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Dimensional Analysis

  1. May 7, 2016 #1
    1. The problem statement, all variables and given/known data
    It is found the terminal velocity ut of a spherical particle in a fluid depends upon the diameter d of particle, the dynamic viscosity μ of fluid and the buoyancy weight W of the particle [given by the difference in density between the particle and the fluid (∆ρ) × gravitational acceleration (g)]. Determine the nature of the relationship between these variables.


    2. Relevant equations

    3. The attempt at a solution

    image.png



    image.png

    I'm not quite sure if I'm on the right track and where to go next from here? Any guidance or a nudge in the right direction would be appreciated. I can't help but think I have gone slightly wrong due to the number of indices to solve for.
     
  2. jcsd
  3. May 7, 2016 #2

    gneill

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    Staff: Mentor

    Perhaps you should make the weight a single term? That is, treat ∆ρ⋅g as one term. That, after all, is how it is described in the problem statement.
     
  4. May 7, 2016 #3
    Thank you. That was a big help. I obviously missed taking ∆ρ⋅g as W and got stuck in a rut. The end equation I've now determined to be as per Stokes law.

    Many thanks.
     
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