Fluid Mechanics
Comprehensive guide to fluid mechanics principles, equations, and applications in engineering.
Bernoulli's Equation
Bernoulli's equation describes the conservation of energy in a flowing fluid. For an ideal fluid with no viscosity, the equation states:
P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
Where:
- P = pressure (Pa)
- ρ = fluid density (kg/m³)
- v = fluid velocity (m/s)
- g = gravitational acceleration (9.81 m/s²)
- h = height (m)
Reynolds Number
The Reynolds number is a dimensionless quantity that helps predict flow patterns in fluid flow situations:
Re = (ρvD)/μ
Where:
- Re = Reynolds number (dimensionless)
- ρ = fluid density (kg/m³)
- v = fluid velocity (m/s)
- D = characteristic length (m)
- μ = dynamic viscosity (Pa·s)
Flow regimes based on Reynolds number:
- Re < 2300: Laminar flow
- 2300 ≤ Re < 4000: Transitional flow
- Re ≥ 4000: Turbulent flow
Darcy-Weisbach Equation
The Darcy-Weisbach equation is used to calculate the pressure drop in a pipe due to friction:
ΔP = f × (L/D) × (ρv²/2)
Where:
- ΔP = pressure drop (Pa)
- f = Darcy friction factor (dimensionless)
- L = pipe length (m)
- D = pipe diameter (m)
- ρ = fluid density (kg/m³)
- v = fluid velocity (m/s)