2. Darcy’s (1856) law forms the foundation of
quantitative groundwater hydrology
Porous
mediu
m
Porous
mediu
m
Datum
To tank
A
B
hA
zA
zB
hB
B
A
B
A
l
l
h
h
l
h
dl
dh
v
L
Along flow direction
lA
lB
Control
valve
g
pA
g
pB
3. v = - k dh /dl
is
h
h
and
is
l
l B
A
B
A
k is the constant of proportionality known as the
hydraulic conductivity (m/d)
v = Q/A
Q = v A= - k A dh / dL flow quantity can be estimated
In Cartesian coordinate system, velocity in x, y and z
direction can be written as
vx= - kxh / x, vy = - ky h / y, vz= - kz h /z
4. Darcy`s law is valid only for laminar flow,
Reynold’s number Re is < 10,
Re = vd10/ ,
where v is Darcy velocity
d10 is the average mean grain
diameter of the porous media (90% retained on the sieve)
and
is the kinematic viscosity of water (= 0.01 cm2
/s at 20
c).
5. In groundwater flow, the groundwater head h is taken as the
summation of the pressure head + velocity head + elevation
head. Since the velocity head is negligibly small compared to
the other two values, h = p/g + z is the head normally used
in groundwater flow problems.
When the flow is not laminar, the hydraulic gradient is not
proportional to the velocity, but involves terms containing
higher powers of velocity vn
, where n is generally ≤ 2. Point
of measurement is the bottom of the piezometer.
6. Schematic representation of the vertical and lateral variation
of hydraulic conductivity
k =50
k =100
Vertical
variation
m/d
fine sand
coarse sand
fine gravel
X
Lateral variation
k =10
Z X
Y
m/d
k =10
k =50
k =100
7. Heterogeneous isotropic
(after Freeze and Cherry 1979)
kx
Aquifer classification based upon the hydraulic conductivity of the
media
K Y
K X
X
Homogeneous anisotropic
Homogeneous isotropic
Heterogeneous anisotropic
K
ky
kx =20m/d
4
ky =10m/d
k=7
11. Average groundwater flow velocity is always
higher than the Darcy velocity
e
e
v
v
A
Q
flow
for
available
area
actual
Q
v
12. Numerical Problem: Assume that three piezometers are
installed very close to each other but penetrate up to
different depths as given below:
Let A, B, and C refer to the points of measurement of
piezometers a, b, and c, respectively. Calculate
Piezometer a b c
Elevation at the
surface (m) amsl
450 450 450
Depth of
piezometer (m)
150 100 50
Depth of water
(m)
27 47 36
(modified from Freeze and Cherry 1979)
13. 1. Groundwater head at a, b, and c in m.
2. The pressure head at A, B, and C in m.
3. The elevation head at A, B, and C in m.
4. The fluid pressure at B(N/m2
).
5. Can you conceive of a hydrogeological situation that
would lead to the directions of flow indicated by these data?
6. If the formation also has two aquitards with a thickness of
15 m (lower) and 20 m (upper) respectively, and hydraulic
conductivity 0.01 m/d, compute the rate of fluid movement
across the two aquitards for an aquifer area of 4 km2
14. Ground surface
Area = 4 km2
400m
k` =.01m/d
Datum
a
Q1
k` =.01m/d
b c
A
B
C
350m
300m
27m
47m 36m
20m
15m
150m 100m
50m
Q2
Aquifer 1
Aquifer 2
Aquifer 3
450m
