Viscous Drag and Terminal Velocity

  • #1

Homework Statement

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.

Homework Equations

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

We have,
v = (approx) 0.3mms^-1.

Is this true?

(@ ehild : Oops. Forgot the negative sign)
Last edited:
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  • #2
"Droplets in a deodorant spray have mass of (4x10^12) kg "

Is this serious?:rofl:

  • #3
Something is still wrong with the data. What is the density of the droplets if the mass is 4^*10^-12 and the radius is 0.1 mm?


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