Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-13T01:34:40.906Z Has data issue: false hasContentIssue false
  • English
  • Français

Sloshing frequencies for cylindrical and spherical containers filled to an arbitrary depth

Published online by Cambridge University Press:  26 April 2006

P. Mciver
P. Mciver
Affiliation:
Department of Mathematics and Statistics, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

The two-dimensional sloshing of a fluid in a horizontal circular cylindrical container and the three-dimensional sloshing of a fluid in a spherical container are considered. The linearized theory of water waves is used to determine the frequencies of free oscillations under gravity of an arbitrary amount of fluid in such tanks. Special coordinate systems are used and the problems are formulated in terms of integral equations which are solved numerically for the eigenvalues. Detailed tables of the sloshing frequencies are presented for a range of fill-depths of the containers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 201 , April 1989 , pp. 243 - 257
Copyright
© 1989 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.
Budiansky, B. 1960 Sloshing of liquids in circular canals and spherical tanks. J. Aero. Sci. 27, 161–173.Google Scholar
Chu, W.-H. 1964 Fuel sloshing in a spherical tank filled to an arbitrary depth. AIAA J. 2, 1972–1979.Google Scholar
Fox, D. W. & Kuttler, J. R. 1983 Sloshing frequencies. Z. angew Math. Phys. 34, 668–696.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 1980 Table of Integrals, Series and Products. Academic.
Henrici, P., Troesch, B. A. & Wuytack, L. 1970 Sloshing frequencies for a half-space with circular or strip-like aperture. Z. angew Math. Phys. 21, 285–317.Google Scholar
Kuttler, J. R. & Sigillito, V. G. 1984 Sloshing of liquids in cylindrical tanks. AIAA J 22, 309–311.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Lebedev, N. N., Skalaskaya, I. P. & Uflyand, Y. S. 1965 Worked Problems in Applied Mathematics. Dover.
Linton, C. M. 1988 Wave reflection by submerged bodies in water of finite depth. Ph.D. thesis, University of Bristol.
Luke, Y. L. 1977 Algorithms for the Computation of Mathematical Functions. Academic.
Mciver, P. & Smith, S. R. 1987 Free-surface oscillations of fluid in closed basins. J. Engng Maths 21, 139–148.Google Scholar
Marichev, O. I. 1983 Handbook of Integral Transforms of Higher Transcendental Functions. Ellis Horwood.
Mei, C. C. 1983 The Applied Dynamics of Ocean Surface Waves. Wiley-Interscience.
Miles, J. W. 1972 On the eigenvalue problem for fluid sloshing in a half-space. Z. angew Math. Phys. 23, 861–869.Google Scholar
Moiseev, N. N. & Petrov, A. A. 1965 The calculation of free oscillations of a liquid in a motionless container. Adv. Appl. Mech. 9, 91–154.Google Scholar
Sneddon, I. H. 1972 The Use of Integral Transforms. McGraw-Hill.