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3.9 P article Analysis 239

The pressure intensity is related to the piezometric pressure p , through the def inition of the
latter quantity:
p p gz (3.589)
I f
where ( z ) is the elee a datum plane. Then ation abo v v

p () p ( z Z p gz + I g Z p ) gZ I f (3.590)
p z
)
z
(
f
f
By using the aboe equations, the eq. (3.448) for the determination of pressure drop in a
v
fluidised bed is deried (Section 3.8.2): v
p Zg ) (3.591)
(1
f
h
f
or
)
Z
p (1 ) ( g (3.592)
h f
The same analysis could be conducted by using forces. Consider a particle of height l and
of projected area perpendicular to flow A pr . The net upthrust on the projected area d A pr is

d
1
gl
p A d
( ) A (3.593)
I pr f h pr
The integration of this equation oer the entire projected area of the particle yields the
v
buoyancy force:
∫
)
F b f (1 g l A p r (3.594)
d
h
A pr
The integral in this equation is equal to the volume of particle. Thus,
F (1 gV (3.595)
)
b f h p
Comparing this equation to that of a single particle (eq. (3.565)), it is evident
that in applying the Archimedes principle to a particle in a fluidized suspension, it is
,
,
v
an aerage suspension density including the particle density rather than that of the
fluid alone, that determines the boscolo and Gibilaro, 1984). The gra uo y force (F yanc vity
force is
F V g (3.596)
g h p
Thus, the drag force is
F ( V g ) (3.597)
d h f p