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Stokes_Law

# Stokes_Law - previous index next Dropping the Ball(Slowly...

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previous index next Dropping the Ball (Slowly) Michael Fowler, UVa 6/12/06 Stokes’ Law We’ve seen how viscosity acts as a frictional brake on the rate at which water flows through a pipe, let us now examine its frictional effect on an object falling through a viscous medium. To make it simple, we take a sphere. If we use a very viscous liquid, such as glycerin, and a small sphere, for example a ball bearing of radius a millimeter or so, it turns out experimentally that the liquid flows smoothly around the ball as it falls, with a flow pattern like: (The arrows show the fluid flow as seen by the ball. This smooth flow only takes place for fairly slow motion , as we shall see.) If we knew mathematically precisely how the velocity in this flow pattern varied near the ball, we could find the total viscous force on the ball by finding the velocity gradient near each little area of the ball’s surface, and doing an integral. But actually this is quite difficult. It was done in the 1840’s by Sir George Gabriel Stokes. He found what has become known as Stokes’ Law: the drag force F on a sphere of radius a moving through a fluid of viscosity η at speed v is given by: 6. Fa v πη = Note that this drag force is directly proportional to the radius . That’s not obvious—one might

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Stokes_Law - previous index next Dropping the Ball(Slowly...

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