Calculate water friction head loss with the Hazen-Williams equation from flow, pipe size, length, and the C roughness coefficient — with a one-click Darcy-Weisbach comparison and clear validity guidance.
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Friction Loss (Hazen-Williams)
Water only — empirical method
Hazen-Williams is reliable only for water near 60 °F, velocities under ~10 ft/s, and pipe ≥ 2 in. For oils, slurries, hot water, or small bore, use Darcy-Weisbach.
in
ft
C
Head Loss2.11ft(0.642 m)
Velocity
4.34 ft/s
Pressure drop
0.914 psi
Loss per length
2.11 ft / 100 ft
C value used
150
Compare with Darcy-Weisbach
Darcy-Weisbach head loss2.1 ft
Hazen-Williams is +0.588% vs Darcy-Weisbach
Darcy comparison assumes water at 60 °F and a representative roughness for the selected material. A large divergence means Hazen-Williams is outside its comfort zone for this case.
Formula & method
hf = 10.44 · L · Q1.852 / (C1.852 · d4.8655) (US: gpm, in, ft)
SI form uses the coefficient 10.67 with Q in m³/s, D and L in m (result in m); it differs from the US-converted value by under ~1%, within Hazen-Williams empirical uncertainty. Pressure drop assumes water (SG = 1).
For preliminary sizing and educational use. Verify final design against manufacturer data and applicable codes; final designs should be reviewed by a licensed professional engineer.
The Hazen-Williams equation is a fast, water-only way to estimate pipe friction loss using a single roughness coefficient C instead of a Reynolds number and relative roughness. Head loss rises with flow to the 1.852 power and falls steeply with diameter: h_f = 10.44 · L · Q¹·⁸⁵² / (C¹·⁸⁵² · d⁴·⁸⁶⁵⁵) in US units, with a higher C meaning a smoother pipe.
Worked example
Water at 100 gpm through 100 ft of 3-inch Schedule 40 PVC (inside diameter 3.068 in, C = 150):
Velocity: 4.34 ft/s
Head loss = 10.44 × 100 × 100¹·⁸⁵² / (150¹·⁸⁵² × 3.068⁴·⁸⁶⁵⁵) ≈ 2.11 ft (0.91 psi)
Darcy-Weisbach on the same pipe gives ≈ 2.10 ft — about 0.6% apart for smooth new pipe
Validity — read before you trust the number
Hazen-Williams is empirical and water-only. It was fitted to cold water (near 60 °F) at ordinary velocities, so it is dependable only for water near room temperature, velocities under about 10 ft/s, and pipe of roughly 2 inches and larger. Applied to oils, slurries, hot water, or small-bore tubing it can be materially wrong because it ignores viscosity entirely. When you are outside that envelope, use Darcy-Weisbach, which derives friction from the Reynolds number and works for any fluid.
Choosing a C value
C describes pipe smoothness and drops as pipe ages and roughens: new plastic and PVC are around 150, new cement-lined or copper about 140, new steel near 140 but older welded steel closer to 120, new cast iron about 130 but decades-old tuberculated cast iron as low as 80–100. Design for the C the pipe will have late in its life, not the day it is installed. Use the built-in “compare with Darcy-Weisbach” to see how far the empirical answer sits from the physics-based one for your case.
