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If two liquid tanks of the same cross-section but different heights have the same liquid up to the same depth, will sloshing be the same or different in both tanks?

I would assume they would be the same because they have the same slosh natural frequency. But if one tank is fully filled for the given liquid height, the damping of the top wall would cause the slosh to be suppressed.

Is this a justifiable observation?

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    $\begingroup$ A full tank doesn't slosh. Is that what you were asking? $\endgroup$ Oct 12, 2022 at 12:20
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    $\begingroup$ I think you've answered your own question up to the level of detail you have given. i.e. there would exist some pair of tank dimensions where the nearly full tank has lower amplitude movements than the tank with more headroom. If you want something more precise it may help to provide the dimensions/viscousity you are interested in, on the off-chance that someone here has over-lapping experience (though that could be quite a long shot). $\endgroup$
    – Puffin
    Oct 12, 2022 at 13:33
  • $\begingroup$ Yes. A full tank doesn't slosh. So just wanted to know if it is due to the "damping" provided by the top wall. I was looking for a source to back my understanding and couldn't find one, so the question here. $\endgroup$
    – Reader
    Oct 15, 2022 at 9:49

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Slosh strongly depends on the shape of the tank, and if baffles are used (or not).

For an unbaffled spherical tank, the slosh frequency varies with the fill level. Changes in the fill level will result in different frequencies. For an unbaffled cylindrical tank, the slosh frequency can vary with fill level as well. When a slosh wave interacts with the top of a cylindrical tank or can "feel" the bottom of the tank results in a significantly different frequency responses than slosh in a somewhat full cylindrical tank. The frequency doesn't change much in a cylindrical tank until the tank gets sufficiently drained such that the principal slosh wave can start to be affected by the bottom of the tank.

The above assumes slosh is small. Highly nonlinear effects come into play when slosh is large. Almost all bets are off when slosh is large. The only bet that is on in the case of significant slosh is that the spacecraft mostly likely is in deep trouble.

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