Mechanical Properties of Fluids - Full Theory

Mechanical Properties of Fluids

1. Density (ρ)

Density is defined as the mass per unit volume of a fluid. It determines how heavy a fluid is for a given volume.

ρ = m / V

Units: kg/m³

Fluids with higher density exert more pressure at the same depth. For example, mercury is denser than water, which is why it is used in barometers.

Example: Water has a density of 1000 kg/m³, while oil has a lower density (~800 kg/m³). Hence, oil floats on water.

2. Pressure (P)

Pressure is the force applied perpendicular to the surface of an object per unit area. In fluids, pressure increases with depth.

P = F / A

Units: Pascal (Pa) = N/m²

Fluids exert pressure equally in all directions. This principle is fundamental in hydraulic systems and submarine design.

Example: At sea level, atmospheric pressure is approximately 101,325 Pa.

3. Pascal’s Law

Pascal's law states that any change in pressure applied to an enclosed fluid is transmitted equally throughout the fluid.

This principle is the basis for devices like hydraulic presses, brakes, and jacks.

Application: In a hydraulic lift, a small force applied at one piston results in a larger force at another piston.

4. Buoyancy & Archimedes’ Principle

Buoyancy is the upward force exerted by a fluid on an object immersed in it. Archimedes' principle states that this force equals the weight of the fluid displaced.

Fb = ρ × V × g

If the buoyant force is greater than the object's weight, it floats; otherwise, it sinks.

Example: Ships float because their overall density (including air space) is less than water.

5. Viscosity (η)

Viscosity is the internal friction between layers of fluid. High viscosity means a fluid flows slowly (e.g., honey), and low viscosity means it flows easily (e.g., water).

η = (F / A) × (dx / dv)

Newtonian fluids (like water) follow this law linearly, while non-Newtonian fluids (like ketchup) do not.

Example: Engine oils have specific viscosity ratings for efficient lubrication.

6. Streamline and Turbulent Flow

Streamline (or laminar) flow is smooth and orderly, with no mixing between layers. Turbulent flow is chaotic and involves eddies and swirls.

The nature of flow depends on the Reynolds number (Re). Low Re indicates laminar flow; high Re indicates turbulence.

Example: Blood flow in narrow arteries is mostly laminar, but can become turbulent in case of blockages.

7. Bernoulli’s Principle

Bernoulli's principle relates the pressure, velocity, and height in a moving fluid. For incompressible and non-viscous flow:

P + ½ ρv² + ρgh = constant

An increase in fluid speed results in a decrease in pressure. This principle is key in aircraft lift and pipe design.

Example: The wings of an airplane are designed to create pressure difference using Bernoulli's principle, resulting in lift.

8. Surface Tension

Surface tension is the property of the fluid surface that allows it to resist external force due to cohesive forces between liquid molecules.

It's responsible for phenomena like water droplets forming spheres and insects walking on water.

Example: Mercury forms spherical droplets due to high surface tension.

9. Capillarity

Capillary action is the ability of a fluid to flow in narrow spaces without the assistance of external forces. It occurs due to surface tension and adhesive forces.

Example: Water rises in a thin glass tube or in plant roots via capillary action.