# Hazen-Williams equation

Hazen-Williams equation is a popular approach for the calculation of head loss of liquid in piping systems. In this method, Hazen-Williams coefficient is introduced to the equation, the coefficient eliminates the need for using Reynolds number. The Hazen-Williams coefficient is mainly used to account for the pipe roughness or efficiency.

## Hazen-Williams equation

Different formats for this equation is specified below

### Equation 1 (US Units)

Hazen-Williams equation for head loss is shown below: Where;
H = frictional head loss, ft
L = length of pipe, ft
D = inside diameter of pipe, ft
Q = flow rate, ft3/s
C = Hazen-Williams C factor or roughness coefficient, dimensionless

### Equation 2 (US Units) Where;

H = friction loss, ft of water per 1000 ft of pipe
Q = flow rate, gal/min
D = inside diameter of pipe, in
C = Hazen-Williams C coefficient, dimensionless

### Equation 3 (US Units) Where;

Pmi = friction loss, psi per mile of pipe
Q = flow rate, gal/min
D = inside diameter of pipe, in
C = Hazen-Williams C coefficient, dimensionless

### Equation 4 (US Units) – Flow rate Where;

H = friction loss, ft of water per 1000 ft of pipe
Q = flow rate, gal/min
D = inside diameter of pipe, in
C = Hazen-Williams C coefficient, dimensionless

### Equation 5 (SI Units) Where;

Q = flow rate, m3/h
D = pipe inside diameter, mm
Pkm = frictional pressure drop, kPa/km
SG = liquid specific gravity (water = 1.00)
C = Hazen-Williams C factor, dimensionless

Common values for the Hazen-Williams coefficient C are listed in the table below:

 Pipe material C Factor Brick 100 Cast iron (old) 100 Iron (worn/pitted) 60 – 80 Polyvinyl chloride (PVC) 150 Smooth wood 120 Smooth masonry 120 Smooth pipes (all metals) 130 – 140 Vitrified clay 110

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