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Hazen-Williams Equation - calculating Head Loss in Water Pipes

Friction head loss (ftH2O per 100 ft pipe) in water pipes can be estimated with the empirical Hazen-Williams equation

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The Darcy-Weisbach equation with the Moody diagram is considered to be the most accurate model for estimating frictional head loss for a steady pipe flow. Since the Darcy-Weisbach equation requires iterative calculation an alternative empirical head loss calculation like the Hazen-Williams equation may be preferred:

h100ft = 0.2083 (100 / c)1.852 q1.852 / dh4.8655                          (1)

where

h100ft = friction head loss in feet of water per 100 feet of pipe (fth20/100 ft pipe)

c = Hazen-Williams roughness constant

q = volume flow (gal/min)

dh = 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" conditions with approximately 1 m/s (3 ft/sec).

Example - Friction Head Loss in Water Pipe

200 gal/min of water flows in a 3 inch PEH pipe DR 15 with inside diameter 3.048 inches. The roughness coefficient for PEH pipe is 140 and the length of the pipe is 30 ft. The head loss for 100 ft pipe can be calculated as

h100ft = 0.2083 (100 / 140)1.852 (200 gal/min)1.852 / (3.048 in)4.8655     

   = 9 ft H2O / 100 ft pipe

The head loss for 30 ft pipe can be calculated

h30ft = h100ft (30 ft) / (100 ft)

        =  9 (30 ft) / (100 ft)

                = 2.7 ft H2O

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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. Default values are from the example above.

l - pipe or tube length (ft)

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

q - flow rate (gal/min)

dh - inside hydraulic diameter (inch)

SI Units

l - pipe or tube length (m)

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

q - flow rate (liter/sec)

dh - inside hydraulic diameter (mm)

The Hazen-Williams equation is not the only empirical formula available. Manning's formula is commonly used to calculate gravity driven flows in open channels.

The flow velocity can be calculated as

v = 0.408709 q / dh2                                (2)

where

v = flow velocity (ft/s)

Limitations

The Hazen-Williams equation is assumed to be relatively accurate for water flow in piping systems when

For hotter water with lower kinematic viscosity (example 0.55 cSt at 130 oF (54.4 oC)) the error will be significant.

Since the Hazen-Williams method is only valid for water flow - the Darcy Weisbach method should be used for other liquids or gases.

  • 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
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  • Engineering ToolBox, (2004). Hazen-Williams Equation - calculating Head Loss in Water Pipes. [online] Available at: https://www.engineeringtoolbox.com/hazen-williams-water-d_797.html [Accessed Day Mo. Year].

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