Page 465 - Water and wastewater engineering

11-38 WATER AND WASTEWATER ENGINEERING

Example 11-8. Determine the depth of the filter box for Ottawa Island’s sand filter. Use the
clean bed headloss from Example 11-2 , and the velocity headloss and the media and underdrain
depths from Example 11-7 . Assume the minimum depth of water above the filter bed is 2.4 m.

Solution:
a. Calculate z 1 using the assumed water depth and other depths from Example 11-7 .
,
,
z water depth depth of sand gravel and uunderdrain
1
.
.
.
.
z 24 m 06 m 0 3 m 0 3 m 3 6 m
.
1
b. The velocity headloss from Example 11-7 is
v 2 ( 18 m/s). 2
. 017 m
0165 or .
(
2g 29 81 m/s ). 2
c. Calculate p 2 / at the beginning of a filter run using the clean bed headloss calculated in
Example 11-2 .
p 2
36 m 017 m 0 76 m 267 or 2 7 m
.
.
.
.
.

d. Estimate the maximum allowable headloss.
p 2
.
.
.
36 m 017 m h L 3 43 m h L

Thus, the maximum headloss that will cause a negative pressure in the filter is one that
is 3.43 m.
e. The filter box depth is estimated as
D depth of water depth of media depth of underdrain
box
factor of safety freeboard

Assuming a factor of safety of 0.6 m and a freeboard depth of 0.6 m
.
.
.
Dbox 24 m 09 m 0 3 m 06 m 06 m 48 m
.
.
.
Comments:
1. The elevation of the maximum water level in the filter box governs the hydraulic profile
of the upstream processes in the plant. This, in turn, has a significant impact on the cost
of the plant. This cost, as well as the cost of the filter itself, favor the design of shallower
rather than deeper filter boxes.
2. The use of low profile drains and those that do not need gravel allow for the design of a
shallower filter box.
3. Though more expensive, a deeper filter box provides for future expansion to deep bed
monomedium.
4. The technique used here for establishing the depth of the filter box is conservative. Monk
(1984) provides a detailed method for optimizing the depth of the filter box.