Hazen-Williams Equation - calculate 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

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 q1.852 / dh4.8655                          (1)


h = 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).

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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:

l - pipe or tube length (ft)

c - design 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)

cdesign 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 common for gravity driven flows in open channels.

The flow velocity can be calculated as

v = 0.408709 q / dh2                                (2)


v = flow velocity (ft/s)

The Hazen-Williams equation is assumed to be relatively accurate for piping systems with Reynolds Numbers 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 = 0.227 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.

Related Topics

  • Fluid Mechanics - The study of fluids - liquids and gases. Involves velocity, pressure, density and temperature as functions of space and time
  • Fluid Flow and Pressure Drop - Pipe lines - fluid flow and pressure loss - water, sewer, steel pipes, pvc pipes, copper tubes and more

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