What is the most important figure in calculating the free surface constant of a tank carrying liquids?

In calculating the free surface constant of a tank carrying liquids, the breadth is the most significant factor. The free surface effect becomes important when liquids are carried in tanks, affecting the vessel's stability. This effect arises due to the movement of liquid within the tank, which can change the center of gravity and, consequently, the metacentric height of the vessel.

The breadth of the tank directly influences the area of the free surface available for liquid to move. A greater breadth means a larger surface area for the liquid, which can lead to more significant movement and a more pronounced free surface effect. This movement as the vessel tilts reduces stability because the center of gravity shifts, making it crucial to consider the breadth when calculating the free surface constant.

While length, depth, and volume are also important in tank design and liquid dynamics, they do not have the same direct impact on the free surface area as breadth does. Therefore, the breadth is critical in determining how the free surface constant affects a vessel's stability.