Question

The settling rate of particulates in air is directly proportional to the square of their diameters (Stokes’ Law), provided that their densities are equal. If emitted particulates with a specific diameter are found to settle out after two days, how long would it take particulates of the same material with half the diameter to settle out if emitted from the same tall chimney?

Answer 1

Answer:

It will take 12 hours to settle out same particulate with half the diameter from same chimney.

Explanation:

The settling rate of particulates = S

Diameter of the particulate = d

$S\propto d^2$

The settling rate of one type of particulates = $S_1$

Diameter of the one type of particulate = $d_1$

The settling rate of other type of particulates = $S_2$

Diameter of the other type of particulate = $d_2=0.5d_1$

$\frac{S_1}{(d_1)^2}=\frac{S_2}{(d_2)^2}$

$\frac{S_1}{(d_1)^2}=\frac{S_2}{(0.5d_1)^2}$

$S_1=4S_2$

$S_2=\frac{S_1}{4}$

Given that settling of one type of particulate from chimney is 2 days.So settling of other type of particulate from  same chimney:

$S_2=\frac{2 days}{4}=0.5 days$

1 day = 24 hours

0.5 days = 0.5 × 24 hours = 12 hours

It will take 12 hours to settle out same particulate with half the diameter from same chimney.