Discharge through a Permeable Rubble Mound Weir

The hydrodynamics of a rubble-mound weir are theoretically and experimentally examined. This type of weir is considered to be environmentally friendly, since its permeability allows substances and aquatic life to pass through longitudinally. By performing a one-dimensional analysis on a steady nonuniform flow through the weir, discharge is described as a function of related parameters, such as flow depths on the up- and downstream sides of the weir, porosity, and grain diameter of the rubble mound, weir length, etc. A laboratory experiment is carried out to determine the empirical coefficients included in the analytical model. The theoretical solution of the discharge is compared with the experimental data to verify the analysis. It is confirmed that agreement between theory and experiment is satisfactory for a wide range of flow conditions. The present study makes it possible to apply the rubble mound weir for practical use as a discharge control system.     

Multislit Weir Characteristics

The slit weir has been recently shown to be effective in measuring very small discharge rates. In this study, the slit weir concept is extended to permit one to measure both very low and very high discharge rates accurately. For this purpose, the hydrodynamic concept of images is adopted to form a bank of multislit weirs in which the individual slit weirs have nearly identical flow characteristics. The discharge coefficient of multislit weirs is determined experimentally using the measured discharges and the corresponding heads causing weir flow. The relationship between the discharge coefficient and the main dimensionless parameters is investigated. It is concluded that the discharge coefficient can be represented solely as a function of the Reynolds number.     

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.     

Discharge Relation for Cutthroat Flume under Free-Flow Condition

A cutthroat flume is commonly used as flow measuring device for open-channel flow due to ease of fabrication and installation. In most of the cases it is difficult to calibrate the flume in the field. Therefore, accurate relation between discharge and upstream head applicable for all sizes of cutthroat flume is needed. Seven different sizes of cutthroat flumes, having different length to throat width ratios, are fabricated and tested in the laboratory under free-flow condition. Selecting groups of different variables describing flow through a cutthroat flume number of dimensionless parameters are formed. Regression analysis of experimental data is carried out between all possible combinations of pairs of dimensionless parameters and the pair giving the best correlation is selected. Using the selected pair, relation between dimensionless parameters of discharge and head is developed. The relation is simple and convenient to use and, at the same time, more accurate compared to methods available in literature for prediction of discharge.     

Measurement of Small Discharges in Open Channels by Slit Weir

A rectangular slit weir is designed for measurement of small (<0.005 m3/s) discharges. The discharge coefficient is determined experimentally using the measured discharges and the corresponding heads over the weir. The relationship between the discharge coefficient and all relevant dimensionless parameters is investigated. It is concluded that the discharge coefficient can be represented solely as a function of Reynolds number.     

Discharge Coefficient of a Triangular Side-Weir Located on a Curved Channel

This study aims to obtain sharp crested triangular side-weirs discharge coefficients both in the straight channel and along the bend by using a total of 1,735 experiments. It was found that triangular side-weirs discharging coefficients along the bend depend on the upstream Froude number in the main channel (F), the apex angle of side-weir (θ), and the bend angle (α). Because there is much greater intensity of secondary flow created by lateral flow with an increase of the overflow length, sharp crested triangular side-weirs discharge coefficients of the apex angle θ = 120° were achieved more frequently than the others even at the straight channel in subcritical flow conditions. In a curved channel, the path of maximum velocity and the secondary current created by the bend both cause a much greater deviation angle towards the side-weir which is involved within F and L/b. Therefore, triangular side-weirs discharging coefficients along the bend are greater than the values obtained in the straight channel.     

Use of Brink Depth in Discharge Measurement

The behavior of free surface flow at a rectangular free overfall is studied experimentally to obtain a relation between the brink depth and the flow rate. A series of experiments were conducted in a tilting flume with wide range of flow rates covering subcritical, critical, supercritical regimes, and two different roughnesses in order to develop a relationship between the discharge and the brink depth. An equation is proposed to determine the flow rate using the brink depth for a channel of known roughness and bed slope.     

Behavior of Submerged Ogee Crest Weir Discharge Coefficients

Weir head-discharge relationships are typically described using the discharge coefficient-dependent standard weir equation. The submerged weir (tailwater exceeds the weir crest elevation) head-discharge relationship can vary from the free-flow head-discharge relationship, particularly at high submergence levels. The accuracy associated with predicting the upstream head or discharge, corresponding to submerged weir flow conditions, is dependent upon the accuracy with which a representative submerged discharge coefficient can be determined. A submerged ogee crest weir discharge coefficient predictive method developed by the U.S. Bureau of Reclamation (USBR) is reviewed and its predictive accuracy compared to laboratory-scale submerged ogee crest weir experimental data associated with a wide range of submerged flow conditions for nine different ogee crest weir geometries. Discussion is presented in an effort to partially explain the relatively poor correlation between the USBR method and the experimental data set. Alternative submerged discharge coefficient relationships are also presented.     

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.     

Performance of Slit Weir

Slit weirs designed to measure small discharges in open channel flows are investigated. Experimental data available in the literature are added to study the effect of the slit width. An explicit relation for the discharge coefficient is obtained by a conventional Reynolds number definition. The discharge coefficient is modified to increase the working range of slit weirs for small values of head to slit-width ratios.     

Generalized Head-Discharge Equation for Flow over Sharp-Crested Inclined Inverted V-Notch Weir

The sharp-crested weir is the most commonly used device in channels for flow measurement and flow regulation due to its simplicity. Attempts have been made to study in detail the flow over different shapes of normal conventional weirs, side weirs, and oblique weirs. Most of the investigators have expressed the discharge coefficient as a function of various parameters. The concern of this paper is to study flow over an inclined inverted triangular notch weir. Based on experimental work on 0° (normal) and 15, 30, 45, and 60° weirs, the writers have established an equation for discharge in terms of the inclination angle of the weir plane with the plane normal to the flow axis. A new general algebraic optimization procedure has been developed for evolving a linear head-discharge relationship for an inclined inverted V-notch (IIVN), which is relatively superior to similar procedures developed earlier. It has been shown that the IIVN does not lose its near-linear discharging characteristics even when it is inclined to the channel bed. The discharge estimated by the linear discharge-head relationship has been found to be in good agreement with the actual discharges well within a ±5% error. Further, the advantages of the IIVN as a flow measuring and flow control device have been highlighted.     

Experiments on Discharge Equations of Compound Broad-Crested Weirs

A linear combination of traditional discharge equations for simple rectangular and/or triangular weirs is proposed to describe the discharge equations of compound broad-crested (CBC) weirs. The CBC weirs are composed of rectangular, triangular, and/or truncated triangular weirs. Dimensionless discharge equations have been also derived. Laboratory experiments on discharge relations for flows over four CBC weirs were conducted in this study in order to calibrate the proposed discharge equations. The experiments were carried out under the conditions of the H1/H2-ratio of water heads above upper and lower crests less than 0.54, and a dimensionless discharge less than 2.174. The result shows that the differences between the calculated discharges by the proposed equations and the measured ones are less than 3% for flows over these CBC weirs under the present experimental conditions.     

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.     

Calculation of Contraction Coefficient under Sluice Gates and Application to Discharge Measurement

The contraction coefficient under sluice gates on flat beds is studied for both free flow and submerged conditions based on the principle of momentum conservation, relying on an analytical determination of the pressure force exerted on the upstream face of the gate together with the energy equation. The contraction coefficient varies with the relative gate opening and the relative submergence, especially at large gate openings. The contraction coefficient may be similar in submerged flow and free flow at small openings but not at large openings, as shown by some experimental results. An application to discharge measurement is also presented.     

Combined Flow over Weir and under Gate

Problems related to sedimentation and deposition can be minimized by using a system where weirs and gates are combined. Given its applications, the hydraulics of simultaneous flow over weir and under gate, in particular, the determination of the stage–discharge relationship, is of interest. Although previous approaches have been based on regression or dimensional analysis, the current work describes a physically based approach. Models of sharp-edged weirs and gates with no lateral contraction are combined. To calibrate and validate the proposed model, experiments have been carried out in a laboratory flume applying different submergence conditions. It was found that the model is able to predict the stage–discharge relationship with reasonable accuracy.     

Flow through Side Sluice Gate

The hydraulic characteristics of a side sluice gate were studied experimentally. It was found that the specific energy remains constant along the side sluice gate. The coefficient of discharge for the side sluice gate is related to the main channel Froude number and the ratio of upstream depth of flow to sluice gate opening for free flow. It also depends on an additional parameter: the ratio of tailwater depth to the gate opening for submerged flow. Suitable equations for discharge coefficient are obtained.     

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.     

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.     

Effect of Weir Face Angles on Circular-Crested Weir Flow

The standard circular-crested weir is often found in engineering applications and is used as a discharge measurement device or as an overflow structure. This research determines the discharge coefficients for ten circular-crested weir configurations with various combinations of up- and downstream angles. Two different weir heights and four different overflow depths are considered for each weir shape. For free overflow, the discharge coefficient is determined experimentally by using the total head of the approach flow. The results indicate that the upstream weir face angle has only a small effect on the discharge coefficient. In contrast, increasing the downstream weir face angle increases the discharge coefficient notably. A new formula for the discharge coefficient is presented, including both the up- and downstream weir face angles. Further, the hydraulic performance of the circular-crested weir, the resulting discharge reduction from tailwater submergence, and transition flow are discussed.     

Discharge Capacity of Labyrinth Side Weir Located on a Straight Channel

Side weirs, also known as lateral weirs, are flow diversion devices widely used in irrigation as a head regulator of distributaries and escapes, land drainage, and urban sewage systems. The studies on the subject have been generally focused on rectangular and triangular side weirs located on a straight channel. However, the same is not true for labyrinth side weirs. The current studies deal with sediment transport and scour problems around side weirs and lateral structures. The investigation of the hydraulic effects of labyrinth side weirs to increase discharge capacity of them has been studied in this particular work. In the study, 2,830 laboratory tests were conducted for determining discharge coefficient of labyrinth side weirs, and results were analyzed to find the influence of the dimensionless weir length L/b, the dimensionless effective length L/?, the dimensionless weir height p/h1, triangular labyrinth side weir included angle θ, and upstream Froude number F1 on the discharge coefficient, water surface profile and velocities in the channel along the side weir. It has been found that discharge coefficient of labyrinth side weirs gives pretty higher coefficient value compare to that of classical side weirs and a reliable equation for discharge coefficient of labyrinth weirs is presented. Discharge coefficient of the labyrinth side weir is 1.5–4.5 times higher than rectangular side weir.