Environmental Engineering Reference
In-Depth Information
where
α
is the thermal coefficient of expansion of
water, Δ
T
is the temperature difference between
the epilimnion and the hypolimnion,
c
k
f
is a
dimensionless constant that is typically taken as
0.13, and
u
f
is the freefall velocity of induced ther-
mals given by
Depth
T
1
T
2
Δ
T
1
/Δ
z
Δ
T
2
/Δ
z
(m)
(°C)
(°C)
(°C/m)
(°C/m)
15
11.0
12.1
2.290
0.225
14
12.1
12.3
0.275
0.142
13
12.1
12.4
−0.0917
0.167
12
12.1
12.7
−0.0083
0.483
11
12.1
13.3
0.042
0.475
1 3
/
=
α
ghH
c
10
12.2
13.7
0.158
0.625
e
(7.99)
u
f
9
12.4
14.7
0.208
1.510
ρ
p w
8
12.6
16.4
0.200
1.040
7
12.8
16.8
0.208
0.792
At the beginning of September, the temperature
of the 15-m-deep epilimnion of Lake Ontario is
17.74°C, and the temperature of the 75-m-deep
hypolimnion is 5.2°C. At the beginning of Fall, the
daily average heat loss is 100 W/m
2
. Use Equation
(7.98) to calculate the change in depth of the epi-
limnion at each step, using also Equations (7.96)
and (7.97). Continue your calculations until the
temperature of the epilimnion no longer exceeds
the temperature of the hypolimnion. Based on this
result, when do you expect Lake Ontario to be
well mixed? Use a time step of 10 days, and assume
that the physical properties of the water are con-
stant:
α
= 2.57 × 10
−4
°C
−1
,
c
p
= 4179 J/(kg°C), and
ρ
w
= 997 kg/m
3
.
7.31.
A nearshore discharge of a contaminant from a
single-port outfall into a lake results in a con-
taminant concentration of 10 mg/L at a distance
of 10 m from the discharge location. The lake
currents are negligible, the dispersion coefficient
in the lake is 5 m
2
is and the decay rate of the
contaminant is 0.01 d
−1
. Estimate the contami-
nant concentration 100 m from the discharge
location.
6
13.0
18.0
0.158
0.650
5
13.1
18.0
0.033
0.017
4
13.1
18.2
0.042
0.117
3
13.2
18.2
0.083
−0.0167
2
13.3
18.2
0.267
0.000
1
13.7
18.2
0.450
0.763 × 10
−5
Source of data
: Lung (2001).
Estimate the variation of the vertical diffusion
coefficient over the depth of the lake on May 21
and June 6, 1974.
7.30.
Consider a lake with an epilimnion of thickness
h
and temperature
T
e
, a hypolimnion of thickness
H
and temperature
T
h
, and the thermocline has neg-
ligible thickness. If over a time interval, Δ
t
, the
epilimnion mixes with a depth Δ
h
of the hypolim-
nion, the temperature of the epilimnion can be
expected to decrease by Δ
T
e1
, where
(
T T
h
−
)
e
h
(7.96)
∆
T
1
=
∆
h
e
If the rate of heat loss from the epilimnion is
H
e
,
the temperature of the epilimnion over time inter-
val Δ
t
is given by
7.32.
Measurements in the vicinity of a nearshore
outfall in a lake indicate that the contaminant con-
centration 20 m from the outfall is approximately
twice the concentration at a distance 40 m from
the outfall. Observations also indicate that the
currents in the lake are negligible, and the decay
constant of the contaminant is 0.05 d
−1
. Estimate
the dispersion coefficient.
H t
c
∆
e
∆
T
2
=
(7.97)
e
ρ
h
p w
where
c
p
and
ρ
w
are the specific heat and density
of water, respectively. A dynamic two-layer model
for estimating the growth of the epilimnion during
a season where the reservoir is cooling is given by
7.33.
A pollutant is released at a rate of 0.5 kg/s on the
side of a lake that is 2.0 m deep and 30 m wide.
The lake has a dispersion coefficient of 1.5 m
2
/s,
an alongshore velocity of 10 cm/s, and the first-
order decay constant of the pollutant is 0.10 min
−1
.
What is the steady-state concentration 50 m
downstream of the source?
α∆
Tgh
dh
dt
f
3
(7.98)
=
c u
k
f
Search WWH ::
Custom Search