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Viscous media

solid spheres


For solid spheres we can relate the radius r of the sphere and its terminal velocity vterm as follows.
The mass m of a sphere is related to its density ρs (not to be confused with the density ρfluid of the medium in which the sphere vertically moves) by

m = 4πρsr3/3 ∝ r3


In regime I we have for the terminal velocity

vterm = mg/C1r ∝ r2


In regime II we have for the terminal velocity

vterm = √(mg/C2r2) ∝ √r


Hence, one may deduce the regime by using falling metal bearing balls with the same density, but of different diameter, and measure their terminal velocities. If the terminal velocity is proportional to r2, then one is dealing with regime I, whereas, when it is proportional to √r, one is dealing with regime II.


massive spheres