Environmental Engineering Reference
In-Depth Information
Taking the surface area,
A
L
(L
2
), of a lake as a measure
of its volume,
V
L
(L
3
), and taking the drainage area,
A
D
(L
2
), as a measure of the average inflow and outflow
rate,
Q
o
(L
3
T
−1
), from the lake, the detention time,
t
d
(days), of a natural lake can be estimated by the empiri-
cal relation (Bartsch and Gakstatter, 1978)
which leads to
A
D
=
2 8 10
5
.
×
m
2
Hence, the estimated drainage area is about 3.3 times
the size of the lake.
The reciprocal of the residence time is called the
flushing rate
. Impoundments with longer residence
times (in months and years) typically have water-quality
problems, such as excessive biological productivity. The
minimum residence time required for algae growth and
development is at least several weeks (Novotny, 2003).
With low velocities and long detention times, most
lake environments are favorable to sedimentation,
resulting in most of the incoming sediments, and many
of the organisms that grow and die in the lake, accumu-
lating at the bottom of the lake. Over extended periods
of time, sedimentation can change the character of a
lake permanently, greatly increasing its organic content
and ultimately converting it to a silted pond, swamp,
marsh, or other type of wetland.
The
hydraulic loading
and
shape factor
are two
parameters that are useful indicators of the biological
productivity potential of lakes. Hydraulic loading,
Q
s
(m/yr), is defined by the relation
A
A
D
log
t
=
4 077 1 177
.
−
.
log
1
day
<
t
<
6000
days
10
d
10
d
L
(7.2)
This empirical equation applies only to natural lakes
with uncontrolled discharges. Long detention times do
not necessarily correspond to large lakes, since small
lakes with small outflow rates can have detention times
comparable with those of large lakes with large outflow
rates. Most natural lakes are fed by one or more streams
and emptied by one outflow channel (Ramaswami
and Luthy, 1997). A large ratio of lake drainage area
to surface area,
A
D
/
A
L
, usually indicates the potential
for high sediment and nutrient loads on the lake
(Ji, 2008).
EXAMPLE 7.2
Q
A
A natural lake has an estimated volume of 9 × 10
5
m
3
, a
surface area of 85,000 m
2
, and an average uncontrolled
outflow rate of 310 m
3
/d. Estimate the hydraulic deten-
tion time in the lake and the drainage area that contrib-
utes runoff into the lake.
(7.3)
Q
s
=
where
Q
is the annual inflow to the lake (m
3
/yr) and
A
is the surface area of the lake (m
2
). The biological pro-
ductivity potential of an impoundment is inversely pro-
portional to the hydraulic loading,
Q
s
. The shape factor
is defined as the length of the impoundment divided by
its width. Elongated valley reservoirs (shape factors >> 1)
are less amenable to excessive biological productivity
than are circular open lakes (shape factor ≈ 1).
The shallow water near the shore of an impoundment
in which rooted (emergent) water plants (macrophytes)
can grow is called the
littoral zone
. Littoral zones in
lakes and reservoirs are essential for spawning and fish
development, and therefore desirable lake depths
should not be uniform, and the bottom relief should
provide a variety of landscapes. Deeper oxygenated
zones are used for escape from summer warmer tem-
peratures in the littoral zone.
Solution
From the given data,
V
L
= 9 × 10
5
m
3
,
Q
o
= 310 m
3
/d,
and Equation (7.1) gives the hydraulic detention time,
t
d
, as
5
V
Q
9 10
310
×
L
t
=
=
=
2900
days
=
8 0
.
years
d
o
The detention time can be related empirically to
the drainage area,
A
D
, by Equation (7.2). Taking
A
L
= 85,000 m
2
, Equation (7.2) gives
A
A
D
log
t
d
=
4 077 1 177
.
−
.
log
10
10
L
7.2 PHYSICAL PROCESSES
or
7.2.1 Circulation
A
D
Water movement in lakes influence the distribution of
nutrients, microorganisms, and plankton, and therefore
log
2900
=
4 077 1 177
.
−
.
log
10
10
85 000
,
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