WikiEngineer :: Water-Resources :: Hazen Williams Equation

How to use the Hazen-Williams Eqn:

The Hazen Williams Equation can be used for a variety of purposes, but the two main reasons it's used under normal conditions is to calculate head loss and flow rate (aka flow velocity).

In order for the Hazen-Williams formula to be valid::

Ambient Temperatures
Turbulent Flow

The Main Equations:

Hazen-Williams has been reworked into a multitude of different variants. The most common are explained below.

To solve for friction loss:

h_f = {{3.022v^{1.85}_{ft/sec} L_{ft}}\over {C^{1.85} D^{1.17}}}

h_f = {{10.44 L_{ft} V^{1.85}_{gpm}}\over {C^{1.85} d^{4.87}_{inches}}}

To solve for velocity:

v = {1.318Cr^{0.63}s^{0.54}} \quad [U.S.]

v = {0.85Cr^{0.63}s^{0.54}} \quad [S.I.]

where:

h_f = frictional head loss
v = Velocity of the fluid
L = Length
C = Hazen-Williams Roughness Coefficient C
D = Diameter of pipe
r = Radius of the pipe
s = Slope of the Channel

Note: These equations will work as long as you keep your units straight. That way you can use either SI or US as long as you keep everything in order. Your h_f should end up in units of length (e.g. feet, meters, etc.)

Other Variations of the Hazen-Williams Formula::

Mean Fluid Velocity:

Friction Coefficient:

C = {v\over {1.318r^{0.63}s^{0.54}}}

Hydraulic Radius:

r = {\left(v\over {1.318Cs^{0.54}}\right)^{1\over {0.63}}}

Hydraulic Grade Line on Slope:

s = {\left(v\over {1.318Cr^{0.63}}\right)^{1\over {0.54}}}

Fluid Flow Rate:

Friction Coefficient:

C = {Q\over {0.285D^{2.63}s^{0.54}}}

Pipe Diameter:

D = {\left(Q\over {0.285Cs^{0.54}}\right)^{1\over {2.63}}}

Hydraulic Grade Line on Slope:

s = {\left(Q\over {0.285CD^{2.63}}\right)^{1\over {0.54}}}

where:

Q = Flow rate or Discharge

References:

P. Aarne Vesilind, J. Jeffrey Peirce and Ruth F. Weiner. 1994. Environmental Engineering. Butterworth Heinemann. 3rd ed.