Download Modeling drag for the coffee filter

Modeling drag for the coffee
filter
Dr. Fisher, 15 Sept 2010
(ref Brueningsen et al, The Physics
Teacher, 32, Oct 1994, p 439)
Some charts
A simplified view of filter movement
through air
• For low Re: the air slips around the filter
• For High Re: Filter, mass M, moves through air,
and it collides with an air molecule, mass m,
initially at rest.
• For the filter, change in momentum is
Dp = mv(2M/M+m)
• Which for M>>m, becomes ?
• Dp = 2vm
As the filter moves through air..
• It sweeps a volume, V, of air
V= AvDt where A is x-sectional area, v is velocity,
and t is time
The Mass of air swept out or displaced is r(AvDt)
• So, the average force applied to the filter due
to collisions is Fd = Dp/Dt
– Another form of Newton’s second law
• Thus, for all the air Fd = (2r(AvDt)v)/Dt
– Which means Fd = kv2
Models to test
• For low Reynolds Number, Stokes flow, we
expect Fd = kv
• And for high Re, we expect Fd = kv2
• So we should check them both to see which
model works
• If we don’t have enough data to test it, then
we can get more data!