Fluid Mechanics Guide

The Darcy-Weisbach Equation for Pipe Friction Loss & Head Drop

Reviewed by PipeSizingCalculator Engineering Team Updated October 31, 2026 Reading Time: 7 min

1. Physical Formulation of Pipe Friction Loss

The Darcy-Weisbach equation is the fundamental theoretical relationship governing head loss due to friction in pipe flow:

$h_f = f \cdot \frac{L}{D} \cdot \frac{v^2}{2g} \quad \text{or} \quad \Delta P = f \cdot \frac{L}{D} \cdot \frac{\rho v^2}{2}$

Where:
• $h_f$: Head loss in meters of fluid column (m)
• $f$: Dimensionless Darcy friction factor
• $L$: Pipe length (m)
• $D$: Internal pipe diameter (m)
• $v$: Mean flow velocity (m/s)
• $\rho$: Fluid density (kg/m³)
• $g$: Acceleration due to gravity ($9.80665 \text{ m/s}^2$)

2. Darcy-Weisbach vs Hazen-Williams

While Hazen-Williams is widely cited in civil water mains, it is an empirical approximation calibrated strictly for cold water at ~15°C. For HVAC heating (60°C–80°C) or chilled water (4°C–6°C), viscosity shifts cause Hazen-Williams errors exceeding 20%. The Darcy-Weisbach equation is universally valid across all fluid temperatures and viscosity regimes.

3. Explicit Swamee-Jain Friction Factor

In turbulent flow ($Re \ge 4000$), the implicit Colebrook-White equation is solved accurately without iterations via the Swamee-Jain formula:

$f = \frac{0.25}{\left[ \log_{10}\left( \frac{\varepsilon}{3.7D} + \frac{5.74}{Re^{0.9}} \right) \right]^2}$

1. Physical Formulation of Pipe Friction Loss

2. Darcy-Weisbach vs Hazen-Williams

3. Explicit Swamee-Jain Friction Factor

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