Consider a cylindrical vessel, open from the top and floating in fresh water (specific gravity SG_w= 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 SG_v= 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 L_min 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.