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

normal_depth(So, n, Q, yopt, Cm, B, SS)

## Arguments

So Channel slope [$$L L^{-1}$$]. Manning's roughness coefficient. Flow rate [$$L^3 T^{-1}$$]. Initial guess for normal depth [$$L$$]. Unit conversion coefficient for Manning's equation. For SI units, Cm = 1. Channel bottom width [$$L$$]. Channel sideslope [$$L L^{-1}$$].

## Value

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

## Details

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

## Examples

normal_depth(0.001, 0.045, 250, 3, 1.486, 100, 0) # rectangular channel#> [1] 1.711301normal_depth(0.0008, 0.013, 126, 5, 1, 6.1, 1.5) # trapezoidal channel with sideslope 3H:2V#> [1] 3.2864