Hello,
My student has an empirical project on the terminal velocity of a small
sphere (radius about 4 cm) falling through water in a tube. He changed the
mass (the sphere is hollow) and measured the terminal speed using video
analysis. The result is a linear dependency between mass and terminal
velocity.
His model is as follows: weight = buoyant force + drag force. The drag force
is estimated using Stoke's law: F(drag) = 6*pi*viscosity*radius*velocity.
Interestingly, the solution of the force equation w.r.t. terminal velocity
is also linearly dependent on mass, consistent with the empirical data. So
far, so good.
The viscosity of water is about 0.001 Pa*s (it depends on temperature). When
the force equation is solved with respect to the terminal velocity, the
answer is a few hundred m/s, whereas the measured terminal velocities are a
few m/s. What might explain the huge difference? One apparent reason is
turbulence, which the model ignores. Another is the edge effect, although
the tube is clearly larger in diameter than the sphere. Anything else?
Thanks for your thoughts in advance!
Antti Savinainen, PhD
Finland
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