Agriculture Reference
In-Depth Information
9.3.3.3 Resultant Conductivity of Horizontal and Vertical Direction
Resultant conductivity of horizontal hydraulic conductivity (
K
H
) and vertical
hydraulic conductivity (
K
V
) can be obtained as
K
H
×
K
=
K
V
(9.10)
9.3.4 Laplace's Equation for Groundwater Flow
Groundwater flow can be described by Laplace's equation. Laplace's equation
combines Darcy's equation and equation describing mass continuity.
In general form, Darcy's equation can be written as
K
d
h
d
S
q
=
V
×
1
=
K
i
×
1
=
(9.11)
where
K
is the hydraulic conductivity,
i
is the hydraulic gradient, d
h
is the head
difference with the distance d
S
.
For a three-dimensional system, it can be written as
K
d
h
d
z
For steady-state condition (no change in storage), mass continuity equation can be
written as
K
d
h
K
d
h
V
x
=
d
x
,
V
y
=
d
y
,
V
z
=
d
V
y
d
y
+
d
V
x
d
x
+
d
V
z
d
z
=
0
Putting the values of
V
x
,
V
y
, and
V
z
, we get
d
2
h
d
x
2
d
2
h
d
y
2
d
2
h
d
z
2
K
x
+
K
y
+
K
z
=
0
(9.12)
For homogeneous and isotropic soil system,
K
x
=
K
y
=
K
z
Thus, the above equation reduces to
d
2
h
d
x
2
d
2
h
d
y
2
d
2
h
d
z
2
+
+
=
0
(9.13)
which is the well-known Laplace's equation for groundwater flow.
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