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New derivations of Darwin's theorem

Published online by Cambridge University Press:  20 April 2006

Chia-Shun Yih
Chia-Shun Yih
Affiliation:
The University of Michigan, Ann Arbor, Michigan
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Abstract

Two new derivations of Darwin's theorem on the equality of the added mass for translation of a body moving in an ideal fluid of infinite extent and the drift mass are given. The first is based on the idea of time lag, used by Rayleigh (1876), Ursell (1953), and Longuet-Higgins (1953) to study fluid drift. The second is truly elementary, relying only on the concept of continuity and Newton's second law of motion. A geometrical interpretation of the result in the first derivation is given, and a few examples are provided.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 152 , March 1985 , pp. 163 - 172
Copyright
© 1985 Cambridge University Press

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