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FAQs > Manning
Formula
Q: What values of coefficient of roughness
“n” are typically used in the Manning’s
formula when designing open channels and spillways with soil-cement
(SC) or roller-compacted concrete (RCC)?
A: Several equations have been published
and proven adequate for the design of open channels but the Manning
formula has been the most favored and regarded by many as the most
convenient. The formula is applied in the following form:
V = (1.486R2/3 S 1/2)/n
Where
V = velocity of flow, fps
n = coefficient of roughness
R = hydraulic radius = flow area divided by wetted perimeter,
ft
S = surface slope
In SI units, the formula is as follows:
V = (R2/3S 1/2)/n
Where V is in m/s, R is in m, and the value of n remaining
the same.
Values for n have been published in many textbooks and
reference books for channels with natural earth surface and grassed
surface, and for channels lined with conventional portland cement
concrete, bituminous concrete, brick, etc. In addition to surface
characteristics, factors affecting the n value include
geometric shape of channel, depth of flow, flow volume, and sediment
load. For concrete channels, most reference books list n
values ranging from 0.013 for smooth concrete to 0.023 for rough,
wavy concrete. However, research for determining the n
values for SC and RCC has been very limited.
Overtopping Application
In 1988, the Federal Highway Administration issued research and
development Report No. FHWA/RD-88/182 titled “Minimizing Embankment
Damage during Overtopping Flow.” In Table 24 of the FHWA report,
the authors recommend the following ranges of n values
for soil-cement overtopping protection:
Overtopping Application |
Manning “n”
Values |
| Plated soil-cement parallel to the slope |
0.017 – 0.035 |
| Stairstepped soil-cement 3H:1V |
0.050 – 0.065 |
| Stairstepped soil-cement 2H:1V |
0.085 – 0.100 |
It should be noted that the reported n values for stairstepped
construction are significantly higher than what should be considered
for open channel flow. In the FHWA research concerning overtopping
applications, the flow is perpendicular to the SC steps whereas
in open channels the flow is parallel to the SC steps.
Open Channel Application
 There
is very little documentation regarding estimated n values
for SC or RRC for open channel applications. Generally, conventional
concrete is smoother and less wavy than SC or RCC, so the n
values for SC and RCC would be expected to be slightly higher. Therefore
it is suggested that n values for SC and RCC would be on
the order of 0.015 to 0.024, depending on the type of construction
(stairstepped or plated) and surface texture.
As mentioned earlier, several factors influence the Manning coefficient
of roughness number. It is the responsibility of the designer to
consider all factors of the design including channel width, depth
of water, design flow, sediment loads, etc. prior to selecting n
values. Until further research is done and new information becomes
available, designers may want to consider the suggested ranges of
n values listed in the table below.
Open Channel Application |
Soil-Cement or Roller-Compacted
Concrete (n-value) |
| Plated bottom and side slopes |
0.015-0.020 |
| Plated bottom and stairstepped side slopes |
0.018-0.024 |
| Soft bottom and plated or stairstepped side slopes* |
0.018 and higher |
* Wide variations of n values
are possible depending on the condition of the unlined channel bottom.
The values are also dependent on the depth of flow. Shallower flows
will result in increasing the effective n value if the
soft bottom is covered with large boulders or thick, high brush.
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