OCEANS AND ESTUARIES - Water Quality Engineering in Natural Systems - page 337

The density of the wastewater can be taken as
998 kg/m 3 , the seawater density is 1024 kg/m 3 , and
the outfall is to be designed for stagnant ambient
conditions. Design the diffuser length, port spacing,
number of ports, and the diameter of the most
upstream port in the diffuser.

(a) What is the conservative contaminant dilution
on the boundary of the mixing zone?
(b) If a contaminant has a 90% decay time of 2
hours in seawater, what is the dilution of this
contaminant on the boundary of the mixing
zone?

9.10. A 15-kg slug of Rhodamine WT dye is released
instantaneously at one point into the ocean, and
the concentration distribution of the dye is mea-
sured every 3 hours for the 12-hour duration of
daylight when the dye can be seen. The horizontal
variance of the dye cloud as a function of time is
as follows:

9.15. Why is decay not considered in near-field dilution
models?

9.16. A near-field ocean outfall dilution model indicates
that the length, L (m), of a diffuser required to
achieve a minimum initial dilution S is given by

L = 0 277 . S

3 2 /

Time,
t (h)

The outfall is to be located 20 km from a popular
beach, and winds are expected to induce a
maximum current of 30 cm/s toward the beach.
The fecal coliform concentration in the effluent is
80,000 CFU per 100 ml, and the maximum allow-
able fecal coliform count on the beach is 200 CFU
per 100 ml. Estimate the minimum outfall length
required. How would you justify neglecting fecal
coliform decay in your analysis? What other con-
siderations would govern selection of the diffuser
length?

0 3 6 9 12

1.1 × 10 4 3.3 × 10 7 1.5 × 10 8 4.1 × 10 8 7.9 × 10 8 σ 2 (cm 2 )

σ 2 (cm 2 ) 1.2 × 10 4 3.0 × 10 7 1.6 × 10 8 3.9 × 10 8 7.7 × 10 8

Estimate the apparent diffusion coefficient as a
function of time. Compare your results to the
Okubo relation (Eq. 9.59).

9.11. (a) Compare the apparent diffusion coefficient of
a contaminant cloud that has a characteristic
size of 100 m with the apparent diffusion coef-
ficient of a contaminant cloud whose size is
200 m.
(b) Estimate how long it would take for a small
contaminant spill to grow to a size of 100 m.

9.17. (a) The city of Hollywood, Florida, discharges
treated domestic wastewater through a single-
port outfall located 3.05 km offshore. This
outfall is simply an open-ended pipe of diam-
eter 1.52 m at a depth of 28.5 m. The 10-
percentile current at the outfall location is
8 cm/s, and the discharge from the outfall
varies in the range 0.88 to 1.93 m 3 /s, with an
average value of 1.40 m 3 /s. The average density
of the seawater is 1.024 g/cm 3 , and the average
density of the effluent is 0.998 g/cm 3 . Use a
length-scale analysis to assess whether the
ambient current has a significant effect on the
near-field plume dilution. Estimate the dilu-
tion expected at the outfall. Compare the cal-
culated dilution to the dilution when the
currents are totally neglected. Does this result
confirm your length-scale analysis? The
Florida Administrative Code 62-4.244(3)(c)
has the following requirements for all outfalls
in the state of Florida: “Rapid dilution shall
be ensured by the use of multiport diffusers,
or a single port outfall designed to achieve a
minimum of 20:1 dilution of the effluent prior
to reaching the surface.” Is the Hollywood
outfall in compliance with these regulations?
(b) An engineer working for the city of Holly-
wood proposes replacing the single-port

9.12. A 50-m-long multiport diffuser discharges effluent
at a rate of 6.5 m 3 /s and at a depth of 32 m. If the
ambient current is 20 cm/s, estimate the distance
downstream of the diffuser to where the dilution
is equal to 150. Assume that the initial wastefield
thickness is 30% of the depth.

9.13. If the near-field mixing at the outfall described in
Problem 9.12 is analyzed more closely using the
Roberts line plume model, compare the assumed
wastefield thickness (30%) with that derived
from using the near-field dilution model. Assume
that the current is perpendicular to the outfall,
the density of the discharge is 998 kg/m 3 , the
density of the seawater is 1025 kg/m 3 , and
the average dilution in the plume is 2 times the
minimum dilution.

9.14. A regulatory mixing zone has a boundary that is
500 m away from an ocean outfall when the
ambient current is 15 cm/s. Within the mixing
zone, near- and far-field models indicate dilutions
of 18 and 40, respectively, for conservative con-
taminants contained in the wastewater effluent.