Question

Small, slowly moving spherical particles experience a drag force given by Stokes' law: Fd = 6πηrv where r is the radius of the particle, v is its speed, and η is the coefficient of viscosity of the fluid medium.

(a) Estimate the terminal speed of a spherical pollution particle of radius 9.00 10-6 m and density of 2166 kg/m3.
cm/s

(b) Assuming that the air is still and that η is 1.80 10-5 N · s/m2, estimate the time it takes for such a particle to fall from a height of 100 m.
h

Answer 1

mass = 2166 * (4/3)pi r^3
weight = 9.81 (2166)(4/3)pi r^3

balance weight with Stokes force

weight = 6 pi η r v

so
6piη r v=9.81 (2166)(4/3)pi r^3

9 η v=9.81 (2166)(2)(9*10^-6)^2


9 η v=9.81 (2166)(2)(9*10^-6)^2

v = 382472 *10^-12/η

have to know η to estimate v, see part b

v =382472 *10^-12 /1.8*10^-5
= 212485 *10^-7
= 0.0212485 m/s

v is constant so time= 100/.021