Science of Water : Concepts and Applications

Water Treatment Calculations 379
Select 4 m.
The surface area (a) for each fi lter 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.
Step 3. If a 6-m × 7-m fi lter is installed, the normal fi ltration rate is
FILTER MEDIUM SIZE
u Q
A
3
0.30 m s 86,400 sd 46 m7 m
3 2
154.3 m (md)
Filter medium grain size has an important effect on the fi ltration effi ciency 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 the fi lter medium are effective size (ES) and uniformity coeffi cient (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 as d 10 . The UC is the ratio of the 60-percentile (d 60 ) to the 10-percentile. The
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 fi lter backwash rate for a fi lter 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-probability plot is assumed, the values can be interrelated by Equation
10.81 (Cleasby, 1990).
Example 10.97
1.67log UC
d d (10 )
(10.81)
90 10
Problem:
A sieve analysis curve of a typical fi lter sand gives d10 = 0.52 mm and d60 = 0.70 mm. What are its
uniformity coeffi cient and d90 ?
Solution:
Step 1.
Step 2. Find d 90 using Equation 10.81.
d60
0.70 mm
UC 135
.
d 0.52 mm
10
d d
1.67 log UC
90 10(10
)
1.67 log1.35
0.52 mm(10 )
0.218
0.52 mm(10 )
0.86 mm