Environmental Engineering Reference
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the longitudinal, horizontal-transverse, and
vertical-transverse directions are 5, 1, and 0.01 m 2 /s,
respectively. The tracer has a first-order decay
constant of 0.01 min −1 . Estimate the concentration
at a point 30 m downstream of the release location
after 5 minutes.
3.23. A tracer is released into the ocean at a rate of
50 kg/s, where the mean ocean current is 30 cm/s
and the diffusion coefficient is 0.5 m 2 is in the verti-
cal direction and 2 m 2 /s in the horizontal. Estimate
the concentration 500 m downstream from the
source under the following conditions: (a) the
source is far below the ocean surface and
the tracer is conservative; (b) the source is far
below the ocean surface and the tracer undergoes
first-order decay with a rate constant of 0.04 min −1 ;
and (c) the source is 3 m below the ocean surface
and the tracer undergoes first-order decay with a
rate constant of 0.04 min −1 .
3.24. A conservative tracer is released into a large body
of water at a rate of 15 kg/s for 5 minutes. The flow
velocity is 5 cm/s and the estimated diffusion coef-
ficient is 10.0 m 2 is in all three coordinate direc-
tions. (a) Estimate the concentration after 15
minutes at two points of interest 100-m down-
stream of the release point, one point is on the
plume centerline and the other point is 40 m offset
from the centerline. (b) If the tracer release is
continuous at 15 kg/s, what is the steady-state con-
centration at the points of interest, and how do
these concentrations compare with those calcu-
lated using the approximate slab solution?
3.25. A tracer is released at a rate of 10 kg/s from the
center of a wide channel that is 2.0 m deep. The
flow velocity in the channel is 15 cm/s, and
the transverse diffusion coefficient is 1 m 2 is If the
contaminant is initially well mixed over the depth,
estimate the contaminant concentration 200 m
downstream and 3 m from the center of the
channel.
3.26. A tracer is released at a rate of 0.1 kg/s from a
point source in the ocean where the horizontal
diffusion coefficient of a tracer can be estimated
by
3.27. Fifty kilograms of a tracer is released instanta-
neously over a 10-m vertical depth in an environ-
ment where the current is 20 cm/s and the diffusion
coefficients are 1, 0.1, and 0.01 m 2 /s in the longitu-
dinal,horizontal-transverse,andvertical-transverse
directions, respectively. If the first-order decay
coefficient of the tracer is 0.04 min −1 , estimate the
maximum concentration of the tracer 80 m down-
stream of the release location after 5 minutes.
3.28. Eight kilograms of a contaminant in the form of
a 1 m × 1 m × 1 m parallelepiped is released into
the deep ocean. If the N-S, E-W, and vertical dif-
fusion coefficients are 15, 10, and 0.1 m 2 /s, respec-
tively, find the concentration as a function of time
at a location 25 m north, 25 m east, and 5 m above
the centroid of the initial mass release.
3.29. The suspended solids in a 200 m × 200 m lake is
measured to be 45 mg/L, and the average settling
velocity is estimated as 0.1 m/day.
(a) Estimate the rate at which sediment mass is
accumulating on the bottom of the lake.
(b) If the suspended solids concentration remains
fairly steady and the water leaving the lake
does not have a significant suspended sedi-
ment content, at what rate is sediment mass
entering the lake?
3.30. The phytoplankton Coscinodiscus lineatus has a
typical diameter of 50 μ m and an estimated density
of 1600 kg/m 3 . Assuming that the phytoplankton
is approximately spherical and the water tempera-
ture is 20°C, estimate the settling velocity using
the Stokes equation. Compare your result with the
settling velocity given in Table 3.2, and provide
possible reasons for any discrepancy.
3.31. A stormwater outfall discharges runoff into a pris-
tine river (with negligible dissolved solids), such that
the suspended solids concentration of the combined
water just downstream of the outfall is 100 mg/L. The
settling velocity of the sediment is estimated to be
2 m/day, the flow velocity in the river is 0.4 m/s, and
the river is 10 m wide and 2 m deep.
(a) How far downstream from the outfall will it
be before all of the suspended sediment settles
out?
(b) Estimate the rate at which sediment is accu-
mulating downstream of the outfall.
1 15
.
D
= 3 5
.
L
,
where D is the diffusion coefficient in the horizon-
tal plane (cm 2 /s) and L is the distance traveled by
the tracer plume (m). The vertical diffusion coef-
ficient is 3.0 cm 2 is Estimate the maximum concen-
tration 50 m downstream of the source.
3.32. Consider the (common) case in which an outfall
discharges treated domestic wastewater at a rate
of 80 L/s with a suspended solids concentration of
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