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Mathematical Problems in Engineering
Volume 2017, Article ID 9795286, 8 pages
https://doi.org/10.1155/2017/9795286
Research Article

Initial Velocity Effect on Acceleration Fall of a Spherical Particle through Still Fluid

Engineering College, Ocean University of China, Qingdao, China

Correspondence should be addressed to Bingchen Liang; nc.ude.cuo@nehcgnib

Received 10 October 2016; Accepted 4 January 2017; Published 6 February 2017

Academic Editor: Sébastien Poncet

Copyright © 2017 Zegao Yin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A spherical particle’s acceleration fall through still fluid was investigated analytically and experimentally using the Basset-Boussinesq-Oseen equation. The relationship between drag coefficient and Reynolds number was studied, and various parameters in the drag coefficient equation were obtained with respect to the small, medium, and large Reynolds number zones. Next, some equations were used to derive the finite fall time and distance equations in terms of certain assumptions. A simple experiment was conducted to measure the fall time and distance for a spherical particle falling through still water. Sets of experimental data were used to validate the relationship between fall velocity, time, and distance. Finally, the initial velocity effect on the total fall time and distance was discussed with different terminal Reynolds numbers, and it was determined that the initial velocity plays a more important role in the falling motion for small terminal Reynolds numbers than for large terminal Reynolds number scenarios.