Buoyancy and Buoyant Force

Introduction to Buoyancy

Buoyancy is the upward force exerted by a fluid on an object immersed in it. This force is responsible for objects floating or sinking in fluids and is governed by Archimedes’ Principle.

• Buoyant Force (FB): The net upward force on an object in a fluid, equal to the weight of the fluid displaced.

• Archimedes’ Principle: An object immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces.

Key Equations:

• Pressure at depth :

• Buoyant force:

• Alternatively:

Example: A man with mass 80 kg and density 955 kg/m3:

• Volume:

• Buoyant force from air:

• Weight:

• Ratio:

Example: Bird bone with air pockets:

• Mass in air: 45.0 g; apparent mass in water: 36.0 g

• Mass of water displaced:

• Volume:

• Average density:

Fluid Flow

Streamline and Laminar Flow

Fluid flow can be classified as laminar (smooth, orderly) or turbulent (chaotic, mixing). Most introductory physics problems focus on laminar flow, where fluid particles follow smooth paths called streamlines.

• Streamline: Path followed by fluid particles in laminar flow.

• Turbulent Flow: Irregular, mixing flow (not covered in detail here).

Equation of Continuity

The equation of continuity expresses conservation of mass for fluids. For an incompressible fluid, the product of cross-sectional area and velocity is constant along a streamline.

• Equation:

• Volume rate of flow:

Bernoulli’s Theorem

Conservation of Energy in Fluid Flow

Bernoulli’s Theorem relates pressure, velocity, and height in a moving fluid, expressing conservation of energy per unit volume.

• Bernoulli’s Equation:

• Between two points:

• Applications: Explains lift in airplane wings, blood flow in arteries, and fluid speed in pipes.

• Torricelli’s Theorem: For fluid exiting a hole:

Example: Power Output of the Heart

The left ventricle pumps blood, increasing its pressure, speed, and height. The power output can be calculated using Bernoulli’s equation and the rate of energy transfer.

• Power:

• Example calculation yields

Summary Table: Key Fluid Equations

Additional info: These notes cover topics from Chapter 10 (Fluids) and Chapter 21 (Bernoulli’s Theorem) in a typical college physics curriculum. All equations are presented in SI units unless otherwise noted.