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The enormous energy carried by discharged water poses a serious threat to the Piano Key Weir (PKW) and its downstream hydraulic structures. However, previous research on energy dissipation in PKWs has mainly focused downstream effects, and the research methods have been largely limited to physical model experiments. To deeply investigate the discharge capacity and hydraulic characteristics of PKW, this study established a PKW model with universally applicable geometric parameters. By combining physical model experiments and numerical simulations, the flow pattern of the PKW, the discharge at the overflow edges, and the variation in the energy dissipation were revealed for different water heads. The results showed that the discharge of the side wall constitutes the majority of the total discharge at low water heads, resulting in a relatively high overall discharge efficiency. As the water head increases, the proportion of discharge from the inlet and outlet keys increases, while the proportion from the side wall decreases. This change results in less discharge from the side wall and a consequent reduction in the overall discharge efficiency. The PKW exhibits superior energy dissipation efficiency under low water heads. However, this efficiency exhibits an inverse relationship with an increasing water head. The overall energy dissipation efficiency can reach 40% to 70%. Additionally, the collision of the water flows inside the outlet chamber and the mixing of the overflow jet play a primary role in energy dissipation. The findings of this study have significant implications for hydraulic engineering construction and PKW operational safety.

A compound channel’s discharge capacity and boundary shear force can be predicted as a sum of the discharge capacity of different sub-regions once the apparent shear stress of the dividing line is reasonably quantified. The apparent shear stress was usually expressed as a coefficient multiplied by the difference between two squared velocities of two adjacent regions. This study investigated the range of the coefficient values and their influencing factors. Firstly, the optimal values of the coefficient were obtained based on experimental data. Then, comparisons between the optimal values and several parameters used in quantifying the apparent shear stress were conducted. The results show that the coefficient is mainly related to a morphological parameter of the floodplain and the ratio of resistance coefficients between the floodplain and the main channel. An empirical formula to calculate the coefficient was developed and introduced to calculate the flow discharge and boundary shear stress. Experimental data, including 142 sets of test data of symmetric-floodplain cases and 104 sets of one-floodplain cases, have been used to examine the prediction accuracy of discharges and boundary shear stress. For all these tests, the ranges of water depth of the main channel and the total width of the compound cross-section are about 0.05~0.30 m and 0.3~10 m, respectively; the Q range and the range of Froude numbers of the main channel flow are about 0.0033~1.11 m3/s and 0.3~2.3, respectively. Comparison with other methods and experimental data from both rigid and erodible compound channels indicated that the proposed method not only provided acceptable accuracy for the computation of discharge capacity and boundary shear stress of compound channels in labs but also gave insights for calculating discharge capacity in natural compound channels.

The piano key (PK) weir is a cost-effective structure for flood discharge. Its typical layout comprises a rectangularly cranked crest in planform with up- and downstream overhangs. With the intention to enhance its hydraulic efficiency, the conventional weir is improved. The sloping floor of each key is modified with a downward semi-circle in the cross-section; each overhanging apex is thus assigned an elliptical crest. Thus, the developed crest length of the resulting weir becomes considerably extended. Experiments are performed to compare the hydraulic behaviors of the improved weir with a reference one. The models are 3D-printed to attain high manufacture precision. For the model dimensions chosen in the study, the developed crest is ~36% longer. The study demonstrates that the improvements in geometry lead to appreciably enhanced flow discharge capacity. Within the hydraulic range examined, the augment in flow discharge varies within a range from 30% to 53%. In terms of both discharge capacity and flow patterns, the improved weir clearly outperforms the conventional one. The elliptical overhang apexes noticeably extend the developed crest length. The streamlined upstream overhang without singularity and the lowered inlet key floor reduce the entrance energy loss and improve the inflow to the inlet key and the flow over the crest. The lowered floor also gives rise to extra water volume, which administers to the flow motion towards the crest. For the outlet key, its lowered floor facilitates the outflow and alleviates the liableness of local submergence at high discharges. If the footprint for spillway construction is limited or the increase in the reservoir water stage must be controlled, the use of a more effective PK weir for flood discharge has significant engineering implications.

This paper focuses on Piano Key Weirs (PKWs) as an effective solution for improving the discharge capacity of spillway systems. The flow behavior in inlet and outlet keys is experimentally studied to analyze the discharge capacity of PKWs with different plan shapes (i.e., rectangular, trapezoidal, and triangular). The results show that in outlet keys, the flow aeration regimes extend to higher values of headwater ratios (Ho/P) by increasing the length magnification ratio (B/w) and apex width ratio (A/w). In addition, the local submergence length is a decreasing function of A/w, especially in high flow heads. While the total interference length enlarges by reducing A/w in lower Ho/P values (Ho/P < 0.5), a reverse trend is observed in higher headwater ratios. PKW performance may also be impacted by the flow contraction and recirculation zone in inlet keys, which intensify in higher values of Ho/P, B/w, and A/w. According to the obtained results, while the discharge coefficient is a decreasing function of A/w in Ho/P > 0.4, it may have a reverse trend in lower head conditions. In addition, a trapezoidal PKW has the highest discharge efficiency in a wide range of the studied domain (Ho/P > 0.25 and B/w ≥ 2). It can improve the discharge efficiency by around 5%, while its body volume is almost 7% smaller than the traditional rectangular PKW. However, for low-length and high-head conditions (B/w = 1 and Ho/P > 0.5), the efficiency a rectangular PKW exceeds that of the other shapes.

Storm drainage inlets transport urban runoff and discharge to underground sewer systems. If the inlet structure is blocked, the urban drainage system is hampered, leading to urban flooding. To quantitatively analyze the influence of clogging conditions on inlet discharge capacity, laboratory experiments were conducted to address the impact of different inlet clogging conditions on inlet discharge capacity under different upstream discharge conditions. These were based on a two-layer platform that mimicked a complete inlet structure including a drainage grate, a rainwater well, and a connecting pipe. The results show that the water flow near the inlet was similar to weir flow when the rainwater well was not full, whereas the water flow state near the inlet behaved similarly to orifice flow after becoming full. In addition, it was found that the clogging extent and position can significantly influence the comprehensive discharge capacity of the street inlet. The experimental dataset was used to calculate the inlet discharge coefficients of the weir and orifice flow states under different clogging conditions. The results are applicable to research addressing the formation mechanisms of urban floods. Additionally, this study is of practical significance for early warning systems and emergency response support during heavy rainfall.

This paper presents the findings of a study into how different inlet designs for stormwater culverts increase the discharge rate. The objective of the study was to develop improved inlet designs that could be retro-fitted to existing stormwater culvert structures in order to increase discharge capacity and allow for changing rainfall patterns and severe weather events that are expected as a consequence of climate change. Three different chamfer angles and a rounded corner were simulated with the software ANSYS Fluent, each of the shapes tested in five different sizes. Rounded and 45 ∘ chamfers at the inlet edge performed best, significantly increasing the flow rate, though the size of the configurations was a critical factor. Inlet angles of 30 ∘ and 60 ∘ caused greater turbulence in the simulations than did 45 ∘ and the rounded corner. The best performing shape of the inlet, the rounded corner, was tested in an experimental flume. The flume flow experiment showed that the optimal inlet configuration, a rounded inlet (radius = 1/5 culvert width) improved the flow rate by up to 20% under submerged inlet control conditions.

Culverts, as an essential part of drainage networks worldwide, provide an efficient solution for flowing waters to cross man-made barriers including roads. Existing structures can be many years old and changes in rainfall patterns due to global warming might not have been considered in their original design. While correctly designed culverts can effectively drain water during high-intensity rainfall events, poorly designed or outdated structures could cause upstream flooding resulting in costly damage and losses. Hydraulic improvements to prepare existing culverts for greater discharge rates could be a favorable alternative to rebuilding every failing structure. Modern design guidelines calculate the performance for inlet and outlet controlled flows on the basis of established hydraulic theories. After calculating the headwater levels for both flow controls, the inferior one is then chosen, based on the assumption that the culvert will operate in its least efficient state. Flow improvements could be made by enforcing the better performing option. Outlet control can be ensured by raising the tailwater levels as high as the outlet thereby utilizing the entire cross-sectional area of the culvert. It was found that, in some cases, an enforced outlet control enables culverts to perform better than operation under inlet control. However, only smooth and short culverts with high losses at the inlet were identified as benefiting from this approach and many existing structures could be improved by better inlet designs.

Gullies are sewer inlets placed in pavements usually covered by bar grates. They are the most common linking-element used to drain a wide range of flows from surface runoff into the buried drainage system. Their hydraulic behavior and their overall hydraulic performance is dependent on the flow conditions, the gully dimension, geometry, and location of the outlet device. Herein a numerical research based on Volume Of Fluid ( V O F ) to detect the interface, and on the Shear Stress Transport S S T k - ω turbulence model was conducted to study the importance of the outlet location and characterize flows through them in drainage conditions. Results provided detailed information about flow features, discharge coefficients, and efficiencies for different outlet locations. The authors identified three different regimes, R 1 , R 2 , and R 3 , and concluded that the outlet location influences the velocity field along the gully, the discharge coefficient, and the drainage efficiency. This allows for the estimation of uncertainty and its variation for different outlet positions.

Combined orifice-weir flow is a complex phenomenon in hydropower and the discharge capacity of a structure affects the safety of the structure. It is essential to propose an equation for computing the discharge coefficient of combined orifice-weir flow. Based on theoretical analyses and physical experiments, 284 laboratory tests were performed to determine the discharge coefficient. The parameters affecting the discharge coefficient were determined and the relationships between the coefficient and four parameters, that is, the ratio of the water head to the upstream water level, the ratio of orifice height to orifice-weir height, the ratio of orifice height to the water head, and the ratio of the length to the height of the orifice-weir structure, were established. According to the dimensional analysis and the linear-fitting method of multidimensional ordinary least squares, five models were constructed to analyze the sensitivity of the model’s accuracy by using different parameters. The sensitivity to each parameter was also evaluated. The results were examined with statistical indices and they showed that one model yielded the best results, which were consistent with the experimental values. Thus, the proposed model is effective in estimating the discharge coefficient of combined orifice-weir flow.

Sedimentation commonly occurs in urban drainage systems, disrupts flow, and is one of the major causes of inundation. The complicated phenomena that alter the cross-section of sewer conduits include transportation, precipitation, and sedimentation, and need to be analyzed for the proper design and efficient maintenance of urban drainage systems. In this study, the discharge capacity of urban drainage systems is simulated and analyzed by considering the pattern of flow of sediments in sewer conduits through a numerical analysis model. The sites of the highest and lowest accumulation of soil were examined as sedimentation occurred, as was discharge due to accumulation in sewer conduits. The purpose of this study is the examination of mathematical models for two-phase fluid flow analysis and the prediction of sedimentation in urban sewer conduits. An expression for the height of the sedimentation was obtained to assess the discharge capacity of urban drainage systems, and a model to predict accumulation in sewer conduits was developed using non-dimensional variables for inlet velocity, inlet particle volume fraction, and particle size. When subjected to linear regression analysis, the model yielded a high correlation coefficient (R2) of 0.899. This satisfied the aims of this study, to obtain a higher discharge capacity and a plan for the design of urban drainage systems.