Environmental Engineering FOURTH EDITION

148 ENVIRONMENTAL ENGINEERING

Column 2: From Eq. (7.7)

1 - 0.4

f = 150 (7) + 1.75 = 51.75.

Columns 3 and 4: For the first size, x = 1.10% and d = 3.28 x

x (51.75)(0.011)

d 3.28 x

f-= = 174.

The last column is summed 1 f(x/d) = 113,977, and from Eq. (7.14), we have

hL=- (' - - 0'4) ( (8*9 (113,977) = 5.78 ft.

0.95 (0.4)3 32.2

The deposition of material during the filtering process increases the head loss

through the filter. A method of predicting head loss takes advantage of this limitation,

predicting head loss as

n

HL = JaL + (hi)t. (7.15)

i=l

Here, HL is the total head loss through the filter, h~ is the clear water head loss at time
zero, and (h~)~ is the head loss in the ith layer of the medium in the filter at time t.
All values are in meters. Head loss within an individual layer, (h&, is related to the
amount of materials caught by the layer

Here (qi)r is the amount of material collected in the ith layer at time t (in mg/cm3),

and x and y are experimental constants. Head loss data for sand and anthracite are

summarized in Fig. 7-10.

A filter run is the time a filter operates before it must be cleaned. The end of a filter

run is indicated by excessive head loss or excessive turbidity of the filtered water. If

either of these OCCUIS, the filter must be washed.

EXAMPLE 7.3. The filter described in Example 7.2 is run so that it reduces the suspended

solids from 55 to 3 mg/L during a filter run of 4 h. Assume this material is captured

in the first 6 in. of sand, where the sand grain size is adequately described as 0.8 mm.

What is the head loss of the dirty filter?