On a vessel of 7000 tons displacement, a tank 35 ft. long, 30 ft. wide and 46 ft. deep is half filled with liquid cargo (S.G. 0.923) while the vessel is floating in saltwater (S.G. 1.026). What is the free surface constant for this tank?
• Free surface effect and how it reduces GM (metacentric height) • Second moment of area of a rectangular tank surface: I = (L × B^3) / 12 • Effect of different specific gravities (S.G.) of cargo and outside water on the free surface constant
• Identify which tank dimensions actually affect free surface (does depth matter, or only the dimensions of the liquid surface?) • Write the formula for the free surface constant used in many stability exam problems and plug in L, B, displacement, and the S.G. ratio step by step. • Consider why the ratio of cargo S.G. to seawater S.G. must be applied, and in which direction (multiply or divide?).
• Be sure you are using breadth (transverse width) as the dimension being cubed in the second moment of area, not the length or depth. • Confirm you have converted units and constants correctly (watch for factors like 12 or 420 that convert feet to inches and weight-volume relationships). • Check that you have applied the S.G. of the liquid and the S.G. of the outside water in the right places in the formula before comparing to the answer choices.
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