JEE Physics Notes: Mechanical Properties of Fluids

Introduction

Fluids are substances that can flow and conform to the shape of their containers. The study of the mechanical properties of fluids includes concepts such as pressure, viscosity, buoyancy, and surface tension. These properties are crucial for understanding fluid behavior in various physical and engineering applications.

1. Pressure in Fluids

• Definition: Pressure is the force exerted per unit area by a fluid.
• Formula: P = F/A, where F is force and A is area.
• SI Unit: Pascal (Pa).
• Hydrostatic Pressure: P = ρgh, where ρ is fluid density, g is acceleration due to gravity, and h is depth.

2. Pascal’s Law

• Statement: The pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid.
• Applications:
  • Hydraulic brakes and lifts.
  • Hydraulic presses.

3. Buoyancy and Archimedes’ Principle

• Definition: Buoyancy is the upward force exerted by a fluid on an object submerged in it.
• Archimedes’ Principle: A body immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced.
• Formula: Fb = ρfluid × g × Vdisplaced.
• Applications: Ship floating, hot air balloons, submarines.

4. Equation of Continuity

• Statement: The mass flow rate remains constant in a steady flow of an incompressible fluid.
• Formula: A₁v₁ = A₂v₂, where A is the cross-sectional area and v is the velocity.
• Applications: Water flowing through a pipe, blood flow in arteries.

5. Bernoulli’s Theorem

• Statement: The total mechanical energy of an incompressible, non-viscous fluid in a streamlined flow remains constant.
• Equation: P + (1/2)ρv² + ρgh = constant.
• Applications:
  • Flight of airplanes.
  • Venturi meter for fluid speed measurement.
  • Atomizers and sprayers.

6. Viscosity

• Definition: Viscosity is the internal friction within a fluid that resists its flow.
• Newton’s Law of Viscosity: F = ηA (dv/dx), where η is the coefficient of viscosity.
• Stokes’ Law: The force of viscosity on a small sphere moving in a fluid is given by F = 6πηrv.
• Applications: Lubrication, blood flow in veins.

7. Surface Tension

• Definition: Surface tension is the property of a liquid surface to contract and resist an external force.
• Formula: T = F/L, where F is force and L is length.
• Capillarity: The rise or fall of a liquid in a narrow tube due to surface tension.
• Applications: Capillary action in plants, detergents and soaps reducing surface tension.

Conclusion

The mechanical properties of fluids govern the behavior of liquids and gases in motion and at rest. Understanding these properties is essential for solving problems in fluid mechanics and engineering applications.