Hydrostatics: Buoyancy & Stability

Buoyancy

Archimedes' Principle: A body immersed in a fluid experiences a vertical upward buoyant force equal to the weight of the fluid it displaces.

$F_B = \gamma V_{displaced}$

• Floating Body: Weight of body = Buoyant Force ($W = F_B$)
• Submerged Body: Apparent Weight = True Weight - Buoyant Force

Stability

Stability refers to the ability of a body to return to its original position after a small disturbance (tilt).

Submerged Bodies

• Stable: Center of Gravity ($G$) is below Center of Buoyancy ($B$).
• Unstable: $G$ is above $B$.

Floating Bodies

Stability is determined by the Metacenter ($M$). The Metacenter is the intersection of the buoyant force vector before and after rotation.

Solved Problems