Geog 427/527: Fluvial Geomorphology
Winter 1999, University of Oregon
[Back to Exercise 2] [Go to photos and cross-sections for each site]
Exercise 2: Method for Estimating Manning's n
This method is extracted from:
Arcement, G.J., Jr., and Schneider, V. R., 1989. Guide for selecting Manning’s
roughness coefficients for natural channels and floodplains. U. S. Geological Survey Water
Supply Paper 2339.
Manning equation for feet, feet/sec: V = (1.486/n) R0.67S0.5
Background on the method:
"The roughness coefficient is applied to a longitudinal reach of channel and (or) floodplain… The flow may be confined to one or more channels, and, especially during floods, the flow may occur in both channel and in the floodplain. Cross sections are typically divided into subsections at points where major roughness or geometric changes occur, such as at the juncture of… the floodplain and channel. Roughness coefficients are determined for each subsection… (Note: In this exercise you will only be estimating roughness for flow in channels, and division into subsections is not necessary.) Roughness values for floodplains can be quite different from values for channels… Seasonally variability of roughness coefficients should be considered. Floods often occur during the winter when there is less vegetation…"
Channel n values:
Manning n is estimated using the following formula, developed by Cowan (1956):
n = (nb+n1+n2+n3+n4)m, where
nb = a base value of n for a straight, uniform, smooth channel in natural
materials,
n1 = a correction factor for the effect of surface irregularities,
n2 = a value for variation in the shape and size of the channel cross section,
n3 = a value for obstructions,
n4 = a value for vegetation and flow conditions, and
m = a correction factor for meandering of the channel.
Step A. Select base n value from the table below, on the basis of channel
material. Sand values in the table apply only to channels experiencing upper flow regime;
channels experiencing lower flow regime often have mush larger n values. Thus, for
sand-bedded channels, it is necessary to determine whether or not upper flow regime is
occurring, after roughness has been estimated. Arcement and Schneider present a simple
equation for this purpose. Note: In this exercise, only use the stable channel part of
Table 1.
A range of values for each material class is given, because it is difficult to separate
the effects of channel materials from other effects on roughness.
Table for nb: Base value of n |
|||
| Smooth channel 2 | |||
| Bed material | D50 |
Straight uniform channel | Smooth channel |
Sand channels, upper flow regime |
|||
| Sand | 0.2 |
0.012 |
--- |
0.4 |
0.020 |
--- |
|
0.6 |
0.023 |
--- |
|
0.8 |
0.025 |
--- |
|
1.0 |
0.026 |
--- |
|
Stable channels and floodplains |
|||
| concrete | --- |
0.012 – 0.018 |
0.011 |
| rock cut | --- |
--- |
0.025 |
| firm soil | --- |
0.025 – 0.032 |
0.020 |
| coarse sand | 1 – 2 |
0.026 – 0.035 |
--- |
| fine gravel | --- |
--- |
0.024 |
| gravel | 2 – 64 |
0.028 – 0.035 |
--- |
| coarse gravel | --- |
--- |
0.026 |
| cobble | 64 – 256 |
0.030 – 0.050 |
--- |
| boulder | > 256 |
0.040 – 0.070 |
--- |
(Note: All cross-sections in this exercise are fairly regular, straight cross-sections that were selected as sites to validate n values. Therefore you will not use the very high values for any of the categories below.)
Step B: Select an adjustment factor for irregularity using the table below.
Where the ratio of width to depth is small, roughness caused by eroded and scalloped
banks, projecting points, and exposed tree roots along the banks must be accounted for by
fairly large adjustments. (If the ratio of width to depth is large, bank irregularities
will exert less or no influence on the overall channel roughness.)
Table for n1: Degree of irregularity |
||
| smooth | 0.000 | smoothest channel attainable in 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 | dredged channels having moderate to considerable bed roughness and moderately sloughed or eroded side slopes |
| severe | 0.011 – 0.020 | badly sloughed or scalloped banks of natural streams; badly eroded or sloughed sides of canals or drainage channels; unshaped, jagged, and irregular surfaces of channels in rock |
Step C: Select a value for variation in channel cross section shape using the table below. "The value of n is not affected significantly by relatively large changes in the shape and size of cross sections if the changes are gradual… The degree of the effect of changes in the size of the channel depends primarily on the number of alternations of large and small sections, and secondarily on the magnitude of the changes. The effects of abrupt changes may extend downstream for several hundred feet. The n value for a reach below a disturbance may require adjustment, even though none of the roughness-producing factors are apparent in the study reach. A maximum increase of 0.003 will result from the usual amount of curvature in designed channels and in the reaches of natural channels used to compute discharge…"
Table for n2: Variation in channel cross-section |
||
| gradual | 0.000 | size and shape of channel cross sections change gradually |
| alternating occasionally | 0.001 – 0.005 |
large and small cross sections alternate occasionally, or the main flow occasionally shifts from side to side owing to changes in cross-section shape |
| alternating frequently | 0.010 – 0.015 | large and small cross sections alternate frequently, or the main flow frequently shifts from side to side owing to changes in cross-section shape |
Step D: Select a value for obstructions using the table below.
"Obstructions – such as logs, stumps, boulders, debris, pilings, and bridge
piers – disturb the flow pattern in the channel and increase roughness. The amount of
increase depends on the shape of the obstruction; the size of the obstruction in relation
to that of the cross section; and the number, arrangement, and spacing of
obstructions."
Table for n3: effect of obstructions |
||
| negligible | 0.000 – 0.004 | a few scattered obstructions, which include debris deposits, stumps, exposed roots, logs, piers, or isolated boulders, that occupy less than 5 percent of the cross-section area. |
| minor | 0.005 – 0.015 |
Obstructions occupy less than 15 percent of the cross-section area, and the spacing between obstructions is such that the sphere of influence around one obstruction does not extend to the sphere of influence around another obstruction. Smaller adjustments are used for smooth-surfaced objects than are used for sharp-edged objects. |
| appreciable | 0.020 – 0.030 | Obstructions occupy from 15 to 50 percent of the cross-sectional area, and the spacing between obstructions is small enough to cause the effects of several obstructions to be additive, thereby blocking an equivalent part of a cross-section. |
| severe | 0.040 – 0.050 | Obstructions occupy more than 50 percent of the cross-sectional area, or the space between obstructions is small enough to cause turbulence across most of the cross-section. |
Step E: Select a value for the influence of vegetation on the flow, using
the table below.
"The extent to which vegetation affects n depends on the depth of
flow, the percentage of the wetted perimeter covered by vegetation, the density of the
vegetation below the high water line, the degree to which the vegetation is flattened by
high water, and the alignment of vegetation relative to the flow... The adjustment values
in the table below apply to constricted channels that are narrow in width. In wide
channels having large width to depth ratios and no vegetation on the bed, the effect of
bank vegetation is small, and the maximum adjustment is about 0.005. If the channel is
relatively narrow and has steep banks covered by dense vegetation that hangs over the
channel, the maximum adjustment is about 0.03. The larger adjustment values given in the
table apply only in places where vegetation covers most of the channel."
Table for n4: Amount of vegetation |
||
| small | 0.002 – 0.010 | dense growths of flexible grass, such as Bermuda, or weeds
growing where the average depth of flow is ³ 2 times the
height of the vegetation; or supple tree seedlings such as willow, cottonwood, arrowweed, or saltcedar growing where the average depth of flow is ³ 3 times the height of vegetation. |
| medium | 0.010 – 0.025 |
turf grass growing where the average depth of flow is ³ 2 times the height of the vegetation; or moderately dense stemmy grass, weeds, or tree seedlings growing where the depth of flow is 2 to 3 times the height of vegetation; or brushy, moderately dense vegetation, similar to 1 to 2 yr old willows in the dormant season, growing along the banks, and no significant vegetation is evident along the channel bottoms where the hydraulic radius exceeds 2 ft. |
| large | 0.025 – 0.050 | turf grass growing where the average depth of flow is about
equal to the height of the vegetation; 8- to 10-yr old willow or cottonwood trees intergrown with some brush or weeds (none of the vegetation is in foliage) where the hydraulic radius exceeds 2 ft.; bushy willows about 1 yr old intergrown with some weeds along side slopes (all vegetation in full foliage), and no significant vegetation exists along he channel bottom where the hydraulic radius exceeds 2 ft. |
| very large | 0.050 – 0.100 | turf grass growing where the average depth of flow is <
half the height of the vegetation; or bushy willow trees about 1 yr old intergrown with weeds along side slopes (all vegetation in full foliage), or dense cattails growing along channel bottoms; or trees intergrown with weeds and brush (all vegetation in full foliage) |
Step F. Select a value for meandering of the channel, using the table below.
"The degree of meandering depends on the ratio of the total length of meandering
channel in the reach being considered to the straight length of the reach… The
meander adjustment should be considered only when the flow is confined to the channel.
There may be very little flow in a meandering channel when there is flood-plain
flow."
Table for m: degree of meandering |
||
| minor | 1.00 | Ratio of channel length to valley length is 1.0 to 1.2. |
| appreciable | 1.15 | Ratio of channel length to valley length is 1.2 to 1.5. |
| severe | 1.30 | Ratio of channel length to valley length is >1.5. |
Step G: Determine your estimated value of n using the equation:
n = (nb+n1+n2+n3+n4)m
Floodplain n values: These are estimated separately from channel n values. See Arcement and Schneider (1989) for details.
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last update: 03/25/00 11:05 AM
Department of Geography, University of Oregon, Eugene OR, 97403-1251