Physics

Introduction to Fluid Mechanics

Fluid mechanics is the study of fluids (liquids and gases) and the forces on them. It includes concepts like pressure, buoyancy, and flow behavior.

Key Concepts

Density (ρ)

Mass per unit volume.
ρ = m/V

Density

Pressure (P)

Force per unit area.
P = F/A

Pressure

Buoyant Force

Upward force by fluid.
F_b = ρVg

Buoyancy

Important Equations

Density

ρ = m / V

Pressure

P = hρg

Buoyancy

F_b = ρVg

Bernoulli's Equation

P + ½ρv² + ρgh = constant

Pascal's and Archimedes' Principles

Principles

Example Problems

1. What is the pressure at 10 m depth in water?

Solution: P = hρg = 10 × 1000 × 9.8 = 98000 Pa

2. Find buoyant force on 2 m³ object in water.

Solution: F_b = ρVg = 1000 × 2 × 9.8 = 19600 N

3. Calculate density if m = 500 kg, V = 0.5 m³

Solution: ρ = m/V = 500 / 0.5 = 1000 kg/m³

4. Use Bernoulli: If P₁ + ½ρv₁² = P₂ + ½ρv₂²

Application: Used in airplane wings, pipe flow, etc.