The Physics of Pipe Friction Loss
When fluid flows through a closed pipe, it experiences resistance due to shear stresses along the inner walls and internal viscosity. In hydraulics, this is represented as head loss or pressure drop.
This calculator estimates losses based on the fundamental **Darcy-Weisbach** equation:
ΔP = f × (L / D) × (ρ × v² / 2)
Where: ΔP = Pressure Drop (Pa) | f = Friction Factor | L = Pipe Length (m) | D = Inside Diameter (m) | v = Velocity (m/s)
The Flow Regimes & Friction Factor:
- Laminar Flow (Re < 2300): Fluid particles move in parallel straight sheets. Friction factor is purely a function of viscosity and is calculated as: \(f = 64 / Re\).
- Turbulent Flow (Re > 4000): Fluctuation and rapid mixing are present. Friction factor depends on both relative roughness (\(\epsilon/D\)) and Reynolds number. It is solved using the Haaland approximation: $$\frac{1}{\sqrt{f}} \approx -1.8 \log_{10} \left( \left(\frac{\epsilon/D}{3.7}\right)^{1.11} + \frac{6.9}{Re} \right)$$