(455) Buoyancy and drag in fluids [IB Physics SL/HL]

Buoyancy and Drag in Fluids

Definition of Fluids

  • Fluids include both liquids and gases (e.g., water, air).

Introduction to Buoyancy

  • Buoyancy refers to the ability of an object to float in a fluid.

  • Common misconception: lighter objects float while heavier ones sink.

  • Archimedes' Principle explains buoyancy:

    • An object experiences an upward buoyant force equal to the weight of the fluid it displaces.

    • If the weight of the displaced fluid equals the object's weight, the object floats.

Archimedes' Principle Explained

  • Displacement is the volume of fluid moved aside by the submerged object.

  • The upward buoyant force is derived from pressure differences on the object.

  • Neutral buoyancy occurs when the object's density equals the fluid density.

  • Equation for buoyancy force (FB):

    • FB = ρ × V × g

      • Where:

        • ρ = density of the fluid (kg/m³)

        • V = volume of fluid displaced (m³)

        • g = acceleration due to gravity (9.81 m/s²)

Practical Demonstration

  • Putting a hand in water displaces water, illustrating the concept of buoyancy.

  • Objects with shapes that displace more fluid can still float even if made of heavy materials.

Stokes' Law and Drag Force

  • Stokes' Law describes the drag force experienced by an object moving through a fluid.

  • Drag force (FD) is opposite to the object's motion, such as a sphere falling through a fluid.

  • Equation for drag force:

    • FD = 6 × π × η × R × V

      • Where:

        • FD = drag force (N)

        • η = viscosity of the fluid (Pa·s)

        • R = radius of the sphere (m)

        • V = speed of the sphere (m/s)

Key Concepts about Viscosity

  • Viscosity measures a fluid's resistance to flow; higher viscosity means slower flow (e.g., maple syrup).

  • Some materials (e.g., glass) appear solid but behave as fluids over time.

Forces Acting on a Falling Object

  • When an object drops in a fluid, it experiences:

    • Downward gravitational force (FG = mg).

    • Upward buoyant force (FB = ρ × V × g).

    • Upward drag force (FD from Stokes' Law).

  • For constant speed, upward forces (FB + FD) equal downward force (FG).

Final Notes

  • Understanding buoyancy and drag is essential in fluid dynamics for both liquids and gases.