Spatial and Temporal Variation of Manning’s Roughness Coefficient in Furrow Irrigation

Manning’s roughness coefficient is one of the input parameters in many surface irrigation simulation models. It affects the velocity of flow and thereby its variation with time and distance along the field length influence water application. In this study, variation of Manning’s roughness coefficient was studied for a furrow plot consisting of three 40 m long free drained furrows of parabolic shape and having a top width of 0.30 m, a depth of 0.15 m and a slope of 0.5%. The irrigation experiments were carried out with the inflow rates of 0.2, 0.3, 0.4, and 0.5?L?s1; and 0.3, 0.4, 0.5, 0.6, and 0.7?L?s?1 under bare; and cropped field conditions, respectively. Furrow cross-section data were collected before each irrigation event at 0.5, 13, 26 and 39.5 m from the head end along the center furrow using a profilometer. During the irrigation event, water depth and velocity of flow were measured at these locations at an interval of 15 min using point gauge and color dye, respectively. The furrow cross-section data were fitted into a second-degree polynomial equation to determine the furrow shape parameters that were used along with the flow depth data for determining the wetted area and wetted perimeter. The wetted area, wetted perimeter, and the velocity data were used to estimate Manning’s roughness coefficient spatially and temporally. It is found that for both bare and cropped field conditions, Manning’s roughness coefficient was more at second and last quarter of the furrow due to soil erosion at these locations. Manning’s roughness coefficient at these locations varied from 0.019 to 0.022 and 0.015 to 0.018 for bare field whereas from 0.02 to 0.024, and 0.019 to 0.022 for cropped field, respectively. The temporal variation of Manning’s roughness coefficient for both bare and cropped furrow conditions decreased with the elapsed time. However, these decreasing trends were observed more for lower inflow rates. Further, the average Manning’s roughness coefficient for the subsequent irrigations was varied from 0.018 to 0.02 and from 0.019 to 0.0245 for bare and cropped conditions, respectively. Thus, the values of Manning’s roughness coefficients were more for cropped furrow conditions than for bare furrow.     

Flow Structure at Different Stages in a Meander-Bend with Bendway Weirs

Streambank erosion is an important management issue, particularly for meandering rivers. Recently, bendway weirs have become popular control measures for bank erosion along small meandering streams in the agricultural Midwest. Although these structures have successfully mitigated bank erosion in some cases, there is evidence that the weirs do not always perform as anticipated. Scientific understanding of how bendway weirs influence flow dynamics, streambank erosion, and aquatic habitat is limited. Current design criteria are based primarily on expert judgment rather than a formalized technical design procedure. At field-scale studies, the present paper represents a first step toward an integrated geomorphological and engineering evaluation of the performance of bendway weirs in rivers. To accomplish this initial phase, three-dimensional (3D) velocity data were collected on Sugar Creek at Brookside Farm, Ill., and 3D numerical simulations for low-flow conditions were performed to validate the computational fluid dynamic model. Overall results show good agreement between measured and simulated data for streamwise velocities and turbulence kinetic energy. The model is less accurate at predicting the velocity and turbulence kinetic energy in the shear layer immediately downstream from the weir tips. Based on the validation for low-flow condition, 3D simulations were carried out for medium and high flows where the bendway weirs are completely submerged. These simulations indicate that 3D patterns of flow, especially flow near the outer bank, change dramatically with changes in flow stage. Flow patterns at high-flow condition indicate that bank retreat over the tops of weirs is associated with locally high-shear stresses, thus producing a “shelf” along the base of the outer bank as observed in the field.     

Method of Solution of Nonuniform Flow with the Presence of Rectangular Side Weir

An iterative step method for solving the nonlinear ordinary differential equation, governing spatially varied flows with decreasing discharge, like the flow over side weirs, is developed. In the procedure, starting at a known flow depth and discharge in the control section, the analytical integration of the dynamic equation with bed and friction slope is carried out. The specific energy, the weir coefficient and the velocity distribution coefficient are considered as local variables, then for the explicit integration, the respective average values along the short side weir elements are assumed. The water surface profiles and the discharges for flow over side weirs, obtained with the proposed relation and valid for rectangular channels, are compared with experimental data for subcritical and supercritical flow conditions. The validation of the method is accomplished by the comparison with the solution obtained by De Marchi’s classical hypothesis, about the specific energy, which is constant along a side weir. In addition, the influence of the coefficient velocity distribution is considered.     

Identification of Manning’s Roughness Coefficients in Shallow Water Flows

A numerical method based on optimal control theories for identifying Manning’s roughness coefficients (Manning’s n) in modeling of shallow water flows is presented. The coefficients are difficult to be determined especially when the spatial variation is significant, and are usually estimated empirically. The present methodology is applied to determine the optimal values of the spatially distributed parameters, which give least overall discrepancies between simulations and measurements. Through a series of systematic studies to identify the n values in both a hypothetical open channel and a natural stream stretch, several identification procedures based on unconstrained and constrained minimizations are analyzed. It is found that the limited-memory quasi-Newton method has the advantages of higher rate of convergence, numerical stability and computational efficiency. Although the identification of Manning’s n is chosen as an example, the identification methods can be applied to numerical simulations of various flow problems.     

Numerical Study of Flow Affected by Bendway Weirs in Victoria Bendway, the Mississippi River

It has been observed that submerged weirs in bendways realign the flow and in general improve navigation conditions. This qualitative observation has been the basis for field design. This paper presents a study of hydrodynamics in the Victoria Bendway in the Mississippi River using three-dimensional numerical simulations. A numerical model, CCHE3D, was applied and computational results were compared to three-dimensional velocity data provided by the U.S. Army Corps of Engineers with reasonable agreement. The numerical simulation results were then used to analyze helical currents due to the channel curvature and the presence of submerged weirs. The simulated flow realignment near the free surface indicates that the flow conditions in the bendway were improved by the submerged weirs, however, the effectiveness of each weir depends on its alignment, local channel morphology, and flow conditions.     

Flow Velocity and Pier Scour Prediction in a Compound Channel: Big Sioux River Bridge at Flandreau, South Dakota

The two-dimensional (2D) depth-averaged river model Finite-Element Surface-Water Modeling System (FESWMS) was used to predict flow distribution at the bend of a compound channel. The site studied was the Highway 13 bridge over the Big Sioux River in Flandreau, South Dakota. The Flandreau site has complex channel and floodplain geometry that produces unique flow conditions at the bridge crossing. The 2D model was calibrated using flow measurements obtained during two floods in 1993. The calibrated model was used to examine the hydraulic and geomorphic factors that affect the main channel and floodplain flows and the flow interactions between the two portions. A one-dimensional (1D) flow model of the bridge site was also created in Hydrologic Engineering Centers River Analysis System (HEC-RAS) for comparison. Soil samples were collected from the bridge site and tested in an erosion function apparatus (EFA) to determine the critical shear stress and erosion rate constant. The results of EFA testing and 2D flow modeling were used as inputs to the Scour Rate in Cohesive Soils (SRICOS) method to predict local scour at the northern and southernmost piers. The sensitivity of predicted scour depth to the hydraulic and soil parameters was examined. The predicted scour depth was very sensitive to the approach-flow velocity and critical shear stress. Overall, this study has provided a better understanding of 2D flow effects in compound channels and an overall assessment of the SRICOS method for prediction of bridge pier scour.     

Physical Modeling of Sheet Flow on Rough Impervious Surfaces

This paper presents results from an extensive experimental study of sheet flow on rough impervious surfaces that are used to represent highway pavement. Experiments were performed on three surfaces under no-rainfall and simulated rainfall conditions, and with slopes of 1, 2, and 3%. Measurements include flow depth and unit discharge. Turbulent boundary layer theory for a rough surface is used to describe the depth-discharge relationship, resulting in a model with a single parameter directly related to the surface roughness. Comparisons are made with Manning’s equation, and the variability of the Manning coefficient is assessed. Hydraulic effects of rainfall are generally found to be small compared to other factors.     

Minimum Specific Energy and Critical Flow Conditions in Open Channels

In open channels, the relationship between the specific energy and the flow depth exhibits a minimum, and the corresponding flow conditions are called critical flow conditions. Herein they are reanalyzed on the basis of the depth-averaged Bernoulli equation. At critical flow, there is only one possible flow depth, and a new analytical expression of that characteristic depth is developed for ideal-fluid flow situations with nonhydrostatic pressure distribution and nonuniform velocity distribution. The results are applied to relevant critical flow conditions: e.g., at the crest of a spillway. The finding may be applied to predict more accurately the discharge on weir and spillway crests.     

Distributed Sensitivity Analysis of Flood Inundation Model Calibration

Uncertainties in hydrodynamic model calibration and boundary conditions can have a significant influence on flood inundation predictions. Uncertainty analysis involves quantification of these uncertainties and their propagation through to inundation predictions. In this paper the inverse problem of sensitivity analysis is tackled, in order to diagnose the influence that model input variables, together and in combination, have on the uncertainty in the inundation model prediction. Variance-based global sensitivity analysis is applied to simulation of a flood on a reach of the River Thames (United Kingdom) for which a synthetic aperture radar image of the extent of flooding was available for model validation. The sensitivity analysis using the method of Sobol’ quantifies the significant influence of variance in the Manning channel roughness coefficient in raster-based flood inundation model predictions of flood outline and flood depth. The spatial influence of the Manning channel roughness coefficient is analyzed by dividing the channel into subreaches and calculating variance-based sensitivity indices for each subreach. Replicated Latin hypercube sampling is used for sensitivity analysis with correlated input variables. The methodology identifies subreaches of channel that have the most influence on variance in the model predictions, demonstrating how far boundary effects propagate into the model and indicating where further data acquisition and nested higher-resolution model studies should be targeted.     

Laboratory Investigation of Mean Drag in a Random Array of Rigid, Emergent Cylinders

This paper investigates the drag exerted by randomly distributed, rigid, emergent circular cylinders of uniform diameter d. Laboratory measurements are presented for solid volume fraction ? = 0.091, 0.15, 0.20, 0.27, and 0.35 and cylinder Reynolds number Rep ≡ Upd/ν = 25 to 685, where Up=temporally and cross-sectionally averaged pore velocity and ν=kinematic viscosity. These ranges coincide with conditions in aquatic plant canopies. The temporally and cross-sectionally averaged drag coefficient, CD, decreased with increasing Rep and increased with increasing ? under the flow conditions investigated. The dimensionless ratio of the mean drag per unit cylinder length 〈〉H to the product of the viscosity, μ, and Up exhibits a linear Rep dependence of the form 〈〉H/(μUp) = α0+α1Rep, consistent with Ergun’s formulation for packed columns. In the range of experimental conditions, α1 increases monotonically with ?. In contrast, α0 is constant within uncertainty for 0.15 ? ? ? 0.35, which suggests that viscous drag per unit cylinder length is independent of ? in this range.     

Unsteady Friction in Rough Pipes

An energy dissipation model is presented for the computation of unsteady friction losses adapted to smooth-to-rough transition and fully rough pipes. The eddy viscosity model used to compute the Reynolds stresses in turbulent flow is modified to include the effect of roughness, which is considered in the computation of the velocity profiles. The model is tested by comparing the computed transient pressures with measured data from a laboratory test facility and a prototype test. Details of the experimental setup, pressure-head measurements, and valve characteristics during transient flow conditions are presented. The quasi-steady approximation gives an inaccurate prediction of the pressure head history; however, significantly better results are obtained if the unsteady friction effects are included.     

Distribution of Discharge Intensity along Small-Diameter Collector Well Laterals in a Model Riverbed Filtration

Experiments were performed to evaluate flow and head variations along perforated screens (10–30?mm in diameter) using sand tanks which were connected and a perforated screen extended through these tanks to form a model collector well lateral up to 2.6?m in length. Hydraulic heads and discharge along the lateral and production rates of the model collector well were measured as the water level in the well, the lateral length, and diameter, and the hydraulic conductivity of the filter sand were varied. A mathematical model was developed to predict the axial flow velocity distribution and the discharge intensity variation along the lateral using the head distribution. Results showed that the production rate increased as the lateral length and diameter and the drawdown at the well increased. However, the production rate increase was not linearly related to these factors. When larger-diameter laterals were used, the axial flow velocity in the laterals decreased. This caused the hydraulic heads along the lateral to become more flattened, resulting in a lateral of high efficiency in terms of water production. This condition is similar to the assumption of the uniform discharge intensity along the lateral that many researchers have used in the analysis of the horizontal wells. Under the conditions of this study, a critical axial flow velocity was determined to be 1?m/s. Hydraulic efficiency decreased drastically when the velocity exceeded 1?m/s. The roughness coefficient (the Manning’s n value) of the lateral varied as a function of factors such as axial velocity and discharge intensity, and it ranged from 0.010 to 0.015.     

Critical Flow over Circular Crested Weirs

The critical flow principle is a useful approach for the hydraulic analysis of round-crested weirs due to their single head-discharge relationships. The hydraulics of circular-crested weirs is examined using simplified models incorporating streamline curvature effects, comparing their predictions with experimental data. A generalized one-dimensional model based on the critical flow in curvilinear motion has been developed. The discharge coefficient increases with the specific energy normalized with the radius of curvature, E/R, when streamline curvature effects are included. The relative flow depth at the crest decreases as E/R increases. The flow at the weir crest is only critical for a normalized specific energy value of E/R ≈ 0.5–0.6. For larger heads, the flow at the weir crest has been found to be supercritical.     

Application of Several Depth-Averaged Turbulence Models to Simulate Flow in Vertical Slot Fishways

Vertical slot fishways are hydraulic structures which allow the upstream migration of fish through obstructions in rivers. The velocity, water depth, and turbulence fields are of great importance in order to allow the fish swimming through the fishway, and therefore must be considered for design purposes. The aim of this paper is to assess the possibility of using a two-dimensional shallow water model coupled with a suitable turbulence model to compute the flow pattern and turbulence field in vertical slot fishways. Three depth-averaged turbulence models of different complexity are used in the numerical simulations: a mixing length model, a k?ε model, and an algebraic stress model. The numerical results for the velocity, water depth, turbulent kinetic energy, and Reynolds stresses are compared with comprehensive experimental data for three different discharges covering the usual working conditions of vertical slot fishways. The agreement between experimental and numerical data is very satisfactory. The results show the importance of the turbulence model in the numerical simulations, and can be considered as a useful complementary tool for practical design purposes.     

Rational Coefficients for Steeply Sloped Watersheds

When computing peak discharges for the design of drainage systems using the rational method, it is important to have an accurate value for the rational coefficient (C). For steeply sloped watersheds the origin of values of the rational coefficient are unknown and lack even modeling verification. A model that shows the relationship between the rational coefficient and watershed slope was developed for steeply sloped watersheds. Using Horton’s infiltration equation, Manning’s equation, the velocity method for computing times of concentration, and generalized intensity-duration-frequency curves, a model was developed to test the effect of variation of several watershed characteristics on the relationship between slope and the rational coefficient. Analyses with the model showed that both Manning’s coefficient and land use had the greatest effect on the relationship between C and slope. A mathematical function was then developed from data generated from the Horton–Manning model. This model allows C to be estimated for a given slope and a value of Manning’s coefficient for the land cover. A rational coefficient at a 6% slope is also required input. The model was tested using several watersheds with moderate to steep slopes. This relationship should be used to better estimate values of C on steep slopes, and thereby, lead to more accurately hydrologic designs.     

Streamflow Properties from Time Series of Surface Velocity and Stage

Time series of surface velocity and stage have been collected simultaneously. Surface velocity was measured using an array of newly developed continuous-wave microwave sensors. Stage was obtained from the standard U.S. Geological Survey (USGS) measurements. The depth of the river was measured several times during our experiments using sounding weights. The data clearly showed that the point of zero flow was not the bottom at the measurement site, indicating that a downstream control exists. Fathometer measurements confirmed this finding. A model of the surface velocity expected at a site having a downstream control was developed. The model showed that the standard form for the friction velocity does not apply to sites where a downstream control exists. This model fit our measured surface velocity versus stage plots very well with reasonable values of the parameters. Discharges computed using the surface velocities and measured depths matched the USGS rating curve for the site. Values of depth-weighted mean velocities derived from our data did not agree with those expected from Manning’s equation due to the downstream control. These results suggest that if real-time surface velocities were available at a gauging station, unstable stream beds could be monitored.     

Effect of Covers for Soil and Water Conservation Using Tilting Flume

The effect of stone and vegetative covers was evaluated for soil and water conservation in a waterway on alfisols. Experiments were conducted on a hydraulic tilting flume under simulated flow (93 and 40 cm2?s?1) and slope (0.1, 1.0, 3.0, and 5.0%) conditions. The depth of soil was maintained at 0.35 m over a perforated bed to facilitate deep drainage. A comparative study of bare soil, stone cover (50%), and vegetative cover (50%) is made to evaluate soil loss, deep drainage, Manning’s roughness coefficient, and the Froude number. The study has revealed that stone cover is more effective than vegetative cover at lower discharge in reducing the flow velocity, and thereby soil erosion. Deep drainage has been reduced from lower to higher discharge for all the slopes with cover measures, including bare soil. It is found that cover measures are necessary beyond 3% slope in order to prevent rill erosion in alfisols.     

Secondary Flow Correction for Depth-Averaged Flow Calculations

A secondary flow correction has been added to the depth-averaged computer program, RMA2. The program solves a transport equation for streamwise vorticity and converts it to accelerations due to secondary currents. The inclusion of these additional accelerations results in improved predictions of depth-averaged velocity. In particular, their effect is to reduce depth-averaged velocities on the inside of curves and increase them on the outside of curves. The bendway correction has been tested on experimental data from the Riprap Test Facility at the U.S. Army Engineer Waterways Experiment Station.     

Study of Penetration Depth and Droplet Behavior in the Case of a Gas Jet Impinging on the Surface of Molten Metal using Liquid Ga–In–Sn

To study the penetration depth in the case of a gas jet impinging on the surface of liquid steel, cold model experiments were carried out using a liquid alloy Ga–In–Sn, which had similar physical properties as liquid steel. A HCl solution was used to simulate the top slag. The top phase was found to have appreciable effect on the penetration depth. Comparison of the experimental data with the predictions of the existing models indicated that most the model predictions deviated from the experimental results at higher lance heights and gas flow rates. New model parameter was suggested based on the present experimental data. The observation of the formation and movement of metal droplets generated by the gas jet was also made. The velocity of the droplet was found to be at a level only about 1% of the terminal velocity. This low velocity suggested that the turbulent viscosity played important role and the droplets could have long resident time in the slag.     

Turbulence Modeling of Flows over Circular Spillways

To predict the characteristics of flows over circular spillways, a turbulence model based on the Reynolds stress model (RSM) is presented. Circular spillways are used to regulate water levels in reservoirs. The flow over the spillway is rapidly varied with highly curvilinear streamlines. The isotropic eddy-viscosity models such as k-ε models are based on the Boussinesq eddy viscosity approximation that assumes the components of the turbulence Reynolds stress tensor linearly vary with the mean rate of strain tensor. Hence, they cannot very precisely predict the characteristics of flows over the spillway. On the other hand, the non-isotropic turbulence models such as the turbulence Reynolds stress models (RSM) that calculate all the components of the Reynolds stress tensor can accurately predict the characteristics of these flows. The k-ε models and RSM were applied in the present study to obtain the flow parameters such as the pressure and velocity distributions as well as water surface profiles. The previously published experimental results were used to validate the simulation predictions. For flow over a circular spillway, RSM appears to properly validate the characteristics of the flow under various conditions in the field, without recourse to expensive experimental procedures.