A cargo vessel of 9,000 tons displacement is carrying a slack deep tank of molasses (SG 1.4). The tank measures 20 feet long and 30 feet wide. What will be the reduction in metacentric height due to free surface, with the vessel floating in sea water (SG 1.026)?
• Free surface effect (FSE) and how it reduces metacentric height (GM) • Moment of inertia of a rectangular free surface: I = (L × B³) / 12 or I = (B × L³) / 12 (be careful which side is breadth) • Relationship between reduction in GM, moment of inertia of free surface, and displacement volume (Δ) in the correct units
• What is the correct formula that links free surface moment of inertia to the reduction in GM, and in what units must displacement be expressed? • For a tank 20 ft by 30 ft, which dimension is the ship’s transverse breadth and which formula for I should you use to get the correct axis? • How does the specific gravity of molasses and sea water affect the effective free surface moment (do you need a correction factor or an equivalent hull form displacement in cubic feet)?
• Be sure to convert displacement in tons to displacement volume in cubic feet before using it in the GM reduction formula. • Confirm you are using the transverse second moment of area about the ship’s centerline (breadth cubed), not the longitudinal one. • Check if you need to adjust the free surface moment for the difference between liquid SG and sea water SG before dividing by displacement volume.
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