Dimensional Analysis:Relating Particle Diam, Viscosity, & Weight

[evoke1l1]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

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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.

 

[gneill]

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.

 

[evoke1l1]

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.