04 // Interactive Formula Compendium // ENGINEERINGh_f = f · (L / D) · (v² / 2g)
Darcy-Weisbach Pipe Friction Head Loss Formula
The Darcy-Weisbach equation h_f = f·(L/D)·(v²/2g) determines head loss in meters due to wall shear friction over pipe length L, internal diameter D, flow velocity v, and Darcy friction factor f.
Formula Reference
Main Formula
h_f = f · (L / D) · (v² / 2g)
Rearranged Forms
ΔP = f · (L / D) · (½ρv²)
f_laminar = 64 / Re
Variables & Units
| Symbol | Name | Unit |
|---|---|---|
| hf | Friction Head Loss | m |
| f | Darcy Friction Factor | dimensionless |
| L | Pipe Length | m |
| D | Internal Pipe Diameter | m |
| v | Flow Velocity | m/s |
Inputs & Parameters
[dimensionless]
[m]
[m]
[m/s]
Calculated Result (Friction Head Loss)
hf =6.373226m
Formula Notes & Background
- Balances axial pressure force ΔP·(πD²/4) against wall shear force τ_w·(πDL) and defines Darcy factor f = 4·C_f = 8τ_w/(ρv²).
- Do not confuse Darcy friction factor f with Fanning friction factor f_F (f = 4·f_F).
Step-by-Step Examples
#1: Find head loss in a 100 m steel pipe (D = 0.10 m, f = 0.020) carrying water at v = 2.5 m/s.
f = 0.020L = 100 mD = 0.10 mv = 2.5 m/s
h_f = 0.020 × (100 / 0.10) × (6.25 / 19.6133) = 20 × 0.31866
→ h_f = 6.37 m of head (ΔP ≈ 62.5 kPa)
#2: Doubling velocity from 2.5 m/s to 5.0 m/s in the same pipe with constant f = 0.020.
v = 5.0 m/s
h_f scales with v²: 6.373 × 4
→ h_f = 25.49 m of head
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Frequently Asked Questions
How do I find the Darcy friction factor f?+
For laminar flow (Re < 2300), f = 64/Re exactly. For turbulent flow, use the Colebrook-White equation, Swamee-Jain explicit approximation, or a Moody chart.
How is head loss h_f converted to pressure drop ΔP?+
Multiply head loss by specific weight: ΔP = ρ · g · h_f (in Pascals).
Why is Darcy-Weisbach preferred over Hazen-Williams?+
Darcy-Weisbach applies rigorously to any Newtonian fluid (oil, gas, steam, water) at any temperature and flow regime, whereas Hazen-Williams is an empirical fit restricted to room-temperature turbulent water.