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106 José Renato Coury et al.

2.4. Other Relations of Interest
2.4.1. The Effect of Particle Loading
The pressure drop in cyclones decreases with increasing particle load in the gas, and
collection efficiency increases. This is attributed to the impact of the larger particles
against the smaller ones, forcing them toward the stagnation region near the wall
(17,28,29). This effect can be quantified by the following expressions:
∆P at
= 1 − . 0 013 c . 05 (35)
c in
∆P at c in = 0 in
100 − η  c  0.182
1 0 = in2 (36)
100 − η   c 

2 0 in1
with c in grains per cubic feet.
in
2.4.2. Cyclones in Parallel (Multicyclones)
The pressure drop in multicyclones (dozens, or even hundreds of cyclones associated
in parallel) can be estimated by Eq. (37), which is a function of the total volumetric
flow rate, Q, the geometrical parameters K and K , and the diameter of the cyclone
a b
body, D (7):
c
 ∆ρHQ 2 
∆P =   (37)
4
2
2
2
 2 KK N D 
a
c
b
c
Multicyclones present a ∆P considerably smaller than a single cyclone, for the same
collection efficiency. The division of the total volumetric flow rate among the number
of N cyclones in Eq. (8) gives for collection efficiency of multicyclones:
c
 1 
τ
  GQ  2 n+2 
η = 1 − exp  −2  i ( n + ) 1   (38)
i 3
  ND c  
c
 
Nevertheless, the difficulties arising from distributing the dust-laden gas uniformly
among the cyclones results, in practice, in smaller collection efficiencies than that
predicted by Eq. (38).
2.4.3. Cyclones in Series
In case a second cyclone in series is needed, it is necessary to calculate the size distri-
bution in the exit of the first cyclone, which will be the feed of the next. This size distribu-
tion is easily obtained from a mass balance for each mass fraction that can be expressed in
terms of mass flow rate of particles with diameter D at the exit by the relation
i
m = c Qx (1 − η i ) (39)
i 0 in i
Therefore, the size fraction of a particle of diameter D at the first cyclone exit is
i
m
x i 0 = ∑ m i 0 i 0 (40)