The correct density for use in fluidization equations is the particle density,
defined as the mass of a particle divided by its hydrodynamic volume. This is
the volume "seen" by the fluid in its fluid dynamic interaction with the particle
and includes the volume of all the open and closed pores (see Figure 2).
Figure 2: Hydrodynamic volume of a particle
mass of particle
Particle density = -------------------------------
hydrodynamic volume of particle
For non-porous solids, this is easily measured by a gas pycnometer or specific
gravity bottle, but these devices should not be used for porous solids since
they give the true or absolute density, 
abs , of the material of which the particle
is made and this is not appropriate where interaction with fluid flow is concerned.
mass of particle
Absolute density = ------------------------------------------------
volume of solids material making up the particle
For porous particles, the particle density p
(also called apparent or envelope density) is not easy to measure directly
although several methods are given in Geldart (1990). Bed density is another
term used in connection with fluidized beds; bed density is defined as:
mass of particles in a bed
Bed density = -------------------------------------------------------
volume occupied by particles and the voids between them
For example, 600 kg of powder is fluidized in a vessel of cross-sectional area
1 m2 and achieves a bed height of 0.5 m. What is the bed density?
Mass of particles in the bed = 600 kg.
Volume occupied by particles and voids = 1 x 0.5 = 0.5 m3
Hence, bed density = 600/0.5 = 1200 kg/m3
If the particle density of these solids is 2700 kg/m3, what is the
bed voidage? Bed density B is related to particle
density p and bed voidage 
by Equation 12:
B = (1 - )p . . . . (Eq. 12)
Hence, voidage = 1 - (1200/2700) = 0.555
Another density often used when dealing with powders is the bulk density:
it is defined in a similar way to fluid bed density:
mass of particles
Bulk density = --------------------------------------------------------
volume occupied by particles and the voids between them
The most appropriate particle size to use in equations relating
to fluid-particle interactions is a hydrodynamic diameter; ie. an equivalent
sphere diameter derived from a measurement technique involving hydrodynamic
interaction between the particle and fluid. In practice, however, in most
industrial applications sizing is done using sieving and correlations use
either sieve diameter, xp or volume diameter, xv.
For spherical or near spherical particles xv is equal to
xp. For angular particles, xv 
1.13 xp.
For use in fluidization applications, starting from a sieve analysis
the mean size of the powder is often calculated from:
mean xp = 1 / 
(mi/xi)
. . . . . . (Eq. 13)
where xi is the arithmetic mean of adjacent sieves between
which a mass fraction mi is collected. This is the harmonic mean
of the mass distribution, which is equivalent to arithmetic mean
of a surface distribution.