Hazen-Williams equation calculator

This free Hazen-Williams equation calculator gives the head loss, pressure drop, mean velocity and hydraulic gradient of water flowing in a pressurised pipe from the flow rate, internal diameter, length and the C coefficient. Work in metric or US units (L/s, mm and m, or gpm, inches and feet), and fill the diameter from the standard pipe-size picker (ASME B36.10M schedules). The C coefficient rolls pipe roughness into one tabulated number, higher for smoother pipe, and the C value tables below cover the common materials.

Method

Hazen-Williams is a long-standing empirical method for head loss of water in pressurised pipes, widely used in water distribution and fire-protection design. In SI units the head loss is

h_f = 10.674 L Q^1.852 / ( C^1.852 D^4.871 )

with h_f in m, L in m, Q in m^3/s and D in m. The pressure drop is dp = rho g h_f and the hydraulic gradient is S = h_f / L. Unlike Darcy-Weisbach, it has no explicit friction factor or viscosity term, so C carries all of the roughness.

On the constant. Textbooks round this to 10.67 and D^4.87. The SI constant 10.674 with the exponent 4.871 is the form given in the EPANET 2 Users Manual, and it is the one the solver, this calculator and our published verification cases all use, so every page on this site quotes the same number. The rounded form differs by about 0.2 per cent, which is negligible next to the uncertainty in C itself. The 10.674 already carries standard gravity, which is why no g appears in the formula.

Limits (important). Hazen-Williams is calibrated for water at ordinary temperatures (roughly 4 to 25 degrees C) in the turbulent range. It is not valid for other fluids, for gases, or for viscous or cold liquids, and it is less physically grounded than Darcy-Weisbach. For anything other than everyday water, prefer the Darcy-Weisbach pressure drop calculator. The Studio supports both methods (Hazen-Williams was added in the solver alongside Darcy-Weisbach).

Inputs

• Hazen-Williams coefficient C (see the C value tables below).
• Flow Q (L/s).
• Internal diameter D, typed or from the standard pipe-size picker.
• Length L (m).
• Water is assumed for the fluid.

Outputs

• Head loss and pressure drop.
• Mean velocity.
• Hydraulic gradient S (m/m).

Typical Hazen-Williams C values by pipe material

Compiled from standard water-engineering tabulations, chiefly the C values in the EPANET 2 Users Manual (Rossman, 2000), alongside Hydraulic Institute data and municipal design guides. C falls as pipe ages and the rate depends heavily on water chemistry, so for old unlined metal mains prefer a field-measured value or the low end of the range. Published tabulations disagree by a few points for the same material, which is a fair signal of how precise this coefficient really is.

Fire-protection design values (NFPA 13)

C values as assigned by NFPA 13, Standard for the Installation of Sprinkler Systems, for hydraulic calculation of sprinkler systems. Confirm against the edition in force for your project before using them in a submission.

Worked example

Water with C = 130 (new iron), 50 L/s in a 200 mm pipe, 100 m long:

h_f = 10.674 x 100 x 0.05^1.852 / ( 130^1.852 x 0.2^4.871 ) = 1.28 m

with a mean velocity of 1.59 m/s and a hydraulic gradient of 0.0128 m/m (about 12.6 kPa of pressure drop over the 100 m, converted with water at 20 degrees C). Those are the figures the calculator above returns, and the same head loss the Studio produces when the project head-loss method is set to Hazen-Williams.

Frequently asked questions

What C value should I use?

Use the tables above: about 150 for new plastics and lined pipe, 140 for cement-lined iron, 120 for new steel, and down towards 100 or below for old unlined metal pipe. C falls with age, so pick a value for the pipe's condition over its design life, not its condition on day one.

Hazen-Williams or Darcy-Weisbach?

Hazen-Williams is convenient for water networks where C values are tabulated and temperatures are ordinary, while Darcy-Weisbach is physically based and valid for any Newtonian fluid, temperature and flow regime. For anything other than everyday water, use the Darcy-Weisbach pressure drop calculator instead, and the Studio solves networks with either method.

Does the calculator work in US units like gpm, inches and psi?

Yes. The Metric (SI) / Imperial (US) toggle converts every input in place, so the same physical problem reads in gpm, inches and feet with results in feet of head, psi and ft/s.

Can it solve for pipe diameter or flow instead of head loss?

Not directly, it computes head loss from flow, diameter, length and C. To size a pipe, step through the standard sizes in the built-in ASME B36.10M picker until the head loss and velocity are acceptable, or model the system in the Studio, which solves flows from the driving heads.

Does temperature matter?

The Hazen-Williams formula is calibrated for water at ordinary temperatures, roughly 4 to 25 degrees C, and has no viscosity term, so it cannot correct for hot or very cold water. This calculator converts head loss to pressure using water at 20 degrees C, and Darcy-Weisbach is the better choice outside that range.

Can I use it for fire sprinkler calculations?

NFPA 13 hydraulic calculations use the Hazen-Williams formula with assigned C values, listed in the fire-protection table above, and this calculator computes that same friction loss for a single pipe run. A full sprinkler demand calculation also needs fittings, elevation and the discharge density, so treat this as a per-pipe check rather than a complete NFPA calculation.

References

• Williams, G. S. and Hazen, A., Hydraulic Tables, John Wiley and Sons. The original tabulation the formula and its C coefficient come from.
• Rossman, L. A. (2000), EPANET 2 Users Manual, US Environmental Protection Agency. The source of the SI constant 10.674 and the exponent 4.871 used here, and of much of the C-value table. epa.gov/water-research/epanet
• NFPA 13, Standard for the Installation of Sprinkler Systems, National Fire Protection Association, for the assigned fire-protection C values. nfpa.org
• Crane Co., Technical Paper No. 410: Flow of Fluids Through Valves, Fittings and Pipe, for the comparison with Darcy-Weisbach. tp410.com

Related

• Pipe pressure drop calculator (Darcy-Weisbach)
• Pipe velocity calculator
• Darcy friction factor calculator
• Branched water distribution example and the looped network example
• Modelling a water network? Open the Studio to solve it with Hazen-Williams or Darcy-Weisbach.