Hazen-Williams equation is a widely used empirical equation (derived by Allen Hazen and Gardner Stewart Williams in 1906) for calculating the friction (major) head losses \ pressure of fluids in different piping systems.

The Hazen-Williams coefficient C is mainly used to account for the pipe roughness or efficiency. This coefficient is a function of the pipe material and status (old pipes have different Hazen-Williams coefficients than the new ones).

## Hazen-Williams equation (English Units) :

\[{h_f} = 4.73 \times {\left( {\frac{Q}{C}} \right)^{1.852}} \times \frac{L}{{{D^{4.87}}}}\]

Where :

h_{f} is the friction (major) head loss in ft

L is the pipe length in ft

Q is the discharge (flow rate) passing through the pipe in ft^{3}/sec

C is the Hazen-Williams coefficient (Dimensionless)

D is the pipe diameter in ft

## Hazen-Williams equation (SI Units) :

\[{h_f} = 10.7 \times {\left( {\frac{Q}{C}} \right)^{1.852}} \times \frac{L}{{{D^{4.87}}}}\]

Where :

h_{f} is the friction (major) head loss in meters

L is the pipe length in meters

Q is the discharge (flow rate) passing through the pipe in m^{3}/sec

C is the Hazen-Williams coefficient (Dimensionless)

D is the pipe diameter in meters

## Advantages of Hazen-Williams equation :

- Unlike Darcy-Weisbach equation, Reynolds number is not required. Hazen-Williams coefficient is used instead of the friction factor.
- More simple and easy to use than the Darcy-Weisbach equation.
- Hazen-Williams coefficient is dimensionless.

## Disadvantages of Hazen-Williams equation:

- Valid only for water at ordinary temperatures* (between 40 to 75
^{o}F). - Does not account for the temperature and viscosity of water.
- Valid only for turbulent flow conditions.
- Empirical equation.

*For hot water with low kinematic viscosity (0.55 cSt at 130 ^{o}F (54.4 ^{o}C)), using the Hazen-Williams equation would result in significant error.

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