Date of Award

1982

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Abstract

Measurements are presented for the drag on a torus moving along its axis of rotational symmetry at low Reynolds number. If D is the outside diameter of the torus, and d is the thickness in the axial direction, then the measurements cover the range s(,o) = 1 (the closed torus) to s(,o) = 135, where s(,o) (TBOND) (D/d) - 1. The effect of a coaxial cylindrical boundary (diameter H) is taken into account by an empirical correlation. The values of drag obtained by extrapolating to a fluid of infinite extent are in good agreement with the exact solution obtained by Majumdar and O'Neill. When (pi)d(s(,o))(' 1/2) << H, the empirical boundary correlation is consistent with the result of Brenner for small particles. Measurements with outer boundaries of square and circular cross-section indicate that the relative effect of the two boundary shapes on the drag is the same for the torus as that found by Happel and Bart for a sphere. Empirical results are presented for the case in which the torus is strongly influenced by a coaxial cylindrical boundary. The combined inertial and boundary effect for the torus has been related to the combined inertial and boundary effect for a sphere by an empirical equation.

Pages

107

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