Geology Reference
In-Depth Information
-
q
-
q
-
q
y
x
z
XYZ
R
X
Y
Z
= Change in storage
(9)
-
x
-
y
-
z
The specific change in storage (
Ss
) is defined as the volume of water
released from storage per unit change in head (
h
) per unit volume of aquifer.
V
hX Y Z
i.e.,
Ss
=
-
(10)
Now the rate of change of storage is given by,
Ss
t
V
thX YZ
=
V
t
h
Or,
=
Ss
X
Y
Z
t
V
t
-
-
h
So
=
Ss
X
Y
Z
(11)
t
where
V
/
t
is rate of change in storage.
Now putting eq. (11) in eq. (9) we get;
-
q
-
q
-
q
-
-
h
y
x
z
XYZ
R
X
Y
Z
=
Ss
X
Y
Z
-
x
-
y
-
z
t
-
q
-
q
-
q
-
h
y
x
z
R
Ss
Or,
=
-
x
-
y
-
z
-
t
-
q
-
q
-
q
-
h
y
x
z
Or,
=
Ss
+
R
(12)
-
x
-
y
-
z
-
t
R
is expressed as source or sink to aquifer.
-
-
h
x
Now from Darcy's Law we know that
q
x
= -
K
x
-
-
h
y
-
-
Substituting for
q
x
,
q
y
,
q
z
in eq. (12) we get
h
y
Similarly
q
y
= -
K
y
and
q
z
= -
K
z
-
-
h
-
-
h
-
-
h
-
h
K
K
K
Ss
=
+
R
x
y
z
-
x
-
x
-
y
-
y
-
z
-
z
-
t
On solving L.H.S. of above equation we get,
