Hazen-Williams Equation - calculating Friction Loss in Water Pipes

Friction loss in water pipes can be obtained by using the empirical Hazen-Williams equation

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 solution, an alternative empirical head loss calculation that do not require the trial and error solutions, as the Hazen-Williams equation, may be preferred:

f = 0.2083 (100/C)^1.852 Q^1.852/d_i^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_i = inside diameter (inches)

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

• Hazen-Williams equation on an Excel template

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

The flow velocity may be calculated as:

v = 0.4087 Q / d_i²

where

v = flow velocity (ft/s)

The Hazen-Williams formula can be assumed to be relatively accurate for piping systems where the Reynolds Number is 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 = 0.0227 m³/h = 0.0631 dm³(liter)/s = 2.228x10^-3 ft³/s = 0.1337 ft³/min = 0.8327 Imperial gal (UK)/min

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