Journal of Fluid Mechanics

Forces on a sphere accelerating in a viscous fluid

Fuat  Odar a1 and Wallis S.  Hamilton a2
a1 U.S. Army Cold Regions Research and Engineering Laboratory Hanover, New Hampshire
a2 Northwestern University, Evanston, Illinois

Article author query
odar f   [Google Scholar] 
hamilton ws   [Google Scholar] 


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.

(Published Online March 28 2006)
(Received April 5 1963)
(Revised September 21 1963)