Your vessel displaces 750 tons and measures 151'L by 35'B. What is the reduction in GM due to free surface if the fish hold (60'L by 31'B by 10'D) is filled with 3.5 feet of water? (Each foot of water weighs 53.1 tons)
• Free surface effect and how it reduces GM (metacentric height) • Formula for free surface moment: area of surface × density factor, then divided by displacement to find reduction in GM • How to convert the water depth and tank dimensions into volume, weight, and free surface area
• First, focus on the surface area of the water in the fish hold, not the total volume. Which dimensions of the tank define the free surface? • Think about how to use the given: displacement (750 tons), tank dimensions, and weight per foot of water (53.1 tons). Which of these helps you find the free surface moment, and which is used to find the reduction in GM? • Ask yourself: Do you need the entire 10 ft depth of the hold for this calculation, or just the 3.5 ft of water? How does that affect the numbers you use?
• Be sure you are using the correct free surface formula: reduction in GM = free surface moment ÷ ship’s displacement • Double‑check which tank dimension is length and which is breadth, and square the correct one in your calculation • Verify that your final GM reduction is in feet, and that the magnitude is reasonable for a 750‑ton vessel with a large slack tank
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