Page 139 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

4.5 Aerosol Particle Size Distribution 113

In an engineering practice, log probability paper is often used in engineering
practice to determine the aerosol particle size distribution. One kind of log prob-
ability paper is given in Fig. A.1 as an example. Note that the x-axis is for the
probability and the y-axis is for the particle diameter.

4.6 Practice Problems

1. Calculate the aerodynamic diameter for an iron oxide spherical particle with
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geometric equivalent diameter, d p = 0.21 μm and density, ρ p = 5,200 kg/m .
2. Calculate the aerodynamic diameter for a sand particle with geometric equiv-
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alent diameter, d p = 0.3 μm and density, ρ p = 3,500 kg/m .
3. A spherical grain of concrete dust is falling down to the floor through standard
calm air. The particle geometric diameter is 2 μm and the particle density is
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2,500 kg/m . Determine
(a) the aerodynamic particle diameter of the particle
(b) how long it will take for the particle to reach its terminal velocity
(c) terminal settling velocity of the particle
(d) flow condition around this particle, laminar or turbulent
(e) how long it will take this particle will take to fall down a distance of 1 m?
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Given: standard room air density = 1.21 kg/m , viscosity = 1.81 × 10 −5 Pa s.
Air mean free path = 0.066 μm.
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4. A spherical particle with a diameter of 2 μm and a density of 5,200 kg/m is
released from rest in still air. How long it will take to reach its terminal
velocity?
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5. A dust grain with a diameter of 5 μm and a density of 5,000 kg/m is released
from rest in still air. Calculate the terminal settling velocity and drag force
exerted on this particle.
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6. A particle with a diameter of 0.08 μm and a density of 2,000 kg/m is released
from rest in still air. What is the terminal velocity and drag force if particle is
released from rest in still air?
7. Calculate the diffusion coefficient of a 2-μm particle in air at 25 °C and 1 atm.
8. Calculate the diffusion coefficient of a smoke particle having 0.05 μm diameter
in air at 45 °C and 1 atm.
9. Calculate the Cunningham correction factor for the following particles at 373 K
and 1 atm. (a) 0.055 μm, (b) 0.55 μm, and (c) 5.5 μm.
10. A dust particle having 0.75 µm diameter escapes through a filter of vacuum
cleaner at a height 1 m above the floor. Assume that the particle is spherical and
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its density is 1,200 kg/m . How long it will take to settle on the floor?
11. Two particles having diameters 1 and 10 µm, respectively, are released from a
height of 25 m above the ground. Assume that the particles are spherical with
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1,200 kg/m of density and ambient air is still. How long will they take to settle
on the ground?