Compute friction head loss in a pressurized water pipe with the Hazen-Williams equation, the standard empirical method for water-distribution and fire-protection design. Enter flow rate, diameter, length, and the pipe's C-factor; the calculator returns head loss, velocity, and the hydraulic gradient in SI units.
The Hazen-Williams equation is the most widely used empirical formula for sizing water-distribution mains, service lines, and fire-protection systems. Unlike the more general Darcy-Weisbach approach, it folds all the friction behaviour into a single roughness coefficient C, requires no Reynolds number or viscosity, and is valid specifically for water near room temperature. This calculator returns the friction head loss, the average velocity, and the hydraulic gradient (slope of the energy line) from just four inputs.
h_f = 10.67 ยท L ยท Q^1.852 / (C^1.852 ยท D^4.87).
Here h_f is the friction head loss (m), L the pipe length (m), Q the volumetric flow (mยณ/s), D the inside diameter (m), and C the Hazen-Williams roughness coefficient (dimensionless). The constant 10.67 is the SI form of the equation. Note the strongly non-linear exponents: head loss rises with flow to the 1.852 power and falls with diameter to the 4.87 power, so diameter is by far the most influential variable.
C is a measure of pipe smoothness โ higher C means smoother pipe and less friction (the opposite sense to Manning's n). Typical design values: PVC and smooth plastic โ 150, new ductile or cast iron and new steel โ 130, average steel โ 120, ordinary cast iron โ 100, and old, corroded, or tuberculated pipe โ 80 or lower. Because head loss scales with C^1.852, an aging main whose C drops from 130 to 80 loses roughly 2.4 times more head at the same flow โ a major reason utilities reline or replace old water mains.
Darcy-Weisbach is the theoretically rigorous, dimensionally consistent equation valid for any fluid, temperature, and flow regime, but it requires the Reynolds number and a friction factor from the Moody chart or Colebrook equation. Hazen-Williams trades that generality for simplicity: it is purely empirical, calibrated for clean water at ordinary temperatures (about 4โ25 ยฐC) and turbulent velocities. For routine water-supply design it is faster and accurate enough; for other fluids, hot water, or research-grade accuracy, Darcy-Weisbach is preferred.
Hazen-Williams should only be used for water โ not oils, slurries, sludges, air, or other fluids whose viscosity differs from water. It is calibrated for diameters above roughly 50 mm and velocities in the normal turbulent range (about 0.6โ3 m/s); outside that band, and at very low temperatures, accuracy degrades. It also captures only straight-pipe (major) friction loss โ minor losses through valves, bends, and fittings must be added separately using loss coefficients or equivalent lengths to get the total head a pump must supply.
Use Hazen-Williams for pressurized water-distribution, transmission, and fire-protection design at ordinary temperatures โ it is the industry standard there and avoids friction-factor iteration. Switch to Darcy-Weisbach for non-water fluids, hot or cold water far from room temperature, laminar flow, or any case where dimensional rigor and accuracy across regimes matter.
Choose C for the expected condition over the pipe's service life, not just when new. New PVC and plastic run about 150 and new metal pipe about 130, but utilities commonly design with a lower aged value (often 100โ120 for metal) to account for tuberculation, scaling, and biofilm that reduce C over decades. Always check local design standards.
Because the diameter exponent is 4.87. At a fixed flow rate, reducing the diameter by half multiplies head loss by roughly 2^4.87 โ 29. This extreme sensitivity is why pipe sizing dominates the energy cost of a water system and why a modest increase in diameter can dramatically cut pumping head and operating cost.
No โ it returns only the straight-pipe friction (major) loss. Minor losses through valves, elbows, tees, meters, and reducers are added separately, typically as KยทVยฒ/2g loss coefficients or by adding an equivalent pipe length to L. The sum of major loss, minor losses, and elevation change gives the total dynamic head for pump selection.
Not reliably. The equation is calibrated specifically for clean water; sludges and slurries have higher and often non-Newtonian viscosity that the single C-factor cannot represent. For those fluids use Darcy-Weisbach with the appropriate viscosity, or specialized slurry-flow correlations. Gravity sewers flowing partly full are handled with Manning's equation instead.