# Hazen-Williams Coefficient

on . Posted in Fluid Dynamics

Hazen-Williams coefficient, abbreviated as C, also called Hazen-Williams friction coefficient or, Hazen-Williams roughness coefficient, a dimensionless number, is used in the Hazen-Williams Equation.  The coefficient is used in fluid dynamics to calculate the resistance of water flow in a pipe network.  The lower the coefficient, the smoother the pipe is.  The higher the coefficient, the less fluid flow is restricted.  By using pipe materials with improved flow characteristics, energy costs for pumping can be reduced or smaller pipes can be used.

The Hazen-Williams coefficient represents the internal roughness of the pipe, taking into account factors such as pipe material, age, and condition.  It is used to incorporate the effect of pipe roughness on the flow characteristics.  The higher the coefficient, the smoother the pipe surface, resulting in a higher flow rate for a given pressure drop.  The Hazen-Williams coefficient varies depending on the pipe material, and it is typically determined through empirical testing.  The coefficient values for different pipe materials are usually available in engineering references and design manuals.

It's important to note that the Hazen-Williams equation is an empirical approximation and is most accurate for steady, uniform flow conditions in water supply systems.  For more complex or non-uniform flow situations, other equations, such as the Darcy-Weisbach equation, may be more appropriate.

Note that the Hazen-Williams Coefficient is '''not''' the same as the Darcy-Weibach-Colebrook friction factor, f.  These are not in any way related to each other.

## Hazen-Williams coefficient formula

$$\large{ C = \frac {v}{ 1.318 \; r_h^{0.63} \; m^{0.54} } }$$     (mean flow velocity
Symbol English Metric
$$\large{ C }$$ = Hazen-Williams Coefficient, see below for values $$\large{ dimensionless }$$
$$\large{ v }$$ = mean flow velocity $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$
$$\large{ r_h }$$ = hydraulic radius $$\large{ ft }$$ $$\large{ m }$$
$$\large{ m }$$ = hydraulic grade line slope $$\large{ dimensionless }$$

## Hazen-Williams coefficient formula

$$\large{ C = \frac {Q}{ 0.285 \; d^{2.63} \; m^{0.54} } }$$     (fluid flow rate)
Symbol English Metric
$$\large{ C }$$ = Hazen-Williams Coefficient, see below for values $$\large{ dimensionless }$$
$$\large{ Q }$$ = flow rate $$\large{\frac{ft^3}{sec}}$$ $$\large{\frac{m^3}{s}}$$
$$\large{ d }$$ = pipe inside diameter $$\large{ in }$$ $$\large{ mm }$$
$$\large{ m }$$ = hydraulic grade line slope $$\large{ dimensionless }$$

## Hazen-Williams Coefficient

Material Coefficient
Aluminum 130 - 150
Asbestos Cement 120 - 150
Asphalt-lined iron or steel 140
Brass 130
Cast Iron, cement lined 140
Cast Iron, coated 110 - 140
Cast Iron, new unlined 130
Cast Iron, old unlined 40 - 120
Cast Iron, uncoated 100 - 140
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
Cement lining 140
Concrete 100 - 140
Concrete, old 100 - 110
Copper 130 - 140
Corrugated Metal Pipe 60
Corrugated Steel 60
Deteriorated old pipes 60 - 80
Ductile Iron 120 - 145
Fiberglass 150
Galvanized Iron 100 - 120
Glass 130
Polyethylene 140
PVC, PE, GRP 120 - 150
Steel, new unlined 120
Steel, 15 years 200
Steel, riveted joints 95 - 110
Steel, welded joints 100 - 140
Steel, welded joints, lined 110 - 140
Steel, welded or steamless 100 - 120
Tin 130
Wood Stave 110 