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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!