Fundamentals of Groundwater Hydrogeology - Introduction to Phytoremediation of Contaminated Groundwater - page 98

v ¼ iK = n e (4.6)

such that the average linear velocity of groundwater, v , can
be estimated with knowledge of the head gradient, i ,as
measured using at least two wells, the hydraulic conductiv-
ity, K , and effective porosity, n e , from laboratory

measurements or reference values.
Darcy's Law is similar to an earlier empirical expression
that describes the flow of electrons in conductive
materials—Ohm's Law. In 1827 Georg Ohm stated that the
flow of current, I , in amps is directly proportional to the
potential difference in voltage, V , across two points and is
inversely proportional to the resistance, R , between these
two points. Moreover, the hydraulic conductivity term
Darcy used is analogous to that discussed in Chap. 3 with
respect to soil hydraulic conductivity, root hydraulic con-
ductance, and even stomatal conductance, although this lat-
ter instance deals with the movement of water vapor. In all
cases, however, the central issue is the rate of water move-
ment either through a cell membrane or through a porous
media.

Fig. 4.3 Relation between discharge and hydraulic gradient for differ-
ent geologic media. Under a given hydraulic gradient, greater flow
occurs in sandy sediments or aquifers relative to aquifers with finer
sediments. To support a constant rate of flow a steeper head gradient is
required in aquifers with finer sediments.

Law has a few limitations, particularly from the perspectives of
mathematics or fluid mechanics. First, the equation is more
useful to describe the large-scale properties of flow relative to
describing flow on a small scale. This is because Darcy's Law
assumes that an aquifer acts as a homogeneous continuum of
porous material, much like one big column. This in fact is in
contrast to most aquifers, which tend to be heterogeneous on a
smaller scale because of the sedimentary processes that lead to
aquifer formation, such as layers of sand adjacent to layers of
silts and clays. This approach averages all the variations of
hydraulic conductivity inherent in a particular aquifer into one
hydraulic conductivity value that can be used to calculate
discharge.
As a result, even though the hydraulic conductivity value
in Darcy's Law has units of velocity (L/T) and Q has units of
flux (L 3 /T), it does not indicate a velocity of groundwater but
rather a volume of water moving through a cross-section area.
This is because only part of the cross-sectional area, A ,is
available for fluid movement; the rest of the area being filled
with solid matter. Darcy's Law also cannot be used to inves-
tigate water flow in the unsaturated zone or if flow is turbu-
lent. To further investigate these shortcomings of Darcy's
Law, attempts have been made to derive a similar equation
for fluid flow through porous media from physical laws, such
as the Navier-Stokes equation (see Gray and Miller 2004).
Although many groundwater scientists are well versed in
applied mathematics, most are more interested in expressions
that consist of parameters than can be readily measured—a
nod to Darcy's original experimental approach.
Even with these concerns the usefulness of Darcy's Law
to solving complex groundwater-flow problems is its simpli-
fication of parameters that control flow, in particular

4.1.2 Plants and Groundwater

Not only did Darcy experimentally determine a fundamental
relation between water and its movement through porous
media, Darcy also may have been the first hydrologist to
recognize the important relation between certain plants and
groundwater. That Darcy was aware of at least a general
relation between plants and groundwater is evident in quotes
made by a Chief Engineer in Dijon, who stated that in some
Morvan forests, springs could be found were alder trees were
growing (Darcy 1856). Darcy himself also discussed the
observations made by the French abbot Paramelle and his
observations about springs and plants. Darcy stated that
Paramelle could find groundwater discharging as springs
by the following method:
As Father Paramelle slowly walks through a valley or continu-
ous depression to find a spring there, it is obvious that he looks
carefully at plants and at the ground, from which he seeks to
infer the nature of and the strength of the plants, the consistency
of the soil, the probable presence of water, and even the approx-
imate depth of the water below the ground surface.
Darcy (1856), translated
by Bobeck (2004)

Paramelle obviously had knowledge about plant and
water relations and must have been aware of the previous
work related to the movement of water through plants, as
described in Chap. 1. Paramelle stated
Plants draw the material that feeds them from the soil and the
atmosphere. Roots withdraw from the earth water, salts, and
organic substances provided by manure. We know that this