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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