Hazen-Williams Equation

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Hazen-Williams Equation

Hazen-Williams Equation

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 :

hf 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 ft3/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 :
hf 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 m3/sec

C is the Hazen-Williams coefficient (Dimensionless)

D is the pipe diameter in meters

Advantages of Hazen-Williams equation :

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

Disadvantages of Hazen-Williams equation:

  1. Valid only for water at ordinary temperatures* (between 40 to 75 oF).
  2. Does not account for the temperature and viscosity of water.
  3. Valid only for turbulent flow conditions.
  4. Empirical equation.

*For hot water with low kinematic viscosity (0.55 cSt at 130 oF (54.4 oC)), using the Hazen-Williams equation would result in significant error.