Manning's Coefficient Research Articles

Geometrical and roughness effects on compound channel resistance

This paper presents an analysis of resistance coefficients derived from measurements taken in phases A, B and C of the research programme of the UK Flood Channel Facility (FCF). The FCF is a large-scale compound channel facility and the programme has included straight and meandering planforms, smooth and mobile main channel roughnesses and smooth and rod-roughened floodplain boundaries. Floodplain roughness consisted of 25 mm surface-penetrating dowel rods. Data were also obtained for straight trapezoidal channels for comparison by confining flow to the main channels. Stage–discharge relationships were derived which enabled calculation of Manning's roughness coefficient values for a range of selected relative depths for each geometry, planform and roughness case. Graphs are presented of the variation with depth of Manning's coefficient for each geometry and roughness expressed as a ratio of smooth straight compound, or straight trapezoidal channel data. These presentations quantify the increase or decrease of roughness coefficient resulting form cross-sectional geometry, planform and boundary roughness. It is suggested that this represents a possible valid approach to the estimation of Manning's roughness coefficient in compound channels and rivers.

Integrated two-dimensional macrophytes-hydrodynamic modeling

Lake Saint-Francois is the first fluvial lake downstream of the Great Lakes. Aquatic macrophytes are abundant because of water level stabilization and increased nutrient loads. The influence of plants on flow modification is very important and must be considered in order to simulate hydrodynamic conditions. The spatial distribution of plant species is linked to their instream flow preferences. Several abiotic variables are of importance: light penetration, wave energy, current velocity, nutrients in substrate and physical characteristics of the substrate are controlling the species and their biomass. Field characterization of macrophytes was performed using echosounder transects in association with a submersible video camera. This technique allowed the calibration of each echofacies for species identification and their relative proportion, height and density. The main eleven assemblages appear to be strongly correlated with abiotic conditions. A basic interpretation key was set up in order to describe plant distribution over the entire lake. Species, relative proportion, density and plant height were interpolated between transects. This information is used to adjust the Manning's friction coefficient for each assemblage. Simulations of the flow fields with plants and in absence of plants show a contrasted pattern. During the summer (with plants), the flow is mainly concentrated in deep channels where velocities are clearly increased by approximately 20% compared to spring-fall simulation (without plants).

Transport, Mixing and Stirring Processes in a Louisiana Estuary: A Model Study

Transport and mixing processes in a broad and shallow estuary in Louisiana, Terrebonne/Timbalier Basin, are examined using a depth-integrated two-dimensional numerical model. Using current meter records previously obtained, the model calibration yielded correlation coefficients between simulated and observed current components of 0·89–0·95. It appears that the bottom friction in the bay is relatively large with a Manning's coefficient of 0·07 producing the best results. The large bottom friction appears to be due to a combined effect of currents and the surface wave field which is not explicitly accounted for in the numerical model. Despite the small tidal range, tidal forcing dominates circulation in the bay. During equatorial tides, tidal currents on the order of 20cms−1could develop in a broad area of the bay while in tidal passes currents could reach 50–60cms−1. During tropic tides, strengths of the currents in the bay could easily be double those during equatorial tides. Local wind forcing is also important in controlling general flow direction inside the bay, in particular during equatorial tides. Flushing time, estimated by a particle tracking technique, was 27 days, that appears to be in agreement with observations. Horizontal diffusivities computed using tracer particles are comparable to the previous estimates of horizontal diffusion coefficients compiled by Okubo (1974). The larger values appear to be due to coastal trapping. Mixing of water masses, based on particle tracking, is found to consist of continuous stretching, folding and break-up of material lines due to interaction of wind-driven and tidal currents with bottom and coastal topography. Time evolution of the boundary between the two water masses depends on the initial tidal phase. However, this dependence lasts only until coastal trapping becomes dominant in controlling the time evolution of the boundary. Coastal trapping appears to be an important process by which stirring and mixing processes are enhanced, thus making stirring and mixing ‘more efficient’ and ‘chaotic’. Those observations point to the need to resolve small-scale shear flow patterns, in both space and time, and detailed bottom and coastal topography in order to understand transport, stirring and mixing processes in the broad, shallow estuaries typical of the northern Gulf of Mexico.

Research on Resistance Properties of Gutter with Reductive Functions of Fluid Velocity

In order to investigate the fundamental properties of resistance of gutter with a step-like bottom boundary as an energy dissipator and, in addition to that, with spur dikes, we carried out some measurements of Manning's coefficient of artificial roughness by physical model experiments. As a result, it is found that the step-like bottom boundary is effective for dissipating energy of flow in case of low water depth. It is also found that the spur dikes attached to side walls are effective in case of high water depth flow. This fact suggests that we can control the flow in a gutter by suitable combinations of those two dissipators.

A fully conservative Beam and Warming scheme for transient open channel flows

A fully conservative Beam and Warming scheme that uses Roe's approximate Jacobian is presented for solving transient open channel flows. A general treatment for satisfying entropy inequality condition is incorporated which always leads to a physically realistic solution. Details of the Beam and Warming scheme, inclusion of the source terms and proposed modifications for achieving full conservation are presented. Improvement in accuracy achieved with the proposed treatment is demonstrated by comparing numerical results by different versions of the scheme with analytical solutions. The applicability of the scheme is examined by comparing numerical results with experimental data and numerical results from existing studies. The scheme's response (o the Courant number and Manning's coefficient is also investigated.

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.

Modélisation hydrodynamique du lac Saint-Pierre, fleuve Saint-Laurent : l'influence de la végétation aquatique

The macrophytes (aquatic plants) can have a substantial effect on the hydrodynamics of some watercourses. A mathematical formulation for the resistance effect of macrophytes on the current is inserted in a two-dimensional finite element hydrodynamic model. The method introduced herein allows to take into account the morphology, the density, and the growth curve of the different species of macrophytes present in the river. The Lake Saint-Pierre between Sorel and Trois-Rivières (Québec, Canada) in the St. Lawrence River is used to demonstrate the approach. The mathematical aspect of the model is first briefly presented. The field surveys of macrophytes and some other data sets used with the model are then analyzed. Finally, after the calibration–validation step, which insures the good behavior of the model, some results are presented to show the effect of the macrophytes on the flow structure. Key words: hydrodynamics, aquatic plants, St. Lawrence River, Lake Saint-Pierre, two-dimensional modelling, simulation, finite element method, Manning's coefficient.

Runoff Process of Rainwater in Small Mountainous Basin

The channel flow is considered as the rainfall which passes through the infiltration area, where the distribution of pores is assumed as fractal. Using these assumption and the estimation of the characteristics of slope distribution, the method of the lumping of a hillside and the value of fractal number δ of the pores of the infiltration area in a hillside (δ=1.8) are obtained. It is also found that in mountainous basins where the areas are less than 0.2km2 the delay of runoff is nearly 20 minutes and that the Manning's coefficient n is nearly 0.05 (m-1/3·s).

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.

Stream-floodwave propagation through the Great Bend alluvial aquifer, Kansas: Field measurements and numerical simulations

The hypothesis is explored that groundwater-level rises in the Great Bend Prairie aquifer of Kansas are caused not only by water percolating downward through the soil but also by pressure pulses from stream flooding that propagate in a translatory motion through numerous high hydraulic diffusivity buried channels crossing the Great Bend Prairie aquifer in an approximately west to east direction. To validate this hypothesis, two transects of wells in a north-south and east-west orientation crossing and alongside some paleochannels in the area were instrumented with water-level-recording devices; streamflow data from all area streams were obtained from available stream-gaging stations. A theoretical approach was also developed to conceptualize numerically the stream-aquifer processes. The field data and numerical simulations provided support for the hypothesis. Thus, observation wells located along the shoulders or in between the inferred paleochannels show little or no fluctuations and no correlations with streamflow, whereas wells located along paleochannels show high water-level fluctuations and good correlation with the streamflows of the stream connected to the observation site by means of the paleochannels. The stream-aquifer numerical simulation results demonstrate that the larger the hydraulic diffusivity of the aquifer, the larger the extent of pressure pulse propagation and the faster the propagation speed. The conceptual simulation results indicate that long-distance propagation of stream floodwaves (of the order of tens of kilometers) through the Great Bend aquifer is indeed feasible with plausible stream and aquifer parameters. The sensitivity analysis results indicate that the extent and speed of pulse propagation is more sensitive to variations of stream roughness (Manning's coefficient) and stream channel slope than to any aquifer parameter.

On the Formation of Hydrograph and Its Characteristics of Flood wave

The objective of the present study is to clarify the processes of the formation of hydrograph and its characteristics in actual basins. From the field observation and numerical analysis, the followings are concluded.(1) The linearity between the discharge in a river and the catchment area is assured in the basin with the catchment area less than 4000km2.(2) The effects of Manning's coefficient for the deformation of hydrograph is smaller than the magnitude of the discharge from large tributaries and its timing.

Flow resistance in compound channels

Preliminary results from the Flood Channel Facility sponsored by the British Science and Engineering Research Council and Hydraulics Research Ltd. are presented. The Facility takes the form of a large compound channel and the first series of experiments have been analysed to assess flow resistance characteristics of simple and compound channels having smooth boundaries. The effects of momentum transfer from main channel to flood plains on the capacity of the compound and main channel sections have been demonstrated. Flow resistance relationships for the compound section, main channel and flood plains have been presented in terms of Manning's and Darcy-Weisbach resistance coefficients, and compared with simple channel shapes. This has emphasised the complexity of compound channel flow resistance, while also pointing out the likely errors involved in applying simple channel methods of analysis and design to rivers and channels of compound geometry.

Uncertainty in Dam Break Flow Simulation

The flow caused by a dam breaking across its entire length can be approximated by a one-dimensional, unsteady flow model in form of the St. Venant equations. In this model, the flow is governed by the river geometry and the river roughness, which is quantified by Manning's coefficient. The roughness characteristics are generally difficult to estimate under natural conditions. Thus, the estimates of the Manning's coefficient will in general be subject to uncertainty. In this paper, the uncertainty in the discharge and depth hydrographs due to the uncertainty in estimating the roughness characteristics of a river, is investigated. A specific case of the Noppikoski dam in Sweden that failed in 1985 is used to illustrate the sensitivity of the flow simulation on the roughness coefficient. The analysis shows that the uncertainty in the dam break flow simulation due to the uncertainty in estimating Manning's coefficient, is significant. The uncertainty is larger at greater distances from the dam, and is greater for the discharge hydrograph than for the depth hydrograph.

RESISTANCE TO FLOW OVER RIPRAP IN STEEP CHANNELS1

ABSTRACT: A series of flume tests were conducted to determine the flow resistance of angular shaped riprap in steep channels. Flow resistance was expressed in terms of the Darcy‐Weisbach friction factor and the Manning's roughness coefficient. Prototype channels of 4 ft. (1.2 m) and 12 ft. (3.7 m) in width were constructed at slopes ranging from 0.01 to 0.20. The channel beds were comprised of angular riprap of median diameters of 1, 2, 4, 5, and 6 inches (2.59, 5.59, 10.41, 12.95, and 15.75 cms). The Darcy‐Weisbach and Manning's coefficients were determined for each test condition prior to bed failure.The resulting Darcy‐Weisbach coefficients were related to the channel energy gradient and the bed relative submergence for highly turbulent flow. Also, Manning's roughness coefficients were related to the product of the median stone diameter and energy gradient. Because of the angular shape of the riprap and the wedging and/or packing of the bed materials, the resistance to flow was found to exceed the flow resistance values predicted by previous studies. Expressions were presented for estimating the resistance to flow for angular riprap in steep channels.

Closure to “Manning's Coefficient for Smooth Pipes”

Closure to “Manning's Coefficient for Smooth Pipes”

Discussion of “Manning's Coefficient for Smooth Pipes”

Discussion of “Manning's Coefficient for Smooth Pipes”

Resistance Relationships for Alluvial Channel Flow

The problem of resistance to flow over alluvial beds has received considerable attention during the post-war years. Almost all the problems associated with alluvial channels—e.g., preparation of stage-discharge curves, determination of sediment transport rates, design of stable channels, prediction of aggradation and degradation due to the presence of hydraulic structures—require an accurate resistance law for their solution. The resistance of channels with a rigid bed has been defined accurately by relationships given by Keulegan and Manning. But the extensive data collected an alluvial channels in recent years have indicated large variations in the values of n, Manning's coefficient, and K S , the equivalent sand-grain roughness of the bed, for a particular channel under different flow conditions; also, the variation of these parameters with the flow conditions has not yet been satisfactorily predicted.

Tolkmitt's Backwater and Dropdown Curve Tables

Tables and formulas, published originally by G.TOLKMITT, are presented in slightly enlarged form, for computation of backwater and dropdown curves for channels of parabolic section; use of Manning's coefficient of roughness and velocity formula in cases when considerable variations in depth and water volumes have to be considered.