A block of wood (SG=0.6) floats in fluid X in Fig. P 2.126...

Key Concepts

Archimedes’ Principle

This principle states that a body immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. It is used to determine the fraction of an object’s volume that must be submerged so that its buoyant force exactly balances its weight. In problems involving flotation, setting the weight of the object equal to the buoyant force (which is the product of the fluid density, gravitational acceleration, and displaced volume) is the basic starting point for analysis.

Hydrostatic Pressure and Pressure Distribution

Fluid pressure increases with depth according to the hydrostatic relation, and surfaces immersed in a fluid experience pressures that vary with depth. In configurations where the object is only partially immersed, both the pressure on the submerged surfaces (which depends on the depth below the fluid’s free surface) and the pressure on the surfaces exposed to the surrounding gas come into play. Understanding how these pressures act on different parts of the body is essential for accurately performing a force?balance analysis.

Force Balance on Floating Bodies

For a floating object, the condition of equilibrium is obtained when the net upward forces (buoyant forces due to fluid pressure on the immersed portion and any forces acting due to the ambient gas pressure on surfaces originally exposed to the fluid) exactly balance the weight of the body. When the external gas pressure deviates from a standard value (for example, in a partial vacuum), the pressure on the exposed portion of the object changes, altering the net force balance and thereby changing the fraction of the volume that must be submerged for equilibrium.

Specific Gravity and Density Relationships

Specific gravity is the ratio of a material’s density to a reference density (usually that of water). In flotation problems, the specific gravity of the object compared to that of the fluid determines the submerged fraction under ordinary conditions. Any deviation from this expected submergence (such as an object submerging more than predicted) may indicate additional forces at work – for example, differences in the pressure acting on surfaces that are normally exposed to atmospheric pressure.

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