# Open Channel Flow Calculations Include Determining Manning Roughness Coefficient n equation.

## Introduction

There are several approaches in use for determining Manning roughness coefficient, n, to be used for Manning equation open channel flow calculations for water flow in a natural channel. All of the methods use a description of the river or stream channel and its surfaces. There are tables available that give maximum, minimum and average Manning roughness (n) values for various channel descriptions. (See ‘Use of the Manning Equation for Open Channel Flow in Natural Channels’ for an example.) There is also an approach that uses pictures of many natural open channels with known n value that can be matched to the channel of interest.

The approach to be discussed here uses a base n value determined by the general type of channel and then modifies the base n value on the basis of various descriptors of the channel and its surface. The original reference for the method is Cowan, 1956. There is also a good description with details of the method in McCuen, 1998.

## The Base Roughness Coefficient, n1

The first step in determining Manning roughness coefficient, n, for use in the Manning equation is selecting a value for the base roughness coefficient, n1, from the following list based on the general character of the channel.

- Character of Channel………………………Basic n value, n1
- Channels in earth……………………………………0.02
- Channels cut into rock……………………………..0.025
- Channels in fine gravel……………………………..0.024
- Channels in coarse gravel…………………………0.028

## Irregularity Modifier, n2

The second step is selection of a value for the ‘irregularity modifier,’ n2 from the table below.

- Degree of Irregularity……………………………………………………………………………………….Modifier, n2
- Smooth (Surface comparable to the best attainable for the materials involved)……………………..0.000
- Minor (good dredged channels; slightly eroded or scoured side slopes of canals)………………….0.005
- Moderate (fair to poor dredged channels; moderately sloughed or eroded canal side slopes)……0.010
- Severe (Badly sloughed banks of natural streams; badly eroded or sloughed sides of canals or drainage channels; unshaped, jagged and irregular surfaces of channels excavated in rock……..0.020

## Cross Section Modifier, n3

The third step is selection of a value for the ‘cross section modifier,’ n3, from the table below.

- Character of Variations of Size & Shape of Cross Section………………………………………Modifier, n3
- Change in size or shape occurs gradually……………………………………………………………….0.000
- Large & small sections alternate occasionally or shape changes cause occasional shifting of main flow from side to side………………………………………………………………………………………….0.005
- Large & small sections alternate frequently or shape changes cause frequent shifting or main flow from side to side…………………………………………………………………………………………0.010-0.015

## Obstructions Modifier, n4

The fourth step is selection of a value for the ‘obstruction modifier,’ n4, from the table below.

- Relative Effect of Obstruction………………………………………………………Modifier, n4
- Negligible……………………………………………………………………………………0.000
- Minor……………………………………………………………………………………..0.010-0.015
- Appreciable……………………………………………………………………………..0.020-0.030
- Severe…………………………………………………………………………………….0.040-0.060

## Vegetation Modifier, n5

The fifth step is selection of a value for the ‘vegetation modifier,’ n5, from the table below.

- Degree of Vegetation Effect on n………………………………………….Modifier, n5
- Low………………………………………………………………………………0.005-0.010
- Medium…………………………………………………………………………0.010-0.020
- High……………………………………………………………………………..0.020-0.050
- Very High……………………………………………………………………….0.050-0.100

## Meandering Modifier, n6

The sixth step in this procedure is selection of a value for the ‘meander modifier,’ n6.

- Degree of Meander………….Ratio of Meander Length to Straight Length……………Modifier, n6
- Minor…………………………………………………1.0-1.2…………………………………………….0.000
- Appreciable…………………………………………1.2-1.5…………………………………………….0.15ns
- Severe………………………………………………..> 1.5……………………………………………..0.30ns

Where ns = n1 + n2 + n3 + n4 + n5

## Final Estimate of Manning Roughness Coefficient

Finally, determining Manning roughness coefficient, n, can be done with the equation:

n = n1 + n2 + n3 + n4 + n5 + n6

## References

Cowan, W.L., “Estimating Hydraulic Roughness Coefficients,” *Agricultural Engineering,* Vol. 37: 473-475, 1956.

McCuen, R.H., *Hydrologic Analysis and Design,* 2nd Ed., Prentice Hall, Upper Saddle River, NJ, 1998.

## About the Author

Dr. Harlan Bengtson is a registered professional engineer with 30 years of university teaching experience in engineering science and civil engineering. He holds a PhD in Chemical Engineering.

## This post is part of the series: Uniform Open Channel Flow and the Manning Equation

The Manning equation is widely used for uniform open channel flow calculations with natural or man made channels. The Manning equation is used to relate parameters like river discharge and water flow velocity to hydraulic radius, and open channel slope, size, shape, and Manning roughness.

- Introduction to the Manning Equation for Uniform Open Channel Flow Calculations
- Calculation of Hydraulic Radius for Uniform Open Channel Flow
- Use of the Manning Equation for Open Channel Flow in Natural Channels
- Determining the Manning Roughness Coefficient for a Natural Channel
- Calculating Uniform Open Channel Flow/Manning Equation Solutions