Environmental Engineering FOURTH EDITION

Water Treatment 147

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EXAMPLE 7.2. A sand consisting of the following sizes is used'

Sieve % of sand retained Geometric mean sand

number on sieve, x lo2 size, ft x 10-~

14-20

20-28

28-32

32-35

3542

42-48

48-60

60-65

65-100

1.10

6.60

15.94

18.60

19.10

17.60

14.30

5.10

1.66

3.28

2.29

1.77

1.51

1.25

1.05

0.88

0.75

0.59

The filter bed measures 20 x 20 ft2 and is 2 ft deep. The sand has a porosity of 0.40
and a shape factor of 0.95. The filtration rate is 4 gal/min-ft2. Assume the viscosity is
3 x lb-s/ft2. Find the head loss through the clean sand.
The solution is shown in tabular form:

Reynolds number, R Friction factor,f x/d f(x/d)

1.80

1.37

1.06

0.91

0.75

0.63

0.53

0.45

0.35

51.7

67.4

86.6

100.6

121.7

144.6

171.5

201.7

258.8

3.4

28.8

90.1

123.2

152.8

167.6

162.5

68.0

28.1

174

1,941

7,802

12,394

18,595

24,235

27,868

13,715

7,272

Column I : The approach velocity is

For the first particle size, d = 3.28 x ft, and

= 1.80.

(0.95)( 1.94)(89)( (3.28)(

R=

3 x 10-5

lAdapted from J. W. Clark, W. Viessman, and M. J. Hammer, Water Supply and Pollution Control, 3rd
ed., Thomas Crowell, New York, 1977.