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describe the problem of free surface effect

Liquid that only partially fills a compartment is said to have a free surface that tends to remain horizontal (parallel to the waterline). When the ship is inclined, the liquid flows to the lower side (in the direction of inclination), increasing the inclining moment.
If the tank contains a solid weight, and the ship is inclined, the center of buoyancy shifts in the direction of the inclination and righting arms (GZ) are formed.
Replacing the solid with a liquid of the same weight, when the ship is inclined, the surface of the liquid remains horizontal. This results in a transfer of "a wedge of water," which is equivalent to a horizontal shift of weight, causing gravity to shift from G0 to G2.
The wedge of water transferred increases as the angle of inclination increases, therefore, the center of gravity shifts a different amount for each inclination.
Due to the horizontal shift of the center of gravity, the righting arm is now G2Z2. To determine the effect on stability, a vertical line is projected upward through G2 (see below). Where this line crosses the ship�s centerline is labeled G3. The righting arm G3Z3is the same length as the righting arm G2Z2. Therefore, moving the ship�s center of gravity to position G2 or G3 yields the same effect on stability. Movement from G0 to G3 is referred to as a Virtual Rise of the center gravity.

To calculate the virtual rise in the center of gravity due to the Free Surface Effect, use the following equation:

B = The breadth (width) of the compartment
L = The length of the compartment
WF = The ship�s final displacement (after flooding water added)

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