Hazen-Williams equation

The Hazen-Williams formula can be used to calculate the pressure loss per one foot of pipe of a known diameter due to friction dependent on the flow. This equation is commonly used for pressure drop calculations in fire sprinkler systems, water distribution systems, and irrigation systems.

The equation in U.S. customary units

:$P\_d=frac\{4.52quad\; Q^\{1.85\{C^\{1.85\}quad\; d^\{4.87$

where:

P_d = pressure drop in pounds per square inch / foot

Q = flow in gallons per minute

d = inside pipe diameter (inch)

C = factor (roughness or friction loss coefficient) - the higher the C factor, the smoother the pipe. Typical C factors used in design, which take into account some increase in roughness as pipe ages are as follows:
*Asbestos-cement - 140
*Cast iron - 100
*Cement-Mortar Lined Ductile Iron Pipe - 140
*Concrete - 100
*Copper - 150
*Steel - 120
*Galvanized steel - 120
*Polyethylene - 150
*Polyvinyl chloride (PVC) - 150
*Fibre-reinforced plastic (FRP) - 150

An alternative form of the Hazen-Williams equation is:

:$V=1.318quad\; Cquad\; R\_h^\{0.63\}quad\; S^\{0.54\}$

where:

V = Velocity (in feet per second)

C = as above

R_h = Hydraulic Radius (in feet)

S = Energy Gradient or Friction Slope (h_f/L)

The equation in SI units

:$P\_d=frac\{102627quad\; Q^\{1.85\{C^\{1.85\}quad\; d^\{4.87$

where:

P_d = pressure drop in Pa/m of pipeline

Q = volumetric flow rate in m³/s

d = inside pipe diameter in m

C = as above

Alternatively:

:$Q\; =\; 0,849\; ;\; C\; ,\; A\; ,\; R\_h^\{0,63\}\; ,\; S^\{0,54\}$

Q = Volumetric flow rate

C = factor (friction loss coefficient)

A = Cross-sectional area of flow

R_h = Hydraulic Radius

S = Slope of energy grade line

ee also

*Darcy-Weisbach equation
*Fluid dynamics
*Friction
*Pressure
*Volumetric flow rate
*Water pipe

References

* Turf Irrigation Manual, 5th Ed., by James A. Watkins, published by Telsco, 1987.
* Fluid Mechanics, 10th Ed., by E. John Finnemore and Joseph B Franzini, published by McGraw Hill, 2002.

External links

* [http://www.engineeringtoolbox.com/hazen-williams-water-d_797.html Engineering Toolbox reference]
* [http://www.engineeringtoolbox.com/hazen-williams-coefficients-d_798.html Engineering Toolbox Hazen Williams Coefficients]
* [http://www.calctool.org/CALC/eng/civil/hazen-williams_g Online Hazen-Williams calculator for gravity-fed pipes.]
* [http://www.calctool.org/CALC/eng/civil/hazen-williams_p Online Hazen-Williams calculator for pressurized pipes.]