Introduction to Health Physics: Fourth Edition - Ruang Baca FMIPA UB

RADIATION SAFETY GUIDES 359
collisions with air molecules lead to diffusion of very small or molecule-sized particles.
The released particle also falls under the influence of gravity. For particles
greater than about 1 μm, the gravitational effects and inertial effects are much
greater than the diffusional effects. Thus, the motion of this particle relative to the
air is determined mainly by the aerodynamic properties of the particle. For particles
smaller than 0.1 μm, diffusional effects predominate and particle motion relative
to air is determined by thermodynamic properties of the particle. Particles between
these two sizes are influenced by both aerodynamic and thermodynamic factors.
Aerodynamic Properties
When aerodynamic properties predominate, a released particle is acted upon by
two forces: f g, the downward force of gravity, and f r, the upward retarding force
due to the resistance to free fall offered by the air (Fig. 8-4). When the retarding
force is equal to the gravitational force, there is no unbalanced force to accelerate
the falling particle, and a constant velocity, called the terminal velocity, v t, is attained by
the falling particle. Equating f r to f g and solving for the terminal velocity, we have
fr = 3πηdv = πd3
6 (ρ − ρair)g = fg
(8.15)
v = vt = d2 (ρ − ρair)g
. (8.16)
18η
Since the air density is very much less than the particle density, that is, ρair ≪ ρ, Eq.
(8.16) may be written as
vt = d2ρg . (8.17)
18η
Retarding force, f r = 3πηdv
Gravitational force, f g = Mg = πd (p-pair)g 3
6
Figure 8-4. The forces acting on a particle falling through air. η = viscosity of air = 185μP at room
temperature (1 P = 1 g/cm/s); d = particle diameter (cm); v = velocity of fall (cm/s); M = particle
mass (g); g = acceleration due to gravity = 980 cm/s 2 ; ρ = particle density (g/cm 3 ); ρair = air density
(g/cm 3 ).