# Mixing of fluid in a rotating barrel

A barrel/drum with a diameter of 60cm is rotating at 20RPM to get a good mixing of the fluid contained (type thick oil).

At what RPM should a barrel of 30cm rotate to get the same mixing efficiency with the same fluid? To get the same peripheral velocity, the RPM should be 40RPM, but will this give the same mixing of the fluid? I guess gravitational and centripetal forces play a role her...

The barrel is rotating around the length axis and the degree of fill is 90%.

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This actually sounds like a fun question, and should be approachable by scaling/dimensional analysis arguments. Mixing is a microscopic kinetic effect, so is really something to do with vicosity. Clearly, the size of the container matters, perhaps both radius and height. Finally, there is the rotation speed. What dimensionless quantities may be made with these? Are there other factors which might be important (density? I don't have a very good intuition about fluids...) – genneth Jan 28 '11 at 11:53
The orientation of the drum relative to gravity is still missing: ie does the drum stand upright or does it lie horizontally with respect to its axis of symmetry? – Georg Jan 28 '11 at 12:47
It lies horizontally.. just like a barrel rolling down a hill. – williamx Jan 28 '11 at 14:07

Knowing a bit about process engineers' attitude to science I would say you just need to have same Reynolds number. $U\approx\Omega R$, $L\approx R$, then $Re\approx\frac{\Omega R^2}{\nu}$ so 80RPM.