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Engineering ToolBox > Hazen-Williams Equation - calculating Friction Head Loss in Water Pipes

Friction head loss (ft H2O per 100 ft pipe) 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_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 physical basis. Be aware that the roughness constants are based on "normal" condition with approximately 1 m/s (3 ft/sec).

Online Hazens-Williams Calculator

The calculator below can used to calculate the head loss:

l - pipe or tube length (ft)

c - design coefficient determined for the type of pipe or tube

q - flow rate (gal/min)

d_h - inside hydraulic diameter (inch)

• Hazen-Williams equation in 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_h²

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

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.