Comments on “Study and application of discharge calibration for submerged radial gates” by Guo X., Guo Y., Wang T., Fu H., Li J. Flow Meas. Instrum. 78 (2021) 101912, https://doi.org/10.1016/j.flowmeasinst.2021.101912

This paper discusses the capability of Guo et al.'s (2021) equations to determine the discharge of radial gates under submerged flow conditions. It was concluded that Guo et al.'s (2021) equations are associated with error reduction compared to the Incomplete Self-Similarity (ISS) theory and the calibration method. However, it does not have a significant advantage over Energy-Momentum (E-M) approach. Employing E-M principles, new equations were proposed to determine the discharge of radial gates, which has some advantages compared to Guo et al. (2021), such as (1) error reduction under partially and fully submerged flow conditions, (2) least dependence on the empirical constants, (3) uniformity of form over the entire submerged condition, and (4) no need to classify the submerged flow. Field calibration showed that the proposed equations in the present study for a single gate predict the discharge of parallel radial gates with a mean absolute error of less than 4.5% subject to the submerged operation of all open gates.     

Rotary gate: Submerged flow condition

The rotary gate is a recently proposed gate for application in semicircular elevated irrigation networks. In this study, the hydraulics of rotary gate submerged flow was theoretically and experimentally investigated. Two approaches for estimating the submerged flowrate were considered, namely the stage-discharge based on the superposition rule and the dimensional analysis principles. The results revealed that the gate opening angle and the submergence ratio affect the submerged discharge the most. Based on the compiled experimental data relationships for estimating the discharge in such flow conditions were presented. Statistical analysis indicated that both approaches yielded satisfactory results for discharge estimation. Also, the submerged threshold condition of the rotary gate was investigated and a relationship was proposed whose results concurred with the observed data. In addition, the gate discharge coefficient and its head loss were studied and relationships for determining the discharge coefficient and the relative head loss in submerged flow condition were proposed.     

Effective parameters for calculating discharge coefficient of sluice gates

The present work demonstrates the characteristics of flow from sluice gates under free and submerged flow conditions using Energy and Momentum Equations (EMEs). The experimental data was used from the research works reported by different investigators to calibrate the proposed equations. An equation for estimation energy loss factor of sluice gate at free flow was presented and effect of this parameter on increasing discharge coefficient's accuracy was demonstrated. It was derived a theoretical equation for variations of sluice gate's discharge coefficient with relative opening and relative tailwater depth. Effects of energy loss factor on discharge coefficient and distinguishing limit were investigated. In this research the concepts of submergence limit of the gate and the submergence limit of hydraulic jump will be distinguished. By determining effective pressure on the gate and using EMEs, equations for variations of sluice gate's contraction coefficient with relative opening and relative submergence were presented. The result shows that at free flow condition, a minimum contraction coefficient obtained under a certain value of relative gate opening. At submerged flow condition, contraction coefficient would be either increased or decreased depending on the level of flow submergence. This paper carefully considered stage-discharge relationships for estimation gate discharge under free and submerged flow conditions.     

Stage-discharge relationship for slide gates installed in partially full pipes

Sluice/slide gates are widely used for flow depth control and flow discharge measurements in open channels. The hydraulic behavior of the sluice gates located in the rectangular open channels is well documented in the literature. This study reports the results of an investigation conducted to establish the stage-discharge relationship for the sluice gates located in horizontal, circular open channels/pipes under free outflow conditions. Different stage-discharge models were proposed based on the Buckingham's theorem of dimensional analysis and orifice theory. A comprehensive series of laboratory experiments (729 runs) were performed to study the sluice gates located at the middle, and at the end of two circular pipes. Using the data collected from two circular open channels of nominal diameters 20 and 30 cm, the proposed models were calibrated. For the middle slide gates, the experimental results showed that the discharge prediction can be improved by introducing the Reynolds number. For the slide gates located at the middle of the channel, the best proposed model has an average error of 1.40% with a maximum error of 7.12%. For the slide gates located at the end of the channel, the Reynolds number has no significant effect and best proposed model has an average error of 2.47% with a maximum error of 6.59%. The results also showed that the flow discharge of the end slide gate (with unconfined free jet under gravity) is higher than the flow discharge of the middle slide gate for the same gate opening areas and upstream flow depths. The proposed sluice/slide gate for circular open channels offers a simple and reliable discharge measurement approach with acceptable accuracy.     

Discharge estimation for submerged parallel radial gates

Seven hundred ninety-seven field-measured data points were collected to calibrate multiple parallel radial gates. Data were collected from three control structures (i.e., Al-Tawfiki, Al-Menoufi, and Abasi regulators), which are located in the Delta irrigation district of Egypt. Upstream and downstream water depths, gate opening size, and flow discharge was measured at each structure. Additionally, previous calibration methods were reviewed and evaluated. Dimensional analysis with application of the incomplete self-similarity concept demonstrated the best results for the study area. Based on the field measurement data, a simple formula that implicitly considers the discharge coefficient is proposed for estimating the flow rate through submerged parallel radial gates.     

Distinguishing condition curve for radial gates

Identifying the free or submerged flow condition and the threshold between the two regimes is vital for accurate flow measurement through a gate. In this paper, analytical findings about distinguishing condition curve of radial gates are presented. The generality of the available calibration methods of the radial gates has been analyzed. Then, based on the assumption of starting the transition zone right at the interception point of the free and submerged flow relationships, a comprehensive equation is developed to distinguish the flow condition through a radial gate. Using ample high quality available experimental data, the accuracy of the proposed distinguishing curve was verified. The results indicated that the proposed distinguishing curve accurately identified observed flow condition data. Finally, by defining a suitable sensitivity index, the effects of downstream channel width, energy loss through the gate, Reynolds number, and contraction coefficient on the distinguishing condition curve have been evaluated. Also, the results promise the application of the proposed method for situations where only one of some parallel radial gates is operating under the submerged flow condition.     

Parameter identification for discharge formulas of radial gates based on measured data

Calibrating the coefficients of discharge formulas of gates has great significance for the simulation and control of water flow. By investigating three discharge formulas derived from the energy equation and one discharge formula derived from dimensionless analysis of radial gates, the new parameter identification models for these discharge formulas were established using the least squares method, and the coefficients of discharge formulas were obtained. Followed by that, these discharge formulas of radial gates were applied through a case study. The results showed that the mean relative errors of the four formulas were 18.99%, 34.26%, 24.10% and 21.11%, respectively; while the mean relative errors were reduced to 3.54%, 3.54%, 1.90% and 1.09% by the use of parameter identification technique, respectively, indicating that the accuracy was greatly improved. The results proved that the parameter identification method may have potential application to improve the accuracy of calculating the discharge under the radial gates, and can also be applied to the sluice gates.     

The hydraulics of parallel sluice gates under low flow delivery condition

In this paper the flow through parallel sluice gates under low flow conditions and with some of the gates closed resulting in symmetrical or asymmetrical gate installations was studied experimentally. The current stage–discharge formula for single sluice gates cannot be used for either free flowing or submerged parallel sluice gates. Then, on the basis of experimental observations, the effect of the closed gates was considered to develop a submergence distinguishing condition curve formula. For both free and submerged regimes, the Π-theorem along with the incomplete self-similarity concept was used to develop head–discharge formulas for symmetrical and asymmetrical gate installations. The proposed formulas were then calibrated using the compiled experimental data. The new approach is shown to be applicable within the entire range of operation, i.e. from free to submerged flow regimes as well as the transition zone.     

Experimental study on rectangular cut-throated flume: Effects of flume walls slopes and channel longitudinal slope

This research conducted to study the flow through a rectangular cut-throated flume (RCTF). The flume is simply formed by placing two vertical triangular prisms (two vertical folded plates) on either side of a rectangular open channel. Both channel and flume cross-sections are rectangular. The investigated flume is inexpensive, easy to install and does not require high maintenance. A wide experimental investigation, carried out under free outflow conditions and under upstream subcritical flow regime to investigate the effects of the channel longitudinal slope, the flume throat width, and slopes of upstream and downstream flume walls on the stage-discharge relationship. The stage-discharge relationships were deduced by applying the dimensional analysis and were calibrated using the data of this study. The proposed stage-discharge equation for horizontal channel has an average absolute relative error of 2.97% with the relative errors restricted in the range of ±10%, and 80% of the data points are in the error range of ±5%. The proposed stage-discharge equation for sloping channel has an average absolute relative error of 3.97% with the relative errors restricted in the range of ±10%, and 66% of the data points are in the error range of ±5%. The measurements indicate that slopes of upstream and downstream walls affect the stage-discharge relationship of the CTFs only in sloping channels and flow discharge is not influenced by the flume walls slopes in a horizontal channel. The proposed unified stage-discharge equation for both horizontal and sloping channels has an average absolute relative error of 3.38% with the relative errors restricted in the range of ±10%, and 74% of the data points are in the error range of ±5%. The proposed stage-discharge model demonstrates favorable accurate and convenient estimation of discharge for flows through the CTFs.     

Flow through lateral circular orifice under free and submerged flow conditions

Open channels, with flow diversion structures such as orifices, weirs and sluice gates; are prevalent in irrigation systems, both for conveying water from the source to the irrigated areas, and for distributing the water within the irrigated area. The present study was broadly aimed at to investigate the flow characteristics of sharp-crested side circular orifices under free and submerged flow conditions through analytical and experimental considerations. It was also intended to develop relationships for coefficient of discharge for orifices under free and submerged flow conditions. The computed discharges using developed relationships were within ±5% and ±10% of the observed ones for free and submerged orifices, respectively. Sensitivity analysis reveals that the discharge through side orifice is more sensitive to the low head above the center of the orifice. Various parameters affecting the jet angles have been identified and relevant parameters are used for proposing relationships for the jet angle under different flow conditions.     

New stage-discharge relationship for cylindrical and semi-cylindrical edged sluice gates

Gates are simple hydraulic structures which have been widely used for flow control and measurement in irrigation networks. In this paper new sluice gates with cylindrical and semi-cylindrical edges were introduced and the flow movement below these types of gates was experimentally investigated for both free- and submerged-flow conditions. The Buckingham theorem of dimensional analysis and the self-similarity theory were applied for developing the stage-discharge relationships for the two investigated flow conditions. For these cylindrical and semi-cylindrical edged gates and a free-flow condition, the proposed stage-discharge relationship was characterized by an estimate error less than or equal to 5% for 96.0% and 93.7% of the calculated values, respectively. Finally, an equation for calculating the maximum tail water depth allowing free flow condition was proposed.     

Unified discharge coefficient formula for free and submerged triangular labyrinth weirs

The flow through a triangular plan labyrinth weir is studied for both free and submerged flow conditions experimentally and theoretically. The free flow condition is studied using a new experimental data set collected in this study. For the submerged flow condition, the threshold between free and submerged flow regimes is studied experimentally. Then Buckingham analysis is employed to determine the submerged head-discharge formula of the triangular plan labyrinth weir. Finally, a step by step calibration method is proposed to find the unified discharge coefficient. The proposed discharge coefficient can be used for both free and submerged flow conditions continuously and within the transition zone.     

Experimental study on free and submerged multi-jets

The flow characteristics of the hydraulic jump due to parallel jets are different from the classical jump emerging from a single gate. Due to the highly complex flow field at the downstream pool, deciding about the tailwater measuring location is a challenging issue affecting the flow measuring accuracy. Experiments are conducted herein, on different parallel jets’ configurations for both free and submerged flow conditions. To quantify the flow uniformity, for any downstream cross section, the associated momentum correction factors, β₂, were estimated for the free-flow condition. It is found that β₂-values depend significantly on the measuring location, and consequently the available conjugated depths relationship results in poor estimation when measuring location moves downstream. Employing Buckingham analysis, a general formula is proposed to calculate the momentum correction factors associated with the free hydraulic jump at different downstream measuring locations. The experimental results of this study indicated that such a formula enhances distinguishing between free and submerged flow conditions of the gates installed in parallel. Finally, a dimensionless stage-discharge formula is presented to predict the submerged flow rate through parallel gates of different gate openings and widths.     

Evaluation of 1-D and 2-D models for discharge prediction in straight compound channels with smooth and rough floodplain

Accurate estimation of discharge capacity of flooding rivers is extremely important in flood control projects. Floodplains are often covered with vegetation which generally increases the flow resistance, and affects the conveyance capacity. Several numerical methods have been proposed by researchers for predicting the stage-discharge relationship in compound channels. The hydraulic behavior of compound channel flow with vegetated floodplains is very complex. Hence, the accuracy of numerical discharge prediction methods must be investigated in compound channels with vegetated floodplain. In this paper, experimental results are presented for flow capacity of an asymmetric compound channel with vegetated and non-vegetated floodplain. An attempt has been made to compute the discharge with different 1-D and 2-D methods, including Single Channel Method (SCM), Divided Channel Methods (DCMs), Coherence Method (COHM) and Shiono and Knight Method (SKM). The results are then compared with experimental data. The results show that the SKM model is more accurate in discharge prediction than other models studied in the present study. Also, the DCM-ID model is found to be less accurate in discharge prediction in compound channels with smooth or rough floodplain.     

Flow over gabion weir under free and submerged flow conditions

A gabion weir is considered more environmentally friendly than a solid weir, as its porosity allows aquatic life and physical matter to move through it. In the present study, a series of laboratory experiments were conducted on flow over gabion weir and solid weir under free flow and submerged flow conditions. The collected data have been used to develop equations for the coefficient of discharge of gabion weir and solid weir. Two approaches are developed for the estimation of discharge over the gabion weir. Approach-I shows better results for the estimation of the discharge over gabion weir under free-flow and submerged flow conditions. Further, water surface profiles over the solid weir and gabion weirs with different porosities are observed during experimentation. It is also observed that the ratio of head over the gabion weir to crest height is an effective parameter for the coefficient of discharge of gabion weir.     

Discharge coefficient relationship for the sharp-edged width constriction new theory and experiment

In the field of flow measurement, what is needed in general rule is to design devices that are inexpensive, fairly accurate, and easy to implement. Some devices are more accurate than others but are very expensive.The present study examines a device for measuring flow in rectangular open channels that combines the three abovementioned advantages. It is made up of two separate vertical thin plates arranged in such a way that they form a central opening of width b less than the rectangular channel width B in which they are inserted. It is the simplest device ever imagined and designed for flow measurement in open channels.It is planned to derive the stage-discharge relationship by borrowing a rigorous theoretical development based on classical hydraulic formulas, accounting for the effect of the approach flow velocity. The intended stage-discharge relationship will allow us to derive the resulting discharge coefficient equation of the device.It is established that the resulting theoretical discharge coefficient is formally identified as being exclusively dependent on the contraction rate β = b/B, and this finding is predicted by dimensional analysis. Both dimensional and experimental analyses show no effect of the upstream water depth on the discharge coefficient for the selected values of β. The derived theoretical discharge coefficient relationship is straightforward, although it contains trigonometric functions that are somewhat cumbersome when the designer needs to perform a rapid field calculation.The theoretical and mean-experimental discharge coefficients of the eight tested devices are carefully compared using the one hundred and fifty-seven experimental values collected. An excellent agreement, even perfect, is observed since the maximum deviation worked out over the tested range of β is only 0.05%. This confirmed the validity of the theoretical relationship governing the discharge coefficient, which does not need any correction.     

Stage-discharge relationship for triangular and curved-edge triangular weirs

A sharp-crested weir with power-law sides is a general form, which reduces to the wildly used rectangular, parabolic, and triangular weirs. This general form allows modeling the weirs with different shapes. Up to now, the hydraulic performance of the power-law weirs with the exponent n in the range of 1 ≤ n ≤ 2 has not been studied. In this study, the triangular (n = 1) and curved-edge triangular (n > 1) weirs are studied experimentally and theoretically. For this, weir and critical flow theories along with Buckingham's theorem of dimensional analysis are used to deduce the stage-discharge relationship of the triangular and curved-edge triangular weirs. A series of laboratory experiments (464 runs) were conducted to calibrate the deduced theoretical stage-discharge relationships under free outflow condition. The proposed general stage-discharge relationship using the weir theory has a mean absolute relative error of 2.51% for 1 ≤ n ≤ 2. For this relationship, the mean absolute relative errors for n = 1, n = 1.5 and n = 2 are respectively as 1.96%, 2.64% and 3.08% whilst for the proposed stage-discharge relationship using the critical flow theory they are as 1.96%, 2.75% and 3.82%, respectively. Thus, the proposed stage-discharge relationship using the weir theory may be preferable due to its accuracy and generality.     

Experimental study on triangular central baffle flume

In this paper the results of the experiments performed to study the flow through a Triangular Central Baffle Flume (TCBF) are reported. The investigated flume consists of a triangular baffle of the apex angle of 75° with a given base width. The theoretical stage-discharge formula was deduced by applying the Buckingham's Theorem and incomplete self-similarity hypothesis and was calibrated using the laboratory measurements carried out in this investigation. The proposed stage-discharge formula is characterized by a mean absolute relative error of 7.4% and 72% of the data points are in an error range of ±5%. The results indicate that TCBF flume is characterized by a flow capacity higher than that of a typical central baffle flume. Experimental observations show that the contraction ratio is a key parameter to distinguish between free and submerged flow regimes through a TCBF. Finally, to identify the flow condition, submergence threshold condition was formulated.     

Discharge prediction for rectangular sharp-crested weirs by machine learning techniques

The stage-discharge relationship of a weir is essential for posteriori calculations of flow discharges. Conventionally, it is determined by regression methods, which is time-consuming and may subject to limited prediction accuracy. To provide a better estimate, the machine learning models, artificial neural network (ANN), support vector machine (SVM) and extreme learning machine (ELM), are assessed for the prediction of discharges of rectangular sharp-crested weirs. A large number of experimental data sets are adopted to develop and calibrate these models. Different input scenarios and data management strategies are employed to optimize the models, for which performance is evaluated in the light of statistical criteria. The results show that all three models are capable of predicting the discharge coefficient with high accuracy, but the SVM exhibits somewhat better performance. Its maximum and mean relative error are respectively 5.44 and 0.99%, and 99% of the predicted data show an error below 5%. The coefficient of determination and root mean square error are 0.95 and 0.01, respectively. The model sensitivity is examined, indicative of the dominant roles of weir Reynolds number and contraction ratio in discharge estimation. The existing empirical formulas are assessed and compared against the machine learning models. It is found that the relationship proposed by Vatankhah exhibits the highest accuracy. However, it is still less accurate than the machine learning approaches. The study is intended to provide reference for discharge determination of overflow structures including spillways.     

Non-contact flood discharge measurements using an X-band pulse radar (II) Improvements and applications

This paper presents and applies an improved method of determining cross-sectional depth and discharge of a river. The method used with the universal law and Darcy-Weisbach friction factors to obtain the lateral variation of the roughness height. This method of measurement was successfully used at the Kaoping River during the Xangsane typhoon in Taiwan, and the results show that the surface velocity obtained using an X-band pulse radar system were close to that obtained by the float method. The estimated discharges at four stages were within 3% of the recorded values of the stage-discharge rating curve in the gauging station.