On a vessel of 6,000 tons displacement there are two slack tanks of carbon tetrachloride (SG 1.6). Each tank is 40 feet long and 25 feet wide. What is the reduction in metacentric height due to free surface with the vessel in sea water (SG 1.025)?
• Free surface effect and metacentric height (GM) correction on a vessel • How to compute the second moment of area (I) for a rectangular tank: I = (b^3 × l) / 12 • Effect of liquid density (specific gravity) ratio between tank liquid and outside seawater on free surface correction
• Which tank dimension should be used as the breadth (b) for free surface (athwartships) and which as the length (l)? • How do you adjust the free surface moment to account for the liquid’s specific gravity being 1.6 while the surrounding seawater is 1.025? • After finding the free surface moment for one tank, how do you combine the effect of two identical tanks and relate that to the ship’s displacement to find the GM reduction?
• Be sure you are using the athwartships dimension (breadth) of the tank raised to the 3rd power in the I = (b^3 × l) / 12 formula, not the length • Confirm that you apply the specific gravity ratio (1.6 / 1.025) correctly when computing the free surface moment • Verify that you have included both tanks and then divided the total free surface moment by the vessel’s displacement (6,000 tons) to get the GM reduction in feet
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