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.     

Study and application of discharge calibration for submerged radial gates

Sophisticated stage-discharge rating curves for radial gates are essential to modernization efforts in water conservancy and irrigation projects. However, it is a challenging hydraulic issue to accurately determine discharges through radial gates, especially when subjected to highly submerged flow conditions. According to the variation trend of jet Froude number and the mechanism of energy dissipation subjected to submerged flows, a new criterion was proposed to subdivide submerged flow into partially submerged and totally submerged flows. Thus, the three stage-discharge equations were developed for free flow, partially submerged flow and totally submerged flow, respectively. With the aid of the experimental data of single radial gate and the field data of multi-radial gates, the proposed discharge calibration method, referred to as the identification method, was tested and verified. The results indicated the discharge prediction accuracies were satisfactory, in which the mean absolute percentage errors were less than 10%. The proposed method is feasible and easily programmed.     

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.     

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.     

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.     

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.     

Computation of discharge for simultaneous flow over weirs and below gates (H-weirs)

Simultaneous flow over weirs and below gates for free flow condition is experimentally investigated. Combination of a sharp-crested rectangular weir and rectangular gate is considered as a flow measurement structure which is named as H-weirs. H-weirs are defined by the width of the weir and gate openings, the height of the gate opening and the vertical distance between bottom of the weir and top of the gate. Laboratory experiments are conducted by measuring the discharge and the depth of water at upstream for different H-weirs. The present study aims to determine the discharge for a given H-weir simply by reading the depth of water at upstream of the combined structure. The compatibility of various formulations of the discharge–depth of water relationship is investigated by using the collected data and two new formulations are suggested based on the analysis of these data. After obtaining and comparing percentage errors of each equation, it is concluded that the new proposed equations can be used to accurately predict the discharge through H-weirs within the given ranges of the experimental study.     

Experimental analysis of combined side weir-gate located on a straight channel

Flow measurement and control in open channel system for lateral flow is important to support the system management. The flow characteristics of combined side weir-gate are complicated due to changes in flow conditions along the side weir-gate section. Experimental investigation of the flow characteristics of both weir and sluice gates is crucial for predicting the flow through a combined side weir-gate structure. Although weir-gate structures are widely used for frontal flow in hydraulic structures, the same is not true for lateral flows. In this study, 650 laboratory tests were conducted to determine the flow characteristics of combined side weir-gate for subcritical flow, and the experimental results were analyzed to determine the effect of these characteristics and weir-gate geometry on discharge capacity. Interaction factor of combined side weir-gate is a function of the upstream Froude number, the ratio of gate opening to upstream flow depth, the ratio of distance between the top of the sluice gate and the weir crest to gate opening, the ratio of weir and gate length to upstream flow depth, and the ratio of weir and gate length to main channel width. Consequently, more discharge is passed through combined side weir-gate compared to side weir and sluice gates. The empirically derived equations for the discharge of combined side weir-gate show good compatibility with the experimental data.     

Discharge coefficient for vertical sluice gate under submerged condition using contraction and energy loss coefficients

A novel method is suggested for the determination of flow discharge in vertical sluice gates with considerably small bias. First, in order to derive an equation for the discharge coefficient, energy-momentum equations are implemented to define the physical realization of the phenomenon. Afterward, the discharge coefficient is presented in terms of contraction and energy loss coefficients. Subsequently, discharge coefficient, contraction, and energy loss coefficients were determined through an implicit optimization technique on the data. Data analysis illustrated that there is a meaningful power relationship between the contraction and energy loss coefficients. Thereafter, dimensional analysis is performed and an explicit best-fit regression equation is developed for defining the energy loss coefficient. The obtained equations for contraction and energy loss coefficients were then used in the computation of the discharge coefficient and determination of the flow discharge in the vertical sluice gate. The performance of the developed approach is validated against the selected benchmarks existing in the literature.     

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.     

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.     

An experimental device for measuring radial flow velocity profiles of yield stress fluids

Measuring the radial flow velocity field of yield stress fluids (YSFs) between two parallel disks provides crucial data to understand the underlying flow phenomena. However, direct velocimetry of YSFs in the radial flow configuration remains a challenge, due to the complex fluid rheology and geometry constraints. In this paper, we present an experimental device for measuring YSF radial flow velocity profiles. Ultrasound Velocity Profiling (UVP) is used to non-intrusively measure the velocity profiles. The Tikhonov regularization method is implemented to obtain smooth velocity profiles, which are used to calculate the plug-flow region. Compared to our previous work on radial flow, the current contributions include: (i) additional structural frame members to maintain a constant aperture, (ii) wall slip reduction, and (iii) an improved velocity profile plug-detection algorithm. The results show that the experimental device and the measurement method are effective for further studying radial flow behavior of YSFs for industrial applications.     

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.     

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.     

Experimental and theoretical modeling of a quarter-circular gate flow

Gates are important hydraulic structures and used for flow measurement, water delivery, and water level regulation in open channels and irrigation networks. In this study, the quarter-circular gate is introduced and investigated. The cross section of this gate consists of a quarter circular arc and the lip angle of the gate equals to zero. Discharge coefficient, variation of downstream flow depth, and velocity distribution at opening section of gate were experimentally measured. Using potential flow theory supported by dimensional analysis, equations for discharge coefficient and velocity distribution at gate opening section of quarter-circular gate were derived and then validated using experimental data. The mean percentage error (MPE) of obtained equation for discharge coefficient of quarter-circular gate was calculated as 2.24%, indicating the high precision of the proposed theory. Based on obtained results, downstream flow depth of quarter-circular gate is uniform. Also, velocity distribution at gate opening section is nearly uniform. Discharge coefficient of quarter-circular gate was averagely obtained 55% larger than that of sluice gate. It was also obtained larger than that of radial gate. Elimination of contraction section at downstream of gate opening, which is the main source for energy loss and therefore discharge capacity reduction, is the main reason for larger discharge coefficient of quarter-circular gate.     

Application of the submerged experimental velocity profiles for the sluice gate's stage-discharge relationship

Sluice gates have been widely used and intensively studied, however their submerged flow conditions still call for in depth attention. A large scale experimental setup equipped with Acoustic Doppler Velocimetry, ADV, and electromagnetic flow-meter was used to thoroughly investigate various aspects of the hydraulics of submerged sluice gate. In this study, new experimental data sets are provided, that help better understand and quantify the flow features for submerged sluice gates. According to the experimental data generic fitting are provided for the velocity profiles from which the velocity correction factors can be obtained. Then, the experimentally obtained submerged head loss coefficient is presented and discussed. The results of this study showed that current classical Energy-Momentum methods (EM) failed to accurately determine the flow rate for the cases of highly submergences, while employing the interaction of the energy correction factors and head loss values in the EM model would result in more accurate head-discharge estimation. The new data set provided in this work can be used effectively for the validation of numerical modeling of submerged sluice gates.     

Automated classification and visualization of fluorescent live cell microscopy images

Robotic, high‐throughput microscopy is a powerful tool for small molecule screening and classifying cell phenotype, proteomic and genomic data. An important hurdle in the field is the automated classification and visualization of results collected from a data set of tens of thousands of images. We present a method that approaches these problems from the perspective of flow cytometry with supporting open‐source code. Image analysis software was created that allowed high‐throughput microscopy data to be analysed in a similar manner as flow cytometry. Each cell on an image is considered an object and a series of gates similar to flow cytometry is used to classify and quantify the properties of cells including size and level of fluorescent intensity. This method is released with open‐source software and code that demonstrates the method's implementation. Accuracy of the software was determined by measuring the levels of apoptosis in a primary murine myoblast cell line after exposure to staurosporine and comparing these results to flow cytometry.     

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.     

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.     

Application of a portable measuring system with acoustic Doppler current profiler to discharge observations in steep rivers

Obtaining discharge measurements during high flows is very difficult in steep rivers (slopes greater than about 0.1%) because of the highly unstable free surfaces and bed elevations. In this study, a portable flow measuring system with an acoustic velocimeter was developed. The proposed system has been proved to be better than existing systems for streamflow measurements in steep rivers. Field data collected by conventional velocimeters were analyzed, and compared with the flow measurements using the portable system with an ADP (acoustic Doppler profiler) or ADCP (acoustic Doppler current profiler). The effects of channel patterns on the applicability of the highly efficient discharge estimation method, as proposed by C.L. Chiu [An efficient method of discharge measurement in rivers and streams. In: Lecture of the workshop for development and application of discharge measurement in Taiwan. Taichung (Taiwan): National Chung-Hsing University, 1996. p. 55 [in Chinese]], were also discussed. In general, the method was applicable to higher flows where the measuring verticals were reasonably stable.