Environmental Engineering Reference
In-Depth Information
tives within each time step. Under initial condi-
tions, the O
2
concentration in the layer of interest
is 6.5 mg/L and the concentrations above and
below this layer are 7.5 and 4.5 mg/L, respectively.
After the first iteration, the estimated O
2
concen-
tration in the layer of interest is 5.7 mg/L, and the
concentrations above and below this layer are 7.0
and 3.7 mg/L, respectively. Determine the next
iterative estimate of the concentration of O
2
in the
layer of interest.
Q
= 1.0
×
10
6
m
3
/d
c
= 10 mg/L
Q
= 0.5
×
10
6
m
3
/d
c
= 50 mg/L
Reservoir 1
(Volume = 10
8
m
3
)
Reservoir 2
(Volume = 10
9
m
3
)
D
7.27.
Temperature measurements in a lake indicate that
the epilimnion temperature is normally constant
in the summer, and the heat transfer coefficient
between the epilimnion and hypolimnion is
approximately 5.0 cm/d. Typical thicknesses of the
thermocline and hypolimnion are 0.8 and 20.0 m,
respectively. If the temperatures at the beginning
of a particular summer stratification season are 16
and 14°C in the epilimnion and hypolimnion,
respectively, estimate the temperature in the
hypolimnion 90 days after the beginning of
summer conditions. If the 90-day temperature is
subsequently measured as 14.6°C, estimate the
corresponding heat transfer coefficient and verti-
cal diffusion coefficient in the thermocline.
Figure 7.21.
Two reservoirs discharging into a common
stream.
tions, and volumes are shown, and the substance
is conservative. Assume that the flow and influent
concentrations have been entering the reservoir
for a long enough time to reach steady state in the
entire system. At time
t
= 0, the influent concen-
tration to reservoir 1 drops to zero. The flow
remains the same. How many days will it take
before the concentration at point D is reduced by
50% of the steady-state pre-reduction value?
7.24.
A lake has a surface area of 1 km
2
, and an average
inflow and outflow rate of 8000 m
3
/d. Under
typical conditions, the wind speed is 10 km/h, the
relative humidity is 80%, the air temperature is
20°C, and the net solar radiation incident on the
lake is 750 W/m
2
. If the average temperature of
the inflow is 15°C, estimate the steady-state tem-
perature of the lake.
7.28.
A lake has a plan area of 50 m × 100 m and a
depth of 3 m. Measurements in similar lakes indi-
cate that the Rast and Lee (1978) relationship
between TP and biomass is applicable to this
lake. (a) Assuming that light attenuation in the
lake is only due to algae and that the depth of
oxygenated water can be approximated by the
compensation depth, estimate the upper limit of
the TP concentration that would correspond to
the entire lake having adequate oxygen levels.
What is the trophic state of the lake under this
condition? (b) If the lake is well protected by a
surrounding forest and the depth of the epilim-
nion is equal to the depth at which 90% of the
incident sunlight is attenuated, estimate the depth
of the epilimnion. (c) Normally, the temperature
in the epilimnion is 23°C and the temperature in
the hypolimnion is 21°C. At the end of a particu-
larly hot day, the temperature of the epilimnion
reaches 25°C while the temperature in the hypo-
limnion remains at 21°C, estimate the increase in
the temperature of the hypolimnion after 12
nighttime hours (caused by downward diffusion
of heat).
7.25.
Measurements of DO are taken at 1-m depth
increments in a lake that has a plan area of
approximately 5000 m
2
. At around mid-depth, the
DO in successive layers are found to be 8, 7, and
6.5 mg/L, respectively, in order of increasing depth.
One week later, the measurements in these layers
are repeated and are found to be 7.2, 6.4, and
5.1 mg/L respectively. If the vertical diffusivity is
estimated to be 1 cm
2
/s, determine the rate at
which oxygen is being added or consumed in the
mid-layer of these three layers. What might be
responsible for this source/sink?
7.26.
A 10-ha lake is discretized into 0.5-m layers to
estimate the distribution of oxygen (O
2
) in the
lake. Phytoplankton are estimated to generate O
2
at a rate of 4.0 (mg/L)/day and the diffusion coef-
ficient of O
2
is estimated as 0.20 cm
2
is There is
negligible lateral inflow and outflow, and vertical
advection in the lake is negligible. Time steps of 1
day are to be used in the simulation, and a weight
of 0.5 is to be used in calculating the partial deriva-
7.29.
Temperature profiles measured in White Lake,
Michigan, on May 21 (
T
1
) and June 6, 1974 (
T
2
)
are as follows:
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