A shaft alley divides a vessel's cargo hold into two tanks, each 20 ft. wide by 60 ft. long. Each tank is filled with saltwater below the level of the shaft alley. The vessel's displacement is 7,000 tons. What is the reduction in GM due to free surface effect?
• Free surface effect (FSE) and how it reduces GM (metacentric height) • Formula for free surface moment of inertia: I = (breadth³ × length) / 12 for a rectangular tank • How to convert moment of inertia of the free surface into a GM correction using ship displacement
• Start by finding the free surface moment of inertia for ONE tank, then consider whether you need to account for both tanks created by the shaft alley. • Think about whether the shaft alley actually stops the liquid from flowing side-to-side, or just divides the tank into separate free surfaces. • After you find the combined free surface moment(s), recall how to turn that into a loss of GM using the vessel's displacement (in long tons).
• Be sure to use feet consistently for all dimensions and convert displacement from tons to long tons only if needed by your formula convention. • Verify whether the fluid is saltwater and if that affects density assumptions in your GM reduction formula. • Double-check that you are using breadth of each free surface (not total ship beam) and that you are correctly handling having two separate tanks.
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