Hydraulic radius is used in various engineering applications, particularly in the calculation of pipe and channel flow. It is defined as the flow area divided by the wetted perimeter.

$latex r_h = \frac{Flow Area}{Wetted Perimeter}&s=2$

## Flow Area

This is the cross-sectional flow area of the channel or pipe. When a pipe is flowing under pressure, this is the full internal area of the pipe.

## Wetted Perimeter

This is the length of the line representing the interface between the fluid and the pipe or channel. It does not include the free surface length.

## Example – Circular culvert flowing full

A circular culvert flowing completely full has a flow area of *πr ^{2}* and a wetted perimeter of

*2πr*, meaning the hydraulic radius is:

$latex r_h = \frac{\pi r^{2}}{2\pi r} = \frac{r}{2}&s=2$

## Interpretation

The greater the hydraulic radius, the greater the efficiency of the pipe (or channel) and the greater the volume of flow it can carry.

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