Chapter 17: Hydrostatics

Buoyant Force

The upward force exerted by a fluid on a submerged or partially submerged object.

Archimedes’ Principle

A fluid exerts an upward buoyant force on an object equal to the weight of the displaced fluid.

Buoyant Force Formula

Formula

$F_{\text{buoyant}}={\rho }_{\text{fluid}}g{V}_{\text{displaced}}$

Variables

• F_buoyant: Buoyant force (N).
• ρ_fluid: Density of the fluid (kg/m³).
• V_displaced: Volume of the displaced fluid (m³).
• g: Acceleration due to gravity (m/s²).

Applications of Buoyancy

• Ships and Submarines: Design based on the principle of buoyancy to float or dive.
• Hot Air Balloons: Use the difference in air density to lift off the ground.
• Hydrometers: Measure the specific gravity of liquids by floating at a level proportional to the fluid’s density.

Example 17-1: Calculating Buoyant Force

A 0.05 m³ block is fully submerged in water (ρ = 1000 kg/m³). What is the buoyant force acting on the block?

• Given: V_displaced = 0.05 m³, ρ_fluid = 1000 kg/m³, g = 9.8 m/s².
• F_buoyant = ρ_fluid × g × V_displaced.
• F_buoyant = 1000 × 9.8 × 0.05 = 490 N.
• Answer: 490 N

Questions for Students

1. Define buoyant force and state Archimedes’ principle.
2. Explain how a ship’s design utilizes buoyancy to float.
3. Calculate the buoyant force on a 0.1 m³ object submerged in a liquid with a density of 800 kg/m³.
4. Describe the role of buoyancy in the operation of a hot air balloon.
5. How does a hydrometer measure the specific gravity of a liquid?