The hydraulic radius is variable used in open channel flow for the Manning Equation and the Hazen Williams Equation.

 In general, the Hydraulic Radius of a system can be solved by: R = \frac{\text{cross-sectional flow area}}{\text{wetted perimeter}} = \frac{A}{s}

where:

• R = the Hydraulic Radius
• wetted perimeter = perimeter where water touches a solid surface

### Hydraulic Radius for Common Channel Shapes:

The following common channel/pipe shapes have been simplified to easily find their hydraulic radius'.

#### Rectangular Channel (partially full):

For a rectangular Channel, given h depth and b width:

R = \frac{bh}{b+2h}

#### Circle (half full):

For a half filled circle, given r radius & D diameter:

R = \frac{\frac{\pi r^2}{2}}{\frac{2\pi r}{2}} = \frac{r}{2} = \frac{D}{4}

#### Circle (full):

For a full circle, given r radius & D diameter:

R = \frac{\pi r^2}{2\pi r} = \frac{r}{2} = \frac{D}{4}

#### Square (full):

For a full square, given s side:

R = \frac {s^2}{4s} = \frac{s}{4}

## Resources:

1. Stephen Elmer Slocum, "Elements of Hydraulics", 1915 (Read Online Here)

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