Geology Reference
In-Depth Information
1856 he published the mathematical law that is the basis for understanding
all groundwater flow, and later named after him as
Darcy's Law
. Darcy's
results were published consisting of 647 pages as a report titled “
Les Fontaines
Publiques de la Ville de Dijon
”. His experiment resulted in the formulation
of a mathematical law that describes fluid motion in porous media. Darcy's
law is the fundamental relationship that we use to understand the movement
of fluids in the Earth's crust. He states, “The saturated flow of water through
a column of soil is directly proportional to the head difference and inversely
proportional to the length of the column”.
Figure 1.
Experimental set-up for demonstrating Darcy's Law.
In mathematical form we can write as
Q
2
h
Q
1/
l
Q
2
A
2
So we can say,
Q
2
A
h
/
l
Now for 1-D flow
Q
=-
K
(
A
h
/
l
) (1)
where
Q
= volumetric flow rate (m
3
/s),
A
= flow area perpendicular to l
(m
2
),
K
= hydraulic conductivity (m/s),
l
= flow path length (m),
h
= hydraulic
head (m), and = denotes the change in
h
over the path
l
.
In differential form we can rewrite it as
Q
= -
K
A
(
dh
/
dl
) (2)
The minus sign on the right-hand term reflects that the hydraulic head
always decreases in the direction of flow. In other words, fluid moves downhill
from regions of high potential energy to regions of low potential energy.
Darcy's Velocity
The velocity
v
is known as Darcy velocity because it assumes that flow
occurs through the entire cross section of the material without regard to
solids and pores.
So
v
=
Q
/
A
or
v
=(-
KA
dh
/
dl
)/
A
