The liquid mud tanks on your vessel measure...

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Question 1 of 2066636eec28f7522a1c51c659

The liquid mud tanks on your vessel measure 24'L by 16'B by 8'D. The vessel's displacement in salt water (specific gravity 1.025) is 864 T and the specific gravity of the mud is 1.47. What is the reduction in GM due to a pair of these tanks (p/s) being slack?

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Question 1 of 20

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🔍 Key Concepts

• Free surface effect and how it reduces GM (metacentric height) when tanks are slack • Using the second moment of area of the liquid surface: I = L × B³ / 12 for each rectangular tank (about the ship’s centerline) • How specific gravity (SG) of the liquid in the tank versus seawater changes the magnitude of the correction

💭 Think About

• First, find the free surface moment for ONE tank using its plan dimensions. Which dimension creates heeling moment: length or breadth? • Then account for the fact that there are two tanks, port and starboard. How does that affect the total free surface moment? • Finally, relate the total free surface moment to the vessel’s displacement to find the reduction in GM. How does the mud’s SG compared to seawater enter that relationship?

✅ Before You Answer

• Be sure you are using the breadth (16 ft) as the dimension that is cubed when you compute the second moment of area, not the depth or length • Apply a factor to account for the heavier mud (SG 1.47) compared with seawater (SG 1.025); don’t treat it as if it were fresh water or seawater • After you compute the GM reduction, check that the value is reasonable: it should be less than a few feet and in the same order of magnitude as the answer choices

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