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 [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}]. |
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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