Page 140 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

114 4 Properties of Aerosol Particles

12. Starting from Eq. (4.55) derive the fractional distribution equation the surface
and volume distributions to show that both surface and volume also follow
lognormal distributions with the same standard deviation but with different
median diameters.
13. A 1-µm cubic particle discharged from a 20-m tall stack travels with a hori-
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zontal wind at a constant speed of 10 m/s. Assuming its density is 1,500 kg/m ,
estimate
(a) its volume equivalent diameter,
(b) its aerodynamic diameter, and
(c) the horizontal distance it travels before it falls to the ground.
14. Calculate the half-value time of spherical monodisperse aerosol with initial
3
6
concentration of 10 particles/cm and initial particle diameter of dp = 100 μm.
Assume standard condition and only Brownian coagulation is considered.
15. The figure below shows the cumulative mass distribution of a sample taken
from coal fly ash. Assume the particles are lognormally distributed. Find the
geometric standard deviation, and mass median diameter using the figure
below.

99.99
99.95
99.9
99.8
Cumulative % Less Than Indicated Size 90
99
98
95
80
70
60
50
40
30
20
10

2 5
1
0.5
0.2
0.1
0.055
0.01
0 1 10 100
Particle Diameter (µm)