Does anyone know this equation? (fluid dynamics, Stokes law)

[astro111]

I was doing some research into my coursework (don't worry, this isn't a real 'help!' thread) on Stokes law, and I found this equation on this forum (posted in 2010), regarding the effect of the walls of a pipe on the calculated value for viscosity when a sphere is dropped through that pipe (sorry if that doesn't make sense!). The equation supposedly gives an approximate correction for that value of viscosity, taking into account the diameter of the pipe.
The equation is: mu_c = mu[1 - 2.104 d/D + 2.09 (d/D)^3 - 0.95 (d/D)^5]
where mu_c is the corrected viscosity, d is the diameter of the sphere and D the diameter of the pipe.

Does anyone know the origin of this equation, or whether it is accepted? I've been googling it for the past half an hour, but I'm yet to find anything! Thanks.

 

[Doc Al]

I believe this is the thread you are referring to: https://www.physicsforums.com/threads/please-help-viscosity-using-stokes-law.455280/

 

[astro111]

Indeed, however I was wondering if anyone knew where the equation originally came from (or whether it was simply devised by the website linked in that thread).

I've heard something about it being derived by someone called Faxen?

 

[Vagn]

Without knowing anything about it, that equation looks very much like a Taylor series expansion of some odd function.

 

[Chestermiller]

Check out this link: http://www.engr.uky.edu/~egr101/ml/ML3.pdf .
Better yet, check out page 73 of this reference: http://books.google.com/books?id=TD...q=falling ball viscometer corrections&f=false