Page 172 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Sedimentation 127

1 9:81 m=s 2
projected to the horizontal plane. Conversions between the 2:30 10 4 m=s ¼ 6 2
expressions are seen in Equations 6.43 through 6.45. 18 1:004 10 m =s
2
Willis (1978, p. 334), in an article on tube-settlers, draws (1:05 1:00) d(floc) (Ex6:7:2)
attention to the issue of clearly defining the hydraulic loading
d(floc) ¼ 0:092 mm (Ex6:7:3)
rate and suggests as a criterion, HLR(horiz-plane) 2.5
2
gpm=ft -face-area-of-tubes, with ‘‘face-area’’ defined as the 0:1 mm (Ex6:7:4)
area of the tubes intersecting the horizontal plane. For refer-
ence, the Colorado Department of Health (1987, p. 32) gives
3 2 In other words, d(floc) 0.1 mm will be 100%
as a criterion HLR(horiz plane) 0.102 m =min=m (2.5 removed and d(floc) < 0.1 mm will be partially
2
gpm=ft ) and defines the term as the total tube or face area
removed.
of the plane containing the open end of all tubes. An equiva-
b. Determine R
lent interpretation is that the HLR(horiz plane) is the flow per First, apply Equation 6.36 to calculate v P :
basin divided by the plan area of the basin.
d(plate)
v o
=
¼
v P (L(plate) cos u þ d(plate) sin u)
Example 6.7 Floc Particle Sizes Removed (Ex6:7:5) (6:36)
by Plate Settlers
2:30 10 4 m=s 0:080 m
Given ¼
v P [2:0m cos558þ(0:080 m=sin558)]
Consider the Fort Collins Colorado Water Treatment Plant (Ex6:7:6)
for which v o SOR ¼ 19.9 m=day (Table 6.12). Plate
dimensions are (Kamp, 1989), i.e., dimensions, L(plate) ¼
3.0 m, w(plate) ¼ 1.2 m, d ¼ 80 mm, and u ¼ 558; also, the v P ¼ 0:00358 m s = (Ex6:7:7)
flow enters each plate from the sides 1.0 m from the
bottom. Assume T ¼ 208C. Calculate R at T ¼ 208C:
Required r(T ¼ 20 C) v P d(plate)

(Ex6:7:8)
a. Floc size: Determine the smallest size of floc particle, R ¼ m(T ¼ 208C)
d(floc), removed 100% by the plate settlers, assum- 3
(998 kg=m )(0:00358 m=s)(0:08 m)
ing Stokes’ law applies. (Ex6:7:9)
¼ 2
b. Laminar flow check: Check to determine whether (0:001002 Ns=m )
the flow between the plates is laminar, i.e., R 100. ¼ 285 (Ex6:7:10)
Solution
Discussion
a. Calculate d(floc)
Overflow velocity, SOR, is given as, Laminar flow in a pipe requires, R 1000; the same
criterion is assumed to apply for flow between two flat
plates. Thus, since R(plate) ¼ 285, the flow between the
v o ¼ SOR ¼ 19.9 m=day ¼ 2.30 10 4 m=s plates is laminar. The limitation in the accuracy of the
calculation is the assumed value of floc-specific gravity,
Particles having fall velocity, v s v o , will be i.e., SG(floc) ¼ 1.05. Also, as noted, the parabolic velocity
removed 100%; particles having v s < v o will be par- profile between the plates was neglected. A spreadsheet
may be set up to calculate d(floc) to test the sensitivity of
tially removed. Therefore, particles for which v s ¼ v o
are the smallest that will be 100% removed for a the value to SG(floc).
given SOR and for a particular plate design, which is
depicted by Figure 6.28. 6.10.2 TUBE SETTLERS
If the flow between the plates is laminar, i.e.,
R(plate flow) 1000, the particle size associated The tube settler system was developed by Neptune Microfloc,
with a particle fall velocity, v s ¼ v o , is given by Stokes’ Inc. and appeared on the scene during the mid-1960s; their
law, Equation 6.7. By definition, Stokes’ law applies to experimental program started in 1964 (Hansen and Culp,
a particle falling in the range, R(particle) 1. For 1967; Culp et al., 1968). The two versions of tubes were (1)
such Reynolds number range, turbulence is not a hexagonal tubes, each tube 760 mm (30 in.) long and 51 mm
factor. Also, the parabolic velocity distribution (2 in.) across the flats and u ¼ 58, and (2) square tubes, each
between the plates is neglected as a factor in the tube 610 mm long and 51 mm (2 in.) square, and u ¼ 608. The
particle trajectory.
hexagonal tube type was designed for the settling of floc prior
To apply Stokes’ law, assume the specific gravity,
to filtration with cleaning of accumulated solids by rapid
SG(alum floc) ¼ 1.05. For the conditions stated,
application of Stokes’ law to yield d(floc) is draining timed to occur simultaneously with filter backwash.
The square tube type was designed for the self-cleaning of
1 g 2 solids as they accumulate. For the square tubes inclined at 608,
(SG s SG f )d (Ex6:7:1) (6:7)
v s ¼
18 n the bundle was fabricated of PVC plastic with tubes arranged,