Small, slowly moving spherical particles experience a drag force given by Stokes’ law: where r is the radius of the particle, 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 1.00 x 10-5 m and density of 2000 kg/m3. (b) Assuming that the air is still and that η is 1.80 x 0-5 N · s/m2, estimate the time it takes for such a particle to fall from a height of 100 m.

Question

Small, slowly moving spherical particles experience a drag force given by Stokes’ law:  where r is the radius of the particle,  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 1.00 x 10-5 m and density of 2000 kg/m3. (b) Assuming that the air is still and that η is 1.80 x 0-5 N · s/m2, estimate the time it takes for such a particle to fall from a height of 100 m.

drwls · Answer

You need Stokes' law to do that problem. You did not include it in the question, but I assume you have it or can look it up. (See also below) (a) The terminal speed of the particle is the value for which the Stokes' drag equals the weight minus the buoyancy force. (b) For the time to fall 100 m, divide 100m by the terminal speed.

The equations you need can be found at

http://en.wikipedia.org/wiki/Stokes'_law