# Hydraulic Radius for a Channel

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**Formula:** `R_h = A / P`

The hydraulic radius, ** R_{h}**, is used in fluid mechanics to relate the shape of a channel to its resistance to flow. It is defined as the cross-sectional area of the flow,

**, divided by the wetted perimeter,**

*A***, which is the perimeter of the cross-section that is in contact with the fluid (excluding the free surface). This concept is important for the calculation of flow properties such as velocity, discharge, and frictional energy losses in open channels.**

*P*The hydraulic radius is particularly useful in equations such as the Manning formula for open channel flow, where a larger hydraulic radius suggests less resistance posed by the channel. It's also applicable in the Darcy-Weisbach equation to calculate the friction factor in pipe flow.