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Forces on a sphere accelerating in a viscous fluid

Published online by Cambridge University Press:  28 March 2006

Fuat Odar  and
Wallis S. Hamilton
Fuat Odar
Affiliation:
U.S. Army Cold Regions Research and Engineering Laboratory Hanover, New Hampshire
Wallis S. Hamilton
Affiliation:
Northwestern University, Evanston, Illinois
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Abstract

A detailed equation is proposed for the force exerted on a sphere that accelerates rectilinearly in an otherwise still fluid. In addition to the buoyant force, the fluid exerts forces that depend on (a) the velocity of the sphere, (b) the acceleration of the sphere and (c) the history of the motion. The equation reduces to the known theoretical solution for low velocity and large acceleration.

The proposed equation was tested and found most satisfactory for a particular case in which the velocity was not small, viz. the case of simple harmonic motion along a straight line. The acceleration (added mass) and history coefficients in the equation were evaluated experimentally. They were found to depend on the ratio of the convective acceleration to the local acceleration as measured by the parameter V2/aD, in which V, a and D are the velocity, acceleration and diameter of the sphere, respectively. The Reynolds numbers varied from 0 to 62 during the tests.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 18 , Issue 2 , February 1964 , pp. 302 - 314
Copyright
© 1964 Cambridge University Press

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References

Basset, A. B. 1888 A Treatise on Hydrodynamics, Vol. 2, Ch. 21. Cambridge: Deighton, Bell and Co. (Also New York: Dover Publications, Inc., 1961.)
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Odar, F. 1962 Forces on a sphere accelerating in a viscous fluid. Ph.D. Dissertation, Northwestern Univ., Evanston, Illinois.
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Stokes, G. G. 1851 Mathematical and Physical Papers, 3, 1.
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