# Hazen-Williams Equation

Written by Jerry Ratzlaff. Posted in Fluid Mechanics

Hazen Williams method is only valid for water flowing at ambient temperatures, the Darcy-Weisbach method should be used for other liquids or gases. The Hazen-Williams Equation can be used for flow through an open channel or through a pressurized pipe.

## flow through an open channel formula

$$v = 1.318C r^{0.63} m^{0.54}$$

Where:

$$v$$ = mean flow velocity

$$C$$ = Hazen Williams Coefficient, see below for values

$$r$$ = hydraulic radius

$$m$$ = hydraulic grade line slope

$$Q$$ = discharge or flow rate

$$d$$ = pipe diameter

Solve for:

$$C = \frac {v} { 1.318r^{0.63} m^{0.54} }$$

$$r = \left( \frac {v} { 1.318C m^{0.54} } \right) ^{\frac {1}{0.63} }$$

$$m = \left( \frac {v} { 1.318C r^{0.63} } \right) ^{\frac {1}{0.54} }$$

$$Q = 0.285C d^{2.63} m^{0.54}$$

$$C = \frac {Q} { 0.285d^{2.63} m^{0.54} }$$

$$d = \left( \frac {Q} { 0.285C m^{0.54} } \right) ^{\frac {1}{2.63} }$$

$$m = \left( \frac {Q} { 0.285C d^{2.63} } \right) ^{\frac {1}{0.54} }$$

## flow through a pressurized pipe formula

$$\Delta p_{100} = \frac{452Q^{1.85}} {C^{1.85} d^{4.86}}$$

Where:

$$\Delta p_{100}$$ = pressure drop per 100 feet

$$Q$$ = flow rate, gpm

$$C$$ = Hazen Williams Coefficient, see below for values

$$d$$ = inner diameter of pipe, in

Solve for:

$$C = \frac {v} { 1.318r^{0.63} m^{0.54} }$$

$$r = \left( \frac {v} { 1.318C m^{0.54} } \right) ^{\frac {1}{0.63} }$$

$$m = \left( \frac {v} { 1.318C r^{0.63} } \right) ^{\frac {1}{0.54} }$$

$$Q = 0.285C d^{2.63} m^{0.54}$$

$$C = \frac {Q} { 0.285d^{2.63} m^{0.54} }$$

$$d = \left( \frac {Q} { 0.285C m^{0.54} } \right) ^{\frac {1}{2.63} }$$

$$m = \left( \frac {Q} { 0.285C d^{2.63} } \right) ^{\frac {1}{0.54} }$$

## hazen-williams coefficient

The following values are used in the Hazen-Williams Equation. The lower the coefficient, the smoother the pipe is. The higher the Hazen-Williams 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.

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.

MaterialHazen Williams Coefficient
Asbestos Cement 120 to 150
Asphalt-lined iron or steel 140
Cast Iron, Coated 110 to 140
Cast Iron, Uncoated 100 to 140
Concrete 100 to 140
Copper or brass 130
Corrugated steel 60
Deteriorated old pipes 60 to 80
Ductile Iron 120 to 145
Fiberglass 150
Galvanized Iron 100 to 120