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#### Floating vessel

Consider a cylindrical vessel, open from the top and floating in fresh water (specific gravity SGw= 1), as shown in the figure. The inner diameter of the vessel is D = 1 m, its height is H = 1 m, its wall thickness is δ = 0.10 m and the specific gravity of its material is SGv= 0.9. The vessel contains a liquid with specific gravity SG2= 1.2, up to a depth L.
a) If L = 0.5 m, determine the depth h of the vessel bottom below the free surface of the water.
b) Determine the minimum depth Lmin of the inner liquid above which the vessel would sink.
c) Now assume that, instead of the above, you use some other inner liquid with a specific gravity SG3. Is it possible for the vessel not to sink, even if it is completely full? If so, determine the corresponding maximum value of SG3.

Contributed by Stavros Tavoularis, Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada.

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