15.8 : Design Example: Application of Archimedes' Principle

Archimedes' principle is fundamental in analyzing the buoyant force and stability of floating bodies. In this example, a wooden block with a rectangular section floats in seawater. Based on the block's dimensions, its specific gravity and the specific weight of seawater are used to find the volume of water displaced and the center of buoyancy.

The volume of seawater displaced by the block is determined by first calculating the block's weight. This is done by multiplying the block's volume by its specific gravity. According to Archimedes' principle, the weight of displaced water is equal to the weight of the block. The volume of displaced water is then found by dividing the block's weight by the unit weight of seawater.

The center of buoyancy, which is the centroid of the displaced water volume, indicates where the buoyant force acts. To locate this point, the immersed depth is calculated by equating the submerged portion's volume to the volume of displaced water. The center of buoyancy is positioned at half the immersed depth from the bottom of the block, representing the equilibrium point where the buoyant force balances the weight of the block.