### 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:*

*where:*

_{f}= 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 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:**

**Hydraulic Radius:**

**Hydraulic Grade Line on Slope:**

#### Fluid Flow Rate:

**Friction Coefficient:**

**Pipe Diameter:**

**Hydraulic Grade Line on Slope:**

*where:*

### References:

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