Page 443 - Water and wastewater engineering

11-16 WATER AND WASTEWATER ENGINEERING

The last column is summed and the headloss calculated using Equation 11-9 :

2
.
(
1 067 0 0025 m/s ) ( 0 5 . m )
.
h ( , 1 )
75 025 m
L 2 2 4
.
( 082 9 81 m/s )( .
. )(
045)

1
( . 5 2 )( 75 0 , 25m ) 076 m
1 0119 10 m
.
2
Comments:
1. This headloss is large for clean bed filtration. It should be less than 0.6 m for the specified
loading rate. Comparison of the effective size and uniformity coefficient for this sand (from
Example 11-1 ) with the typical values in Table 11-1 reveals that the uniformity coefficient
is too high. As noted later in this chapter (see p. 11-22), the loading rate is high for a stan-
dard sand filter. Either the loading rate should be lowered, the fraction of fines should be
reduced, or some combination of less fines and a lower loading rate should be employed.
2. Note that the equation used to calculate C D changed when the Reynolds number dropped
below 0.5.
3. As may be noted from the number of significant figures presented, this calculation was
performed on a spreadsheet.
Terminal Headloss. As the filter clogs, the headloss will increase so that the results calculated
using the clean bed equations are the minimum expected headlosses. There is no method to pre-
dict the increase in headloss as the filter becomes plugged with accumulated solids without full-
scale or pilot plant data. The phenominological model ( Equations 11-7 and 11-8 ) provides a way
to obtain estimates of the time to reach terminal headloss using pilot plant data. More typically,
terminal headloss pressure is selected based on experience and the hydraulic profile of the entire
treatment plant.

Backwashing Hydraulics
The expansion of the filter bed during backwash is calculated to provide a starting point in
determining the placement of the backwash troughs above the filter bed. Fair and Geyer (1954)
developed the following relationship to predict the depth of the expanded bed:
f
D e (1 )( D) (11-11)

(1 e )

where D e depth of the expanded bed, m
porosity of the bed
D depth the unexpanded bed, m
f mass fraction of filter media with expanded porosity
e porosity of expanded bed
The conditions during backwash are turbulent. A representative model equation for estimating e
is that given by Richardson and Zaki (1954):
.
⎛ b v ⎞ 0 2247R 01 .
e ⎜ ⎟ (11-12)
⎝ s v ⎠