3 replies to this topic

[Rich19]

Okay, I've done an investigation into viscosity and am analysing the data using things like Stokes' law. In this particular bit I'm working on, I dropped spheres of various radii through a viscous liquid and measured their terminal velocity. After doing a bit of research and looking at the data, I've come to the conclusion I need to apply a correction to the measured terminal velocity, as Stokes' law assumes the fluid is infinite in all directions.

The problem is that I haven't been able to find a single source that agrees on what that correction factor should be:

An old physics textbook (first published 1964) quotes something called the Ladenburg Correction, which is supposedly:

v(infinite) = v(measured) * (1+(2.4r/R)) * (1+(3.3r/h)

Where r is the radius of the sphere, R is the radius of the cylindrical tube through which it is dropped, h is the height of said cylinder, and v is velocity.



This website quotes something slightly different:

v(infinite) = v(measured) * (1+(2.4r/R)) * (1+(1.65r/h)


A completely different correction, this time for the viscosity, can be found at the top of page 7 here.



Does anyone have another textbook they could look up this correction factor in? Every single other place on the internet seems to want you to pay to view a journal in order to find out what this thing is.

Edited by Rich19, 19 March 2009 - 17:21.

[Dauth]

Why not derive your own correction factor?

It looks like a binomial correction around a sine rule from the ones I've seen, you could probably solve for the resulting polynomial in Excel (to a reasonable degree) or something better if you write the code and compute it.

You might need to have a binomial in both height and radius which could be more difficult but for a high viscosity you reach terminal velocity so fast that the contribution from the pressure wave in the depth is probably not worth calculating.

[Rich19]

I'm afriad that's probably a bt above my level - I'm not really quite sure what a binomial correction around a sine rule is, or how to derive the correction factor from that. Nevertheless, I appreciate the help, so thanks.

The liquid I was using is glycerol, so it is rather viscous.

Edited by Rich19, 19 March 2009 - 18:47.

[Dauth]

You can calculate the infinite viscosity can't you? The corrected value is the one you get from experiment.

Corrected = Infinite*Correction factor

Then just find an appropriate correction factor as a numerical value, would be an interesting start point and you can play with the algebra from there.