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Homework Help: Viscous Drag and Terminal Velocity

  1. Mar 9, 2010 #1
    1. The problem statement, all variables and given/known data

    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.

    2. Relevant 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)

    3. 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: Mar 9, 2010
  2. jcsd
  3. Mar 9, 2010 #2


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    "Droplets in a deodorant spray have mass of (4x10^12) kg "

    Is this serious?:rofl:

  4. Mar 10, 2010 #3


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    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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