Darcy-Weisbach Head Loss Calculator
Friction loss is the backbone of every pipe sizing and pump head calculation. Enter flow, pipe size, length, and roughness to get Darcy-Weisbach head loss with the friction factor solved for you.
Friction Head Loss
| Item | Value |
|---|
How the calculation works
Darcy-Weisbach equation
hf = f · (L / D) · (V² / 2g)
V = Q / A, A = πD² / 4, g = 32.2 ft/s²
Reynolds number Re = V · D / ν
Haaland approximation (turbulent flow, explicit form of Colebrook-White):
1/√f = −1.8 · log10[ (ε/D / 3.7)1.11 + 6.9/Re ]
Laminar flow (Re < 2,300): f = 64 / Re
Dynamic viscosity from the Vogel-type water correlation μ = 2.414×10−5 · 10247.8/(TK−140) Pa·s; ν = μ/ρ
psi = ft of head × 0.4333
hf = f · (L / D) · (V² / 2g)
V = Q / A, A = πD² / 4, g = 32.2 ft/s²
Reynolds number Re = V · D / ν
Haaland approximation (turbulent flow, explicit form of Colebrook-White):
1/√f = −1.8 · log10[ (ε/D / 3.7)1.11 + 6.9/Re ]
Laminar flow (Re < 2,300): f = 64 / Re
Dynamic viscosity from the Vogel-type water correlation μ = 2.414×10−5 · 10247.8/(TK−140) Pa·s; ν = μ/ρ
psi = ft of head × 0.4333
| Pipe material | Typical roughness ε (mm) |
|---|---|
| PVC / HDPE | 0.0015 |
| Commercial steel | 0.045 |
| Cement-lined ductile iron | 0.10–0.15 |
| Cast iron, unlined | 0.26 |
| Concrete | 0.3–3.0 |
Notes & limitations
The Darcy-Weisbach equation with the Colebrook-White friction factor (via the Haaland explicit approximation, 1983) is the standard for pressurized pipe flow — see any fluid mechanics text (e.g., Munson, Young & Okiishi) or Crane Technical Paper No. 410. Roughness values are typical new-pipe values; tuberculation and scaling raise ε with age.
- For full pipe flow only. Partially-full gravity sewers use Manning’s equation instead.
- Aged pipe can have several times the new-pipe roughness — field-verify with pressure-drop tests on old mains.
- Add minor (fitting) losses separately; this page covers friction loss only.
- The Haaland approximation is valid for turbulent flow (Re > 4,000); laminar flow uses f = 64/Re automatically here.
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