On a vessel of 6500 tons displacement, a...

Question 1 of 2707066636eec28f7522a1c51d0a1

On a vessel of 6500 tons displacement, a tank 35 ft. long, 25 ft. wide, and 8 ft. deep is half filled with liquid cargo (S.G. 1.053) 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 impacts a vessel’s stability • Relationship between moment of inertia of the liquid surface and free surface constant • Effect of displacement of the vessel and specific gravity (S.G.) of liquids involved

💭 Think About

• How do you calculate the second moment of area (moment of inertia) of a rectangular free surface, and which tank dimension(s) are used? • Once you have the moment of inertia of the free surface, how is it related to free surface constant and the vessel’s displacement? • Does the S.G. of the liquid in the tank or the surrounding seawater change the free surface constant itself, or does it mainly affect displacement and density relationships?

✅ Before You Answer

• Be sure you are using the correct tank dimensions for the moment of inertia formula for a rectangle about its centerline. • Confirm you are using the vessel’s displacement in consistent units with your moment of inertia (e.g., long tons vs cubic feet of seawater). • Double-check whether specific gravities are actually needed in the final free surface constant calculation, or whether they cancel out in this type of question.