What is the reduction in metacentric height...

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Question 1 of 2066636eec28f7522a1c51caf7

What is the reduction in metacentric height due to free surface when a tank 60 feet long and 30 feet wide is partially filled with salt water, and is fitted with a centerline bulkhead? (The vessel has a displacement of 10,000 tons.)

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🔍 Key Concepts

• Free surface effect (FSE) formula for reduction in metacentric height (GM) using the second moment of area (I) of the liquid surface • Effect of a centerline bulkhead on the effective free surface width of a tank • Relationship between displacement in tons and displacement volume in cubic feet for a salt water vessel

💭 Think About

• First, decide which dimension of the tank (length or width) should be raised to the third power when calculating the second moment of area for transverse stability. • Work out the second moment of area (I) for the full-width tank, then repeat it assuming a centerline bulkhead splits the width into two separate free surfaces and compare the results. • Convert the ship’s displacement in tons to a volume in cubic feet, then apply the standard free surface correction formula to see which answer choice is closest.

✅ Before You Answer

• Confirm you are using the correct formula for free surface correction: reduction in GM is proportional to I / displacement volume. • Make sure the width used in I = (L × B³) / 12 is the transverse width of each free surface, not the total width when a centerline bulkhead is fitted. • Verify that you converted 10,000 tons to cubic feet using the correct factor for salt water (about 35 ft³ per ton) before computing the correction.

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