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On super free fall

Published online by Cambridge University Press:  16 April 2013

A. Torres ,
A. Medina ,
F. J. Higuera  and
P. D. Weidman
A. Torres
Affiliation:
ESIME UA, Instituto Politécnico Nacional, Avenida de las Granjas 180, C.P. 02250, México D.F., Mexico
A. Medina
Affiliation:
ESIME UA, Instituto Politécnico Nacional, Avenida de las Granjas 180, C.P. 02250, México D.F., Mexico
F. J. Higuera
Affiliation:
Escuela Técnica Superior de Ingenieros Aeronáuticos, Plaza del Cardenal Cisneros 3, 28040 Madrid, Spain
P. D. Weidman*
Affiliation:
Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309, USA
*
†Email address for correspondence: [email protected]
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Abstract

Villermaux & Pomeau (J. Fluid Mech., vol. 642, 2010, p. 147) analysed the motion of the interface of an inviscid liquid column released from rest in a vertical tube whose area expands gradually downwards, with application to an inverted conical container for which experimental measurements were carried out. An error in the analysis is found and corrected in the present investigation, which provides the new governing equation for the super-accelerated interface motion down gradually varying tubes in general, and integrated results for interface trajectories, velocities and accelerations down a conical tube in particular. Interestingly, the error does not affect any of the conclusions given in the 2010 paper. Further new results are reported here such as the equation governing the centre of mass and proof that the end point acceleration is exactly that of gravity.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
Papers
Information
Journal of Fluid Mechanics , Volume 723 , 25 May 2013 , pp. 653 - 664
Copyright
©2013 Cambridge University Press 

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References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Paterson, A. R. 1983 A First Course in Fluid Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Villermaux, E. & Pomeau, Y. 2010 Super free fall. J. Fluid Mech. 642, 147–157.Google Scholar