The Hazen-Williams equation is empirical and has long been used to calculate the friction loss in pipework for water-based fire sprinkler protection systems.
This equation uses the coefficient C (C-factor) to specify the pipe roughness, which is independent of the Reynolds number, unlike other pressure-loss equations. However, this has the disadvantage that the equation applies only when water is in the 'turbulent' flow range. Suppose the system is outside the usual pressure and flow range and will have additives such as foam or antifreeze, or unusual temperature conditions. In that case, the Darcy-Weisbach equation may be more appropriate.
Gardner Williams and Allen Hazen first started their Experimentation in the early part of the 20th century. They began recording friction loss through a pipe in numerous experiments as part of their studies, which led to the development of the empirical formula now known as the Hazen-Williams equation. The formula and a series of friction-loss tables were published in 1903.
The Hazen-Williams formula is simple to calculate with a scientific calculator. In contrast, the Darcy-Weisbach equation requires the friction factor 'f', which can only be calculated with several iterations because 'f' appears on both sides. You can use a Moody diagram to find the value of 'f'; however, this is time-consuming and almost certainly not the most accurate method. (Ibrahim & Ibrahim, 2002, pp. 369-374)
The Hazen-Williams formula has now been adopted worldwide as the pressure loss formula for the hydraulic design of fire sprinkler systems. Using the Hazen-Williams formula will provide adequate answers in almost all cases. Care should be taken when using the Hazen-Williams equation to ensure it is not used outside its scope. Otherwise, you may end up with inaccurate calculations. To avoid this, you should limit the velocity when specified in the desired design standard.
The Hazen-Williams formula can also be used to calculate water mist systems where the system pressure does not exceed 12 bar (low-pressure water mist systems) or the water velocity does not exceed 7.6 m/s, and the minimum pipe size is 20mm for intermediate and high-pressure water mist systems. This is stated in NPFA 750. (NFPA 750: Standard on Water Mist Fire Protection Systems, 2023) For other cases and for high-pressure water mist systems, the Darcy-Weisbach equation is more appropriate.
You can use Canute Hcalc's hydraulic calculator or our online Hazen-Williams calculator to visually explore the relationship between flow, pipe diameter, and the pipe C-factor in the Hazen-Williams formula, which will give you a good understanding of the formula. Our Hcalc software is free for you to download and use.
Hazen-Williams equation:
When:
p = pressure loss in bar per meter
Q = flow through the pipe in L/min
C = friction loss coefficient
d = internal diameter of the pipe in mm
L = Length of pipe in m
You can see in the equation above that if Q is raised to the power of 1.85, doubling the flow while keeping all other factors constant would increase the friction loss by almost 4 times. If the flow were to triple, the friction loss would increase by almost 9 times. You can also see that the pipe diameter D is raised to the power of 4.87 and is in the denominator on the right-hand side of the equation. Therefore, increasing the pipe size will reduce friction losses if all other factors remain constant. If the diameters double, the friction loss will be reduced by almost a factor of 1/32. Likewise, if the pipe diameter is tripled, the friction loss would be reduced to about 1/243 of its original value.
The Hayes-Williams formula, which is empirical, yields only approximate results; however, it is considered to be accurate enough to be used for the calculation of fire sprinkler systems, and indeed, the formula is stipulated in all fire sprinkler design standards throughout the world, including NFPA 13, EN 12845, EN 16925 and BS 9251. There are certain cases, such as high-pressure water mist, where the Darcy-Weisbach equation would be more appropriate, as set out in NFPA 750.
Example Calculations Using the Hazen–Williams Formula
Example 1: 105 mm (ID) Mild Steel Pipe — 2000 L/min
Consider a mild steel pipe with an internal diameter of 105 mm, a flow rate of 2000 L/min, and a pipe length of 150 m.
For mild steel, use a C‑factor of 120.
Result:
Pressure loss per metre: 0.016 bar
Total pressure loss: 2.40 bar
Velocity: 3.8 m/s
Example 2: 105 mm (ID) Plastic Pipe — 2000 L/min
Using the same pipe diameter and flow rate as Example 1, but assuming a plastic pipe with a C‑factor of 140.
Result:
Pressure loss per metre: 0.012 bar
Total pressure loss: 1.80 bar
Velocity: 3.8 m/s (unchanged, as diameter and flow rate remain the same)
Example 3: 85 mm (ID) Ductile Iron Pipe — 1560 L/min
Now consider a ductile iron pipe with an internal diameter of 85 mm, a flow rate of 1560 L/min, and a pipe length of 100 m.
For ductile iron, use a C‑factor of 100.
Result:
Pressure loss per metre: 0.039 bar
Total pressure loss: 3.90 bar
Velocity: 4.6 m/s
Value of C-factor for use in the Hazen-Williams formula
The table below lists typical values of coefficient C that can be used in the Hazen-Williams formula for different fire sprinkler design standards. The value of C represents the pipe's roughness, with higher C values indicating lower friction losses. The values specified in the design standards allow for pipe degradation. For instance, a new cast iron pipe has a C coefficient of 130, while EN 12845 gives a value of 100, equivalent to a pipe about 20 years old.
| Type of Pipe | C1 | C EN 12845 |
C BS 9251 |
C NFPA 13 / 13D & 13R |
| Cast iron | 64-130 | 100 | - | - |
| Cement-lined cast iron | - | 130 | - | 140 |
| Copper | 130-140 | 140 | 140 | 150 |
| Ductile iron | 110 | 110 | - | 100 |
| Galvanized steel | 120 | 120 | - | 120 |
| Mild steel | 120-150 | 120 | 120 | 120 |
| Mild steel (dry & preaction) |
- | - | - | 100 |
| Plastic | 140-150 | 140 | 150 | 150 |
| Stainless steel | - | 140 | - | 150 |
| C1 References: Brater, King H, Lindell J. Wei C (seventh edition), Handbook of Hydraulics: McGraw-Hill | ||||
Conclusion
The Hazen–Williams formula is a practical, widely used method for estimating friction loss in fire sprinkler piping. Pipe diameter, flow rate, and the C-factor each play a major role in pressure loss and water velocity. At the same flow rate, a higher C-factor, such as that of smooth plastic pipe, results in much lower friction loss than rough materials like mild steel or ductile iron.
Understanding these relationships helps fire protection engineers make informed choices on pipe materials, sizing distribution networks, and ensuring pressure at remote sprinkler heads. Accurate friction-loss calculations lead to reliable system performance, a better hydraulic balance, and compliance with standards. When engineers observe how these variables interact, they can create safer, more resilient fire protection systems.
