Science of Water : Concepts and Applications

382 The Science of Water: Concepts and Applications
Step 3. Compute total head loss.
h 0.0410 m0.5579 m
0.599 m
HEAD LOSS THROUGH A FLUIDIZED BED
If the upward water fl ow rate through a fi lter bed is very large the bed mobilizes pneumatically
and may be swept out of the process vessel. At an intermediate fl ow rate the bed expands and is
in what we call an expanded state. In the fi xed bed the particles are in direct contact with one
another, supporting one another’s weight. In the expanded bed, the particles have a mean free
distance between particles and the drag force of the water supports the particles. The expanded
bed has some of the properties of the water (i.e., of a fl uid) and is called a fl uidized bed (Chase,
2002). Simply, fl u i d i z a t i o n is defi ned as upward fl ow through a granular fi lter bed at suffi cient
velocity to suspend the grains in the water. Minimum fl uidizing velocity (Umf ) is the superfi cial
fl uid velocity needed to start fl uidization; it is important in determining the required minimum
backwashing fl ow rate. Wen and Yu proposed the Umf equation including the near constants (over
a wide rang of particles) 33.7 and 0.0408, but excluding porosity of fl uidization and shape factor
(Wen and Yu, 1966):
U
mf
05 . 33. 7
( 1135. 690. 0408Gn)
pd
pd
where
µ = absolute viscosity of water, N s/m 2 or lb s/ft 2
p = density of water, kg/m 3 or lb/ft 3
d eq = d 90 sieve size is used instead of d eq
G n = Galileo number
eq
eq
(10.84)
3
2
Gndeqp( ps − p) g
(10.85)
Other variables used are expressed in Equation 10.83.
√ Note: Based on the studies of Cleasby and Fan (1981), we use a safety factor of 1.3 to ensure
adequate movement of the grains.
Example 10.100
Problem:
Estimate the minimum fl uidized velocity and backwash rate for the sand fi lter. The d90 size of sand is
0.90 mm. The density of sand is 2.68 g/cm3 .
Solution:
Step 1. Compute the Galileo number.
From given data and the applicable table, at 15°C:
p = 0.999 g/cm3 µ = 0.0113 N s/m2 = 0.00113 kg/ms = 0.0113 g/cm s
µp = 0.0113 cm2 /s