Reynolds

# Reynolds - previous index next Stokes Law and the Coffee...

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previous index next Stokes’ Law and the Coffee Filters Michael Fowler, UVa 6/12/06 A Problem We found that Stokes’ Law, which we derived in the form drag F Ca v η = from purely dimensional considerations (Stokes did the hard part of proving that 6 C π = ) correctly predicted that for two small steel balls, one having a radius exactly twice the other, the bigger one would fall through a fluid four times faster (it had eight times the weight, and twice the drag force for the same velocity, and the drag force is proportional to the velocity). Now let us ask what Stokes’ Law predicts for the following coffee filter experiment : If we drop a single coffee filter, it reaches a terminal velocity of about 0.8 meters per sec after falling less than a meter. If we drop a stack of four close packed filters, the terminal velocity clocks in at about 1.6 meters per sec. That is to say, the stack of four filters has a terminal velocity twice that of a single filter. Now at terminal velocity the drag force is exactly balancing the weight of the object falling. The stack of four filters is almost indistinguishable in shape and size from the single filter, so it’s difficult to believe there’s any significant difference in the air flow pattern round the falling filters for the same speed. Therefore the Stokes’ drag from the air friction should be the same Ca v for both.

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## This note was uploaded on 12/07/2011 for the course PHYSICS 152 taught by Professor Michaelfowler during the Fall '07 term at UVA.

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Reynolds - previous index next Stokes Law and the Coffee...

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