Manning Resistance Coefficient Research Articles

Manning's roughness coefficient in a truncated triangular open-channel flow section

Abstract In uniform flows, Manning's roughness coefficient n plays an important role in the calculation of the normal depth in the open channels. When calculating uniform flows in open conduits and channels, Manning's coefficient is arbitrarily chosen. This arbitrary choice is not physically justified because the coefficient n must be determined according to the parameters that influence the flow, particularly the normal depth sought. In this paper, a new method is presented to compute Manning's coefficient in a truncated triangular channel section. In the first step, the study proposes to establish the general relationship that allows computing Manning's coefficient in this type of channel. The relationship is presented in dimensionless terms, giving it a character of general validity, including the dimensionless Manning's resistance coefficient, denoted as N. The latter is shown to depend on the aspect ratio of the wetted area, the side slope of the channel, the relative roughness and the modified Reynolds number, which is physically justified since flow resistance is closely related to flow depth. In the second step, the rough model method is proposed to express Manning's coefficient when the horizontal dimension of the channel is not a given data of the problem.

Near surface roughness estimation: A parameterization derived from artificial rainfall experiments and two-dimensional hydrodynamic modelling for multiple vegetation coverages

Roughness is the key parameter for surface runoff simulations. This study aims to determine robust Manning resistance coefficients (n) on the basis of consecutive artificial rainfall experiments on natural hillslopes available in literature, obtained at 22 different sites with different degrees of vegetation cover and type. The Manning resistance coefficient is particularly important in the context of two-dimensional (2D) hydraulic heavy rainfall simulations. Since there is a wide range of possible resistance values available leading to significantly different results regarding the accumulation of surface runoff, especially for shallow water depths. The planning of flood protection structures is directly affected by these uncertainties. This work also improves the knowledge between roughness and the shape of the hydrograph allowing a better calibration of infiltration models. As flow velocity, water depth, and infiltration rate were not observed during the rainfall experiments, only the outflow of the test field and rain intensity are known. For this purpose, a framework was developed to parameterize shallow water depth (<1 cm) -dependent roughness coefficients. To test the robustness of the framework, three different formulations of depth-dependent roughness and a constant Manning coefficient are used by comparing the measured discharge under different rainfall intensities with simulations in a 2D-hydraulic model. We identified a strong dependency of Manning’s n on the degree of vegetation cover and -type as well as an influence of consecutive rainfall events. This finally leads to a more robust parameterization of near surface roughness for hydrodynamic modelling, which is particularly important for the simulation of heavy rainfall events.

Applicability of Flow Resistance Formulae for Sand-Bed Channels: An Assessment Using a Very Large Data Set

Among numerous flow resistance formulae for sand-bed channels, this study selected five for evaluation and in order to cover flow conditions in sand-bed river channels as widely as possible, a total of 1,636 sets of field measures were collected from the hydrological stations of two large river systems of China—the Yellow and Yangtze Rivers, in addition to the data compiled by Brownlie. The performance of the selected formulae in yielding the values of Manning resistance coefficient n was evaluated against the total of 6,805 datasets. In many cases, the formula of Ma et al. yielded unreasonable n values of &amp;lt;0, while that of Deng et al. and formulae 1 and 2 of Zhang et al. yielded n values with large errors. The formula of Wu and Wang yielded n values varying within the scope only in the case of n &amp;lt; 0.04. By dividing the absolute relative errors (AREs) from the selected formulae into six groups of 0–0.05, 0.05–1, 0.1–0.2, 0.2–0.5, 0.5–1, and &amp;gt;1, it can be found that, for all five selected formulae, ARE occurred in the group 0.2–0.5 occupied the largest percentage, while in each of the adjacent groups of 0.5–1 and 0.1–0.2 it also occupied a very large percentage. Hence, all five formulae still need to improve their predicting ability.

Experimental study of depth-limited open-channel flows over a gravel bed

Laboratory experiments of depth-limited open-channel flows over a gravel bed were conducted in the study. Two gravel patches with identical individual element size and different lengths (3.81m and 7.5m) were tested. The depth-limited uniform flow regime with relative submergence Sr (=D/ks) ranging from 2.68 to 5.94 was produced by adjusting the tailgate weir. The velocity profiles were measured by using both an ultra-sound velocity profiler (UVP) and an acoustic Doppler velocimeter (ADV). The conventional methods used to determine the zero-plane displacement and estimate the bed shear velocity were then reviewed and compared. The measured double-averaged (DA) velocity profiles were found to fit well with the log law and defect law with a non-universal Karman constant κ. κ-value remains nearly constant and in the range from 0.2 to 0.3 for the long patch (LP) cases and κ-values are scattered within a wider range from 0.3 to 0.5 for the short patch (SP) cases. While the Br-value in log law remains constant and equal to 8.5 for LP cases, the Br-value was found to decrease with the increase of the dimensionless roughness height ks+ for SP cases. The streamwise turbulence intensity distributions were found to be independent on the patch length and agree well with the available experimental data in the intermediate region and wall region. The Manning resistance coefficient and Darcy–Weisbach friction factor were analyzed. The κ-value decreases to 0.22 for the fitting of the logarithmic flow resistance law under small relative submergence. The value of the integration constant Ar in the logarithmic law falls within the normal range between 3.25 and 6.25.

Evaluation of a Simple Hydraulic Resistance Model Using Flow Measurements Collected in Vegetated Waterways

A simple idealized model to describe the hydraulic resistance caused by vegetation is compared to results from flow experiments conducted in natural waterways. Two field case studies are considered: fixed-point flow measurements in a Green River (case 1) and vessel-borne flow measurements along a cross-section with floodplains in the river Rhine (case 2). Analysis of the two cases shows that the simple flow model is consistent with measured flow velocities and the present vegetation characteristics, and may be used to predict a realistic Manning resistance coefficient. From flow measurements in the river floodplain (case 2) an estimate was made of the equivalent height of the drag dominated vegetation layer, as based on measured flow characteristics. The resulting height corresponds well with the observed height of vegetation in the floodplain. The expected depth-dependency of the associated Manning resistance coefficient for could not be detected due to lack of data for relatively shallow flows. Furthermore, it was shown that topographical variations in the floodplain may have an important impact on the flow field, which should not be mistaken as roughness effects.

Hydraulic resistance to overland flow on surfaces with partially submerged vegetation

This study investigates numerically the characteristics of upscaling the Manning resistance coefficient (nt) for areas covered by partially submerged vegetation elements, such as shrub or tree stems. A number of high‐resolution hydrodynamic simulations were carried out corresponding to scenarios with different domain slopes (S), inflow rates (Q), bed roughness (nb), and vegetation cover fractions (Vf). Using simulations performed at fine space‐time scales, two methods were developed for computing the upscaled Manning coefficient, termed “Equivalent Roughness Surface (ERS)” and “Equivalent Friction Slope (EFS).” Results obtained with these two methods indicate that both yield highly correlated estimates of nt. The effects of four independent variables (Vf, S, Q, and nb) on nt were further investigated. First, as Vf increases, nt also grows. Second, two distinct modes of the relationship between S and nt for a fixed Vf and Q emerge: a positive dependence at low‐flow rates and a negative dependence at high‐flow rates. For a fixed Vf and S, two distinct modes of the relationship between Q and nt are also identified: a positive dependence at mild domain slopes and a negative dependence at steep slopes. A regression analysis shows that the two conflicting trends can occur depending on whether the variability of flow depth with respect to S (or Q) is greater than the ratio of h and S (or Q). Third, a rougher soil bed (i.e., larger values of nb) implies a higher resistance due to vegetation. Last, the study argues that nt increases as h increases and decreases as V increases. A generic regression relation that includes all four of the above variables and the difference nt − nb (i.e., the additional resistance due to partially submerged vegetation representing the sum of the form and wave resistances) was developed. The range of applicability of this relation is given by the following conditions: Vf ≤ 0.5, 0.1 ≤ S ≤ 1.1, and 0.0001 ≤ Q ≤ 0.01. The difference nt − nb computed from the developed regression relation was compared with estimates reported by five different studies. Furthermore, the simulated wave resistance coefficients were compared with those predicted from an equation in a previous study; the estimates were consistent in the range of experimental conditions for which the latter equation was developed. The relationship is sufficiently general and applicable to other flow conditions with partially submerged roughness elements.

Influence of Flow Width on Mean Velocity of Debris Flows in Wide Open Channel

Debris flow in a wide open downstream channel has a significant transverse velocity component that strongly influences its mean longitudinal velocity. Investigation of observation data of debris-flow surges at Jiangjia Ravine in China shows the dependency of Manning resistance of debris flows on the ratio of flow width to depth. Regression fit reveals a power function relationship between the Manning resistance coefficient and the width-to-depth ratio. This derives a new formula of mean velocity incorporating the influence of flow width. The result indicates that the width-to-depth ratio can be viewed as a kind of shape roughness analogous to grain roughness in the Darcy-Weisbach resistance coefficient expression.

Numerical study of the behavior of the vegetated channel flow

An effect of vegetation is as the additional resistance to the riverbed.A formula of equivalent Manning resistance coefficient for the open channel flow with vegetation was deduced in consideration of the secondary flow on the resistance of the vegetated area by an influence coefficient.The modified Manning formula was introduced to the water depth-averaged model to solve the non-symmetrical compound channel flow and rectangular channel flow.The computed velocities were in good agreement with the experiment data,indicating that the numerical model is valid for estimating the velocity distribution of the partially vegetated open channel.The results are useful for the cognition of the vegetation flow structure.

Physically based simulation of dam breach development for Tangjiashan Quake Dam, China

Physically based modeling approach has been widely developed in recent years for simulation of dam failure process resulting from overtopping flow. Due to the lack of field data, there exist few applications to natural quake dams with complex erosion mechanisms. This paper presents a physically based simulation of the failure process of the Tangjiashan Quake Dam formed as a result of the “May 12, 2008” Wenchuan earthquake in China. The one-dimensional model adopted features as cost saving but enables capturing the main characteristics of the failure process, where selective sediment transport and gravitational slope collapse are accounted for. The simulated flow hydrograph and breach progression process are generally in good agreement with the observed data. Unsteadiness and non-uniformity are found to be substantial characteristics of breach progression during the failure process of natural quake dams. Sensitivity analysis showed that the Manning resistance coefficient and the erodibility coefficient in Osman and Thorne’s (J Hydraul Eng 114(2):134–150, 1988) model significantly influences the flow peak discharge but has less influence on its occurrence time, while the velocity lag coefficient associated with bed-load transport may affect the two breaching parameters substantially.

Conveyance estimation for channels with emergent vegetation boundaries

Emergent vegetation strips occur commonly in rivers, especially along the banks, and have a significant influence on channel conveyance. A simple approach is presented for estimating the conveyance in such rivers, and the method is tested against laboratory and field data. Field data are also used to determine a realistic value of the resistance coefficient for marginal vegetation boundaries. Laboratory experiments have shown that the resistance of vegetation strips depends on the number of vegetation/ clear channel interfaces, and that the overall Manning resistance coefficient n varies strongly with flow depth. For practical purposes, conveyance can be estimated by summing the discharges in vegetated and clear channel zones, calculated separately but with allowance made for the interzonal interaction. The clear channel discharge usually makes the major contribution and can be reliably determined by application of familiar composite roughness formulae, accounting for different bed and side boundary resistance. Field data indicate a Manning's n of about 0·13 for a typical emergent vegetation side boundary. The vegetated zone discharge is invariably underestimated by using a basic vegetation resistance equation without accounting for interzonal interaction effects, especially for narrow strips, but its contribution to the total channel discharge is usually relatively small.

Evolution and hydraulic resistance of anchor ice on gravel bed

This paper presents a laboratory study on anchor ice evolution and its hydraulic effect in channels with a gravel bed. The study revealed that anchor ice is initiated by frazil ice accumulation on bed gravel from half a gravel diameter below the crown level of the gravel. No in-situ ice growth within the frazil accumulation or downward growth towards the bed was observed. During the initial stage of growth anchor ice grew in the forms of tails, scales, or balls, depending on the flow velocity and Froude number. During the final stage of growth, when the gravel bed was covered by ice, the growth rate increased with the heat loss rate and Froude number, and inversely proportional to the flow depth. The overall hydraulic resistance of anchor ice was smaller for smaller bed gravel sizes and decreases with the increase in flow rate and flow depth. The rate of increase of the gross Manning's resistance coefficient decreases with the increase in Reynolds number. The bed/ice surface roughness first increases with anchor ice growth, then decreases to a minimum value after the initial stage of growth, when anchor ice grew out of the gravel bed.

Theoretical assessment of changes in design flood peak of an overland plane for two opposing urbanization sequences

By considering urbanization on an overland plane as a process whereby a relatively rough, permeable surface is gradually replaced by a relatively smooth, less permeable surface, the effect of urbanization sequence on the flood peak is theoretically assessed by the kinematic wave method. In the assessment, two opposing urbanization sequences are considered: one from downstream to upstream, and the other from upstream to downstream. The assessment is carried out in terms of the individual effect as well as the combined effect of the Manning resistance coefficient and the runoff coefficient. For both urbanization sequences and for all degrees of urbanization, the assessment shows that surface conversion from rough to smooth, or from permeable to less permeable causes the flood peak to increase. A comparison of the individual effects shows that for equal reductions in surface roughness and permeability, the reduction in permeability causes greater increases in the flood peak compared with the reduction in surface roughness. For a partially urbanized plane and for the same degree of urbanization, due to the partial area effect, urbanization at the downstream end generally causes greater increases in the flood peak. In terms of urbanization sequence, the downstream to upstream urbanization sequence generally causes greater increases in the flood peak. The effect of urbanization sequence on the flood peak, however, is only significant for the larger reductions in surface roughness and permeability. Finally, a comparison of the results of this study with those obtained from drainage basins shows that for most of the results from the basins, they correspond to those for the small reductions in surface roughness and permeability on an overland plane. For these cases, the effect of urbanization sequence on the flood peak is small. Copyright © 1999 John Wiley & Sons, Ltd.

Assessment of changes in overland time of concentration for two opposing urbanization sequences

By considering the urbanization process on an overland plane whereby a relatively rough permeable surface is replaced by a relatively smooth impermeable surface, the effect of urbanization on the time of concentration is assessed. In the assessment, two opposing urbanization sequences are considered: one from downstream to upstream, and the other from upstream to downstream. The assessment is carried out in terms of the individual effect as well as the combined effect of the Manning resistance coefficient and the runoff coefficient. For both urbanization sequences and for all degrees of urbanization, the assessment shows that surface conversion from rough to smooth or from permeable to impermeable causes the time of concentration to be shorter. Urbanization at the upstream end causes the greatest decrease in the time of concentration, and the reduction in surface roughness causes a greater decrease in time of concentration as compared to the reduction in permeability. Depending on the pre- and post-urbanization land surface conditions, the assessment shows that the time of concentration could decrease to 4–39% of its original value. Moreover, the time of concentration for a plane with urbanization from downstream to upstream could be more than four times longer than that for a plane with urbanization from upstream to downstream. Finally, there is a remarkable resemblance between the results of this study with those obtained from drainage basins in earlier studies, and it appears that the results from earlier studies are only applicable for the upstream to downstream urbanization sequence.

Time of Concentration and Peak Discharge Formulas for Planes in Series

Based on the kinematic-wave equations, a time of concentration formula for overland flow over a series of planes is derived. The formula is applicable to a cascade of planes, to planes of different roughnesses, to planes of different flow regimes, to planes of different soil types and infiltration rates resulting in different net intensities, to planes subject to different rainfall intensities, and to planes with a combination of all these variables. For practical applications, the formula is developed in terms of the Manning resistance coefficient that is applicable to turbulent or near turbulent flow only. For the series of planes subject to uniform rainfall excess, under the full-area contribution, the corresponding peak discharge formula in terms of the Manning resistance coefficient is derived. This formula can also be used to estimate the peak discharge under the partial-area contribution. The derived formulas are all consistent with the published formulas for a single plane.

Influence of upstream inflow on wave celerity and time to equilibrium on an overland plane

Abstract Based on the kinematic wave equations, formulae for the wave celerity along an overland plane subject to uniform rainfall excess and with a constant upstream inflow together with the corresponding average wave celerity and time to equilibrium for the entire plane are derived. The formulae are further developed in terms of both the Darcy-Weisbach resistance coefficient and the Manning resistance coefficient. By comparing the wave celerities, the average wave celerities and the time to equilibrium for planes with and without upstream inflow show that the upstream inflow causes the wave celerity and the average wave celerity to be faster and the times to equilibrium to be shorter. The effect of upstream inflow is greater with increasing inflow, but the marginal effect decreases with increasing inflow. The effect is greatest for laminar flow and least for turbulent flow. For the wave celerity, the effect is also greatest at the upstream end of the plane and least at the downstream end of the plane.

TECHNICAL NOTE Time of concentration formulae for planes with upstream inflow

Due to changes in physical characteristics, the valley side of a drainage basin may be represented by a series of overland planes. In such a situation, the downstream outflow from one plane becomes the upstream inflow for the subsequent plane. Based on the kinematic wave equations, two time of concentration (time to equilibrium) formulae are derived for planes subject to uniform rainfall excess and with a constant upstream inflow. For practical applications, the formulae are further developed in terms of the Manning resistance coefficient. The derived formulae are all consistent with those published for the case of zero upstream inflow.

Hydraulic study of a two‐stage river channel

AbstractMany regulated rivers have compound or two‐stage cross‐sections consisting of a deep main channel flanked by one or two floodplains. Existing methods of assessing discharge capacity in such channels can lead to serious errors, and hence there is a need for the acquisition of flow data to validate models suggested as improvements to existing methods. Stage and discharge data, under both steady and unsteady conditions, were collected from a reach of the River Main in Northern Ireland, which has been reconstructed for flood defence purposes to form a two‐stage channel. The data were analysed using a steady flow computational model to yield water surface profiles and values of Manning's resistance coefficient at various flow depths. The complex nature of flow resistance in two‐stage channels is demonstrated. Unsteady stage hydrographs were linked to a computational model which illustrates the magnitude of errors incurred in applying conventional methods of discharge estimation in compound rivers.

Random differential equation modelling for backwater profile computation

Two probabilistic models for backwater profile computation are developed by using the theory of random differential equations. The models can simultaneously consider uncertainties in boundary condition and hydraulic parameters, such as the Manning's resistance coefficient, channel slope, discharge rate, within the equation describing the one-dimensional steady state nonuniform flow. The probability density functions of the water profile are obtained by numerically solving Liouville and Fokker-Planck equations. The results indicate that the method of random differential equations is useful for uncertainty analysis of the water surface profile computations.

Estimation of depression storage and Manning's resistance coefficient from random roughness measurements

Depression storage and values of Manning's n resistance coefficient of tilled soil surfaces were estimated from micro-topographic data measured on micro-catchments subjected to simulated rainfall. Manning's n values were calculated from a simplified momentum equation applied to overland flow combined with the depth discharge relationship. Random roughness was calculated as the standard deviation of micro-relief heights measured with a relief meter. Depression storage was measured for different surface roughness inclined at different slopes. Micro-relief height measurements were taken before and after individual rainfall applications in order to monitor changes in random roughness with cumulative rainfall. Regressing random roughness against rainfall showed that random roughness decreases exponentially with increase in water application. A regression equation which relates depression storage to slope steepness and random roughness was developed. Another regression equation was developed to predict Manning's resistance coefficient from random roughness. This approach of relating Manning's resistance coefficient to dynamic surface parameters can be applied to whole seasons as well as individual rainfall events. These relationships can potentially be incorporated into simulation models of soil water balance, overland flow and erosion on tilled soils.

Field‐Measured Hydraulic Resistance Characteristics in Vegetation‐Infested Canals

Realistic estimates of hydraulic resistance are essential to the proper design and analysis of irrigation canal networks. Extensive field studies in Egypt provide data on the magnitude and variability of hydraulic resistance in earthen irrigation canals infested with aquatic weeds. Values of Manning resistance coefficient, n, were calculated from 280 measurements at selected cross sections in 23 stable canals with emergent ditch‐bank vegetation. The temporal sample mean of monthly values of n estimated within a year ranged from 0.017–0.062 for cross sections where five or more measurements were made. The temporal sample coefficient of variation ranged from 0.03–0.42. Dependence of n on flow regime (hydraulic depth and product of average velocity and hydraulic radius) was explored. Studies also were conducted on nine canals containing submerged vegetation. These studies included 312 sonar measurements of vegetation density as well as 156 measurements to estimate n at selected cross sections. Regression ana...