OCEANS AND ESTUARIES - Water Quality Engineering in Natural Systems - page 321

prevent the deposition of suspended solids. The critical
velocity generally depends on the level of treatment of
the effluent. As effluent is discharged through ports
along the pipe, the flow rate in the diffuser pipe decreases
gradually, and the diffuser diameter has to be reduced
to maintain the pipe velocity above the critical value.
Designing the length and port spacing in shallow
water diffusers is usually a fairly straightforward process
in which the required initial dilution, S , and the diffuser
depth, y are both given, and the required port discharge,
Q 0 , can be calculated using the single-plume equation.
The minimum port spacing is then set such that adjacent
plumes do not merge. Dividing the total effluent dis-
charge by Q 0 gives the number of ports, N p . Practical
considerations usually require a port spacing that is a
multiple or fraction of the length of a pipe section. The
required diffuser length, L , can be calculated using the
relation

seawater density is 1024 kg/m 3 , and the design ambient
current is 11 cm/s. Design the length of the diffuser, port
spacing, number of ports, and the diameter of the most
upstream port in the diffuser.

Solution

From the given data, S = 20, y = 30 m, Q = 5.73 m 3 /s,
ρ e = 998 kg/m 3 , ρ a = 1024 kg/m 3 , and u a = 11 cm/s =
0.11 m/s. The effective gravity, g ′, can be derived from
the given data as

ρ ρ
ρ

− 1024 998

998

−

a e

g ′ = g = (9.81) = 0.256 m/s

2

e

and the plume/crossflow length scale, L b , can be derived
as

L N = ( − 1 ) s

(9.53) p p

B
u

Q g
u

′ = Q (0.256)

0.11

0
3

0 0

L = = = 192 Q

b 0

3 3

a a

There are a wide variety of designs used in practice, with
port diameters typically in the range of 10-30 cm (4-
12 in) and port spacings in the range of 1-10 m (3-30 ft).
The ports may be simple holes cut into the distribution
pipe or they may be nozzles at the tips of risers that
direct flow from the pipe (e.g., Tian and Roberts, 2011).
Designing deepwater outfalls is more complex than
designing shallow water outfalls, since density gradients
in the water column usually cause the effluent plumes
to be trapped below the water surface, and merging of
adjacent plumes is more commonplace.
In practical applications, near-field dilution is assumed
to occur within a designated regulatory mixing zone ,
which might not coincide with the physical extent of the
near-field mixing zone associated with the near-field
dilution equations. In spite of this mismatch, it is com-
monly assumed that the near-field dilution equations
yield the dilution within the regulatory mixing zone. A
common estimate of the regulatory mixing zone is the
zone of initial dilution , which is defined as the region of
initial mixing extending a distance of one water depth
from any point on the diffuser and including the water
column above that area.

The diffuser will be designed as a shallow-water diffuser
with nonmerging plumes. Assume that the plume will
operate in the BDNF regime described by Equation
(9.15), and, according to Table 9.2, values of C BDNF are
in the range of 0.26-0.31, with a mid-range value of
C BDNF = 0.29. Based on these assumptions, the plume
dilution, S = 20, satisfies the relation

5 3 /

SQ
u L

y
L

0
2

= C

BDNF

a b b

5 3 /

20
(0.11)(192

Q 30

192

0

= 0 29 .

2

Q ) Q

0 0

which gives

Q 0 = . m /s 4 35

3

Since the total discharge, Q , is 5.73 m 3 is the required
number of ports, N p , is given by

Q
Q

5.73
4.35

EXAMPLE 9.4

N = = = 1.3 ports

p

0

A diffuser is to be located in 30 m of water, discharge
5.73 m 3 /s of secondary-treated domestic wastewater,
and provide an initial dilution of 20:1. The critical veloc-
ity required to prevent deposition in the diffuser is
60 cm/s, and the total head at the upstream port will be
maintained at 32 m by an onshore pumping station. The
density of the wastewater can be taken as 998 kg/m 3 , the

Therefore, two ports should be used in the diffuser.
Using two ports gives a discharge of 5.73/2 = 2.87 m 3 /s
per port. For Q 0 = 2.87 m 3 /s, L b = 192 Q 0 = 192 (2.87) =
551 m. Since y / L b = 30/551 = 0.05, the BDNF assump-
tion ( y / L b << 1) is validated, and the plume dilution, S ,
using two ports is given by