# normal_depth: Normal depth In rivr: Steady and Unsteady Open-Channel Flow Computation

## Description

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

## Usage

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

## Arguments

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

## 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

.

## Value

The normal depth y_n [L].

## Examples

 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 

### Example output

[1] 1.711301
[1] 3.2864


rivr documentation built on Jan. 21, 2021, 5:06 p.m.