A ship of 5000 tonne displacement has two empty rectangular double bottom tanks with dimensions:
Tank A: length 12 m, width 16 m, and height 2 m
Tank B: length 16 m, width 12 m, and height 2 m
The length of each tank is oriented along the length of the ship. It is required to ballast the ship with 192 m\(^3\) of seawater of density 1025 kg/m\(^3\). Which one of the following scenarios will minimize the free surface effect?
Tank A: length 12 m, width 16 m, and height 2 m
Tank B: length 16 m, width 12 m, and height 2 m
The length of each tank is oriented along the length of the ship. It is required to ballast the ship with 192 m\(^3\) of seawater of density 1025 kg/m\(^3\). Which one of the following scenarios will minimize the free surface effect?
Show Hint
- 100% of the given ballast water is filled in Tank A.
- 100% of the given ballast water is filled in Tank B.
- 50% of the given ballast water is filled in Tank A and the remaining in Tank B.
- 40% of the given ballast water is filled in Tank A and the remaining in Tank B
The Correct Option is B
Solution and Explanation
Step 1: Understanding free surface effect.
The free surface effect depends on the second moment of area (moment of inertia) of the tank's free surface. \[ I = \frac{b^3 l}{12} \] where \( b \) is the breadth of the tank (transverse dimension), and \( l \) is the length.
Step 2: Compare Tank A and Tank B.
Tank A: \( b = 16 \, {m} \), \( l = 12 \, {m} \) \[ I_A = \frac{16^3 \cdot 12}{12} = 4096 \] Tank B: \( b = 12 \, {m} \), \( l = 16 \, {m} \) \[ I_B = \frac{12^3 \cdot 16}{12} = 2304 \] Step 3: Select the tank with smaller free surface moment.
Since \( I_B<I_A \), Tank B contributes less to the free surface effect. Hence, filling 100% of the ballast water in Tank B is the best option.
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