Hazen-Williams estimates the head a water pipe loses to friction from its diameter, its flow and one roughness number, C. The choice of C moves the answer more than the choice of formula. A cement-lined pipe can be given anything from 120, the bottom of EPANET 2.2's row for "concrete or concrete-lined" pipe, to 150, the Cameron handbook's average for "cement-lined iron or steel centrifugally applied". On our arithmetic, C 120 gives about 1.5 times the head loss of C 150. Against Darcy-Weisbach with the Colebrook equation, for smooth plastic pipe at C 150 and water at 30 °C, Hazen-Williams ran from 17% under to 12% over across our sweep.
We were not first to measure that second gap. Liou (1998) showed that C is "a strong function of Reynolds number and pipe size", and Darweesh et al. (2024) tested the formula across temperatures, velocities and diameters.
Cast-iron mains took well over a decade to reach the C value used most
The formula predates its book. The 1920 third edition of Williams and Hazen's Hydraulic Tables opens its review of new data: "It is eighteen years since the Williams-Hazen formula was first used and fifteen since the first edition of these tables appeared." That dates first use to about 1902.
The 1905 first edition calls 130 "a fair value for new pipe" in cast iron and prints the C 100 column in bold, as the one "most often required". Its circled figures, read from the page images, put cast iron at C 100 after 13 years in a 4-inch pipe and 20 years at 42 and 48 inches. By then, the authors wrote, "twice as much head is consumed" as when new; C 140 against C 100 gives 1.86 times the loss, by our arithmetic.
That row is history, no forecast for modern pipe: cast iron carrying "soft and clear but unfiltered river-waters", in figures the authors called "very rough approximations".
Cement-lined pipe changes head loss about 1.5 times with the choice of C table
We compared Williams and Hazen, Table 3.2 of the US EPA's EPANET 2.2 manual, and Cameron Hydraulic Data (Ingersoll-Dresser Pumps, a post-14th edition). The loss ratio, (highest C ÷ lowest C)1.852, is ours.
| Pipe, as each source labels it | C for new pipe | Loss ratio |
|---|---|---|
| Cast iron | 130 (1905); 130–140 (EPANET); 130 average (Cameron) | 1.15 |
| Steel (EPANET); welded or seamless steel (Cameron) | 140–150; 130 average | 1.30 |
| Concrete or concrete-lined (EPANET); cement-lined iron or steel, centrifugally applied (Cameron) | 120–140; 150 average | 1.51 |
| Plastic (EPANET) | 140–150 | 1.14 |
| Vitrified clay | 110 in all three | 1.00 |
The 1905 book has no lined-pipe value: its 120 is for "masonry conduits of concrete or plastered". Cameron keeps lined pipe and plain concrete apart; EPANET merges them. Utilities and national plumbing codes publish their own figures, which we did not open.
A 100 mm test pipe barely moves between the published constants
The original form, v = 0.849 C R0.63 S0.54, gives an SI coefficient of 10.6742, usually printed as 10.67. A 100 mm pipe, 100 m long, carrying 10 L/s at C 130 loses 1.906 m in SI form. The US form with its 4.52 constant comes out 0.24% lower, and Cameron's form 0.47% higher. Rounding stays under half a per cent, while the lined-pipe choice of C moves the same loss by 51%.
Until 19 October 2026 our Hazen-Williams pipe flow calculator accepted bores down to 5 mm without warning. Its six C options cited nothing, and the default, "Cement-lined / PVC field" at 130, sat below EPANET's 140–150 for plastic. It said 100 mm to 150 mm cut the loss to roughly a tenth; the exponent gives 0.139, about a seventh. It credited Williams and Hazen with water near 15 °C and recommended bigger pipes for low pressure.
The revision made that day sources every C option, defaults to "New cast iron" at 130, flags bores under 2 inches and under 1 inch, and takes a custom C. With the inputs above it returns 1.906 m; choose "Other" and enter 120 for 2.211 m, or 150 for 1.462 m, a ratio of 1.51.
Smooth plastic pipe drifts from Colebrook in opposite directions by bore and speed
Our grid crossed ten bores, 15 to 300 mm, with six speeds, 0.3 to 3 m/s. Each C took its roughness height from the same EPANET row, with viscosity from the NIST Chemistry WebBook. It compares two formulas and is no field test.
For smooth plastic at C 150 and 30 °C, Hazen-Williams reads low in small pipes at low speed, 0.83 of the Colebrook loss at 15 mm and 0.3 m/s, and high in large mains at high speed, 1.12 at 300 mm and 3 m/s. Of the 60 cells, 46 fall within 10%. At C 140, still inside EPANET's plastic range, 49 fall outside it.
Rough cast iron at C 130 runs the other way: 0.73 at 50 mm and 3 m/s, 1.11 at 300 mm and 0.3 m/s. One C cannot hold across the Reynolds numbers such a grid spans.
Travis and Mays (2007) linked C to Colebrook roughness with equations "accurate to within 4% error". Alegret Breña and Martínez Valdés (2019) found the two losses "difieren entre sí" unless C is set from Reynolds number and relative roughness. Jaćimović et al. (2015) derived C from Colebrook for DN80 to DN500. Our grid adds smaller bores and warm water.
Pipes under an inch passed up to a tenth less water by the authors' own warning
The authors called the formula "designed primarily for computing the flow of water in pipes", though "reasonably well adapted" to open channels. In 1920 they left pipes under 2 inches out of their exponent fit, since "viscosity is a greater element" there. Under 1 inch they preferred the Saph and Schoder formula and warned that flows "may be as much as 10 per cent less".
Ten per cent less flow at a given head means 1.215 times the head at a given flow, on our arithmetic. Our 15 mm, 0.3 m/s cell has Colebrook at 1.206 times the Hazen-Williams figure, which is consistent. At 15 °C that cell reads 0.75, about a quarter low.
Mains in warm climates run with less friction on Colebrook's reckoning
Hazen-Williams has no temperature term. Neither Williams and Hazen edition gives a temperature for it, only for a separate formula below the critical velocity. Cameron states its basis as water at 60 °F (15.6 °C).
Colebrook responds to viscosity, which NIST puts about 30% lower at 30 °C than at 15 °C. In the same pipe at the same flow, our sweep found 6–10% less head at 30 °C for smooth plastic and 1–4% less for cast iron. The 25–35 °C band is our own choice and no utility's measured mains temperature. Across it, plastic cells beyond 10% at C 150 rise from 7 of 60 at 25 °C to 19 at 35 °C. Seventeen of those 19 sit in wider pipes at higher speeds, where warmer water leaves Hazen-Williams reading high.
View author profile → · Editorial policy
