Environmental Engineering Reference
In-Depth Information
Solution
g
(
ρ ρ
/
−
1
)
d
2
p
w
p
v
=
(7.5)
s
18
ν
From the given data:
U
= 20 mph = 8.94 m/s. Assume
that the density of air is 1.25 kg/m
3
. Since the drag coef-
ficient is 0.001 and 0.0015 at wind speeds of 5 m/s and
15 m/s, respectively, the drag coefficient in this case can
be interpolated as
where
v
s
is the settling velocity (LT
−1
),
g
is gravity (LT
−2
),
ρ
p
is the particle density (ML
−3
),
ρ
w
is the water density
(ML
−3
), and
ν
is the kinematic viscosity of water (L2T−1).
2
T
−1
).
It is apparent from Equation (7.5) that the settling
velocity increases as the square of the particle diameter,
so larger particles settle much faster than smaller par-
ticles. Equation (7.5) is strictly applicable to cohesion-
less sediments when
v
s
d
p
/
ν
≤ 1. For cohesive sediments,
the settling velocity will usually depend on the concen-
tration of suspended sediment.
The vertical distribution of suspended sediment in
the water column depends on both the turbulence inten-
sity and the particle settling velocity. For particles with
higher settling velocities, higher turbulence intensities
are required to keep the particles suspended. For steady
and horizontally uniform flows, the distribution of sus-
pended sediment in the water column is described by
(Ji, 2008)
0 0015 0 001
15 5
.
−
−
.
C
D
=
0 001
.
+
( .
8 94 5
−
)
=
0 0012
.
Hence the shear stress on the surface of the lake,
τ
, is
given by Equation (7.4) as
τ
=
C U
D a
ρ
2
=
( .
0 012 1 25 8 94
)( .
)( .
)
2
=
0 120
.
Pa
The induced velocities will have magnitudes on the
order of the shear velocity,
u
*
. Hence, if the density of
the lake water,
ρ
w
is estimated as
ρ
w
= 998 kg/m
3
(pure
water @20°C), then
τ
ρ
w
0 120
998
.
u
*
=
=
=
0 011
.
m/s
ε
v
dS
dz
= −
v S
(7.6)
s
h
Hence, velocity fluctuations on the order of 1.1 cm/s will
be induced in the surface layer of the lake. These veloci-
ties are on the order of 0.1% of the wind velocity.
where ε
v
is the vertical turbulent diffusion coefficient
(LT
−2
),
h
is the water depth (L),
S
is the concentration
of suspended sediment (ML
−3
),
z
is the vertical coordi-
nate (L), and
v
s
is the sedimentation velocity (LT
−1
). The
solution of Equation (7.6) is
7.2.2 Sedimentation
Deposition of sediment received from the contributing
watershed is an important physical process in lakes.
Because of the low water velocities in lakes, sediments
transported by inflowing waters tend to settle out. Sedi-
ment accumulation rates are strongly dependent both on
the physiographic characteristics of the watershed and
on various characteristics of the lake. In general, sedi-
mentation rates can be estimated by either periodic sedi-
ment surveys or estimation of watershed erosion and
bed load. Accumulation of sediment in lakes can, over
many years, reduce the life of the water body by reducing
the water storage capacity. Sediment flow into a lake also
reduces light penetration, eliminates bottom habitat for
many plants and animals, and carries with it absorbed
chemicals and organic matter that settles to the bottom
and can be harmful to the ecology of the lake. Where
sediment accumulation is a major problem, proper
watershed management including erosion and sediment
control should be considered.
Sedimentation in lakes is described by Stokes equa-
tion, which when applied to uniform spherical particles
is given by
v h
z z
s
ε
(
)
S
=
S
exp
−
−
(7.7)
0
0
where
S
0
is the suspended sediment concentration at
z
=
z
0
. The suspended sediment distribution described
by Equation (7.7) is illustrated in Figure 7.3. It is appar-
z
water surface
h
distribution of suspended sediment
bottom of lake
S
Figure 7.3.
Suspended solids distribution in water column.
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