Hazen-Williams Equation - calculating Friction Head Loss in Water Pipes

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The Darcy-Weisbach equation with the Moody diagram are considered to be the most accurate model for estimating frictional head loss in steady pipe flow. Since the approach requires a not so efficient trial and error iteration an alternative empirical head loss calculation like the Hazen-Williams equation may be preferred:

f = 0.2083 (100/c)^1.852 q^1.852 / d_h^4.8655         (1)

where

f = friction head loss in feet of water per 100 feet of pipe (ft_h20/100 ft pipe)

c = Hazen-Williams roughness constant

q = volume flow (gal/min)

d_h = inside hydraulic diameter (inches)

Note that the Hazen-Williams formula is empirical and lacks a theoretical basis. Be aware that the roughness constants are based on "normal" condition with approximately 1 m/s (3 ft/sec).

Related Mobile Apps from The Engineering ToolBox

• Water Pipes Head Loss Calculator App

- free apps for offline use on mobile devices.

Online Hazens-Williams Calculator

Imperial Units

The calculators below can used to calculate the specific head loss (head loss per 100 ft (m) pipe) and the actual head loss for the actual length of pipe:

SI Units

• Hazen-Williams equation in an Excel template

The Hazen-Williams equation is not the only empirical formula available. Manning's formula is common for gravity driven flows in open channels.

The flow velocity can be calculated as

v = 0.408709 q / d_h²        (2)

where

v = flow velocity (ft/s)

The Hazen-Williams equation can be assumed to be relatively accurate for piping systems with Reynolds Numbers above 10⁵ (turbulent flow).

• 1 ft (foot) = 0.3048 m
• 1 in (inch) = 25.4 mm
• 1 gal (US)/min =6.30888x10^-5 m³/s = 0.227 m³/h = 0.0631 dm³(liter)/s = 2.228x10^-3 ft³/s = 0.1337 ft³/min = 0.8327 Imperial gal (UK)/min

Note! The Hazen-Williams formula gives accurate head loss due to friction for fluids with kinematic viscosity of approximately 1.1 cSt. More about fluids and kinematic viscosity.

The results for the formula is acceptable for cold water at 60 ^oF (15.6 ^oC) with kinematic viscosity 1.13 cSt. For hot water with a lower kinematic viscosity (0.55 cSt at 130 ^oF (54.4 ^oC)) the error will be significant.

Since the Hazen Williams method is only valid for water flowing at ordinary temperatures between 40 to 75 ^oF, the Darcy Weisbach method should be used for other liquids or gases.

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Related Topics

• Fluid Flow and Pressure Drop - Pipe lines - fluid flow and pressure loss - water, sewer, steel pipes, pvc pipes, copper tubes and more
• Fluid Mechanics - The study of fluids - liquids and gases. Involves various properties of the fluid, such as velocity, pressure, density and temperature, as functions of space and time.

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