On a vessel of 12,500 tons displacement,...

Question 1 of 2707066636eec28f7522a1c51d098

On a vessel of 12,500 tons displacement, compute the reduction in metacentric height due to free surface in a hold having free water on the tank top. The hold is 35 feet long and 50 feet wide. What is the reduction in metacentric height?

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Question 1 of 27070

🔍 Key Concepts

• Free surface effect and how it reduces metacentric height (GM) • Formula for free surface moment of a rectangular tank: breadth and length relationship • How to convert free surface moment into a reduction of GM using vessel displacement

💭 Think About

• First, think about the geometric property you need for a free water surface in a rectangular hold. Which second-moment formula applies, and about which axis? • How does the free surface moment scale with the tank dimensions (width vs length)? Which dimension is more important in the formula? • Once you have the free surface moment in ft-tons or ft^4, how do you relate it to the vessel’s displacement (12,500 tons) to get a change in GM in feet?

✅ Before You Answer

• Make sure you are using the correct axis of rotation for the second moment (transverse stability: heel to port/starboard). • Check that your units are consistent: lengths in feet, displacement in tons, GM reduction in feet. • Before picking an answer, see if the magnitude of GM reduction is reasonable for a single large hold compared to the ship’s displacement.