Geoscience Reference
In-Depth Information
With the accumulation of impurities, head loss gradually increases until the filter is backwashed.
The Kozeny equation, shown below, is typically used for calculating head loss through a clean fixed-
bed flow filter:
2
2
h
L
k
µε
ε
(
1
−
)
A
V
=
u
(23.82)
3
gp
where
h
= Head loss in filter depth
L
(m, ft).
L
= Depth of filter (ft, m).
k
= Dimensionless Kozeny constant (5 for sieve openings, 6 for size of separation).
µ = Absolute viscosity of water (N·s/m
2
, lb·s/ft
2
).
ε = Porosity (dimensionless).
g
= Acceleration of gravity (9.81 m/s or 32.2 ft/s).
p
= Density of water (kg/m
3
, lb/ft
3
).
A/V
= Grain surface area per unit volume of grain.
= Specific surface
S
(shape factor = 6.0-7.7).
= 6/
d
for spheres.
= 6/Ψ
d
eq
for irregular grains.
Ψ = Grain sphericity or shape factor.
d
eq
= Grain diameter of spheres of equal volume.
u
= Filtration (superficial) velocity (m/s, fps).
■
EXAMPLE 23.99
Problem:
A dual-medium filter is composed of 0.3 m of anthracite (mean size, 2.0 mm) that is
placed over a 0.6-m layer of sand (mean size, 0.7 mm) with a filtration rate of 9.78 m/hr. Assume
that the grain sphericity is Ψ = 0.75 and the porosity for both is 0.42. Although such values are
normally taken from the appropriate table at 15°C, we provide the head loss data of the filter at
1.131 × 10
-6
m
2
·s.
Solution:
Determine head loss through the anthracite layer using Equation 23.82:
2
2
h
L
k
µε
ε
(
1
−
)
A
V
=
u
3
gp
where
k
= 6.
g
= 9.81 m/s
2
.
µ
p
=
v
= 1.131 × 10
-6
m
2
·s (from the appropriate table).
ε = 0.40.
A/V
= 6/0.75
d
= 8/
d
= 8/0.002.
u
= 9.78 m/h = 0.00272 m/s.
L
= 0.3 m.
Then,
2
−
6
2
1 131 10
981
.
×
(
1042
042
−
.
)
8
0 002
×
×
h
=×
6
×
0 00272
.
×
03
.
=
0.0410 m
3
.
.
.
Search WWH ::
Custom Search