Page 476 - Water and wastewater engineering

GRANULAR FILTRATION 11-49

b. Anthracite coal

E 11 mm
.
v 7 5 m/h ; 12 m/h ; 15 m/h ; 20 m/h 25 m/h
.
;
a
Water temperature 15 C
Use the following equation to calculate the Reynolds number.

d
( )()( ) ()( )
d
va
va
R

3

where density, kg/m
v a approach velocity

d effective diameter of media (E)
dynamic viscosity, Pa · s
2
kinematic viscosity, m /s
11-9. The Ergun equation for calculating clean bed headloss ( Table 11-2 ) has been pro-
posed for use in cases where larger media and higher filtration rates are used such
as deep bed monomedium filters. The first term in the Ergun equation accounts for
viscous forces. The second term accounts for inertial forces. Calculate the ratio of the
inertial term to the total headloss estimate for various filtration rates using a spread-
sheet you have written. Assume the following values:

k v 228
0.50
3
1.14 10 Pa · s
L 1.5 m
3
999 kg/m
d 1.1 mm
2
g 9.81 m/s
k i 4.4

Identify the filtration rate at which the inertial term accounts for half of the clean bed
headloss. See Trussell and Chang (1999) for more on k v and k i.
11-10. The rapid sand filter being designed for Eau Gaullie has the characteristics and sieve
analysis shown below. Using the Rose equation, determine the headloss for the clean
filter bed in a stratified condition.

Depth 0.60 m
3
2
Filtration rate 120 m /d · m
Sand specific gravity 2.50
Shape factor 0.80
Stratified bed porosity 0.42
Water temperature 19 C