River cross-section analysis¶

Introduction¶

The purpose of this notebook is to look up at the hydraulic parameter at a specific cross-section. Especially to compute the potential elevation of water and the velocity in order to pre-design protection work such as dike or rip rap. These basic computations may be done also into spreadsheet. However, the second goals of this notebook is to become familiar with the "R" programming language, starting with a simple example.

Hydraulic considerations¶

Here we will use the so-called Manning-Strickler formula. It is basically the same than the Chézy's formula, but being more accurate due to higher exponent applied to the hydraulic radius (assumed to be better constrained, than the roughness coefficient). It is used worldwide and therefore produce a large amount of supporting documents. The difference between Manning and Strickler is in the way the roughness coefficient is expressed. The Manning coefficient is named "n" and the Strickler one is named "K_s". Their are related trough:

$ n = \frac{1}{K_{s}}$

As it is very difficult getting reasonable guess of the value of the rougness coefficient in the area influenced only by the bed (as you often couldn't oberve it), one could you the following workflow. Although a little more complex than a direct approach, it avoids having to guess this partial roughness in the flow center line (the one on the banks is easier to calibrate because it can be observed directly).

Geometry description¶

Based on your field assessment of:

1. n the roughness coefficient (unit is dimensionless, see below)
2. A the equivalent trapezoidal section A = A_wl + A_s + A_wr (unit is m²)
3. P_s the wetted perimeter in the section influenced inly by the bed (= bed width in m)
4. J the longitudinal gradient of the river at this cross-section (unit is m/m, i.e an angle in radian)
5. d₉₀ the diameter of the equivalent sand roughness