Contents
Introduction
It is simple to calculate the average flow velocities in engineered structures such as pipes. However, it is a tiny bit more challenging to estimate average flow velocities in (natural) open channels. Using the Gauckler-Manning-Strickler equation and parameters is a method to do so. The Gauckler-Manning-Strickler equation is defined as follows:
\( v_{m} = k_{st} \ \frac{m^{\frac{1}{3}}}{s} \cdot R^{\frac{2}{3}} \ m \cdot I^{\frac{1}{2}} \frac{m}{m} \)
where:
\(v_{m} = \text{average velocity} \ \left[\frac{m}{s}\right]\)
\(k_{st} = \text{“Strickler coefficient”, sometimes denoted as a} \ \frac{1}{n} \text{to convert feet to meter} \ \left[\frac{m^{\frac{1}{3}}}{s}\right]\)
\(R = \text{hydraulic radius} \ \left[m\right]\)
\(I = \text{Stream bed slope} \ \left[\frac{m}{m}\right]\)
Examples
Let’s see how different slopes and radii as well as different type of stream beds lead to different average velocities. Therefore, we will use these values and plot them:
| Stream type | $$k_{st} \ \left[\frac{m^{\frac{1}{3}}}{s}\right]$$ |
|---|---|
| Concrete channel | 90 |
| Stream with a high amount of gravel | 30 |
| Weedy stream | 35 |
| Torrent with large boulders | 20 |
*The Engineering ToolBox published many coefficients. However, the do not use values for \(k_{st}\) but for \(n\) which is a coefficient used if we are dealing with velocities in \(\frac{ft}{s}\) instead of \(\frac{m}{s}\) In such a case \(k_{st} = \frac{1.486}{n}\).(
If we want to understand effects of different \(k_{st}\) values and channel geometries, then we have to look at it in 3D: