Finding the Direction of the Groundwater Flow
In groundwater that is open to atmospheric pressure (unconfined aquifers), hydraulic gradient is
the degree of inclination of the water table in the direction of the
flow, usually described as the number of feet the water table drops per
mile.
To determine the gradient under a certain area, we assume that the face
of the groundwater represents a plane in space. In an area with no
faults or fractures, it is a safe assumption, on the order of the
assumption that the face of water in a calm pond is flat.
A point in space cannot be assigned a location but only in relation to
a viewpoint. To establish orientation, we arbitrarily “fix” points in
space from where we view the point in question and derive relative
distances and orientations. For example, in enjoying a beautiful
sunset at the beach, we take Earth as a fixed object, while in
actuality it is rotating in at least five different planes as far as
itself, the solar system and Milky Way galaxy are concerned.
To determine the location of a point in space we fixate a system of
three lines that intersect each other perpendicularly in one point
(Cartesian coordinates, see below) and we measure the shortest distance
to the point from each of these lines.
Rene Descartes (March 31, 1596 – February 11, 1650), also known
as Cartesius, worked as a philosopher and mathematician. He is equally
notable for both his groundbreaking work in philosophy and mathematics.
As the inventor of the Cartesian coordinate system, he formulated the
basis of modern geometry (analytic geometry), which in turn influenced
the development of modern calculus. Read about Rene Descartes.
A line in space is determined by connecting two points.
To determine a plane in space you need to connect three points (or establish two intersection lines).
Thus, to determine the facial plane of the water table, we find three
points on it: we install three wells and measure the elevations of the
water in the wells (usually relative to sea level).
The diagram below shows three wells: MW2, MW3 and MW4. The number
next to each well marks the elevation of the water in the well above
mean sea level. The outer red triangle represents the spatial plane of
the groundwater and with a bit of geometry we fine the direction of the
flow (the southwest turquoise arrow) and the slope of the water table,
that is 47.56 feet per mile.
