Environmental Engineering Reference
In-Depth Information
EXAMPLE 9.11
ocean is typically stratified, with a density of
1025.5 kg/m
3
at the discharge depth and 1023.5
kg/m
3
at the ocean surface. The density of the
freshwater discharge is 998 kg/m
3
. Estimate the
dilution, rise height, and wastefield thickness of
the plume. How would these plume characteristics
be affected by a current of 10 cm/s?
The peak tidal inflow rate to a small estuary during the
flood cycle is estimated as 5.0 × 10
4
m
3
/s, and the the
peak outflow rate during the ebb cycle is estimated as
6.0 × 10
4
m
3
/s. If the flood and ebb cycles have durations
of approximately 12 hours each, estimate the net outflow
from the estuary over each tidal cycle.
9.5.
Consider an outfall that is required to discharge
treated domestic wastewater at 3 m
3
/s in 20 m of
water, where the 10-percentile current is 5 cm/s.
Solution
From the given data:
Q
f
= 5.0 × 10
4
m
3
/s,
Q
e
= 6.0 ×
10
4
m
3
/s, and
T
f
=
T
e
= 12 hours. The flood volume,
V
f
,
ebb volume,
V
e
, and net outflow volume,
V
out
, are as
follows
(a) What would the wastewater dilution be if the
wastewater is simply discharged out of the
end of the 900-mm-diameter outfall pipe?
(b) What would the wastewater dilution be if the
wastewater were discharged through closely
spaced ports along a 12-m-long diffuser?
Assume typical values for the wastewater and
seawater densities.
2
2
V
=
QT
=
π
( .
5 0 10
×
4
)(
12 3600
×
)
=
2 16 10
.
×
9
m
3
f
f
f
π
2
2
V
=
QT
=
π
( .
6 0 10
×
4
)(
12 3600
×
)
=
2 592 10
.
×
9
m
3
e
e e
π
9.6.
Repeat Problem 9.3, treating the diffuser as a line
source.
V
out
=
2 592 10
.
×
9
−
2 16 10
.
×
9
=
4 32 10
.
×
8
m
3
(a) Calculate the dilution for currents perpen-
dicular and parallel to the diffuser.
(b) Determine the effluent discharge rate at which
the plume dilution becomes independent of
the current direction.
Hence, the net outflow volume during each tidal cycle
is 4.32 × 10
8
m
3
. This is 17% of the ebb volume and 20%
of the flood volume, so the estimated outflow volume
might have reasonable accuracy.
9.7.
Use Equation (9.42) to derive an expression for
the dilution of a slot plume in a stagnant environ-
ment. Express the dilution in terms of
y
,
g
′,
L
, and
Q
.
PROBLEMS
9.1.
A single-port outfall discharges treated municipal
wastewater into an unstratified stagnant ocean at
a depth of 15 m. The diameter of the outfall port
is 0.7 m, the discharge velocity is 3 m/s, the density
of the wastewater is 998 kg/m
3
, and the density of
the ambient seawater is 1024 kg/m
3
. Estimate the
plume dilution.
9.8.
An ocean outfall diffuser is to be designed to dis-
charge 1.75 m
3
/s of sewage effluent at a depth of
20 m and achieve a near-field dilution of 25:1. The
effluent density is 998 kg/m
3
and the seawater
density is 1024 kg/m
3
.
9.2.
Repeat Problem 9.1 for the case in which the
ambient current is 15 cm/s. Determine the approx-
imate current speed at which the plume changes
from the BDNF to the BDFF regime.
(a) If the dilution effect of the ambient currents
is neglected, determine the required length of
the diffuser. State your assumption(s) regard-
ing the port spacing.
(b) If the effluent is simply discharged out of the
end of the outfall pipe, what dilution would be
achieved? Based on your analysis, would a
diffuser or end-of-pipe discharge be prefera-
ble in this case?
9.3.
An ocean outfall discharges at a depth of 31 m
from a diffuser containing seven 1-m-diameter
ports spaced 10 m apart. The average effluent flow
rate is 7.5 m
3
is the ambient current is 8 cm/s, the
density of the ambient seawater is 1.024 g/cm
3
,
and the density of the effluent is 0.998 g/cm
3
.
Determine the length scales of the effluent plumes,
and calculate the minimum dilution. Neglect
merging of adjacent plumes.
9.4.
Wastewater is discharged at a rate of 1.5 m
3
is from
a single port 40 m below the ocean surface. The
9.9.
A diffuser is to be located in 28 m of water, dis-
charge 3.90 m
3
/s of primary-treated domestic
wastewater, and provide an initial dilution of 30:1.
The critical velocity required to prevent deposi-
tion in the diffuser is 60 cm/s, and the total head
at the upstream port will be maintained at 31 m.
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