Environmental Engineering Reference
In-Depth Information
ent that the concentration of suspended solids will nor-
mally increase with depth. For large settling velocities,
little suspended sediment will remain in the water
column, while for small settling velocities, much of the
suspended sediment will be uniformly mixed in the
water column.
behavior of fish. The deleterious effects of limited light
penetration are consequences of the fact that oxygen
will be produced by indigenous plants and algae only as
deep as sunlight penetrates. The reduction of light pen-
etration through the water column of a lake is a function
of scattering and absorption. Light transmission is
affected by the water surface film, floatable and sus-
pended particulates, turbidity, populations of algae and
bacteria, and color. In a typical clear lake, 50% of the
incident sunlight is absorbed in the upper 2 m (6 ft), and
very little light energy penetrates more than 10 m (30 ft)
below the water surface.
Light penetration into an open body of water, such
as a lake or reservoir, is described by
Beer's law
, which
can be stated as
EXAMPLE 7.4
Under summer conditions, a 3.0-m deep lake typically
has wind-induced bottom currents of 5 cm/s, a turbulent
diffusion coefficient of 6 cm
2
/s, and a temperature of
20°C. Under these conditions, the suspended sediment
concentration 10 cm above the bottom of the lake is
70 mg/L, and water samples indicate a typical particle
size of 5
µ
m. The density of the individual particles is
estimated as 2650 kg/m
3
. Estimate the suspended sedi-
ment concentration near the surface of the lake under
these conditions.
I d
( ) =
I e
k d
−
(7.8)
e
s
where
I
(
d
) is the solar radiation (P
*
L
−2
) penetrating to
a depth
d
(L) below the water surface,
I
s
is the solar
radiation at the water surface (PL
−2
), and
k
e
is the light
extinction coefficient (L
−1
). The value of
k
e
is largely
influenced by the suspended solids concentration,
and an empirical relationship derived from studies
in Lake Okeechobee (in Florida) is given by (Jin and
Ji, 2005)
Solution
From the given data:
h
= 3.0 m,
V
= 5 cm/s, ε
v
= 6 cm
2
/s
= 6 × 10
−4
m
2
/s,
T
= 20°C,
z
0
= 10 cm,
S
0
= 70 mg/L,
d
p
= 5
µ
m, and
ρ
p
= 2650 kg/m
3
. At 20°C, the density and
kinematic viscosity of water are:
ρ
w
= 998 kg/m
3
, and
ν
= 1.00 × 10
−6
m
2
/s. The settling velocity,
v
s
, of the par-
ticles is given by Equation (7.5) as
k
e
=
0 1219
.
(
TSS
)
+
1 236
.
(7.9)
g
(
ρ ρ
/
−
1
)
d
2
p
w
p
v
=
where
k
e
is in m
−1
and TSS is the suspended solids con-
centration in mg/L.
An important measure based on the transmission of
light is the depth to which photosynthetic activity is
possible. The minimum light intensity required for pho-
tosynthesis has been established to be about 1% of the
incident surface sunlight. The portion of the lake from
the surface to the depth at which the 1% intensity
occurs is called the
euphotic zone
, and the depth at
which net photosynthesis is equal to zero is called the
compensation depth
,
compensation point
, or
compensa-
tion limit
. Below the euphotic zone is the
aphotic zone
,
where light penetration is negligible. Benthic plants do
not exist in the aphotic zone (due to lack of light), and
many lakes are sufficiently deep or turbid to prevent
the development of benthic plants except in the imme-
diate vicinity of the shoreline (i.e., within the littoral
zone). If nutrients are abundant in the aphotic zone,
production in the euphotic zone will subsequently
increase if aphotic zone water is mixed with euphotic
zone water, a process that occurs regularly in all aquatic
systems.
s
18
9 81 2650 998 1 5 10
18 1 00 10
ν
.
(
/
−
)(
×
−
6 2
)
=
( .
×
−
6
)
2 26 10 . m/s
and the suspended sediment concentration near the
surface of the lake, at
z
= 3.0 m, is given by Equation
(7.7) as
=
×
−
v h
z z
s
ε
(
)
S
=
S
exp
−
−
0
0
( .
2 26 10
×
×
−
5
)( . )
3 0
(
)
=
(
70
)exp
−
3
.
0 0 1
−
.
6 10
−
4
=
50
mg/L
Therefore, under the given conditions, it is expected that
the suspended solids concentration near the surface of
the lake will be around 50 mg/L, which is very turbid.
7.2.3 Light Penetration
Transmission of light through the water column influ-
ences primary productivity (growth of phytoplankton
and macrophytes), distribution of organisms, and
*
P indicates units of power.
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