Hazen-Williams pressure drop calculator

The Hazen-Williams equation is a long-standing empirical method for head loss of water in pressurised pipes, widely used in water distribution and fire-protection design because it rolls pipe roughness into a single, tabulated coefficient C. This calculator returns the head loss, pressure drop, velocity and hydraulic gradient for water.

Method

In SI units the head loss is

h_f = 10.67 L Q^1.852 / ( C^1.852 D^4.87 )

with h_f in m, L in m, Q in m^3/s and D in m. The coefficient C describes the pipe smoothness: higher is smoother. Typical values are about 150 for PVC and new steel, 130 for new cast or ductile iron, and 100 or lower for old, tuberculated pipe. The pressure drop is dp = rho g h_f and the hydraulic gradient is S = h_f / L. Citation: the Hazen-Williams empirical formula; values of C are tabulated in water-engineering references.

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 (with a table of typical values).
• Flow Q (L/s).
• Internal diameter D (mm).
• Length L (m).
• Water is assumed for the fluid.

Outputs

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

Worked example

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

h_f = 10.67 x 100 x 0.05^1.852 / ( 130^1.852 x 0.2^4.87 ) = 1.28 m

with a mean velocity of 1.59 m/s and a hydraulic gradient of 0.0128 m/m (about 12.5 kPa of pressure drop over the 100 m).

Frequently asked questions

Hazen-Williams or Darcy-Weisbach?

Hazen-Williams is convenient for water networks where C values are tabulated and temperatures are ordinary. Darcy-Weisbach is more general and physically based, and it handles any fluid and temperature. For general work, prefer Darcy-Weisbach.

What C value should I use?

About 150 for PVC and new steel, 130 for new iron, and down towards 100 for old or fouled pipe. C falls as pipes age.

Does temperature matter?

The method is calibrated near room-temperature water, so it does not correct for viscosity changes with temperature. Cold or hot water is better handled by Darcy-Weisbach.

Related

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