Hazen-Williams Equation - calculating Friction Head Loss in Water Pipes Friction head loss (ftH2O per 100 ft pipe) in water pipes can be estimated by using the empirical Hazen-Williams equation

The Darcy-Weisbach equation with the Moody diagram are considered to be the most accurate model for estimating frictional head loss in steady pipe flow. Since the approach requires a not so efficient trial and error iteration an alternative empirical head loss calculation like the Hazen-Williams equation may be preferred:

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

where

f = 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" condition with approximately 1 m/s (3 ft/sec).

Online Hazens-Williams 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:

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)

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

100

140

200

3

30

140

q - flow rate (litre/sec)

dh - inside hydraulic diameter (mm)

Hazen-Williams equation in an Excel template

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)

where

v = flow velocity (ft/s)

The Hazen-Williams equation can be 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.

Hazen-Williams coefficients are used in the Hazen-Williams equation for friction loss calculation in ducts and pipes. Coefficients for some common materials used in ducts and pipes can be found in the table below:

10

76

MaterialHazen-Williams Coefficient

- c -

ABS - Acrylonite Butadiene Styrene

130

Aluminum 130 - 150

Asbestos Cement 140

Asphalt Lining 130 - 140

Brass 130 - 140

Brick sewer 90 - 100

Cast-Iron - new unlined (CIP)

130

Cast-Iron 10 years old 107 - 113

Cast-Iron 20 years old 89 - 100

Cast-Iron 30 years old 75 - 90

Cast-Iron 40 years old 64-83

Cast-Iron, asphalt coated 100

Cast-Iron, cement lined 140

Cast-Iron, bituminous lined 140

Cast-Iron, sea-coated 120

Cast-Iron, wrought plain 100

MaterialHazen-Williams Coefficient

- c -

Cement lining 130 - 140

Concrete 100 - 140

Concrete lined, steel forms 140

Concrete lined, wooden forms

120

Concrete, old 100 - 110

Copper 130 - 140

Corrugated Metal 60

Ductile Iron Pipe (DIP) 140

Ductile Iron, cement lined 120

Fiber 140

Fiber Glass Pipe - FRP 150

Galvanized iron 120

Glass 130

Lead 130 - 140

Metal Pipes - Very to extremely smooth

130 - 140

Plastic 130 - 150

MaterialHazen-Williams Coefficient

- c -

Polyethylene, PE, PEH 140

Polyvinyl chloride, PVC, CPVC

150

Smooth Pipes 140

Steel new unlined 140 - 150

Steel, corrugated 60

Steel, welded and seamless 100

Steel, interior riveted, no projecting rivets

110

Steel, projecting girth and horizontal rivets

100

Steel, vitrified, spiral-riveted 90 - 110

Steel, welded and seamless 100

Tin 130

Vitrified Clay 110

Wrought iron, plain 100

Wooden or Masonry Pipe - Smooth

120

Wood Stave 110 - 120

Pipe Friction Loss CalculationsFlow of fluid through a pipe is resisted by viscous shear stresses within the fluid and the turbulence that occurs along the internal pipe wall, which is dependent on the roughness of the pipe material.

This resistance is termed pipe friction and is usually measured in feet or metres head of the fluid, which is why it is also refered to as the head loss due to pipe friction.

Head Loss in a Pipe

A large amount of research has been carried out over many years to establish various formulae that can calculate head loss in a pipe. Most of this work has been developed based on experimental data.

Overall head loss in a pipe is affected by a number of factors which include the viscosity of the fluid, the size of the internal pipe diameter, the internal roughness of the inner surface of the pipe, the change in elevation between the ends of the pipe and the length of the pipe along which the fluid travels.

Valves and fittings on a pipe also contribute to the overall head loss that occurs, however these must be calculated separately to the pipe wall friction loss, using a method of modeling pipe fitting losses with k factors.

Darcy Weisbach Formula

The Darcy formula or the Darcy-Weisbach equation as it tends to be referred to, is now accepted as the most accurate pipe friction loss formula, and although more difficult to calculate and use than other friction loss formula, with the introduction of computers, it has now become the standard equation for hydraulic engineers.

Weisbach first proposed the relationship that we now know as the Darcy-Weisbach equation or the Darcy-Weisbach formula, for calculating friction loss in a pipe.

Darcy-Weisbach equation:

hf = f (L/D) x (v2/2g)

where: hf = head loss (m) f = friction factor L = length of pipe work (m) d = inner diameter of pipe work (m) v = velocity of fluid (m/s) g = acceleration due to gravity (m/s²)

or:

hf = head loss (ft) f = friction factor L = length of pipe work (ft) d = inner diameter of pipe work (ft) v = velocity of fluid (ft/s) g = acceleration due to gravity (ft/s²)

The establishment of the friction factors was however still unresolved, and indeed was an issue that needed further work to develop a solution such as that produced by the Colebrook-White formula and the data presented in the Moody chart.

The Moody Chart

The Moody Chart finally provided a method of finding an accurate friction factor and this encouraged use of the Darcy-Weisbach equation, which quickly became the method of choice for hydraulic engineers.

The introduction of the personnel computer from the 1980's onwards reduced the time required to calculate the friction factor and pipe head loss. This itself has widened the use of the Darcy-Weisbach formula to the point that most other equations are no longer used.

Hazen-Williams Formula

Before the advent of personal computers the Hazen-Williams formula was extremely popular with piping engineers because of its relatively simple calculation properties.

However the Hazen-Williams results rely upon the value of the friction factor, C hw, which is used in the formula, and the C value can vary significantly, from around 80 up to 130 and higher, depending on the pipe material, pipe size and the fluid velocity.

Also the Hazen-Williams equation only really gives good results when the fluid is Water and can produce large inaccuracies when this is not the case.

The imperial form of the Hazen-Williams formula is:

hf = 0.002083 x L x (100/C)^1.85 x (gpm^1.85 / d^4.8655)

where: hf = head loss in feet of water L = length of pipe in feet C = friction coefficient gpm = gallons per minute (USA gallons not imperial gallons) d = inside diameter of the pipe in inches

The empirical nature of the friction factor C hw means that the Hazen-Williams formula is not suitable for accurate prediction of head loss. The friction loss results are only valid for fluids with a kinematic viscosity of 1.13 centistokes, where the velocity of flow is less than 10 feet per sec, and where the pipe diameter has a size greater than 2 inches.

Notes: Water at 60° F (15.5° C) has a kinematic viscosity of 1.13 centistokes.

Common Friction Factor Values of C hw used for design purposes are:

Asbestos Cement 140 Brass tube 130 Cast-Iron tube 100 Concrete tube 110 Copper tube 130 Corrugated steel tube 60 Galvanized tubing 120 Glass tube 130 Lead piping 130 Plastic pipe 140 PVC pipe 150 General smooth pipes 140 Steel pipe 120 Steel riveted pipes 100 Tar coated cast iron tube 100 Tin tubing130 Wood Stave 110

These C hw values provide some allowance for changes to the roughness of internal pipe surface, due to pitting of the pipe wall during long periods of use and the build up of other deposits.