If a cargo tank is slack and gasoline is pumped out while sea water is pumped in, what happens to the free surface effect?

When gasoline is pumped out of a slack cargo tank and sea water is pumped in, the free surface effect increases due to several interrelated factors.

Initially, the cargo tank is considered slack, meaning it is partially filled with gasoline, and thus there is a significant free surface area. As gasoline, which has a lower density, is removed, it is replaced with sea water, which has a higher density. This change not only affects the weight distribution but also the volume of liquid in the tank, which creates a larger effective free surface area, leading to increased stability concerns.

The presence of two different liquids with distinct densities adds complexity to the stability calculation, primarily because the movement of the heavier sea water could cause greater shifting and increase the immobility of the center of gravity. Additionally, as the liquid sloshes in the tank, the forces acting on the vessel from the changing liquid distribution create a larger righting arm due to the presence of a greater free surface area, further exacerbating the free surface effect.

In conclusion, the process of replacing the lighter gasoline with heavier sea water increases the free surface effect, thus increasing the potential for instability in the vessel. This understanding is crucial for maintaining proper vessel stability and preventing capsizing.