Flow Velocity: Manning’s Formula

Flow resistance is proportional to flow depth, which modulates the influence of bed roughness. Deeper flows feel the bed less.

Learning Goals

• Understand why deeper flows are disproportionately faster.
• Know where and how to find values for Manning’s \(n\) (and what it is)
• Understand the concerns about the dimensional consistency of the equation

The formula

For quick reference; see course notes and video for derivation:

\[\bar{u} = \frac{1}{n} h^{2/3} S^{1/2}\]

Course notes

Flow mechanics PDF

Manning’s formula and Manning’s \(n\) explained

Manning’s \(n\) references

Page through these to give yourself an idea of what Manning’s \(n\) means and where to look it up. This is likely to come in handy if you ever find yourself working with surface-water flows.

Picture books (not even kidding!)

Barnes (1967), Roughness Characteristics of Natural Channels

Yochum et al. (2014), Photographic Guidance for Selecting Flow Resistance Coefficients in High-Gradient Channels, General Technical Report RMRS-GTR-323, US Forest Service Rocky Mountain Research Station.

USGS Water Resources Division (1984), Guide for Selecting Manning’s Roughness Coefficients for Natural Channels and Flood Plains, FHWA-TS-84-204, US DOT Federal Highway Administration.

Tables

Chow, 1959

Video explanation

This video goes through the comparative method (“picture books”), and also uses a rubric that I do not present here but that is commonly in use when working at field sites. This is not necessary material for the class, but is useful if you want to go on and work on rivers.

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