# Stoke's Law air density calculation

Stokes' Law describing partial sedimentation is given by:

Rate = [(gd^2)(Δρ)]/18η

where g = 9.81 m s^-2 is gravitational acceleration. Δρ is the density difference between particles and the air, air viscosity of η = 1.67E-4 g cm^-1 s^-1 and d is the particle diameter in centimeters.

a. Calculate the weight(g) of one cubic centimeter of air at 1.0 atm and 15 degrees celsius.

b. Assume particles have a density of 2.45 g cm^-3 and are being released by a 100 m smokestack. How long does it take (s) a 25μm particle to settle to the ground?

c. It rains exactly once a week. What is the smallest particle size (μm) that can settle to the grounds before wet removal?

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#### Solution Preview

a. Calculate the weight(g) of one cubic centimeter of air at 1.0 atm and 15 degrees celsius.

if we use the equation alluded to in: http://hypertextbook.com/facts/2000/RachelChu.shtml (Center choice) as "The density of moist air may be determined by a similar relation:

D = 1.2929 (273.13/T) [(B - 0.3783e)/760] where T is the absolute temperature; B, the barometric pressure in mm, and e the vapor pressure of the moisture in the air in mm."

Then in our circumstance D = ...

#### Solution Summary

Solution to problem involving sedimentation/settling rates of airborne particles as per Stoke's Law.