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Experimental evaluation of the drag coefficient for smooth spheres by free fall experiments in old mines

J A Maroto1, J Dueñas-Molina2 and J de Dios1

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Mines of Linares, Jaén, Spain, have been exploited from the age of the Phoenicians, Carthaginians and Romans. These silver and lead mines reached their maximum splendour at the end of the 19th century and at the beginning of the 20th century. Nevertheless, all the mining works finished in the 1970s and the diverse machinery was sold. Only the shafts remain since then which has now permitted carrying out interesting free fall experiments using smooth spheres of both cork and cast iron. The experiments were facilitated by the fact that the tubular shape of the shafts provides excellent transmission of sound, which made feasible the recording of the impact sound of the spheres with water at the bottom of the shafts at distances of up to 200 m. By using these experimental data, we have carried out an evaluation of the drag coefficient for the movement of smooth spheres through the air in the laminar regime with Reynolds number in the interval 103 to 2 × 105. This evaluation was in excellent agreement with the literature data. From the theoretical point of view, the analysis of the free fall movement includes a variety of concepts such as Newton's second law, the drag force, Archimedes principle and the velocity of sound, which makes these experiments very attractive for both physics teachers and physics students at university level. Finally, an easy experiment is proposed in this paper which has permitted an approximate evaluation of the drag coefficient for smooth spheres to be carried out in a laboratory environment.


PACS

47.15.-x Laminar flows

01.50.Pa Laboratory experiments and apparatus

Subjects

Fluid dynamics

Education and communication

Dates

Issue 3 (May 2005)

Received 1 September 2004, in final form 4 January 2005

Published 7 March 2005



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