Relative resistance and effective area¶

When relative resistance is specified for a cross section, the effect of the relative resistance number, r, is included in the hydraulic radius R and the flow area A_fl, while the processed resistance numbers F by default are constant 1 for all levels.

If the hydraulic radius type used is either “Resistance Radius” or “Hydraulic Radius, Effective Area”, an effective area is calculated. The effective area tries to take into account the amount of water that due to resistance is not giving any contribution to the momentum, and is used in the Momentum Equation (4.1b), instead of the geometric area.

The effective flow area, A_e, for a given water level is defined as:

\[ A_e = \int_0^B \frac{y}{r} db \]

Equation: Effective flow area accounting for spatial variation in resistance number.

where, y is the local water depth and B is the width of the cross section at the given water level.

Looping over all line segment in the cross section profile (which equals the number of raw (x,z) values minus one), this converts to a sum on the form

\[ A_{e}=\sum_{i}\!\left(\frac{A_{i}}{r_{i}}\right) \]

Equation: Effective flow area weighted by inverse of relative resistance across cross section segments.

where A_i is the area above the i’th line segment up to the current water level, and r_i is the relative resistance specified for the line segment.

In case the relative resistance value is constant 1 along the entire cross section profile, the effective area will equal the geometric area.

The effect on the hydraulic radius will be described in the next section.