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Accurate determination of grate inlet discharge coefficients is crucial in reducing modeling uncertainties and mitigating urban flooding hazards. This review critically examines the methods, equations, and recommendations for determining the weir/orifice discharge coefficients, based on the inlet parameters and flow conditions. Reviewing previous studies for inlets showed that the discharge coefficient of rectangular inlets under subcritical flow ranges from 0.53 to 0.6 for weirs and from 0.4 to 0.46 for orifices, while in grated circular inlets, it falls between 0.115 and 0.372 for weirs and between 0.349 and 2.038 for orifices. For circular non-grated inlets under subcritical flow, the weir and orifice coefficients are in the range of 0.493–0.587 and 0.159–0.174, respectively. However, the orifice discharge coefficients of grated and non-grated inlets with unknown Froude number range between 0.14–0.39 and 0.677–0.82, respectively. For supercritical flow, the weir and orifice discharge coefficients of grated and non-grated rectangular inlets are 0.03–0.47 and 1.67–2.68, respectively. Previous studies showed that it is recommended to correlate the discharge coefficients with the approaching flow and Froude number under subcritical and supercritical flows, respectively. Yet, additional studies are recommended for a better understanding of the limits and parameters governing the flow transitional stage between weir and orifice and between subcritical and supercritical conditions. Moreover, further research is required to determine the weir and orifice discharge coefficients of circular inlets under supercritical flow as well as the orifice discharge coefficient range of rectangular non-grated inlets under subcritical flow. Finally, it is recommended to increase the road surface roughness to reduce Froude number, and thereby, increase discharge coefficients of street inlets. The aim of this review is to help inlet designers and authorities promote sustainable cities with resilient urban drainage systems and reduce the environmental, economic, health, and social impacts of urban drainage failure.

The Piano Key (PK) weir is a new type of long crested weirs. This study was involved the addition of a gate to PK weir inlet keys. It was conducted by the Department of Water Engineering, University of Tabriz, Iran to determine if the gate increased hydraulic performance. A Gated Piano Key (GPK) weir was constructed and tested for discharge ranges of between 10 and 130 l per second. To this end, 156 experimental tests were performed and the effective parameters on the GPK weir discharge coefficient (Cd), such as gate dimensions (b and d), gate insertion depth in the inlet key (Hgate), the ratio of the inlet key width to the outlet key width (Wi/Wo) and the head over the GPK weir crest (H) were investigated. In addition, application of soft computing to estimate of Cd was carried out using MLP, GPR, SVM, GRNN, multiple linear and non-linear regressions methods using MATLAB 2018 software. This study suggests the relation for Cd with non-dimension parameters. The results of this study showed that H, Wi/Wo, Hgate and b and d, had the greatest effect on the GPK weir discharge coefficient, respectively. The GPR method was introduced as a new effective method for predicting discharge coefficient of weirs with RMSE = 0.011, R2 = 0.992 and MAPE = 1.167% and provided the best results when compared with other methods.

Cavitation is the transition from a liquid to a vapour phase, due to a drop in pressure to the level of the vapour tension of the fluid. Two kinds of cavitation have been reviewed here: acoustic cavitation and hydrodynamic cavitation. As acoustic cavitation in engineering systems is related to the propagation of waves through a region subjected to liquid vaporization, the available expressions of the sound speed are discussed. One of the main effects of hydrodynamic cavitation in the nozzles and orifices of hydraulic power systems is a reduction in flow permeability. Different discharge coefficient formulae are analysed in this paper: the Reynolds number and the cavitation number result to be the key fluid dynamical parameters for liquid and cavitating flows, respectively. The latest advances in the characterization of different cavitation regimes in a nozzle, as the cavitation number reduces, are presented. The physical cause of choked flows is explained, and an analogy between cavitation and supersonic aerodynamic flows is proposed. The main approaches to cavitation modelling in hydraulic power systems are also reviewed: these are divided into homogeneous-mixture and two-phase models. The homogeneous-mixture models are further subdivided into barotropic and baroclinic models. The advantages and disadvantages of an implementation of the complete Rayleigh–Plesset equation are examined.

The micro-flow control system, serving as a critical component of the air-breathing electric propulsion storage and supply system, is responsible for precise delivery of captured rarefied atmospheric gas. As a key technology in air-breathing electric propulsion, its performance directly determines the operational stability and efficiency of the thruster. An essential flow regulation approach involves adjusting upstream pressure and modifying micro-orifice dimensions. Micro-orifices (micron-scale throat-diameter conical entrance sonic nozzles) act as flow output elements in this system. This study investigates the flow characteristics of these micro-orifices under low Reynolds number conditions (Re < 2000), with the upstream side maintained at standard atmospheric pressure and the downstream connected to a vacuum chamber (40-120 μm orifices) via pressure controllers. Experimental analysis revealed that when the Reynolds number is below 2000, the critical back pressure ratio (CBPR) of the micro-orifices is approximately 0.19. The discharge coefficient Cd exhibits an increasing trend at Reynolds numbers below 900, while oscillating between 0.88 and 0.94 when the Reynolds number exceeds 900. Compared to conventional micron-scale arc-shaped sonic nozzles (CBPR = 0.53, Cd = 0.98), the studied micro-orifices demonstrate reduced CBPR and Cd values, indicating greater deviation between actual and theoretical flow rates under low Reynolds conditions. These findings provide theoretical foundation and technical references for optimizing micro-flow control systems in air-breathing electric propulsion applications.

The dynamic properties of a compact hydro-pneumatic suspension strut integrating the gas chamber are investigated analytically and experimentally. A comprehensive experiment was designed to experimentally characterize the dependence of friction force on the strut operating pressure in addition to the pressure/force–displacement and pressure/force–velocity properties of the prototype under broad ranges of excitations. An analytical model of the strut is formulated to incorporate the polytropic gas process, nonlinear and hysteretic friction force and turbulent flows across the piston orifices. Owing to dominant effect of friction due to seals of the floating piston separating the gas and oil media, and strong dependence of friction force on the operating pressure, the Coulomb and Stribeck friction effects are described by a nonlinear function in the operating pressure. Furthermore, the viscoelastic O-ring-type seals contributed to notable hysteresis at very low velocities, which is described by a hyperbolic tangent function in velocity. The discharge coefficient of flows through orifices is also identified from the measured fluid pressures. The validity of the proposed model is demonstrated through comparisons of force–displacement and force–velocity responses of the model with the corresponding measured data under broad ranges of excitations. The comparisons revealed that the model could predict dynamic behavior of the strut reasonably well. The effects of charge pressure and gas volume are further investigated to seek guidance on tuning of the strut for realizing desired load carrying capacity and suspension stiffness.

Accurately quantifying the capacity of sewer inlets (such as manhole lids and gullies) to transfer water is important for many hydraulic flood modelling tools. The large range of inlet types and grate designs used in practice makes the representation of flow through and around such inlets challenging. This study uses a physical scale model to quantify flow conditions through a circular inlet during shallow steady state surface flow conditions. Ten different inlet grate designs have been tested over a range of surface flow depths. The resulting datasets have been used (i) to quantify weir and orifice discharge coefficients for commonly used flood modelling surface–sewer linking equations and (ii) to validate a 2D finite difference model in terms of simulated water depths around the inlet. Calibrated weir and orifice coefficients were observed to be in the range 0.115–0.372 and 0.349–2.038, respectively, and a relationship with grate geometrical parameters was observed. The results show an agreement between experimentally observed and numerically modelled flow depths but with larger discrepancies at higher flow exchange rates. Despite some discrepancies, the results provide improved confidence regarding the reliability of the numerical method to model surface to sewer flow under steady state hydraulic conditions.

The present study used three machine learning models, including Least Square Support Vector Regression (LSSVR) and two non-parametric models, namely, Quantile Regression Forest (QRF) and Gaussian Process Regression (GPR), to quantify uncertainty and precisely predict the side weir discharge coefficient (Cd) in rectangular channels. So, 15 input structures were examined to develop the models. The results revealed that the machine learning models used in the study offered better accuracy compared to the classical equations. While the LSSVR and QRF models provided a good prediction performance, the GPR slightly outperformed them. The best input structure that was developed included all four dimensionless parameters. Sensitivity analysis was conducted to identify the effective parameters. To evaluate the uncertainty in the predictions, the LSSVR, QRF, and GPR were used to generate prediction intervals (PI), which quantify the uncertainty coupled with point prediction. Among the implemented models, the GPR and LSSVR models provided more reliable results based on PI width and the percentage of observed data covered by PI. According to point prediction and uncertainty analysis, it was concluded that the GPR model had a lower uncertainty and could be successfully used to predict Cd.

A side or lateral weir can be defined as a longitudinal weir put in parallel to the main flow direction. A piano key side weir (PKSW) is one of the various side weirs used to control flow level, flow diversion, and flood harm prevention in dams and hydraulic systems. A side weir aims to keep the water level in the main channel at a specific level by discharging the overflow water into a side channel. The discharge coefficient of the PKSW was covered in this study by numerical modeling of a rectangular PKSW type B with various ratios of the crest length to the width in a straight channel. Results showed that the discharge coefficient of the PKSW was more affected by the parameter when the other parameters were constant. It was noted that the PKSW discharge coefficient for equal to 6 demonstrated a significantly higher level of performance and also found that increasing the upstream head above the side weir crest ( ) negatively affected the coefficient of discharge. It was concluded that a high capacity of the discharge coefficient required the ( ) ratio to be smaller than 0.75 or within the range (0.3 ≤ < 0.75).

Gates are useful structures that are widely used in open channels for controlling discharge and water level. In this article, to study the flow passing under a gate, five gates with different-shaped edges are numerically simulated. The contraction coefficient, discharge coefficient, pressure distribution behind the gate, and the pressure distribution on the channel bottom near the gate were investigated with models in free flow conditions. The analyses were performed for six water depths. The results show that the contraction coefficients for standard and jagged-edged shapes increase with an increase in the a/E 1 ratio (where a is the gate opening and E is the energy level), which matches the experimental results. For upward- and downward-facing sharp edges and for rounded-edged gates, the contraction coefficient decreases until a/E 1 < 0.4 and increases for a/E 1 > 0.4. Investigation of pressure distribution behind the gate and on the bottom of the channel under the gate shows that the position of maximum pressure is the same for all models, but its magnitude varies among different models. Comparison of numerical analysis results with experimental and theoretical data showed good agreement.

Triangular orifices are widely used in industrial and engineering applications, including fluid metering, flow control, and measurement. Predicting discharge through triangle orifices is critical for correct operation and design optimization in various industrial and engineering applications. Traditional approaches like empirical equations have accuracy and application restrictions, whereas computational fluid dynamics (CFD) simulations can be computationally costly. Alternatively, artificial neural networks (ANNs) have emerged as a successful solution for predicting discharge through orifices. They offer a dependable and efficient alternative to conventional techniques for estimating discharge coefficients, especially in intricate relationships between input parameters and discharge. In this study, ANN models were created to predict discharge through the triangle orifice and velocity at the downstream of the main channel, and their effectiveness was assessed by comparing the performance with the earlier models proposed by researchers. This paper also proposes a novel hybrid multi-objective optimization model (NSGA-II) that uses genetic algorithms to discover the best values for design parameters that maximize discharge and downstream velocity simultaneously.