Your vessel displaces 645 tons and measures 132'L by 34'B. What is the reduction in GM due to free surface if the fish hold (30'L by 26'B by 8'D) is filled with 3.0 feet of water? (Each foot of water weighs 22.3 tons)
• Free surface effect and how it reduces GM (metacentric height) • How to compute the moment of inertia of the free surface: ( I = \frac{L \times B^3}{12} ) for a rectangular tank with water depth not affecting I • Relationship between free-surface moment and reduction in GM: ( \Delta GM = \frac{\text{Free surface moment}}{\Delta} ) where ( \Delta ) is vessel displacement
• How does the breadth of the free surface affect the free surface moment compared to its length? Which dimension is more important in the formula? • You are given "each foot of water weighs 22.3 tons". How could that help you find the total weight of water in the tank, and then the vertical center of this water? • After finding the free surface moment (or its equivalent), how do you relate it to the ship's total displacement (645 tons) to find the reduction in GM?
• Make sure you use the correct breadth (B) in the free surface formula; remember it is usually breadth cubed. • Confirm that you are using the vessel's displacement (645 tons), not the water weight, in the denominator when finding ( \Delta GM ). • Check that all your units are consistent: tons·feet for moments, feet for distances, tons for displacement.
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