Water Treatment Processes - Mathematics and Statistics for the Environment - page 647

90-percentile, d 90, is the size for which 90% of the grains are smaller by weight. The d 90 size is used
for computing the required filter backwash rate for a filter medium. Values of d 10, d 60 , and d 90 can
be read from an actual sieve analysis curve. If such a curve is not available and if a linear log-prob-
ability plot is assumed, the values can be interrelated by Equation 23.80 (Cleasby, 1990):

d 90 = d 10 (10 1.67logUC ) (23.80)

■ EXAMPLE 23.97
Problem: A sieve analysis curve of a typical filter sand gives d 10 = 0.52mm and d 60 = 0.70 mm. What
are its uniformity coefficient and d 90 ?
Solution:

UC = d 60 / d 10 = 0.70 mm/0.52 mm = 1.35

d 90 = d 10 (10 1.67logUC ) = 0.52 mm × (10 1.67log1.35 ) = 0.52 mm × (10 0.218 ) = 0.86 mm

23.6.14 m fixed m edia
An innovation in filtering systems has offered a significant improvement and economic advantage
to rapid rate filtration: the mixed media filter bed. Mixed media filter beds offer specific advantages
in specific circumstances, but will give excellent operating results at a filtering rate of 5 gal/ft 2 /min.
Moreover, the mixed media filtering unit is more tolerant of higher turbidities in the settled water.
For improved process performance, activated carbon or anthracite is added on the top of the sand
bed. The approximate specific gravities of ilmenite (<60% TiO 2 ), silica sand, anthracite, and water
are 4.2, 2.6, 1.5, and 1.0, respectively. The economic advantage of the mixed bed media filter is
based upon filter area; it will safely produce 2-1/2 times as much filtered water as a rapid sand filter.
When settling velocities are equal, the particle sizes for media of different specific gravities can be
computed by using Equation 23.81:

2/3

d
d

ss
ss

−
−

1
2

2
1

(23.81)

=

where
d 1 , d 2 = Diameter of particles 1 and 2, and water, respectively.
s 1 , s , s 2 = Specific gravity of particle 1, water, and particle 2, respectively.

■ EXAMPLE 23.98
Problem : Estimate the particle size of ilmenite sand (specific gravity = 4.2) that has the same set-
tling velocity as silica sand that is 0.60 mm in diameter (specific gravity = 2.6).

Solution: Find the diameter of ilmenite sand using Equation 23.81:

2/3

26 1
42 1

.
.

−
−

=

d = 0.6 mm × 0.38 mm

23.6.15 h ead l oss For F fixed b ed F loW
When water is pumped upward through a bed of fine particles at a very low low rate the water per-
colates through the pores (void spaces) without disturbing the bed. This is a fixed bed process. The
head loss (pressure drop) through a clean granular-media filter is generally less than 0.9 m (3 ft).