Lecture Notes: Fluid Pressure and Archimedes' Principle

Key Concepts

Pressure in Fluids

• Pressure Dependence on Depth:

  • Pressure at a point within a liquid depends on the depth.
  • Pressure acts in all directions.

• Static System Assumption:

  • Fluids are stationary.
  • Pressure is equal in all directions to ensure no acceleration.

Pressure on an Object in Fluid

• Consideration of a submerged object in fluid:
  • Example: A cube with dimensions d.
  • Pressure varies with depth along the cube.
  • Pressure at Different Points:
    • Pressure at the top (Pt)
    • Pressure at the bottom (Pb) is greater than Pt.

Net Force on a Submerged Object

• Calculation of Net Force (Fn):

  • Fn = Force due to pressure at the bottom - Force due to pressure at the top.
  • Surface area of the bottom = d^2.
  • Formula: Fn = (Pb - Pt) * d^2

• Substitution of Pressure Values:

  • Pt = density * h * gravity
  • Pb = density * (h + d) * gravity
  • Net force simplifies to: Fn = d^3 * density * gravity

Archimedes' Principle

• Volume Displacement:

  • d^3 represents the volume of the cube and the volume of water displaced.

• Buoyant Force:

  • Net force upwards due to pressure difference is called the buoyant force.
  • Weight of Displaced Water:
    • Buoyant force equals the weight of the displaced water.

• Mass and Gravity Relation:

  • Mass of displaced liquid: density * volume
  • Net force: mass of displaced liquid times gravity (i.e., weight of displaced liquid).

• Archimedes' Principle:

  • "The buoyant force on a submerged object is equal to the weight of the fluid that is displaced by the object."

Conclusion

• The buoyant force is what makes objects float.
• Archimedes' Principle is key in understanding buoyancy.

Upcoming Topics

• Application of Archimedes' Principle to solve problems in future sessions.