Page 418 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Rapid Filtration 373

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34
18
Piezometers
16
HGL
14 Δh = 4 units
t = 0 h
12
Headwater
10
A B C D
8
6
Tail-
Mono media water
4
2
0
ΔL=18 units

FIGURE 12.39 Piezometric head along length of clean-bed (Equation E.5).

Equation E.5. A typical value for the initial headloss might be in hydraulic gradient as the bed ‘‘clogs,’’ that is, during a filter-
30 cm (12 in.). Figure 12.39 illustrates the linear hydraulic run. At t ¼ 0, that is, the ‘‘clean-bed’’ condition, the hydraulic
gradient for a clean-bed, oriented horizontally. grade line (HGL) is linear; as in Figure 12.39. As the filter run
progresses, however, the bed clogs with solids, starting in
12.5.2.2 Progression of Headloss with Filter Run the upper levels, and the HGL changes commensurately. The
Figure 12.40a is essentially the same as Figure 12.39, but the clogging effect is illustrated at t ¼ 2, 4, and 6 h, with the HGL
bed is oriented vertically and it shows the progress of changes declining exponentially with vertical depth and progressing

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 0 2 4 6 8 101214161820222426283032
40 50
38 48
HGL 46
36
t = 0 h
44
34
h L (valve E)t = 0 h 42
HGL
32 40 Headwater
Headwater t=2 h Headloss curve
30 h L (valve E)t = 2 h 38
HGL
28 36
h L (valve E)t = 4 h 34
t=4 h
26 A
h L (valve E)t = 6 h 32
HGL
24 30
A t = 6 h B
22 28
20 26 Mono media
C
B 24
18
22
16 Mono media 20 D
C Negative
14 18
Support head at D
12 16 gravel
D Tailwater 14
10 X
8 12 Valve is Tailwater
Support 10
6 open fully
gravel 8
4 6
E
2 X 4
Valve is open fully after 6 h 2
0
0
(a) (b)
FIGURE 12.40 Effect of media clogging filter bed on hydraulic gradient for two conditions. (a) Tailwater at level of bed surface.
(b) Tailwater below level of bed surface (Equation E.6). (Reprinted from Mackay, D. J., Opflow, 14(11), 1, 1988b. With permission.
Copyright ß 1988, American Water Works Association.)