Sloshing Modes in a Cuboidal Tank

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This Demonstration shows the sloshing modes (, ) of a liquid in a partially filled rectangular tank with base .

Contributed by: Enrique Zeleny (February 2013)
Open content licensed under CC BY-NC-SA



Starting from Laplace's equation in Cartesian coordinates, assume that the boundary and free-surface conditions are all equal to zero and that the solution is separable. Let be the height of the liquid when it is still. The solution at time is:


where is the frequency and the gravitational acceleration.


[1] P. Hagedorn and A. DasGupta, Vibrations and Waves in Continuous Mechanical Systems, Chichester, UK: John Wiley & Sons, 2007.

[2] J. Kobine. Sloshing in a Square Tank [Video]. (Jan 31, 2013)

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