Environmental Engineering Reference
In-Depth Information
Temperature (°C)
Temperature (°C)
Temperature (°C)
Depth
Depth
Depth
(m)
Oct
Nov
(m)
Oct
Nov
(m)
Oct
Nov
0
20.0
19.3
6
16.0
17.3
12
14.7
16.2
1
19.8
19.0
7
15.5
17.0
13
14.6
16.0
2
19.4
18.5
8
15.3
16.8
14
14.5
15.9
3
19.0
18.0
9
15.1
16.7
15
14.4
15.7
4
18.5
17.7
10
15.0
16.5
-
-
-
5
17.5
17.4
11
14.8
16.4
-
-
-
Estimate the vertical mixing coefficient as a function of
depth.
n
∑
∆
∆
T
t
z
∂
∂
∂
∂
T
t
dz
T
z
∆
z
∫
(7.81)
−
h
i
=
1
K z
z
( ) =
=
∆
∆
T
z
Solution
From the given data, the density profile changes over
the course of a month, so take Δ
t
= 30 days. Equation
(7.78) will be used to calculate the vertical profile of the
mixing coefficient,
K
z
, and is discretized as follows
where
n
is the number of depth intervals from the
bottom of the lake up to elevation
z
. The computations
to calculate
K
z
(
z
) are summarized in the table below:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
∂
∂
T
z
∂
∂
T
z
∂
∂
T
z
∂
∂
T
t
∂
∂
T
t
∑
T
t
∂
1
2
Depth
T
1
T
2
∆
∆
K
z
(m
2
/d)
(m)
(°C)
(°C)
(°C/m)
(°C/m)
(°C/m)
(°C/d)
(°Cm/d)
(°Cm/d)
0
20.0
19.3
−0.023
0.2
0.3
0.25
−0.025
0.333
1.33
1
19.8
19.0
−0.027
0.4
0.5
0.45
−0.028
0.358
0.80
2
19.4
18.5
−0.030
0.4
0.5
0.45
−0.032
0.387
0.86
3
19.0
18.0
−0.033
0.5
0.3
0.40
−0.030
0.418
1.05
4
18.5
17.7
−0.027
1.0
0.3
0.65
−0.015
0.448
0.69
5
17.5
17.4
−0.003
1.5
0.1
0.80
0.020
0.463
0.58
6
16.0
17.3
0.043
0.5
0.3
0.40
0.047
0.443
1.11
7
15.5
17.0
0.050
0.2
0.2
0.20
0.050
0.397
1.98
8
15.3
16.8
0.050
0.2
0.1
0.15
0.052
0.347
2.31
9
15.1
16.7
0.053
0.1
0.2
0.15
0.052
0.295
1.97
10
15.0
16.5
0.050
0.2
0.1
0.15
0.052
0.243
1.62
11
14.8
16.4
0.053
0.1
0.2
0.15
0.052
0.192
1.28
12
14.7
16.2
0.050
0.1
0.2
0.15
0.048
0.140
0.93
13
14.6
16.0
0.047
0.1
0.1
0.10
0.047
0.092
0.92
14
14.5
15.9
0.047
0.1
0.2
0.15
0.045
0.045
0.30
15
14.4
15.7
0.043
Search WWH ::
Custom Search