Droplets in a deodorant spray have mass of about (4x10^-12) kg and a radius of about 0.1mm. Estimate the terminal velocity of the droplets in Air of Viscosity (2x10^-5)Nsm^-2.
Stoke's Law, F = 6pi rvu
where r = radius, v = velocity and u = viscosity.
Upthrust of an object = vpg (v = volume, p = density, g = gravitational acceleration)
The Attempt at a Solution
Since at terminal velocity, it is obvious that W = F + U. (where W = weight, F = viscous drag, U = upthrust.)
So we have,
F = W-U
6pi (0.1x10^-3)(2x10^-5)(v) = (4x10^-12)(9.8) - (4/3)(pi)(0.1x10^-3)^3(1.24)(9.8)
**Based on the assumption that the droplet is a sphere and the density of air is 1.24kg/m^3
v = (approx) 0.3mms^-1.
Is this true?
(@ ehild : Oops. Forgot the negative sign)