Design Example: Application of Archimedes' Principle

The volume of water displaced equals the block's weight divided by the unit weight of water. First, calculate the block's weight by multiplying its total volume by its specific gravity. According to Archimedes' principle, the weight of displaced water equals the block's weight. Dividing this weight by seawater's unit weight (1025 kg(f)/m³) gives the displaced volume.

Archimedes' principle states that the weight of liquid displaced by a floating block equals the block's weight. This equilibrium condition ensures the block floats stably. For a wooden block with specific gravity 0.64 floating in seawater, the buoyant force balances the block's weight, determining how deeply it submerges and establishing buoyancy and stability for submerged and floating bodies.

The center of buoyancy is located at the centroid of the submerged portion of the block. It is positioned at half the immersed depth from the bottom of the block. This point represents where the buoyant force acts and indicates the equilibrium location where the upward buoyant force balances the downward weight of the block.

The immersed depth is found by equating the volume of the submerged portion to the volume of water displaced. Once you know the displaced volume from dividing the block's weight by water's unit weight, divide this by the block's cross-sectional area. For a 1.25 m wide by 2 m deep block, this calculation yields the depth to which the block sinks into the water.

Specific gravity determines how much of a block's volume must be submerged to achieve equilibrium. A wooden block with specific gravity 0.64 displaces a volume of water equal to 64% of its total volume. This ratio directly controls the immersed depth and the position of the center of buoyancy, making it essential for predicting floating body behavior.

The unit weight of seawater (1025 kg(f)/m³) is the denominator used to convert the block's weight into the volume of water displaced. A higher unit weight means less volume is needed to displace the same weight, causing the block to float higher. This parameter is critical for determining both the displaced volume and the immersed depth in floating body analysis.

Block dimensions determine its total volume and cross-sectional area, which are used to calculate weight and immersed depth. A 1.25 m × 2 m × 4 m block's volume multiplied by its specific gravity yields its weight. The cross-sectional area (1.25 m × 2 m) then divides the displaced volume to find immersed depth, showing how geometry directly influences buoyant force distribution.