Environmental Engineering Reference
In-Depth Information
Table 3.11 Temperature measured in sandy sediments underlying a wetland at depths of 0.2 m
and 0.4 m over a period of 2 days
0.2
m
0.4
m
T
max
Day 1
21
T
min
Day 1
T
max
Day 2
T
min
Day 2
Peak time Day 1
Peak time Day 2
Amplitude, 0.2 m
¼
20
19
(
C)
(
C)
Amplitude, 0.4 m
¼
18
Δt ¼
(h)
(s)
0.2 m
0.4 m
17
0:00
12:00
0:00
12:00
0:00
Accurate estimates of
q
using this method requires pre-processing the signals
using Fourier transform or a dynamic harmonic regression algorithm (Keery
et al.
2007
; Gordon et al.
2012
). In this exercise, a simple graphical technique is
used for demonstration purposes.
The figure embedded in Table
3.11
shows the temperature data collected in
sandy sediments underlying a wetland.
1. Record the maximum and minimum temperature recorded on Day 1 for the 0.2
and 0.4 m sensor depths and enter the values in Table
3.11
. Repeat the procedure
for Day 2.
2. Record the time of peak temperature on Day 1 at 0.2 and 0.4 m depths and enter
the values in the table. Repeat the procedure for Day 2.
3. Estimate the average amplitude of temperature oscillation by calculating (
T
max
T
min
)/2 and taking the average of the 2 days.
4. Estimate the average phase shift
t
by calculating the difference in peak time for
each day and taking the average of the 2 days.
5. Calculate
D
and
H
in Eq.
3.61
assuming:
c
w
¼
Δ
4,160 J kg
1
K
1
,
ρ
w
¼
1,000
2.0 W m
1
K
1
.
6. Calculate all constants in Eq.
3.60
assuming
c
kg m
3
, and
λ
e
¼
1,400 J kg
1
K
1
,
¼
ρ ¼
2,000
kg m
3
. Note that the period of oscillation
is 86,400 s (24 h).
7. Solve Eq.
3.60
for
q
. The third-order polynomial equation has three roots, but
only one is a real number. Various numerical tools are available; for example,
MATLAB
2
software or its freeware equivalents have a line command for
solving polynomial equations. The solution also can be obtained graphically
by treating the left hand side of Eq.
3.60
as a polynomial function
f
(
q
) and
τ
2
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