and below the 70 equipotential surface can be used to approximately
define the 70 equipotential surface. Equipotential surfaces do not have
to be plane or flat, regardless of whether they are in the water table or
in a confined aquifer (we will discuss a confined aquifer later). Equipotential
surfaces can be bent into varied shapes. Bent equipotential surfaces are
more commonly the rule even under naturally occurring hydrogeologic conditions
that are unaffected by pumping of the ground water. We will see this in
future examples. Arrows to define ground-water flow can't be located at
a right angle to the equipotential surface. Arrows to denote ground-water
flow direction are located normal to the constructed equipotential surface.
Remember, that
ground-water flow is typically in 3 dimensions and that equipotential lines
are just the surface expression of a equipotential surface. |
