Which equation is better? Here’s a brief comparison of their use in sprinkler piping sizing.
by Yasser Amer Ahmed, CPD, LEED AP BD+C, CFPS, MIFireE, PMSFPE
The Hazen-Williams and Darcy-Weisbach equations are both used to calculate head loss due to friction in fluid flow. The Hazen-Williams equation is commonly used for water flow through pipes, while the Darcy-Weisbach equation is a more versatile and accurate method for calculating head loss due to friction in fluid flow.
The Hazen-Williams equation is easier to use than the Darcy-Weisbach equation, as it doesn’t require iterative calculations. It estimates friction loss in a pipeline with just a few parameters. However, this equation is only applicable to water flow and cannot be used for other fluids. It also is less accurate for larger pipes and higher flow velocities.
On the other hand, the Darcy-Weisbach equation can be used for various fluids, not just water. It provides more accurate results for a wide range of pipe sizes and flow velocities. However, the equation is more complex, requiring iterative calculations and additional parameters.
Values of the friction loss coefficient, C, used in the Hazen-Williams equation are accurate only if the flow velocity is close to that at which the value of C was measured.
It is a matter of judgment as to what velocity is “too high” for the Hazen-Williams equation. American Water Works Association (AWWA) data list C factors measured at a velocity of 3 feet per second (fps) (0.9 m/s), yet it is standard practice in sprinkler calculations to accept velocities in sprinkler piping between 10 and 20 fps (3.05 and 6.1 m/s). Similarly, the tables of equivalent lengths for fittings and valves used by sprinkler system designers are based on fittings and valve types typical of sprinkler systems. Water mist systems may incorporate different types of fittings and valves for which the equivalent length values based on Hazen-Williams commonly accepted for sprinkler piping will be incorrect.
The Hazen-Williams (H-W) equation contains no terms that allow you to change the temperature, density, or viscosity of the liquid. It assumes that the water contains no additives and is close to 60°F (15.6°C). The Darcy-Weisbach (D-W) equation does allow for variation in fluid properties, and for that reason, it is widely used by mechanical engineers designing fluid systems.
NFPA 750: Standard on Water Mist Fire Protection Systems requires the use of the D-W equation if fluid velocity exceeds 25 fps (7.6 m/s). The limiting velocity was selected after a review of calculations comparing the agreement between H-W and DW calculations and measured head losses in 1- to 3-inch (25- to 80-mm) diameter black steel pipe over a range of velocities.
Finally, the Hazen-Williams formula comes within 10 percent accuracy of the value obtained using the Darcy-Weisbach equation, with significantly less effort. This is considered to be within the range of acceptable values in an engineering exercise involving fire protection system piping.
About the Author
Yasser Amer Ahmed is an accomplished Egyptian Fire Protection and Plumbing Specialist with 30+ years of international experience at Dar Al-Handasah Consultants, an internationally ranked consulting firm providing planning, design, management, and consultancy. As a Fire Protection & Plumbing Specialist, he excels in managing diverse projects and teams, with expertise in strategic leadership, project management, and engineering, and has strong and diversified experience in the design and coordination of plumbing and fire protection systems for mixed-use complexes, airports, educational, healthcare, residential, commercial, high-rise, and governmental buildings. Yasser graduated from Ain Shams University with a bachelor’s degree in Civil Engineering, Public Works Dept., in 1991, and he received a post-graduate diploma in Sanitary Engineering from Ain Shams University in 1996 and an MBA from Brookline Business School (New York) in August 2020. Yasser is a Certified Fire Protection Specialist (CFPS) since December 2016, Certified in Plumbing Design (CPD) since April 2016, and a LEED AP BD+C since April 2014. He is a member of the National Fire Protection Association (NFPA), ASPE, the Society of Fire Protection Engineers (SFPE), the Institution of Fire Engineers (MIFireE), the Egyptian Engineers Syndicate, and the Egyptian Society of Civil Engineers, and he is authorized as a Fire Protection Consultant Engineer from Egyptian Engineers Syndicate.
The opinions expressed in this article are those of the author and not the American Society of Plumbing Engineers.
References: SFPE Handbook of Fire Protection, 5th edition, and Fire Protection Handbook, 20th edition
