Darcy-Weisbach Friction Loss Calculator
Calculate pipe friction head loss using the Darcy-Weisbach equation.
Includes Reynolds number, Darcy friction factor, and pressure drop in Pa and kPa.
Darcy-Weisbach Equation
The Darcy-Weisbach equation calculates the frictional head loss (or pressure drop) in a pipe due to fluid viscosity and pipe roughness. It is the most accurate and widely used pipe flow equation.
Head loss formula:
h_f = f * (L/D) * v^2 / (2g)
Pressure drop formula:
dP = f * (L/D) * (rho * v^2 / 2) [in Pascals]
Variables:
| Symbol | Meaning | Typical Units |
|---|---|---|
| h_f | Head loss | m |
| dP | Pressure drop | Pa |
| f | Darcy friction factor | dimensionless |
| L | Pipe length | m |
| D | Pipe inner diameter | m |
| v | Mean flow velocity | m/s |
| g | Gravitational acceleration (9.81) | m/s^2 |
| rho | Fluid density | kg/m^3 |
Reynolds number:
Re = v * D / nu
where nu = kinematic viscosity (m^2/s)
Friction factor f:
- Laminar (Re < 2300): f = 64/Re
- Transitional (2300-4000): flow is unstable — use caution
- Turbulent (Re > 4000): Swamee-Jain approximation: f = 0.25 / [log10(eps/(3.7D) + 5.74/Re^0.9)]^2
Where eps = pipe absolute roughness (m).
Common pipe roughness values:
- Smooth (PVC, glass): eps ≈ 0.0015 mm
- Commercial steel: eps ≈ 0.046 mm
- Cast iron: eps ≈ 0.26 mm
- Concrete: eps ≈ 1.0 mm
Key insight: Head loss scales with v^2, so doubling the flow velocity quadruples the friction loss. This makes reducing pipe velocity one of the most effective ways to cut pumping energy.