Fundamentals of Groundwater Hydrogeology - Introduction to Phytoremediation of Contaminated Groundwater - page 96

water (Freeze 1994). Darcy passed water through well-
sorted sand grains in a column of known dimensions
(Fig. 4.1 ).
The column or cylinder had a known cross-section area,
A , and was stoppered at both ends, with the exception of a
tube at the elevated end that allowed water to enter, Q in , and
a tube at the bottom that allowed the water to exit, Q out .To
measure the water properties inside the cylinder Darcy fitted
two mercury-filled tubes, or manometers, through the cylin-
der so that they penetrated into the sediment-filled column.
The two tubes were separated by a distance, L . He filled the
column completely with water, turned it on end, and then
added a flow of water, Q in , at the top to equal the flow that
left the bottom. In other words, flow conditions were at
steady state, where Q in ¼

describing solids were just becoming unraveled. The
scientists Poiseuille, of poise fame, and Hagen in 1841
(Freeze and Cherry 1979) both studied the flow of fluid
through pipes with the diameter of capillary tubes and
noted that fluid flow, Q , was proportional to the cross-section
area, A , of the pipe and rate of discharge, v

Q ¼ vA : (4.1)

Darcy must have known of these studies, because Darcy's
observations are a corollary to Eq. 4.1 .
Darcy expanded upon his results of water flow through
columns and demonstrated that the specific discharge,
or velocity, v , of water through the cylinder of cross-section
area, A , was directly proportional to the difference between
h 2 and h 1 , an observation not considered by Poiseuille
and Hagen since they were using pipes with no manometers.
Darcy observed that a greater head difference between
two measuring points gave rise to higher specific discharge
if the distance between the two measurements,

Q out .
As the water flowed through the column, it also rose
inside the manometers. The elevation to which water rose
in each manometer above a common datum is called the
head. Darcy observed that the head in each tube was differ-
ent and decreased in the direction of flow. For example, the
water rose higher in the tube closest to the inflow, h 2 , relative
to the water level in the tube closest to the outflow, h 1 . The
difference between these two water-level elevations was,
therefore, h 2 - h 1 ,or

L , remained
constant. Also, v was indirectly proportional to L (1/

D

D L )if

D h was constant. Combined, Darcy's observations state that

h . As we will see later in this chapter,
Darcy's measurement of head in each tube represent the sum
of the pressure head of the column of water above the
manometer inlet, and the elevation of the manometer inlet
from a common datum.
Darcy was not breaking new ground with this observation
that water flow through a sediment-filled column resulted in
a head difference that could be measured. Water flow had
been studied, albeit in open channels, prior to Darcy. The
flow of fluids through pipes also was an area of great scien-
tific interest, particularly in the time of Newton, when laws

D v ¼ D h =D L ; (4.2)

where h is the hydraulic head and L is the hydraulic

gradient. In much the same way that changes in height of a
mercury-filled capillary tube, or thermometer, indicate
changes in air temperature, changes in the height of water-
filled tubes indicate changes in the water gradient and, there-
fore, discharge. Darcy's studies were important in that until
his work the flow of water had been investigated only in
streams and rivers.

D h / D

4.1.1 Hydraulic Conductivity

Up to this point of Darcy's experiment, the statement could
be made that the flow of water through the sand-filled
columns between two points was controlled solely by the
head gradient. But what if the column contained gravel
instead of sand? Although Darcy packed his columns care-
fully with uniform sand grains characteristic of those that
were in the sand filters of Dijon, he hypothesized that the
flow of water, as specific discharge, v , through a column of
gravel would be different from flow through sand. To
account for the flow of water through different soil types
that might affect the flow rate through the column, Darcy
introduced a constant of proportionality, K , such that Eq. 4.2
becomes

Fig. 4.1 Darcy's miniaturized sand filter, or column, used in his
laboratory experiments to more easily observe the effect of differences
in head, h cross-sectional area, A and hydraulic conductivity, K on
water flow, Q .

v ¼ K D h =D l : (4.3)