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A theory of water-bells

Published online by Cambridge University Press:  28 March 2006

Jean-Yves Parlange
Jean-Yves Parlange
Affiliation:
Department of Engineering and Applied Science, Yale University, New Haven, Connecticut
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Abstract

A theory is developed to determine the shape of water-bells. The motion of the gas induced by the moving walls is taken into account in this analysis. A rapidly converging iterative procedure leads to a theoretical shape which agrees well with the experimental shape of the water-bell.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 29 , Issue 2 , 11 August 1967 , pp. 361 - 372
Copyright
© 1967 Cambridge University Press

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References

Batchelor, G. K. 1956 On steady laminar flow with closed streamline at large Reynolds number J. Fluid Mech. 1, 177.Google Scholar
Boussinesq, J. 1913 Sur la théorie des nappes liquides rétractiles de Savart Comptes Rendus 157, 89.Google Scholar
Burggraf, O. R. 1966 Analytical and numerical studies of the structure of steady separated flows J. Fluid Mech. 24, 113.Google Scholar
Courant, R. & Hilbert, D. 1962 Methods of Math. Physics, Vol. II, 320. New York: John Wiley and Sons.
Gouml;ring, W. 1959 Zur Abhängigkeit der Oberflächenspannung von der Bildungs–-und Alterungsgeschwindigkeit der Oberfläche Z. Elektrochem., Ber. Bunsenges. physik. Chem. 63, 1069.Google Scholar
Jahnke, E. & Emde, F. 1945 Tables of Functions. New York: Dover.
O'Brien, V. 1961 Steady spheroidal vortices–-more exact solutions of the Navier-Stokes equation Quart. Appl. Math. 19, no. 2, 163.Google Scholar
Taylor, Sir Geoffrey. 1959 The dynamics of thin sheets of fluid. I. Water bells. Proc. Roy. Soc. A 253, 289.Google Scholar
Wegener, P. P. & Parlange, J.-Y. 1964 Surface tension of liquids from water-bell experiments Z. für Physikalische Chemie (Neue folge) 43, 245.Google Scholar
Wood, W. W. 1957 Boundary layers whose streamlines are closed J. Fluid Mech. 2, 77.Google Scholar