### 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:

hf = frictional head loss
V = Velocity of the fluid (ft/sec, m/s)
L = Length (ft, m)
C = Hazen-Williams Roughness Coefficient C
D = Diameter of pipe
R = Hydraulic Radius = \frac{\text{cross-sectional flow area}}{\text{wetted perimeter}} (ft)
S = Slope of the hydraulic gradient (ft/ft)

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 hf 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:

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

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