Description Usage Arguments Details Value Examples

Calculate the normal (equilibrium) depth using Manning's equation.

1 | ```
normal_depth(So, n, Q, yopt, Cm, B, SS)
``` |

`So` |
Channel slope [ |

`n` |
Manning's roughness coefficient. |

`Q` |
Flow rate [ |

`yopt` |
Initial guess for normal depth [ |

`Cm` |
Unit conversion coefficient for Manning's equation. For SI units, Cm = 1. |

`B` |
Channel bottom width [ |

`SS` |
Channel sideslope [ |

The normal depth is the equilibrium depth of a channel for a given flow rate, channel slope, geometry and roughness. Manning's equation is used to calculate the equilibrium depth. Manning's equation for normal flow is defined as

*Q = \frac{C_m}{n} AR^{2/3}S_0^{1/2}*

where *Q* is the channel flow, *S_0* is the channel slope, *A* is the
cross-sectional flow area, *R* is the hydraulic depth and *C_m* is a conversion factor
based on the unit system used. This function uses a Newton-Raphson root-finding approach
to calculate the normal depth, i.e.
*y = y_n* when

*f(y) = \frac{A^{5/3}}{P^{2/3}} - \frac{nQ}{C_mS_0^{1/2}} = 0*

.

The normal depth *y_n* [*L*].

1 2 | ```
normal_depth(0.001, 0.045, 250, 3, 1.486, 100, 0) # rectangular channel
normal_depth(0.0008, 0.013, 126, 5, 1, 6.1, 1.5) # trapezoidal channel with sideslope 3H:2V
``` |

```
[1] 1.711301
[1] 3.2864
```

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