Pressure Drop in Pipes — Darcy-Weisbach Equation Explained

The Darcy-Weisbach Equation

Pressure drop in straight pipes is calculated using the Darcy-Weisbach formula:

$\Delta P = f \cdot \frac{L}{D} \cdot \frac{\rho v^2}{2}$

Where:

• $f$ = Darcy friction factor (dimensionless)
• $L$ = Pipe length (m)
• $D$ = Internal diameter (m)
• $\rho$ = Fluid density (kg/m³)
• $v$ = Mean flow velocity (m/s)

Reynolds Number & Flow Regimes

First, determine the flow regime using Reynolds Number:

$Re = \frac{\rho v D}{\mu}$

• $Re < 2300$: Laminar — $f = 64 / Re$
• $Re > 4000$: Turbulent — use Moody chart or Colebrook equation

Haaland Explicit Approximation

For turbulent flow, Haaland's equation provides an accurate explicit approximation:

$\frac{1}{\sqrt{f}} = -1.8 \log_{10} \left[ \left(\frac{\varepsilon/D}{3.7}\right)^{1.11} + \frac{6.9}{Re} \right]$

Minor Losses (Valves & Fittings)

Fittings and valves add pressure drop using K-factors:

$\Delta P_{minor} = \sum K \cdot \frac{\rho v^2}{2}$

Related Tools

• 🧮 Pipe Friction Loss & Pressure Drop Calculator