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Fluid inside a sphere

Hi all!

Imagine you have an ideal sphere (made of steel or plastics). Then fill it completely with some fluid, e.g. water. Then rotate it very fast. What happens to a fluid inside? I suppose that it will try to change its shape (from spherical to flat). But there is no space for any size changes (the sphere is completely filled). Thank you very much!

With kind regards,
Jan

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