Water Treatment Processes - Mathematics and Statistics for the Environment - page 646

23.6.12 F filter l loading r ate
Filter loading rate is the flow rate of water applied to the unit area of the filter. It is the same value
as the flow velocity approaching the filter surface and can be determined by using Equation 23.79:

u = Q / A (23.79)

where
u = Loading rate (m 3 /(m 2 ·day, gpm/ft 2 ).
Q = Flow rate (m 3 /day, f t 3 /day, g pm).
A = Surface area of filter (m 2 , ft 2 ).

Filters are classified as slow sand filters, rapid sand filters, or high-rate sand filters on the basis of
loading rate. Typically, the loading rate for rapid sand filters is 120 m 3 /m 2 ·day (83 L/m 2 ·min or 2 gal/
min/ft 2 ). The loading rate may be up to five times this rate for high-rate filters.

■ EXAMPLE 23.96
Problem: A sanitation district is to install rapid sand filters downstream of the clarifiers. The design-
loading rate is selected to be 150 m 3 /m 2 . The design capacity of the waterworks is 0.30 m 3 /sec (6.8
MGD). The maximum surface per filter is limited to 45 m 2 . Design the number and size of filters
and calculate the normal filtration rate.

Solution: Determine the total surface area required:

3

Q
u

030 . m/sec (85,400 sec/day)

150 m/m

25 920
150

,

m 2

A == = = 173

32 day

⋅

Determine the number of filters:

2

173 m
45 m

No.offilters = = 3.

Select four filters. The surface area ( A ) for each filter is

A = 173 m 2 ÷ 4 = 43.25 m 2

We can use 6 m × 7 m or 6.4 m × 7 m or 6.42 m × 7 m. If a 6-m × 7-m filter is installed, the normal
filtration rate is

3

Q
A

030 . m/sec ×

××

86,400 sec/day

32 ⋅

u == = 154 .m/m day

4m 6m 7m

23.6.13 F filter m edium s ize
Filter medium grain size has an important effect on the filtration efficiency and on backwashing
requirements for the medium. The actual medium selected is typically determined by performing
a grain size distribution analysis—sieve size and percentage passing by weight relationships are
plotted on logarithmic-probability paper. The most common parameters used in the United States
to characterize a filter medium are effective size (ES) and uniformity coefficient (UC) of medium
size distribution. The ES is that grain size for which 10% of the grains are smaller by weight; it
is often abbreviated by d 10 . The UC is the ratio of the 60-percentile ( d 60 ) to the 10-percentile. The