Free Engineering Tool · NFPA 13
Darcy-Weisbach Friction Loss Calculator
Pipe friction loss by the Darcy-Weisbach equation, for water at different temperatures or an antifreeze solution. Enter the flow, the pipe and the fluid properties, and get the Reynolds number, the Colebrook friction factor, the pressure loss and the velocity, with the Hazen-Williams result alongside for comparison.
- Based on NFPA 13
- Free, runs in your browser; your inputs stay on your device
- Screening tool, not reviewed or sealed by a licensed engineer
- Last updated October 2026
Screening tool, not engineering advice. This calculator estimates results with simplified published methods. It has not been reviewed or sealed by a licensed engineer for your project, and DGA does not warrant that its results are accurate, complete or suitable for any use. Check every result independently and have the licensed professional responsible for your project review it before you rely on it. Use is subject to the Terms of Use.
Flow and Pipe
Fluid
For antifreeze, enter the density and viscosity at the lowest expected temperature from the listed solution's data.
Result
Friction Loss Against Flow
About This Tool
The Darcy-Weisbach equation gives head loss as hL = f · (L / D) · v2 / 2g. In the form used for sprinkler piping it reads ΔP = 0.000216 · f · L · ρ · Q2 / d5 (psi, with L in ft, ρ in lb/ft3, Q in gpm and d in inches), and the Reynolds number is Re = 50.6 · Q · ρ / (d · μ) with μ in centipoise. Unlike Hazen-Williams, it accounts for the fluid’s density and viscosity, which is why NFPA 13 calls for it for antifreeze systems.
The friction factor depends on the flow regime. Below a Reynolds number of about 2,000 the flow is laminar and f = 64 / Re. In turbulent flow it follows the Colebrook equation, 1 / √f = −2 log10(ε / 3.7D + 2.51 / (Re √f)), which the Moody diagram plots; the calculator solves it by iteration. Between about 2,000 and 4,000 the flow is transitional and the friction factor is uncertain, so the tool flags it and uses the turbulent value.
Pipe roughness ε is about 0.046 mm for new steel, 0.15 mm for galvanized steel and close to zero for copper and plastic. Water presets cover 40 to 70 °F. For antifreeze, enter the density and viscosity at the lowest expected temperature from the listed solution’s data: viscosity rises steeply in the cold, and that is when friction loss is highest.
Worked example
Water at 60 °F flowing 500 gpm through 100 ft of 4 in. Schedule 40 steel moves at 12.6 ft/s with a Reynolds number of about 350,000; the friction factor is 0.0177 and the loss is 5.6 psi, while Hazen-Williams with C = 120 gives 7.2 psi, the more conservative figure for new pipe. A cold antifreeze solution with a density of 1,040 kg/m3 and a viscosity of 12 cP flowing 200 gpm through 2 in. pipe tells the opposite story: Darcy-Weisbach gives 39.1 psi per 100 ft against 33.9 psi from Hazen-Williams, 15 percent higher, because the viscous fluid loses more energy than the water-based formula expects.
Assumptions and limits
The calculator treats one straight pipe of one size with steady, fully developed flow. Fittings and valves go in as equivalent length, and the equivalent length tables were built for water in steel pipe, so check them for other fluids. Fluid properties must come from data for the actual solution and temperature.
When to bring in an engineer
Antifreeze systems now depend on listed solutions, temperature limits and the right friction method throughout the hydraulic calculation. DGA prepares sealed hydraulic calculations and designs fire protection systems for unheated and freezer spaces.
References
- NFPA 13, Standard for the Installation of Sprinkler Systems, National Fire Protection Association, 2025 edition: hydraulic calculation methods, the Darcy-Weisbach formula and its use for antifreeze systems.
- C.F. Colebrook, “Turbulent Flow in Pipes, with Particular Reference to the Transition Region between the Smooth and Rough Pipe Laws,” Journal of the Institution of Civil Engineers, Vol. 11, 1939.
- L.F. Moody, “Friction Factors for Pipe Flow,” Transactions of the ASME, Vol. 66, 1944.
- National Institute of Standards and Technology, NIST Chemistry WebBook: thermophysical properties of water (density and viscosity presets).
Frequently Asked Questions
When do you use Darcy-Weisbach instead of Hazen-Williams?
Hazen-Williams is calibrated for water at ordinary temperatures in turbulent flow. Darcy-Weisbach works for any fluid because it uses density and viscosity, so it is used for antifreeze solutions, cold or viscous fluids, and wherever laminar or transitional flow is possible. NFPA 13 calls for it in antifreeze systems.
How is the Darcy friction factor found?
For laminar flow (Reynolds number below about 2,000) the friction factor is 64 divided by the Reynolds number. For turbulent flow it comes from the Colebrook equation, which depends on the Reynolds number and the relative roughness of the pipe; the Moody diagram is a plot of the same relationship. This calculator solves Colebrook by iteration.
What roughness should I use for steel sprinkler pipe?
New commercial steel pipe is about 0.046 mm (0.0018 in.). Galvanized steel is rougher, about 0.15 mm, and copper and plastic pipe are close to smooth. Older pipe with corrosion or deposits can be much rougher than these new-pipe values.
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Engineering aid only, provided as is and without warranty. Results depend on the inputs and on the simplifying assumptions of the method summarized on each tool page, and DGA has not verified them for your application. They do not replace code-required design, testing or review by the licensed engineer responsible for the project. Use of the tools is subject to the Terms of Use.
Related Reading
Articles from DGA Insights on the code and the method behind this calculator.