Page 858 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Appendix D: Fluid Mechanics—Reviews of Selected Topics 813

w a Discussion
With a head range of only 10 cm, which corresponds to a
flow of 3 million L=day, the accuracy of flow measurement
H
will be acceptable. At the same time, the rectangular weir
will control the tailwater elevation with only 10 cm
P
change from zero flow to the maximum flow.
(a) Side view Front view
Example D.3 Tailwater Weir Design for 100 Mile
House, B.C.
H θ
Show the required head, H, for the tailwater overflow weir
used in the design at 100 Mile House, British Columbia.

Given data for 100 Mile House, British Columbia,
(b) Side view Front view
The design peak flow for 100 Mile House, British Colum-
bia, for the slow sand filter plant of three cells, was 7.26
FIGURE D.11 Definition sketches for Table D.8. (a) Rectangular
mil L=day (1.92 mgd).
weir-end contractions, (b) triangular weir.
1. Flow per Cell

and Q[cell] ¼ Q[plant]=No. Cells
3
3
Q is the flow (m =s) or (ft =s) 3
¼ 7.260 m =day=3 cells
C w is the weir coefficient (dimensionless)
2
2
3
g is the acceleration of gravity (9.81 m=s ) or (32.2 ft=s ) ¼ 0.028 m =s=cell
w is the length of weir crest (m) or (ft)
H is the height of water level above weir crest upstream 2. Assume that weir is circular, and has a diameter 0.40
from effect of drawdown (m) or (ft) m, and P ¼ 2.0 m. Calculate the head on the weir.
P is the distance from floor of channel to weir crest (m)
or (ft) Substitute numerical data in Equation D.78:
p ffiffiffiffiffiffi 3=2
Figure D.11a is a sketch of a rectangular weir with ‘‘end Q ¼ C W 2g bH
contractions,’’ i.e., the crest does not extend across the chan-
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
3
H p
nel. A ‘‘broad-crested’’ weir is one in which the weir plate 0:028 m =s ¼ 0:40 þ 0:05 2 9:81 p(0:40)Š H 3=2
2:0
½
extends across the channel, with the context being an open
channel. H ¼ 0:25 m (0:82 ft)
Discussion
Example D.2 Rectangular Weir Design Overflow weir: The tailwater overflow weir for one of the
for Tailwater cells at the 100 Mile House plant is circular. The overflow
weir crest is the level of the maximum height of the sand
Calculate the length of rectangular weir, w, for the tail- bed. At the maximum flow, the head on the weir will be
water overflow measurement, taking the entire flow, at about 0.25 m (0.82 ft). The flow from the weir is captured
Empire. Assume that the permissible depth of water by a circular vessel with pipe outflow to the chlorine
above the weir crest, H, is 10 cm (0.328 ft) and that contact basin. A flow meter is located after the exit from
P ¼ 2.0 m (6.6 ft). the filter under-drains.
Valve to control headwater elevation: Shown also is a
Given data for Empire valve on the downstream side of the flow meter. Such a
1. Q(max, 1000 persons) ¼ 3,028 L=person=day valve may be used to raise the headwater elevation, after
1,000 persons ¼ 3,028,000 L=day scraping, to alleviate sand bed erosion. After about 0.5 m
( ¼ 800 gpcd 1,000 persons ¼ 800,000 gal=day)
of headloss, the valve may be opened fully. A valve may be
used in lieu of a vertically movable tailwater weir, but
Calculation requires more operator attention for a few days after the
1. Substitute numerical data in Equation D.78:
bed is scraped and before the initial 0.5 m of headloss.
Backfilling filter bed: A pipe should lead from the chlorine
p ffiffiffiffiffiffi 1:5
Q ¼ C w 2g wH contact basin to the under-drain effluent pipe to backfill the
filter after scraping. Such an ancillary component is easy to

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3
0:10 p
3028=24=3600 ¼ 0:40 þ 0:05 2 9:81w(0:10) 2 w overlook, but is needed to permit start-up after scraping so
2:0 that air-binding can be avoided and that the raw water flow
¼ 0:62 m (2:0 ft) can be re-introduced without eroding the sand bed.