ACCELERATING MOTION OF A VERTICALLY FALLING SPHERE IN INCOMPRESSIBLE NEWTONIAN MEDIA - AN ANALYTICAL SOLUTION

The transient motion of a sphere falling through a Newtonian fluid has been investigated using a drag of the form given by Abraham/Wadell, t he average accuracy of which was found to be 7.6% for a sphere with Re ynolds number Re in the range 0 less than or equal to Re less than or equal to 10(4), 12% for 10(4)<Re<10(5) and 15% for 0 less than or equa l to Re less than or equal to 10(5). The equations of motion have been integrated taking into account the added-mass effects, and exact anal ytical solutions for the time and distance required by the sphere to r each a given velocity are derived. The acceleration of the sphere and the terminal velocity were also determined. It was found that differen t properties of the sphere-fluid combination result in different solut ions for the time and distance, but not for the acceleration. The anal ysis reported herein is, however, restricted to dense spheres falling in less dense fluids, when additional effects arising from the Basset forces can be neglected. (C) 1998 Elsevier Science S.A. All rights res erved.