Re: [Phys-L] Terminal velocity in water
How do you know the drag force is linear in the speed rather than
quadratic? I would think for your dimensions and assuming the sphere is
solid metal that a quadratic dependence is more likely. Have you estimated
the Reynolds number?
On Tue, Oct 24, 2023 at 12:08 PM Antti Savinainen via Phys-l <
phys-l@mail.phys-l.org> wrote:
> 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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