Abstract
An approximate theory is developed to describe the behaviour of a heavy ball passing slowly down a vertical tube having a diameter only slightly exceeding the diameter of the ball, and filled with a viscous fluid. It is shown that according to this theory the equations of motion can be satisfied when the ball takes up any degree of eccentricity in the tube and that any given eccentricity requires a particular velocity of rotation about a horizontal axis. It is found that the eccentricity ratio corresponding to minimum dissipation of energy for given velocity of descent (i.e. to maximum rate of fall for a given weight of ball) is about 0.98, and that the velocity is then rather more than twice the velocity corresponding to zero eccentricity. Experiments are described in which it was shown that provided conditions were such that the ball descended very slowly, the minimum dissipation prediction was verified within the expected accuracy, but that for larger clearances and more rapid fall the predicted angular velocity and eccentricity were not achieved within the times for which observation was possible.
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Schedule a callMore From: Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
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