Your vessel displaces 930 tons and measures 156'L by 38'B. What is the reduction in GM due to free surface if the fish hold (46'L by 28'B by 8'D) is filled with 1.5 feet of water? (Each foot of water weighs 36.8 tons)
• Free surface effect (FSE) and how it reduces GM (metacentric height) • Using the free surface moment (FSM) = area of the free surface × a water weight per foot to find virtual rise of G • Relationship: reduction in GM = Free surface moment ÷ Displacement
• How do you find the free surface area of the water in the fish hold when the depth of water is only 1.5 feet, but the tank is 8 feet deep? Does the depth change the free surface area? • What is the correct way to use the given "36.8 tons per foot" value? Is it per inch of draft over the whole vessel or per foot of depth in that compartment? How does that help convert area into a moment? • Once you compute the free surface moment for the fish hold, how do you convert that to a reduction in GM using the vessel’s displacement of 930 tons?
• Be sure you are using the plan area of the free surface (length × breadth) and not the volume of water to find free surface moment • Verify units when you calculate free surface moment: you should end up with ton-feet, not just tons or cubic feet • Before choosing an answer, confirm that your final GM reduction is a reasonable fraction of the vessel’s size and not unrealistically large or small
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