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Hydromechanics of low-Reynolds-number flow. Part 4. Translation of spheroids

Chwang, Allen T. and Wu, Theodore Y. (1976) Hydromechanics of low-Reynolds-number flow. Part 4. Translation of spheroids. Journal of Fluid Mechanics, 75 (4). pp. 677-689. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:CHWjfm76

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Abstract

The problem of a uniform transverse flow past a prolate spheroid of arbitrary aspect ratio at low Reynolds numbers has been analysed by the method of matched asymptotic expansions. The solution is found to depend on two Reynolds numbers, one based on the semi-minor axis b, R[sub]b = Ub/v, and the other on the semi-major axis a, R[sub]a = Ua/v (U being the free-stream velocity at infinity, which is perpendicular to the major axis of the spheroid, and v the kinematic viscosity of the fluid). A drag formula is obtained for small values of R[sub]b and arbitrary values of R[sub]a. When R[sub]a is also small, the present drag formula reduces to the Oberbeck (1876) result for Stokes flow past a spheroid, and it gives the Oseen (1910) drag for an infinitely long cylinder when R[sub]a tends to infinity. This result thus provides a clear physical picture and explanation of the 'Stokes paradox' known in viscous flow theory.


Item Type:Article
Additional Information:"Reprinted with the permission of Cambridge University Press." (Received 29 Septembor 1975). The authors are greatly indebted to Professor Sir James Lighthill for his invaluable suggestions and comments. This work was partially sponsored by the National Science Foundation and by the Office of Naval Research.
Record Number:CaltechAUTHORS:CHWjfm76
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:CHWjfm76
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:339
Collection:CaltechAUTHORS
Deposited By: Theodore Yao-tsu Wu
Deposited On:03 Jun 2005
Last Modified:26 Dec 2012 08:39

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