# 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_{100ft}= 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_{100ft}_{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)*.

#### 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 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. 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)

d_{h}- inside hydraulic diameter (inch)

#### SI Units

l- pipe or tube length (m)

c-roughness coefficientdetermined for the type of pipe or tube

q- flow rate (liter/sec)

d_{h}- insidehydraulic 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 / 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