The Manning’s roughness coefficient, which is also commonly referred to as Manning’s n, is an empirical parameter that represents energy loss due to a variety of things such as friction losses, flow separation, turbulence, and very sudden contractions or expansions. Manning’s n values are applied to Manning’s equation, which calculates open channel flow.
There are a variety of factors that affect channel roughness including the following:
- Stream bed material and grain size,
- Surface irregularities within the channel bed,
- Channel bedforms (e.g., ripples, dunes, transition, and plane bed),
- Erosion and depositional characteristics,
- Meandering tendencies,
- Channel obstructions (e.g., overtopped trees, root wads, beaver dams, debris),
- Depth of water,
- Change in channel geometry,
- Vegetation along the banks and within the channel, and
- Other abrupt changes in energy and/or momentum.
In many cases, the Manning’s n value applied to a hydraulic model is based on the engineer’s judgment and experience. Cowan’s equation (Cowan, 1956) is a useful equation for generating an estimate of Manning’s n. Cowan (1956) developed this formula by analyzing more than 40 small channels. For this reason, Cowan’s Method is not applicable to streams with a hydraulic radius greater than 15-20 feet.
The equation for Cowan’s Method is as follows:
n = (n0 + n1 + n2 + n3 + n4)m5
where,
n is the final Manning’s roughness coefficient (n) applied to a stream reach,
n0 accounts for the channel material,
n1 accounts for the effect of channel surface irregularities,
n2 accounts for variation in channel cross section shape and size,
n3 accounts for obstructions (e.g., beaver dams, fallen trees, root wads),
n4 accounts for vegetation, and
m5 is a correction factor for channel meandering.
The tables below show the range of values for the coefficients used in Cowan’s Method.
| Material | n0 value |
| Concrete | 0.013 |
| Earth | 0.020 – 0.024 |
| Fine Gravel | 0.024 – 0.027 |
| Rock Cut | 0.025 |
| Coarse Gravel | 0.028 – 0.035 |
| Cobbles | 0.030 – 0.050 |
| Boulders | 0.050 – 0.070 |
| Degree of Irregularity | n1 value | Description |
| Smooth | 0.000 | Smoothest channels attainable for a given bed material. |
| Minor | 0.001 – 0.005 | Carefully dredged channels in good condition but having slightly eroded or scoured side slopes. |
| Moderate | 0.006 – 0.010 | Moderate to considerable bed roughness and moderately eroded or scoured side slopes. |
| Severe | 0.011 – 0.020 | Badly sloughed, eroded, or scalloped banks. Unshaped, jagged, and irregular surfaces for channels made of rock. |
| Variations of Channel Cross Section | n2 value | Description |
| Gradual | 0.000 | Size and shape of the channel cross section change gradually. |
| Alternating Occasionally | 0.005 – 0.010 | Large and small cross sections alternate occasionally, or the main flow occasionally shifts from side to side due to changes in cross-sectional shape. |
| Alternating Frequently | 0.010 – 0.015 | Large and small cross sections alternate frequently, or the main flow frequently shifts from side to side due to changes in cross-sectional shape. |
| Relative Effect of Obstructions | n3 value | Description |
| Negligible | 0.000 | A few scattered obstructions (less than 5 percent of the cross-sectional area), include debris deposits, stumps, exposed roots, logs, piers, or isolated boulders. |
| Minor | 0.010 – 0.015 | Obstructions occupy less than 15 percent of the cross-sectional area. |
| Appreciable | 0.020 – 0.030 | Obstructions occupy less than 15 to 50 percent of the cross-sectional area. |
| Severe | 0.040 – 0.060 | Obstructions occupy more than 50 percent of the cross-sectional area. |
| Vegetation | n4 value | Description |
| Low | 0.005 – 0.010 | Dense growths of flexible turf grass, such as Bermuda, or weeds growing where the average depth of flow is at least two times the height of the vegetation; supple tree seedlings such as willow, cottonwood, arrow weed, or salt cedar growing where the average depth of flow is at least three times the height of the vegetation. |
| Medium | 0.010 – 0.025 | Turf grass growing where the average depth of flow is from one to two times the height of the vegetation; moderately dense stemmy grass, weeds, or tree seedlings growing where the average depth of flow is from two to three times the height of the vegetation: brushy, moderately dense vegetation, similar to 1- to 2-year-old willow trees in the dormant season, growing along the banks and no significant vegetation along the channel bottoms where the hydraulic radius exceeds 2 feet. |
| High | 0.025 – 0.050 | Turf grass growing where the average depth of flow is about equal to the height of vegetation: 8- to 10-year-old willow or cottonwood trees intergrown with some weeds and brush (none of the vegetation in foliage) where the hydraulic radius exceeds 2 feet; bushy willows about 1-year-old intergrown with some weeds alongside slopes (all vegetation in full foliage) and no significant vegetation along channel bottoms where the hydraulic radius is greater than 2 feet. |
| Very High | 0.050 – 0.100 | Turf grass growing where the average depth of flow is less than half the height of the vegetation: bushy willow trees about 1-year-old intergrown with weeds alongside slopes (all vegetation in full foliage) or dense cattails growing along channel bottom; trees intergrown with weeds and brush (all vegetation in full foliage). |
| Degree of Meandering | m5 value | Description |
| Minor | 1.000 | The ratio of the channel length to valley length is 1.0 to 1.2. |
| Appreciable | 1.150 | The ratio of the channel length to valley length is 1.2 to 1.5. |
| Severe | 1.300 | The ratio of the channel length to valley length is greater than 1.5. |
It is not unusual to have zero values for different categories within Cowan’s equation when applying this method to short stream reaches. For reaches several thousand feet in length, most of the categories will have positive values.