The Hazen-Williams formula
p = 4.52 × Q^1.85 ÷ (C^1.85 × d^4.87) psi per foot
Head (ft) = psi × 2.307
Velocity = 0.4085 × Q ÷ d² ft/s
Q = flow (gpm), d = inside diameter (in), C = roughness coefficient
This is the form used in NFPA 13 for sprinkler hydraulics. It's accurate for water at ordinary temperatures in turbulent flow, which covers most building and process water systems.
C-factors
| Pipe | C |
|---|---|
| PVC, CPVC, HDPE | 150 |
| Copper tube | 140 |
| Cement-lined ductile iron | 130–140 |
| New black steel (wet sprinkler, NFPA 13) | 120 |
| Dry-pipe steel or older pipe | 100 |
Velocity guidelines
Keep water velocity under about 5 ft/s in pump suction lines and quiet building services, and under 8 ft/s in general discharge piping. Higher velocities cause noise, erosion at fittings and water hammer when valves close.
Worked example
50 gpm through 100 ft of 2 in Schedule 40 steel (C = 120): velocity is 4.8 ft/s and friction loss is about 2.6 psi, or 6.0 ft of head.
Frequently asked questions
- How do I include elbows and valves?
- Add each fitting's equivalent length to the pipe length. A 2 in standard 90° elbow is roughly 5 ft of pipe, and a gate valve about 1 ft. NFPA 13 publishes equivalent-length tables for sprinkler work.
- Can I use this for oil, glycol or hot water?
- Hazen-Williams is only calibrated for water around 40–75 °F. For other fluids or temperatures, use Darcy-Weisbach with the fluid's viscosity.
- Does elevation change affect the result?
- This calculates friction loss only. Add 0.433 psi for every foot the water rises, or subtract it for every foot it drops.
Results are estimates for planning and education. Verify against the current code edition your jurisdiction has adopted, manufacturer data and a licensed professional before you build or install.