Free Overfall Research Articles

Free Overfall for Discharge Measurement in Channels of Different Shapes: A Review

The end drop in open channels can be considered as a simple and useful tool for the measurement of flow rates flowing in open channels of different shapes. The depth at channel end can be related to the critical depth in the approaching channel and denoted as (EDR). The (EDR) is an essential parameter for measuring end drop discharge (EDD) in open channels. The main target of this paper is to review the previous works done on the end drop in different shapes of channels using the properties of the free end drop flow as basic criteria for the estimation of (EDR) and (EDD). Useful relationships between (EDR) and channel slope are presented which are the outcome results of previous researches done on smooth and rough open channels of different shapes (rectangular, trapezoidal, circular and triangular). Moreover, the correlations of (EDD) depending on end drop depth and characteristics of the upstream approaching channel are presented for channels of different shapes for subcritical and supercritical states of flow. Still there is no unique theoretical solution for the problem of using end depth of free drop as a key for the estimation of flow rates in open channels which needs more theoretical and experimental studies and works on this important field of research.

Estimating discharge coefficient of triangular free overfall using the GMDH technique

Abstract Free overfalls are hydraulic structures used in flood control, water supply, irrigation, and flow measurements. The hydraulic systems of free overfall depend on rectangular end shape. The studies that dealt with triangular crest are few and almost non-existent. In this study, a triangular end-shape design uses multiple linear regression (MLR) and group method of data handling (GMDH) methods for four models with six sub-models. Then, 24 scenarios were chosen and compared. The discharge coefficient (Cd) of a free overfall with a triangular terminal was predicted using experimental data. The triangular end edge shape increased crest length, the discharge coefficient, and discharge passing over free overfall. To this goal, 180 triangular free fall tests were performed. Data were collected for two triangular free overfalls with an opposite flow direction with three angles 600, 750, and 900. Results of Cd acquired using the two ways discussed above show that the algorithm GMDH outperforms the other method. Values for the GMDH approach mod46 testing variables: RMSE, MARE, SI, R2, and NSE are 6.08 × 10−17, 2.65 × 10−17, 6.00 × 10−17, 100.00%, and 1.00, respectively, while these values for MLR are 0.06332, 0.05970, 0.06624, 15.431%, and −3.0419, respectively. The GMDH technique shows the best results concerning MLR and then chooses the best four scenarios from 24 with a Cd percentage error not exceeding ±2%.

Investigation of the free overfall for discharge measurement in stone bed triangular channels

This study utilizes the freefall as a simple and useful tool for measuring end depth discharge EDD in triangular channels having stone beds. For this task, forty-five triangular channel models are constructed and examined all having 360 cm length and end drop fall of 20 cm. In these channel models, three channel side slopes z = 0.7, 1.0 and 1.3, five bed slopes St = 0.00, 0.0033, 0.005, 0.010 and 0.020 and three bed stone diameters ds = 5 mm, 10 mm and 15 mm are tested. The laboratory results demonstrated straight line relationships for the variation of end depth ye with critical depth yc and the variation of end depth with uniform normal depth yn for different values of z, St and ds tested in this study, while, the relation between ye/yc and bed slope St showed a quadratic expression. Moreover, the relationship for the dimensionless discharge with both channel bed slope St and the ratio of end water depth ye to bed stone diameter ds(ye/ds) has been presented by a simple empirical power equation with high determination coefficient which can be applied for subcritical and supercritical states of flow for the range of upstream Froude number Frn between 0.14 and 1.27.

Study the Affecting Factors on Free overfall Flow and Bed Roughness in Semi-Circular Channels by Artificial Neural Network

One of the significant problems facing the water resource engineer is calculating the coefficient of roughness for subsequent design calculations of the discharge amount of a channel or river. In this study, experiments were conducted in a semi-circular, straight channel to investigate the factors affecting bed roughness and flow discharge using Artificial Neural Network (ANN). For this purpose, three semi-circular channel models with free overfall were constructed and installed in a 6-meter-long laboratory flume. The length of these models was 2.50 m with three different diameters (D= 150, 187, and 237mm) and three bed slopes (S=0.004, 0.008, and 0.012). Three sand particle sizes (ds) were used for each semi-circular channel to roughen the bed. The results showed that the Manning roughness coefficient obtained using a rough bed surface was higher than the channel with a smooth bed surface. Also, the results revealed that the Manning roughness coefficient and the Froude number were inversely related. (ANN) analysis showed a good agreement between the experimental and predicted results of flow and roughness. The bring depth (yb) had an 85.8% impact percentage on the free overfall discharge for semi-circular channels, while the bottom slope (S) had only 1.1%.

Experimental Investigation for Free Overfall of Flow in Semi-circular Channels

In the present paper, the effects of diameter, bed slopes, and bed roughness on free overfall flow of semi-circular channels were investigated experimentally. For this purpose, three models of semi-circular channels with free overfall were built and installed in a 6m long laboratory flume. These three models were 250 cm long and had varying diameters 160, 200, and 250 mm. Four different bed slopes (S) were used in each of these models (0, 0.004, 0.008, and 0.012). For each bed slope, three sand particle sizes were used to roughen the bed (1.18mm, 2.36mm, and 4.75mm). For each model, the experimental testing program contained sixteen series of experiments. They were divided into two categories: four smooth beds and twelve rough beds. Different rates of discharge (Q) were examined in a total of 192 tests. According to the experimental results of all models, the Froude number (F r ) of flow decreases as the end depth ratio ( y b / y c ) increases for various bed roughnesses. For varying bed slopes and bottom roughness, a simple linear formula was developed to relate the brink depth ( y b ) with the critical depth ( y c ). For various bed slopes and roughness conditions, simple empirical equations for the flow over the free overfall in semi-circular channels were found. The results demonstrate a good level of agreement.

Investigation of Energy Dissipation Rate of Stepped Vertical Overfall (SVO) Spillway Using Physical Modeling and Soft Computing Techniques

In the present study a physical model of a stepped vertical overfall (SVO) spillway is proposed and designed as a novel combination of a free overfall spillway with horizontal steps. First, the hydraulic design characteristics of the proposed spillway were discussed using a laboratory-scaled model. Effective parameters on the energy dissipation rate were defined as the relative critical depth, Froude number, number of steps, and dimensionless steps' geometry parameter using dimensional analysis. The energy dissipation rate of the stepped vertical overfall spillway is measured using a waterwheel laboratory setup. Different geometry and hydraulic scenarios were used to assess the energy dissipation rate variation of the proposed spillway. Furthermore, Support Vector Regression and Random Forest Regression methods were used to estimate the energy dissipation of the proposed structure. Investigating the energy dissipation rate of 27 geometry scenarios with the available range of discharge revealed that the energy dissipation rate against the water's relative depth inside the SVO spillway follows a gradually increasing trend ranging between 88.53% to 98.06%. Also, random forest regression algorithm showed more accurate prediction performance than support vector regression approach with RMSE = 0.128 and R2 = 0.99 in training stage and RMSE = 0.115 and R2 = 0.99 in testing stage. The support vector regression model estimated the proposed spillway's energy dissipation rate with an accuracy of RMSE = 0.67 and R2 = 0.88 in training stage and RMSE = 0.61 and R2 = 0.9 in testing stage.

Prediction of the key parameters of free over-fall flows within the generalized circular cross-section with varying flat bases

Free over-fall occurring due to the sudden bed drop at the channel end that referred as the brink, facilitates the determination of the flow amount (discharge) by only trailing the value of the water depth at that section. This paper mainly focuses on a new theoretical approach that analysis the free over-fall within a channel of circular cross-section with flat base at different elevation levels by applying the continuity and the energy equations based on one velocity point method. The hydraulic behaviors of the circular cross-section especially having different elevation of the flat base have been investigated in sub-critical flow regime to obtain the end depth ratio (EDR) from which the end depth discharge (EDD) values are computed. The non-horizontal free surface profile at the upstream of the end section due to the accelerated flow velocity is also computed based on the extended energy equation. Subsequently, due to its practical importance direct equations for the free surface profile are provided for each channel cross-section for different values of the non-dimensional critical depth. Furthermore, in order to ease the use of the solution for practitioner in this field, the generalized unique relationships for the EDR, the non-dimensional discharge, and the free surface profile are presented, since there is no direct general equation for all the derivatives of the circular channel as a single solution in the previous studies due to its complexity. Even, relevant experimental and theoretical studies are used to obtain more robust assessment of the applied approach.

Intelligent flow discharge computation in a rectangular channel with free overfall condition

Intelligent flow discharge computation in a rectangular channel with free overfall condition

Numerical simulation of hydraulic performance with free overfall flow

Recently, free overfall flows have attracted attention of many researchers in the world. It is because the free overfall can be used as a tool in measuring the discharges and flows in any open channel systems or water collection systems for various flow regime at different shape of channels. In this study, the hydraulic performances of free overfall flow were explored using numerical simulation for three shapes of open channels including uniform rectangular, rectangular circumscribed, and rectangular inscribed steps. The hydraulic performances discussed in this study are including the flow regime, the maximum pressure, drop length and the energy dissipation rate. Numerical simulations were performed under different discharges Q (between 0.0005 m3/s and 0.0015 m3/s) and excise repair densities (y/H) for 1:2, 1:3 and 1:4. Visual observations identified various flow regimes with largely identical flow patterns in different discharges and configurations. Comparisons of properties indicated that there is a better depressurization and energy dissipation performances at the open channel with the shape of rectangular inscribed steps compare to the uniform rectangular in the small charge. Comparative study also revealed that the large excise repair densities of rectangular circumscribed steps might be optimal in terms of energy dissipation performances.

Numerical Investigation of Rectangular Pipe Free Overfall for Various Upstream Conditions

AbstractThis paper examines the relationship between the flow rate and outflow depth for flow in a rectangular pipe with the outflow running partially full of a free nappe through a series of compu...

Using the Brink Depth in Discharge Measurement for Inverted Semicircular Open Channels

A free overfall at the end of an open channel provides a simple means for measuring flow discharge. The semicircular open channel plays a significant role in various applications, and it is of interest to calculate its discharge. This paper presents the application of the momentum equation to evaluate the use of a smooth inverted semicircular channel end as devised to calculate the discharge if the end depth is known. The experiments were performed in three separate semicircular inverted channels, with diameters of 15.0 cm, 18.4 cm, and 24.2 cm. The experimental data used to develop equations for calculating the discharge from known end depth. Where the end depth is related to the critical depth, and the end depth ratio value was found to be 0.8102 for a critical depth-diameter ratio of up to 0.40. On the other hand, the relationships for end depth ratio and non-dimensional discharge are defined. Two empirical equations are generated for the direct and indirect prediction of discharges from known end depth values.

Hydraulics of free overfall in smooth triangular channels

Abstract The present study deals with the hydraulic behavior of smooth triangular channels with free overfall in order to obtain useful relationships for the estimation of end depth discharge (EDD) in terms of brink depth (yb), channel side slopes (m) and channel bed slope (So). For this purpose, twelve triangular channel models have been built and tested having 3.6 m length and 19 cm drop at brink with different values of side slopes (m = 0.75, 1.0 and 1.25) and different channel bed slopes (So = 0.0, 0.0033, 0.0067 and 0.02). Experimental results of all models showed straight line relationships for the end depth ratio (EDR) for different values of (So) and (m) with high determination coefficients and low values of root mean square error. A quadratic equation is obtained for the variation of EDR with (So). An empirical expression is obtained for a dimensionless discharge in terms of (So) for all channel models tested for both subcritical and supercritical flow conditions with the range of Froude number in the approach channel between 0.64 and 4.15. Two methods (direct and indirect) are proposed for the estimation of EDD in which the outcome results compared quite well with the available data of previous studies.

Nappe oscillations on free-overfall structures, data from laboratory experiments

This paper presents a dataset obtained from fifty-two laboratory experiments of nappe oscillations on free overfall structures. Data were collected on two complementary experimental setups, each consisting of a linear weir model. The dataset covers test configurations involving varied geometric parameters (i.e. weir crest shape, weir width, fall height and nappe confinement) and inflow discharges. The following experimental data were produced: assessment of nappe oscillation occurrence and associated frequencies. The later measurements were performed using characterization techniques (image and sound analysis) developed for this research. Reuse of the collected data will support efforts to improve the understanding of the physical processes underpinning nappe oscillation and to validate numerical modelling of the phenomenon.

Effect of the Vacuum under the Nappe on the Brink Depth in a Rectangular Channel

The author’s method for calculating the brink depth taking into account the vacuum under the nappe is used to evaluate the effect of the vacuum on the brink depth. It should be taken it into account when determining the discharge of water by the end-depth method in channels with a free overfall.

Application of novel data mining algorithms in prediction of discharge and end depth in trapezoidal sections

Flow measurement in irrigation and drainage networks and water conveyance channels have particular importance. Direct methods of flow measurement are costly, time-consuming and are generally associated with losses of energy in flow. In this study, estimation of discharge and end depth of free overfall flows in trapezoidal channels section were investigated. For this purpose, data-driven techniques including dynamic evolving neural-fuzzy inference system (DENFIS), multivariate adaptive regression spline (MARS) and M5 model tree (M5Tree) were developed. 189 laboratory data experiments, six different scenarios based on geometric variables including side slope (m), bed width (B), bed slope (S0), and hydraulic variables including critical depth (Yc), critical slope (Sc) and end depth (YE) or discharge (Q) were applied. The model’s performance was evaluated thorough several statistical indicators and graphical presentations. The accuracy of all three models were apparent in estimation of the discharge and the end depth for most of the scenarios. The results showed that the DENFIS model for the input combination of all variables (Yc, YE, B, S0, m, Sc) with the maximum values of R2 and Nash-Sutcliffe efficiency coefficient (NSE) that were equal to 0.976 and 0.975, respectively, and the minimum values of RMSE, MAE, PBIAS and RSR, that were equal to 0.0015, 0.0989, −1.5906, and 0.1574, respectively, showed the highest estimation accuracy. Regarding the end depth estimation, DENFIS model for the input combination including the variables Yc, Q, Sc, m, B with the highest values of R2 and NSE equal to 0.993 and 0.992 respectively, and the lowest values of RMSE, MAE, PBIAS and RSR equal to 0.0028, 0.1628, 0.7383 and 0.0883, respectively, had a better performance compared to other MARS and M5Tree. The results of this study suggest DENFIS as a suitable and powerful model for estimation of discharge in irrigation and drainage networks.

Application of Fawer Theory to End Depth in Trapezoidal Sloping Channel

AbstractThe Fawer assumption is applied to both energy and momentum equations to analyze free overfalls for a trapezoidal sloping channel in the supercritical flow regime under the assumption of ps...

Hydraulics of free overfall in steeply sloping rough rectangular channel: A general computational approach

All supercritical free overfalls were almost considered as frictionless flow or pseudo-uniform flow before, the effect of friction had not been paid due attention. Currently, a new mathematical model is proposed to analyze supercritical rectangular free overfall by Boussinesq-type energy equation accounting for frictional effect. A computational approach of loop iteration algorithm is utilized to simultaneously calculate the implicit water surface profile by Runge-Kutta method, end-depth-ratio, and discharge. Subsequently, the dependency of discharge on end depth and Nikuradse equivalent sand roughness for different slope is illustrated. Comparison of computed results with experimental observations reveals satisfactory agreement. Additionally, the present energy approach leads to more accurate results than the momentum method for high roughness. Finally, to aid application for engineers, an explicit solution of discharge for practical application in the commonly using range is also proposed. The most important purpose of this study is to present a general computational approach, which could be used for the rough supercritical free overfalls of any other cross-sections.

Flow measurement using free over-fall in generalized trapezoidal channels based on one velocity point method

A free over-fall offers the possibility of being used as a flow measuring device in hydraulic structures with a single depth measurement of the end section. Due to its practical importance, considerable attention has been paid to investigate free over-falls for different channel cross-sections using various approaches. This paper presents a new theoretical approach for computing the end depth ratio (EDR) relationship for the generalized trapezoidal channel cross-sections at free over-falls in sub critical flow regimes from which the end depth discharge (EDD) can be computed. The generalized trapezoidal channel is a geometric shape that is defined mathematically with a single equation where five widely known prismatic channel cross-sectional shapes can be generated (trapezoidal, inverted triangular (Δ), rectangular, parabolic, and triangular). This suggested theoretical approach uses one velocity point at the geometric center of the end section based on the energy and the continuity equations. Relevant experimental and theoretical results were utilized in order to examine the suggested method through the statistical measuring indices (percentage difference and the correlation coefficient (R2)). The computed results show very close agreements with the earlier works. Furthermore, simple equations are also generated using the regression curve fitting technique in order to estimate the direct discharges (Q) using the end depth (ye) for each of the above mentioned channel cross-sections.

Study of Flow Characteristics Over a Rounded Edge Drop Structure in Open Channel

Flow over a drop structure is a form of free overfall called hydraulic drop. Hydraulic drop changes the nature of flow abruptly from sub-critical to super-critical condition. Rapidly varied flow analysis is a complex phenomenon and involves remarkable characteristics. Some of the drop structures constructed in Sindh and Punjab provinces of Pakistan had gone through diverse failures, consequential in interruption of water supply to irrigation fields encountering substantial economic loss. In the present study experiments were carried out in the hydraulic laboratory of Mehran University of Engineering and Technology on round edged drop structure fitted in a horizontal rectangular flume (channel model). Data regarding hydraulic drop and hydraulic jump characteristics were collected during the experiment. The observed data included: flow discharge (Q), radius of rounded edge drop structure (r), height of the structure (h), hydraulic drop length (Ld), hydraulic jump length (Lj), depth of flow at toe of the jump (Y1) and tailwater depth (Y2). Applying dimensional analysis, the non-dimensional parameters of the observed data were calculated. Using statistical analysis, empirical relationships among the non-dimensional parameters were established for the appropriate design of the drop structure. The research results showed that the length and depth indices are functions of D=q2gh3 and r/h values. It was also found that for rounded-edge drop structure, the length of the stilling basin (LSB) reduces as r/h ratio increases

Estimation of discharge with free overfall in rectangular channel using artificial intelligence models

In open channels, free overfall can be used as a flow-measuring device in various flow regimes for different shapes of channels. The aim of this paper is to accurately estimate the discharge in rectangular channels by applying four soft computing models [i.e., artificial neural network (ANN), gene expression programming (GEP), multivariate adaptive regression spline (MARS) and M5 tree model]. The variables including brink depth, roughness coefficient, channel width and channel bed slope taken from earlier published works were used as inputs for the models. Data were divided according to three different splitting scenarios, 50%–50%, 60%–40% and 75%–25%, for training-testing phases to obtain more robust evaluation of the models. The computed discharges were then compared with experimental results. In order to evaluate the accuracy of discharge estimations by ANN, GEP, MARS and M5 tree models, six statistical measures including correlation coefficient (R), mean absolute error (MAE), root mean square error (RMSE), Nash-Sutcliffe (NS), Willmott index (WI) and Legates and McCabe index (LMI) have been applied. For different training-testing scenarios, the performance of the ANN model is better than the other methods. Regarding 50%–50% training-testing scenario, ANN has the best accuracy with R, RMSE, MAE, NS, WI and LMI of 0.994, 0.004 m3/s/m, 0.002 m3/s/m, 0.986, 0.999 and 0.909 by considering all inputs.