HazenWilliams Friction Loss Equation  calculating Head Loss in Water Pipes
Friction head loss (ft_{H2O} per 100 ft pipe) in water pipes can be estimated with the empirical HazenWilliams equation.
The DarcyWeisbach 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 DarcyWeisbach equation requires iterative calculation an alternative empirical head loss calculation like the HazenWilliams equation may be preferred:
h_{100ft} = 0.2083 (100 / c)^{1.852} q^{1.852 }/ d^{4.8655} (1)
where
h_{100ft} = friction head loss in feet of water per 100 feet of pipe (ft_{h20}/100 ft pipe)
c = HazenWilliams roughness constant
q = volume flow (gal/min)
d = inside diameter of pipe (inches)
Note that the HazenWilliams 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
h_{100ft} = 0.2083 (100 / 140)^{1.852} (200 gal/min)^{1.852 }/ (3.048 in)^{4.8655}
= 9 ft H_{2}O / 100 ft pipe
The head loss for 30 ft pipe can be calculated
h_{30ft} = h_{100ft} (30 ft) / (100 ft)
= 9 (30 ft) / (100 ft)
= 2.7 ft H_{2}O
Related Mobile App from The Engineering ToolBox
 free apps for offline use on mobile devices.
Online HazensWilliams 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. Default values are from the example above.
SI Units
The HazenWilliams 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 / d^{2} (2)
where
v = flow velocity (ft/s)
Limitations
The HazenWilliams equation is assumed to be relatively accurate for water flow in piping systems when
 the Reynolds Numbers is above 10^{5} (turbulent flow)
 the water temperature is in the range 40  75 ^{o}F (5  25^{o}C) and the kinematic viscosity is approximately 1.1 cSt
For hotter water with lower kinematic viscosity (example 0.55 cSt at 130 ^{o}F (54.4 ^{o}C)) the error will be significant.
Since the HazenWilliams 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} m^{3}/s = 0.227 m^{3}/h = 0.0631 dm^{3}(liter)/s = 2.228x10^{3} ft^{3}/s = 0.1337 ft^{3}/min = 0.8327 Imperial gal (UK)/min
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