# Hazen-Williams 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 Hazen-Williams equation

_{H2O}per 100 ft pipe

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:

h = 0.2083 (100 / c)^{1.852}q^{1.852 }/ d_{h}^{4.8655}(1)

where

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

### teh Related Mobile Apps from The Engineering ToolBox

- 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 1*00 ft (m)* pipe) and the actual head loss for the actual length of pipe:

#### SI Units

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 / d_{h}^{2}(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

- the Reynolds Numbers is above
*10*(turbulent flow)^{5} - the water temperature is in the range
*40 - 75*and the kinematic viscosity is approximately^{o}F (5 - 25^{o}C)*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 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}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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