# Hydraulic Radius of a Trapezoidal Channel (Unequal Side Slopes)

Hydraulic radius, abbreviated as \(r_h\), is the area cross-section of water in a pipe or channel divided by the wetting perimeter.

## Hydraulic Radius of a Trapezoidal Channel (Unequal Side Slopes) formula |
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\(\large{ r_h = \frac { \frac {h} {2} \; \left( b \;+\; w \right) } { b \;+\; h \; \left( \sqrt { 1 \;+\; z_{1}{^2} } \;+\; \sqrt { 1 \;+\; z_{2}{^2} } \right) } }\) | ||

Symbol |
English |
Metric |

\(\large{ r_h }\) = hydraulic radius | \(\large{ft}\) | \(\large{m}\) |

\(\large{ A_c }\) = area cross-section of flow | \(\large{ft^2}\) | \(\large{m^2}\) |

\(\large{ b }\) = bottom width of fluid | \(\large{ft}\) | \(\large{m}\) |

\(\large{ h }\) = depth of fluid | \(\large{ft}\) | \(\large{m}\) |

\(\large{ g }\) = gravitational acceleration | \(\large{\frac{ft}{sec^2}}\) | \(\large{\frac{m}{s^2}}\) |

\(\large{ w }\) = top width of fluid | \(\large{ft}\) | \(\large{m}\) |

\(\large{ P_w }\) = wetting perimeter | \(\large{ft}\) | \(\large{m}\) |

\(\large{ z_1 }\) = width of channel slope | \(\large{ft}\) | \(\large{m}\) |

\(\large{ z_2 }\) = width of channel slope | \(\large{ft}\) | \(\large{m}\) |

Tags: Hydraulic Equations