Your vessel displaces 740 tons and measures 141'L by 34'B. What is the reduction in GM due to free surface if the fish hold (41'L by 30'B by 9'D) is filled with 2.5 feet of water? (Each foot of water weighs 35.1 tons)
• Free surface effect and how it reduces GM (metacentric height) • How to compute moment of inertia of a rectangular tank about its centerline: I = (l × b³) / 12 • Relationship between free surface moment, displacement, and reduction in GM
• First find the volume and then the total weight of water in the fish hold using the given depth and tons-per-foot value. How does this help you compare to the ship’s displacement? • Think about whether the reduction in GM depends on the actual weight of water in the tank, or on the geometry (length and breadth) of the free surface. • After finding the free surface moment (FSM) from the tank dimensions, how do you convert that FSM into a reduction in GM using the ship’s displacement (in tons)?
• Be sure you are using breadth of the free surface in feet, not the ship’s breadth, when computing the moment of inertia of the water surface. • Confirm that displacement is in tons and distances are in feet, so your GM reduction ends up in feet. • Check that you apply the formula in the correct order: find I for the tank’s free surface, then FSM, then divide by dispacement to get ΔGM.
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