Measurements of Drag Coefficients for Falling and Rising Spheres in Free Motion

Citation

Preukschat, A. Werner (1962) Measurements of Drag Coefficients for Falling and Rising Spheres in Free Motion. Engineer's thesis, California Institute of Technology. doi:10.7907/94MG-ZS76. https://resolver.caltech.edu/CaltechETD:etd-12192005-145326

Abstract

The purpose of this thesis is to investigate the drag coefficient of spheres in free motion, falling and rising, in water. Following the introduction the test set-up, sphere release mechanism, spheres and timing device and recorder are described. Section 3 gives the results of the drag coefficient measurements for free falling spheres which show good agreement with the known measurements, quoted, for instance, in the Handbuch der Experimentalphysik. Section 4 deals with the measurement of drag coefficients of free-rising spheres. It was found that the freely rising spheres move in an oscillatory path of which wavelength and amplitude depend on the ratio of sphere density and water density. The local drag coefficient of the spheres was measured to be the same as for falling spheres. It was found to be independent of the sphere motion. No critical Reynolds number was found for the onset of the oscillatory motion of the sphere. The oscillatory motion appeared to be independent of initial disturbances of the sphere motion. From photographs of the sphere paths Strouhal numbers were formed which are about one third the value given for circular cylinders in the same Reynolds number range. A theoretical oscillatory force coefficient, based on a force balance on the sphere, was obtained. It was found to be of the same order of magnitude as the correspondent, actually measured oscillatory force coefficient on a circular cylinder. The Strouhal number based on the main theoretical frequency was found to be four times as high as the one calculated from the frequency of the sphere path. It could be, dependent on the sphere density, as high as twice the Strouhal number found for circular cylinders in the same Reynolds number range.

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