Civil Engineering Reference
In-Depth Information
headloss allowed between backwashes can be chosen on the basis of several factors,
including cost of available headloss, filter media design, and filter breakthrough. Typ-
ical design headloss valves range from 5 to 10 feet (1.524 to 3.048 m).
The headloss through a clean filter bed can be calculated through the use of a
number of equations, including the Carmen-Koseny, Fair-Hatch, and Rose equations,
which are given below for reference. However, unless a unique filter system is designed
and headloss is critical, the benefit of these equations is questionable. Typical clean
filter beds and underdrain systems, whether mixed- or dual-media, generally impart 1
to 1
1
⁄
2
feet (0.31 to 0.46 m) of headloss. Specific media manufacturers or suppliers
should be consulted when headloss values are determined.
The Carmen-Kozeny equation, for use with uniform-size media, is:
H
11
V
2
L
ƒ
(26-48)
l
d
3
g
where:
H
L
headloss, ft (m)
l
depth of media, ft (m)
particle shape factor, dimensionless
1.0 for sphere
0.28 for mica flakes
0.82 for rounded sand
0.73 for angular sand
d
particle diameter, ft (m)
bed porosity, dimensionless
V
filtration rate of water, ft / sec (m / s)
g
acceleration of gravity, 32.174 ft / sec
2
)
ƒ
friction factor, dimensionless
1
ƒ
150
1.75
Re
Re
Reynolds number, dimensionless
w
Vs
average superficial velocity through an empty bed, ft / sec (m / s)
density, slugs / cu ft (kg / m
3
)
dynamic viscosity, lb
sec/sq ft (N
s/m
2
)
The Fair-Hatch equation for nonuniform media is:
2
HK
V
(1
)
6
n
P
2
L
i
(26-49)
l
g
3
d
2
i
1
pi
where:
H
L
headloss, ft (m)
l
depth of media, ft (m)
K
Kozeny constant,
5
