Environmental Engineering Reference
In-Depth Information
TABLE 4.12. Measurements of Depth and Vertically Averaged Velocity
Distance from side,
y
(m)
0
1
2
3
4
5
6
7
8
9
10
Depth,
d
(m)
0.0
0.30
1.30
1.8
3.1
4.5
3.6
2.2
1.20
0.70
0.0
velocity,
v
(m/s)
0.0
0.45
0.90
1.20
2.1
3.0
2.4
1.5
0.75
0.45
0.0
4.6.
A river is 30 m wide, 3 m deep, and has a typical
roughness height of 5 mm. If the average velocity
in the river is 15 cm/s, determine the values of the
longitudinal and transverse dispersion coefficients
that should be used to make conservative esti-
mates of mixing in the river.
4.10.
Fifty kilograms of a conservative contaminant is
spilled into a river that has an average velocity of
1 m/s, is 10 m deep and 52 m wide, and has a fric-
tion factor on the order of 0.04.
(a) Assuming that the contaminant is initially
well mixed across the river, what maximum
concentration is expected 150 m downstream
of the spill?
(b) What value of
K
L
would you use in your
calculations if the width of the river were
25 m?
4.7.
Stream depths and vertically averaged velocities
at 1-m intervals across a 10-m-wide stream are as
shown in Table 4.12. If the friction factor is
0.04, estimate the longitudinal dispersion coeffi-
cient across the channel using the formulas in
Table 4.1.
4.11.
Fifteen kilograms of a contaminant is spilled into
a stream 4 m wide and 2 m deep.
4.8.
Measurements in a river indicate that the cross
section has an approximately trapezoidal shape
with a bottom width of 20 m, side slopes of 3:1,
longitudinal slope of 0.15%, and a Manning rough-
ness coefficient of approximately 0.021. Assuming
that the longitudinal dispersion coefficient in the
river can be approximated by the Seo and Cheong
(1998) relationship, determine the longitudinal
dispersion coefficient as a function of the flow
depth. If the average flow depth in the dry season
is 2 m and the average flow depth in the wet
season is 4 m, estimate the typical wet season and
dry season dispersion coefficients. If a spill occurs
during the dry season, how long after the spill
would the maximum concentration occur 200 m
downstream of the spill?
(a) If the average velocity in the stream is 0.8 m/s,
the longitudinal dispersion coefficient is
0.2 m
2
/s, and the first-order decay constant of
the contaminant is 0.05 h
−1
, determine the
maximum concentration in the stream at a
drinking water intake 1 km downstream from
the spill.
(b) How would this concentration be affected if
the decay constant is actually one-half of the
estimated value?
4.12.
The plume resulting from a spill of a conservative
contaminant passes an observation point 1 km
downstream of the spill location, where the con-
centration as a function of time is measured. If the
river has a mean velocity of 25 cm/s and the con-
centration distribution is observed to be Gaussian
with a maximum concentration of 5 mg/L, esti-
mate the maximum concentration 1.5 km down-
stream of the spill location.
4.9.
Show that the maximum concentration at a dis-
tance
x
0
downstream from an instantaneous spill
in a river occurs at a time
t
0
given by
2
x
V
K
Vx
K
Vx
4.13.
Derive Equation (4.34).
o
L
L
t
=
−
+
+
1
0
o
o
4.14.
Dye is released instantaneously from a bridge
across a river, and the dye concentrations as a
function of time are measured at locations 500 and
1000 m downstream of the release location. The
measured concentrations at the downstream loca-
tions are given in Table 4.13.
where
V
is the mean velocity in the stream, and
K
L
is the longitudinal dispersion coefficient.
Determine the values of
K
L
/
Vx
0
for which
t
o
does
not deviate by more than 1% from
x
0
/
V
.
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