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and Lee,
1992
). Then the average solute concentration in the drainage water
C
out
(kg
m
-3
) follows from:
½
Lx
L
−
C
=
1
C
=
3
C
=
C
(5.35)
out
in
in
in
½
2
4
Combination of Eqs. (
5.33
) and (
5.35
) gives the solute concentration in the drainage
water as a function of time:
−
Rt
H
φ
(5.36)
CC
=
1
−
e
out
in
We may extend this equation for the case the initial groundwater concentration
amounts
C
orig
(kg m
-3
):
)
−
φ
Rt
H
(
CCCC
=+ −
e
(5.37)
out
in
orig
in
Question 5.15:
Extend Eq. (
5.36
) for the general case with an initial groundwater con-
centration, which should result in Eq. (
5.37
).
Equation (
5.37
) has a much broader application than the concentration luctuations
in drainage water at parallel canals or drains. Also groundwater concentrations of
tube wells, and outlet concentrations of perfectly mixed lakes and reservoirs, can be
described with Eq. (
5.37
) (Van Ommen,
1988
).
Question 5.16:
Consider an area of intensive agriculture with an unsaturated zone of
4 m thick and a root zone of 1 m thick. The mean water content in the unsaturated zone
amounts to 0.20 cm
3
cm
-3
and the precipitation surplus amounts to 300 mm y
-1
.
a) How long is the mean residence time of nitrate in the unsaturated zone? The adsorp-
tion of nitrate is negligible.
The phreatic aquifer is 5 m thick, has a porosity of 0.25 cm
3
cm
-3
and has an aqui-
tard at the bottom. We may neglect the vertical groundwater luxes over the aqui-
tard. Further, the phreatic aquifer is drained with canals with a distance in between of
1 km. Owing to long-term high amounts of fertilizer and manure, the nitrate concentra-
tion in the groundwater has risen towards 50 mg L
-1
.
b) Because of restricted application of fertilizers and manure, the concentration of nitrate
in the percolation water from the root zone decreases from 50 mg L
-1
to 10 mg L
-1
.
How high is the nitrate concentration in the drainage water lowing into the canals
5 years after this decrease in the root zone? You may neglect the nitrate decomposi-
tion in the unsaturated zone below the root zone. Take into account the residence time
in the unsaturated zone.
c) How long will it take from the decrease in the root zone until the nitrate concentration
in the drainage water lowing into the canals has decreased from 50 to 20 mg L
-1
?
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