Hazen-Williams and Darcy-Weisbach Equations: Similarities and Differences

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 is an accomplished Egyptian Fire Protection & Plumbing Specialist with 30+ years of international experience at Dar Al-Handasah Consultants, an internationally ranked consulting Firm providing planning, design, management, and consultancy for the world’s most important and exciting projects.

As a Fire Protection & Plumbing Specialist, He excels in managing diverse projects and teams, with expertise in strategic leadership, project management, engineering and He has a strong and diversified experience in the design and coordination of Plumbing & Fire Protection systems for Mixed-use complexes, Airports, Educational, Healthcare, Residential, Commercial, High-Rise, and governmental buildings. He has been working on a wider variety of Megaprojects.

He graduated from Ain Shams University with a bachelor’s degree in Civil Engineering, Public Works Dept. in 1991, received the Post Graduate Diploma in Sanitary Engineering from Ain Shams University in 1996, and the Master of Business Administration (MBA) from Brookline Business School (New York, USA) in Aug. 2020.

He is also a Certified Fire Protection Specialist (CFPS) from the National Fire Protection Association (NFPA) since Dec. 2016 and Certified in Plumbing Design (CPD) by the American Society of Plumbing Engineers (ASPE) since April 2016. Additionally, He is a LEED AP (BD+C) from United States Green Building Council (USGBC) since April 2014.

Yasser is a member of the National Fire Protection Association (NFPA), the American Society of Plumbing Engineers (ASPE), the Society of Fire Protection Engineers (SFPE), and the Institution of Fire Engineers (MIFireE), and of course, he is a member of the Egyptian Engineers Syndicate, the Egyptian Society of Civil Engineers, and 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

Scroll to Top