Hazen-Williams equation

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

$P_d=\frac{4.52\quad Q^{1.85}}{C^{1.85}\quad d^{4.87}}$

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where:

P_d = pressure drop in pounds per square inch / foot

Q = flow in gallons per minute

C = factor (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

d = inside hydraulic diameter (inch)

An alternate form of the Hazen Williams Equation is:

$V=1.318\quad C\quad R_h^{0.63}\quad S^{0.54}$

where:

V = Velocity (in feet per second)

C = as above

R_h = Hydraulic Radius (in feet) (see Manning formula)

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

In SI units

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

Q =

C = factor (friction loss coefficient)

A =

R_h =

S =

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.

Category: Equations of fluid dynamics