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3.9 P article Analysis 237

w Within the range of Stoks la, e’ Re 1 and C 24/ Re and thus
ter D ter,
gd p 2 ( h f )
u ter (3.575)
18
f

wton’ Within the range of Nes law, Re 1000 and C 0.445, and thus
ter D
gd  ( )  0.5
u 1.73  p h f  (3.576)
ter
 f 
where Re is the Reynolds number based on the terminal particle v. In all the equa- elocity
ter
tions above, SI units should be used. F or u u , the particle is blown out of the bed and
s ter
thus it can be considered as the maximum fluidization v . elocity
Haider and Levenspiel (1989) found a useful relationship for the direct evaluation of the
terminal velocity of particles. They used the following equations on the grounds that
0.5 1:
S
 18 2.335 1.744  1
U  S  (3.577)
ter 2 0.5
D  sph D sph 

where:
 2  13
U u  f  (3.578)
ter ter
 g ( h f ) 

and

 g(  13
)
D d  f h f  (3.579)
sph sph 2


SI units should be used in these equations. Furthermore, the effect of particle sphericity is
included. Here, d could be taken equal to the mean nominal diameter measured by sieve
sph
analysis ( d ).
p
Another useful correlation is the Khan–Richardson correlation (Hilal, 2000):

Ar 2.07 Re ter 0.27 0.33 Re 0.64 3.45 ter (3.580)

where Re is the Reynolds number based on the terminal particle velocity and Ar is the
ter
Archimedes number.
d g )
3
(
Ar p f h f (3.581)

2