On a vessel of 7000 tons displacement, a...

Question 1 of 2707066636eec28f7522a1c51d0a2

On a vessel of 7000 tons displacement, a tank 35 ft. long, 30 ft. wide and 4 ft. deep is half filled with fuel oil (S.G. 0.962) while the vessel is floating in saltwater (S.G. 1.026). What is the free surface constant for this tank?

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Question 1 of 27070

🔍 Key Concepts

• Free surface effect and how it is represented as a constant for a given tank • Relationship between moment of inertia (I) of the liquid surface and the displacement of the vessel • Effect (or non‑effect) of specific gravity of the liquid and surrounding water on the free surface constant

💭 Think About

• How do you compute the second moment of area (moment of inertia) of a rectangular free surface about the ship’s centerline? Which tank dimension(s) are used? • Does the depth of liquid in the tank change the free surface moment when the surface is completely unbroken and extends across the tank? • Once you have the moment of inertia of the free surface, what do you do with the ship’s displacement (in tons) to get a free surface constant with units that match the answer choices?

✅ Before You Answer

• Be clear whether you should use length × breadth³ / 12 or breadth × length³ / 12 for the tank’s free surface moment of inertia about the centerline. • Confirm if the specific gravity of the fuel or seawater actually enters the free surface constant formula, or if it only matters when converting between weight and volume. • Verify that you convert all dimensions to a consistent set of units (feet, long tons, etc.) before comparing with the numerical answer choices.