Journal of Water Resource and Protection, 2012, 4, 838-841 Published Online October 2012 (
Relative Depth Effects on Corrugated Culvert Roughness
Jonathan Scott Toews, Shawn Paul Clark*
Civil Engineering, University of Manitoba, Winnipeg, Canada
Email: *
Received August 20, 2012; revised September 18, 2012; accepted October 20, 2012
Fish passage is important to the overall health of an ecosystem. Therefore, it is important to be able to accurately predict
flow conditions within a stream crossing for high and low flow periods. This paper evaluates the effect of relative water
depth on the hydraulic roughness of culverts at low discharge. A 21 m long, 0.8 m diameter corrugated steel pipe with
0.068 × 0.013 m annular corrugations was used. For relative depths below 0.5, Manning’s n was found to increase with
decreasing relative depth. An equation was developed to predict relative depths below 0.5 within a corrugated steel pipe
based on the corrugation height, slope and culvert diameter. While Manning’s equation does perform reasonably well,
the percent difference from the measured to predicted water levels warrants the use of an additional prediction method
at low flows.
Keywords: Culverts; Fish Passage; Low Flows; Roughness; Manning’s Equation
1. Introduction
The process of fish migration and movement within riv-
ers and streams is important for the health of the local
ecosystem. When fish have the opportunity to move
freely in any habitat they desire, they will generally
flourish. The construction of culverts may become a bar-
rier to fish, which may have a harmful effect on fish pas-
sage. High water velocities commonly present a barrier
to fish passage, typically corresponding to peak flows
from spring run-off. At low flows, however, shallow wa-
ter depths within a culvert may become a barrier to fish
passage, thus requiring a minimum depth within a culvert
[1]. During the spawning period it is recommended by
the Manitoba Stream Crossing Guidelines that the depth
should not exceed half the diameter of the pipe [2]. This
leads to the motivation of this paper, which looks into the
effect of small relative depths (h/D 0.5) on the Man-
ning’s n value within a culvert.
2. Literature Review
The majority of previous work on partially full circular
culverts did not involve evaluation of the effect of rela-
tive depth on Manning’s n. Straub and Morris [3] com-
pleted tests on corrugated metal pipe (CMP) culverts
with three diameters of 0.46, 0.61, and 0.91 m. The cor-
rugation size used for these tests was 0.068 × 0.013 m,
with a slope of 0.20% and a length of 65.8 m. A total of
36 tests were conducted for all three diameters with rela-
tive depths ranging between 0.30 and 0.90. Sterling [4]
completed tests in smooth open channels of circular
cross-section to determine the characteristics of fully
developed turbulent flow. The pipe had a diameter of
0.24 m in a 22 m long tilting flume. Relative depths for
their tests ranged from 0.10 to 0.89. Results showed that
Manning’s n tended to increase with decreasing relative
depth. Ead et al. [5] completed tests on a 0.622 m di-
ameter CMP culvert with 0.068 × 0.013 m corrugations
at slopes of 0.55%, 1.14% and 2.55%. Relative depths
ranged between 0.15 and 0.55.
Kansas Department of Transportation [6] completed
research on helical CMP culverts with 0.068 × 0.013 m
corrugations for three diameters of 0.46, 0.38 and 0.30 m.
These culverts were each tested at a single slope which
was 0.39%, 0.85% and 0.68% respectively for each di-
ameter. The range of relative depths observed within this
study was 0.29 to 0.90. From this data it is also noted that
Manning’s n increases as the depth decreases within a
CMP culvert. Abbs et al. [7] completed work on a 0.5 m
diameter CMP culvert with 0.068 × 0.013 mm corruga-
tions set on a 0.72% slope. For the purpose of the current
paper, results of only two tests have been used.
Mangin [8] compiled numerous data sets to develop an
equation that could predict the water depth within a cir-
cular channel for open channel flow without the need to
predict Manning’s n. Dimensional analysis was per-
formed to determine the most appropriate variables to
predict the relative depth, resulting in Equation (1):
*Corresponding author.
opyright © 2012 SciRes. JWARP
J. S. TOEWS, S. P. CLARK 839
gD K
where h is the water depth, D is the culvert diameter, Q is
the discharge, g is gravity, S is the slope, and Ks is the
roughness height. However, this equation was developed
for h/D > 0.2.
3. Experimental Apparatus and Procedures
The apparatus used at the University of Manitoba’s Hy-
draulics Research & Testing Facility (HRTF) consisted
of a 21 m long, 0.8 m diameter CMP culvert with 0.068 ×
0.013 m annular corrugations. The culvert was supported
on a series of adjustable yokes to allow slope adjustment.
A headwater box along with flow straighteners were used
to provide sufficient length for the flow to develop in the
streamwise direction. A tailwater box with a flap gate
was used to control the tailwater level within the model.
Uniform depth was forced throughout the length of the
culvert to ensure that normal depth was observed. The
water surface profiles were measured using a series of
manometer tubes along the length of the culvert. The
water depth was recorded from the manometers as well
as a point gauge with a vernier scale to ensure accurate
measurement of the flow depth. The flow rate was meas-
aured using a MSR Magnum Standard Magmeter and a
custom designed LabVIEW interface at discharges grea-
ter than 20 L/s, while the low flow rates were measured
using a calibrated triangular sharp-crested weir. The pro-
cedure consisted of setting the desired discharge within
the culvert followed by carefully adjusting the tailgate
setting to achieve uniform depth. The discharge and wa-
ter depth were then measured. Measured relative depths
ranged from 0.03 to 0.67 h/D for each slope tested (0.04,
0.14, 0.27, 0.49 and 0.75%).
4. Results and Analysis
The corrugation type, corrugation size, discharge, depth,
diameter and culvert slope were extracted from the [3],
[5], and [7] to compliment the data collected at the HRTF.
This data was then used to calculate the Manning’s n
value for the culvert at that depth and discharge. It was
found that there was a significant increase in Manning’s
n as the depth within the culvert decreased, which can be
seen in Figure 1, where nf is used to denote Manning’s n
for full pipe flow as determined by the Corrugated Steel
Pipe Institute [9].
Figure 1 shows that the largest variation in Manning’s
n occurs at relative depths below 0.5. Therefore a set of
equations were developed, using a least squares regres-
sion for the variation in Manning’s n, which is shown
below as
0.878for 0.5
for 0.5
nhD hD
By dividing the equation into two portions a slightly
better fit was achieved than simply applying a power
regression to the entire relationship, improving the R2
from 0.58 to 0.62. The proportionality plot in Figure 2
shows that Manning’s Equation using a constant value
for n gives good results over the entire range. However,
using a varying Manning’s n slightly increases the corre-
lation between the observed and predicted relative depths
(Figure 3). This is better represented by Figure 4, which
shows the percent difference between the predicted and
observed data. There is significant improvement for rela-
tive depths below 0.2. Figure 5 shows the predicted re-
sults using the equation developed by Manning, 2010.
As seen it does not do a good job of predicting the
flow depth below a relative depth of a 0.2. This led to the
development of a new equation, using the same dimen-
sionless parameters that were developed by Manning [8]
using dimensional analysis. The dimensionless parame-
QgDters S and were then plotted against the rela-
tive depth to determine the exponential relationship be-
tween them. The exponential relationship for Ks/D could
not be determined in a similar fashion since the tests
were not conducted at the same slopes between each re-
port. Therefore the exponential relationship for Ks/D
Figure 1. Normalized Manning’s n versus relative depth for data collected at the HRTF.
Copyright © 2012 SciRes. JWARP
Figure 2. Proportionality plot of predicted vs observed h/D
using a constant Manning’s n.
Figure 3. Proportionality plot of predicted vs observed h/D
using a varying Manning’s n.
Figure 4. Comparison of predicted and measured relative depth for Ma nning’s Equation using a constant and varying n.
Figure 5. Proportionality plot for Manning’s Equation.
and trend multiplier were then optimized to minimize the
total error between predicted and observed relative
depths. The final form of the equation is
0.247 s
 (3)
As seen in Figures 6 and 7, this equation accurately
predicts relative depths below 0.5. However the model
error tends to increase as the relative depth increases past
this threshold. This was determined not to be an issue
Figure 6. Proportionality plot for Equation (3).
since Manning’s Equation is accurate in this region.
5. Conclusions
Results indicate that Manning’s Equation using a
constant n value does a reasonable job of predicting the
uniform depth within CMP culverts over a wide range of
water depths despite the fact that the roughness
coefficient has been shown to increase with decreasing
h/D. At very low water depths (h/D < 0.15) Equation (3)
performs better than Manning’s Equation, and may be a
Copyright © 2012 SciRes. JWARP
J. S. TOEWS, S. P. CLARK 841
Figure 7. Comparison of predicted and measured relative depth for Manning’s Equation and Equation (3).
more accurate means of estimating minimum flow depths
for fish passage at low discharge. At these very shallow
flows the resistance from the corrugations seem to act as
form drag, rather than merely a uniform skin friction.
The difficulty with Equation (3) is that its accuracy has
not been verified over a significant range of corrugation
heights and culvert diameters. The advantage of using
this equation is that a varying roughness coefficient does
not need to be developed. It also has been shown to be
accurate up to the mid-depth of the culvert, which corres-
ponds to the upper depth limit in the Manitoba Stream
Crossing Guidelines for culverts. Some recommended
future works include testing other corrugation sizes at
similar slopes to determine the variation of Manning’s n
for different CMP culvert types. This would also allow
for a better determination of the relative depths reliance
on the relative roughness.
6. Acknowledgements
The authors wish to thank the NSERC, Manitoba Hydro,
Manitoba Infrastructure and Transportation, and the Cor-
rugated Steel Pipe Institute of Canada for their support.
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US Department of Transportation Federal Highway Ad-
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[3] L. G. Straub and H. M. Morris, “Hydraulic Tests on Cor-
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Copyright © 2012 SciRes. JWARP