LAKES AND RESERVOIRS - Water Quality Engineering in Natural Systems - page 282

998 kg/m 3 , estimate the density difference between
the top and the bottom of the lake for the lake to
be strongly stratified. What temperature differ-
ence could be responsible for such a density
variation?

7.18. A eutrophic lake is estimated to have a mean
total phosphorous concentration of 47 µ g/L that
fluctuates by ±50% during the year.

(a) Estimate the corresponding percentage fluc-
tuation in biomass in the lake.
(b) If the lake is 200 m long × 100 m wide × 3 m
deep, the average inflow (and outflow) rate is
0.1 m 3 is and the decay rate for phosphorus is
0.03 d −1 , compare the detention time in the
lake with the time scale for phosphorus decay.
What can you infer from this result regarding
the fate of phosphorus in the lake?
(c) If the inflow concentration of phosphorus is
reduced to 20 µ g/L, what is the concentration
of phosphorus that can ultimately be expected
in the lake?
(d) How long will it take for the mean phos-
phorus concentration to be decreased by
one-half?

7.14. Bubble plumes generated by the injection of
1.0 m 3 /s of air are intended to destratify a 7.0-m-
deep lake that has an average temperature of
15°C and a buoyancy frequency of 0.1 Hz. Atmo-
spheric pressure at the lake site is 101 kPa. What
are the values of M M and C M ?
7.15. Synoptic measurements of chlorophyll a (Chl a )
and TP in Lake Woebegon are as follows:

TP Chla

( µ g/L) ( µ g/L)

10 3.99

15.8 4.50

25.1 12.7

7.19. If the mass loading of TP in Problem 7.17 sud-
denly drops to zero at the end of the first week,
estimate the daily TP concentration during the
second week.
7.20. If the mass loading of TP in Problem 7.17 doubles
at the end of the first week, estimate the daily TP
concentration during the second week.
7.21. A recreational lake is approximately circular with
a diameter of 700 m and an average depth of 3 m.
Cultural eutrophication has caused the lake to
have an excessive concentration of algae. The TP
concentration is measured at 40 µ g/L, and it is
estimated that the first-order decay factor for
phosphorus in the lake is 0.008 d −1 . Average annual
inflow into the lake is 37.6 L/s, annual rainfall is
150 cm, and annual evaporation is 130 cm.

39.8 14.4

63.1 40.7

100.0 45.9

Determine an approximate empirical relationship
between these parameters. How does your empiri-
cal relationship compare with others?

7.16. you have been appointed to be the project engi-
neer to direct the cleanup of a polluted lake in an
urban development. Congratulations! The lake is
approximately circular with a radius of 100 m and
an average depth of 5 m. The target biomass con-
centration in the lake is 5 µ g Chl a /L, and the
current biomass concentration is estimated to be
15 µ g Chl a /L. If the average inflow and outflow
from the lake is 5 L/s, estimate the allowable con-
centration of TP in the lake inflow such that the
target biomass concentration is reached in 6
months. The decay rate for phosphorus can be
taken as 0.01 d −1 .

(a) Estimate the current mass loading of phos-
phorus in kilograms per year, and the mass
loading that is required to reduce the algae
concentration in the lake by one-half.
(b) With the reduced mass loading, how long will
it take for the phosphorus concentration in
the lake to be within 5% of the equilibrium
concentration of phosphorus?

7.17. The average concentration of TP in a flood-control
lake is 25 µ g/L, and daily flows into and out of the
lake are typically on the order of 0.13 m 3 /s.

(a) If the decay rate of TP is 0.2 d −1 and the
volume of the lake is 2.8 × 10 5 m 3 , estimate
the mass loading that must be maintained to
ultimately bring the TP concentration down to
15 µ g/L.
(b) If this mass loading is maintained for 1 week,
estimate the TP concentration at the end of
each day.

7.22. The surface area of the lake described in Problem
7.17 is 28,000 m 2 . If the effective settling velocity
of TP is 0.1 m/day, repeat Problem 7.17 to
assess the effect of sedimentation on the TP
concentrations.

7.23. Two reservoirs discharge to a common stream as
shown in Figure 7.21. The flow, influent concentra-