Flow over Gabion Weirs

A conventional weir typically consists of an impermeable body constructed of concrete, since its primary functions are to heading up water and efficiently regulate flow. However, an impermeable body prevents the longitudinal movement of aquatic life and transportation of physical and chemical substances in water, eventually having a negative impact on the water environment. One of the advantages of gabions as a building material is that the motion of individual stones comprising the gabion is not of much concern. The wire mesh of the gabion basket serves to restrain any significant movement. Also, gabion weirs offer an alternative design that could be adopted for flash flood mitigation. In this study, a series of laboratory experiments was performed in order to investigate the flow over gabion weirs. For this purpose, two different gabion weir models were tested in two horizontal laboratory flumes of 10-m and 17-m length, 0.3-m width, and 0.3- and 0.5-m depth, respectively, for a wide range of discharge, upstream water depth, downstream water depth, weir height, weir length, and gabion filling gravel material size. The results of the gabion weir were compared with those of experiments carried out on solid weirs having the same dimension and it was found that there is a large deviation when the solid weirs equation is applied to gabion weirs (permeable weirs). So, using one of the existing solid weir flow formulas would lead to an erroneous calculated value. Multiple regression equations based on the dimensional analysis theory were developed for computing the discharge over gabion weirs for both free and submerged flow regimes. Also, equations were introduced for computing the discharge coefficient to be applied with the traditional solid weir equation.     

Critical Depth Relationships in Developing Open-Channel Flow

Doubts have been expressed about the validity of the critical depth defined in terms of the minimum specific energy head of the free-surface streamline when dealing with developing open-channel flows. This note examines the two approaches for defining critical flow, that based on the minimum specific energy of the free-surface streamline and that based on the mean energy head of the whole flow section. Large differences for the dimensionless critical depths are obtained with the two methods due to each critical depth proving to be a different control point on the free-surface profile. It is argued that both methods are different alternatives, although the critical depth concept was different in each case. Theoretical support to critical flow computations based on the free streamline is provided. An alternative approach for computing the discharge characteristics of broad-crested weirs based on the energy loss inside the boundary layer is also proposed.     

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.     

Optimal Design of Open Channel Section Incorporating Critical Flow Condition

The flow at critical condition of an open channel is unstable. At critical condition, a small change in specific energy will cause abrupt fluctuation in water depth of the channel. This is because the specific energy curve is almost vertical at critical state. Therefore, if the design depth of the channel is near or equal to critical depth of the channel, the shape of the channel must be altered to avoid a large fluctuation in water depth. In the present study, a nonlinear optimization model is presented for designing an optimal channel section incorporating the critical flow condition of the channel. The optimization model derives the optimal channel section at a desirable difference from the critical condition of the channel so that a small change in the specific energy of the channel will not cause an abrupt change in flow depth. The objective of the optimization model is to minimize the total construction costs of the channel. Manning’s equation is used to specify the uniform flow condition in the channel. The developed optimization model is solved by sequential quadratic programming using MATLAB. Applicability of the model is demonstrated for a trapezoidal channel section with composite roughness. However, it also can be extended to other shapes of channel.     

Transition Effects in Flow Over Side Weirs

The effect of water surface slope in the lateral direction on flow over side weirs was studied. Water surface elevation on the weir plane was expressed by a parameter ψ based upon the hydraulic profile on the channel axis. Two different relationships of ψ as a function of the Froude number were used to calculate side weir discharges. Results were compared with the experimental data. It was shown that better results are obtained when transition conditions of ψ = 1 at the ends of the side weirs with no lateral surface slope are taken into account. However the effect of water surface slope in lateral direction is of secondary importance as compared to the angle of the deflected water jet along the side weir.     

Discharge Characteristics of Weirs of Finite Crest Length

This technical note presents a critical analysis flow over weirs of finite crest length, with square-edged or rounded entrance, for free-flow conditions. Using the flow equation for the broad-crested weir with parallel flow in the critical state as the basis, we have defined the discharge coefficient Cd, with the head on the weir as the length scale. Based on an extensive analysis of the experimental observations in the literature, we have confirmed the classification of finite crest length weirs into four classes of long-crested, broad-crested, short-crested, and sharp-crested weirs. For the square-edged entrance, we have developed robust correlations for Cd when the Weber number is greater than 1. For weirs with a rounded entrance, for which the data set is not that extensive compared to the square-edged case, we have developed good correlations for Cd.     

Bernoulli Theorem, Minimum Specific Energy, and Water Wave Celerity in Open-Channel Flow

One basic principle of fluid mechanics used to resolve practical problems in hydraulic engineering is the Bernoulli theorem along a streamline, deduced from the work-energy form of the Euler equation along a streamline. Some confusion exists about the applicability of the Bernoulli theorem and its generalization to open-channel hydraulics. In the present work, a detailed analysis of the Bernoulli theorem and its extension to flow in open channels are developed. The generalized depth-averaged Bernoulli theorem is proposed and it has been proved that the depth-averaged specific energy reaches a minimum in converging accelerating free surface flow over weirs and flumes. Further, in general, a channel control with minimum specific energy in curvilinear flow is not isolated from water waves, as customary state in open-channel hydraulics.     

Hydraulic Relations for Clinging Flow of Sharp-Crested Weir

Available discharge coefficient formulas for sharp-crested weirs are only applicable to the free-flow regime. To extend the range of discharge measurement by a rectangular sharp-crested weir, critical heads of the transition flow regime, the head-discharge relation for clinging and free flow, and the discharge coefficient for clinging flow were investigated experimentally based on more than 300 experimental points with head ranging from 0.0048 to 0.0455 m. The results indicate that the transitions from clinging to free flow and vice versa do not occur at the same head. Upper and lower critical heads, Hu,crit and Hl,crit, can be identified at which these transitions occur. For the condition studied, the head relation between clinging and free flow is found to be linearly correlated at the same discharge. Expressions for the discharge coefficient for clinging flow are developed.     

Open Channel Flow Resistance

In 1965, Rouse critically reviewed hydraulic resistance in open channels on the basis of fluid mechanics. He pointed out the effects of cross-sectional shape, boundary nonuniformity, and flow unsteadiness, in addition to viscosity and wall roughness that are commonly considered. This paper extends that study by discussing the differences between momentum and energy resistances, between point, cross-sectional and reach resistance coefficients, as well as compound/composite channel resistance. Certain resistance phenomena can be explained with the inner and outer laws of boundary layer theory. The issue of linear-separation approach versus nonlinear approach to alluvial channel resistances also is discussed. This review indicates the need for extensive further research on the subject.     

Exact Equations for Critical Depth in a Trapezoidal Canal

Critical depth is an important parameter in the analysis of varied flow in canals and natural streams. For triangular, rectangular, and parabolic channel sections it is possible to express critical depth analytically. However, for many practical sections, including the trapezoidal section, the governing equations are implicit in the critical depth. For these sections the critical depth is presently obtained either by trial and error procedure, or by using empirical equations based on curve fitting. In this Technical Note exact analytical solutions of critical depth for the trapezoidal open channel section have been obtained in the form of fast converging infinite series.     

Large-Eddy Simulation of Turbulent Flow over a Fixed Two-Dimensional Dune

Turbulent open-channel flow over a two-dimensional dune is studied using an established large-eddy simulation code. The free surface is approximated as a shear free boundary. Turbulence statistics and instantaneous flow structures are examined. Numerical results from two computational grids agree with each other, and are also in good agreement with recently obtained experimental data. The mean velocity profiles show significant changes along the dune and there is no region that conforms to the standard law-of-the-wall. Profiles of the Reynolds stresses show distinct peaks marking the shear layer that originates from flow separation at the dune crest. Secondary peaks found further from the dune are ascribed to the shear layer over the upstream dune. Details of the separated flow and development of the flow after reattachment are well predicted. Quadrant analysis of the Reynolds shear stress shows that turbulent ejections dominate the near-wall motions. Complex water surface flow structures are visualized.     

Hydraulics of Broad-Crested Weirs with Varying Side Slopes

The flow of water over a trapezoidal, broad-crested, or embankment weir with varying upstream and downstream slopes has been investigated. Data are presented comparing the effect of slopes of 2H:1V, 1H:1V and vertical in various combinations on the upstream and downstream faces of the weir. Pressure and surface profiles were self-similar for all cases tested. Increasing the upstream slope to the vertical decreased the height of the surface profile and, hence, the static pressure of the crest. It also reduced the discharge coefficient. The variation in downstream static pressures was negligible though. Varying the downstream slope had a negligible effect on the surface and pressure profiles over the weir. Changes in flow were constrained to the region downstream of the crest. Cavitation could occur at the downstream corner of the weir if the upstream head was sufficiently high and a sloped face was used. This paper presents data that will be of use in the design of hydraulic structures for flow control and measurement.     

Lateral Weir Flow Model using a Curve Fitting Analysis

A numerical approach is considered for flow over side weirs as a substantial part of distribution channels in irrigation systems and treatment units. The model is based on the energy principle and a curve-fitting technique. For this purpose, the side weir was divided into elementary strips to develop generalized equations for discharge and surface profile. The change in water surface elevation towards the weir crest and the inclination of the deflected flow over the weir were also taken into account. Dimensionless parameters were used and the normalized equations solved to obtain the hydraulic parameters of side weirs. The results were plotted to determine general relationships based on the curve-fitting technique. A practical application of the derived equations to obtain hydraulic parameters of side weirs is performed using literature data.     

Uniform and Critical Flow Computations

The application of theory developed for direct integration of gradually varied flow equations to uniform and critical flow computation greatly reduces the computational effort. A small generalized subroutine is able to compute accurately the various parameters involved in the computation for all types of natural and constructed cross sections. Although the equations are implicit, in a majority of cases the number of iterations needed to achieve the required accuracy is less than 3. The method is even useful for computation by hand held calculators.     

Periodic Oscillation Caused by a Flow over a Vertical Drop Pool

The flow patterns of various dropping flows were investigated and classified experimentally for subcritical approach flows passing a vertical drop pool. A wave gauge was used to measure the free surface fluctuations in the pool. A flow visualization technique was employed to reveal the flow structure of the dropping flows qualitatively. It was discovered that, under certain conditions, the dropping flow forms a switching jet that oscillates up and down periodically and impinges on the bed and the downstream pool wall alternately. The switching jet switches between an impinging jet (a napped flow) and a sliding jet (a skimming flow), causing it to oscillate periodically with a unique period. The primary frequency of the periodic oscillation was determined by applying spectral analysis to the time series of the gauge measurements. Since a large number of air bubbles was entrained in the oscillatory flow, particle image velocimetry, and bubble image velocimetry were used for quantitative velocity determination in the liquid region and the aerated region, respectively. The mechanism causing the periodic oscillation in the pool was elucidated, and variables affecting the oscillation frequency were identified. An empirical relation between a weighted Strouhal number and a grouped dimensionless parameter was proposed to predict the primary frequency of the periodic oscillatory flow.     

Conditional Assessment of Flow Measurement Accuracy

A study conducted by the Utah Water Research Laboratory assessed the accuracies of a wide variety of flow measurement devices currently in service. During the study, a wide variety of flow measurement devices, including flumes, weirs, and rated sections in open channel systems, were evaluated; magnetic and ultrasonic meters in closed-conduit systems were also tested. The specified design accuracies for each device are presented. Actual flow measurements were determined at 70 sites and were compared with the theoretical discharges of each device. Comparison of actual and theoretical flow indicates that only 33% of the measurement devices tested currently measure flow within manufacturer-designed specifications. Field data is presented, and possible reasons for the flow measurement errors and their corrections are discussed.     

Hydraulic Characteristics of Gabion-Stepped Weirs

Experimental studies on the hydraulics of flow through and over gabion-stepped weirs are presented. Two flow components were observed, i.e., base flow through the void between filled stones and overflow on the gabions. The energy loss ratios in the gabion-stepped weirs are greater than those in the corresponding horizontal stepped weirs by approximately 7, 10, and 14% for weir slopes of 30, 45, and 60°, respectively. As a result, the velocity at the outlet is lower. Stone size and shape have little influence on the energy loss and flow velocity as compared to the increasing effect of the weir slope. The pressure acting on the step face for the gabion-stepped weirs is less than that of the horizontal steps owing to the cushioning effect generated by filled stones. To reduce pressure on a step face at a fixed discharge for different weir slopes, the void ratio of the filled stones should be low to allow a small amount of base flow. The pressure distribution pattern on the horizontal face of a step is provided.     

Broad-Crested Weirs with Rectangular Compound Cross Sections

A series of laboratory experiments was performed in order to investigate the effects of width of the lower weir crest and step height of broad-crested weirs of rectangular compound cross section on the values of the discharge coefficient, the approach velocity coefficient, and the modular limit. For this purpose, nine different broad-crested weir models with rectangular compound cross sections and a model with a rectangular cross section were tested in a horizontal laboratory flume of 11.0 m length, 0.29 m width, and 0.70 m depth for a wide range of discharges. The compound cross sections were formed by a combination of three sets of step heights and three sets of lower weir crest widths. The sill-referenced heads at the approach channel and at the tailwater channel were measured in each experiment. The dependence of the discharge coefficient, approach velocity coefficient, and modular limit values on model parameters was investigated, and these quantities were compared with those of the broad-crested weir models with a rectangular cross section.     

Two-Dimensional Simulation of Subcritical Flow at a Combining Junction: Luxury or Necessity?

Classically, in open-channel networks, the flow is numerically approximated by the one-dimensional Saint Venant equations coupled with a junction model. In this study, a comparison between the one-dimensional (1D) and two-dimensional (2D) numerical simulations of subcritical flow in open-channel networks is presented and completely described allowing for a full comprehension of the modeling of water flow. For the 1D, the mathematical model used is the 1D Saint Venant equations to find the solution in branches. For junction, various models based on momentum or energy conservation have been developed to relate the flow variables at the junction. These models are of empirical nature due to certain parameters given by experimental results and moreover they often present a reduced field of validity. In contrast, for the 2D simulation, the junction is discretized into triangular cells and we simply apply the 2D Saint Venant equations, which are solved by a second-order finite-volume method. In order to give an answer to the question of luxury or necessity of the 2D approach, the 1D and 2D numerical results for steady flow are compared to existing experimental data.     

Transcritical Flow due to Channel Contraction

The singular point is a physical phenomenon consistent with critical flow conditions, and, consequently, the real control section of a water surface profile. A general method to study the location, type, and water surface slope of a singular point is described. This method, in addition to improving the classic gradually-varied flow theory, can be used for the design of channel contractions involving transcritical flows, as in the case of chute spillways and inlets to river diversion tunnels. The method is explained in the case of a chute spillway and verified against experimental data recorded in a Venturi channel.