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In this paper, the scour downstream of a trapezoidal Piano key weir (PKW) is investigated under free and submerged flow conditions. For this purpose, an experimental model was used in a laboratory channel with a length of 10 m, width of 0.75 m, and height of 0.8 m at various discharges and tailwater depths. The results showed an increase and decrease in the maximum scour depth with an increase in the discharge and submergence ratio, respectively. In addition, increasing the particle Froude number enhanced the geometric features of the scour hole downstream of the PKW. The rate of bed changes slowed down over time. The average values of maximum scour depth, the distance of the maximum scour depth from the weir toe, maximum scour hole length and weir toe scour depth increased in the free flow compared to the submerged flow. The scour hole volume and scour hole area in the submerged flow were less compared to the free flow. The average maximum level of the sedimentary ridge in the free flow is less than the submerged flow. New equations for calculating the geometric characteristics of the scour hole downstream of the trapezoidal PKW are presented with acceptable accuracy.

This study experimentally investigated the temporal evolution of the scour parameters downstream of a trapezoidal piano key weir. The densimetric Froude number (Frd50) in the range of 0.39–0.57 and the relative vertical distance of the sediment bed level to the weir toe (Δz/P) in the range of 0.025–0.5 were taken into consideration. In general, with an increase in Frd50, the scouring rate, maximum scour depth, scour hole area and scour hole volume enhanced over time. The increases in the scour parameters were greater at the initial stages of the tests. About 87, 80, 65 and 70% of the maximum scour depth, weir toe scour, scour hole area and scour hole volume occurred within the first 20% of the durations of the tests, respectively. Any increase in Frd50 and Δz/P augmented the scour depth at the weir toe. The results also indicated that the distance of maximum scour depth from the weir increased for greater values of Δz/P and Frd50. The amounts of scour downstream of the outlet keys were greater than those downstream of the inlet keys. The trend of variations of the longitudinal bed profiles remained nearly unchanged over time. New equations were developed to predict the temporal variations of scour parameters, with acceptable accuracy. [ABSTRACT FROM AUTHOR]

This study examines the scouring effect downstream of a type-A trapezoidal stepped Piano key weir using experimental methods. The experiments were performed on weirs, both with and without steps at the outlet keys, while considering various discharge rates, tailwater depths, and bed material sizes. The study scrutinized three unique weir configurations, each with different dimensions and step counts at the outlet keys: the first, second, and third weirs had 5, 10, and 15 steps respectively. The findings indicate that the maximum scour depths in the Piano key weirs with 5, 10, and 15 steps were, on average, 17.5%, 31%, and 19% less than those in the non-stepped weir. It was also noted that an increase in discharge and a decrease in tailwater depth and bed material size led to an increase in the maximum scour depth. Moreover, an increase in the number of steps and a decrease in the size of the bed materials resulted in a reduction in sediment ridge height. The analysis suggests that the average scour index values in the 10-stepped weir were about 21% lower compared to the non-stepped weir. These insights contribute to the design and optimization of hydraulic structures to effectively mitigate scouring effects. [ABSTRACT FROM AUTHOR]

The assessment of scour depth downstream of weirs holds paramount importance in ensuring the structural stability of these hydraulic structures. This study presents groundbreaking experimental investigations highlighting the innovative use of baffles to enhance energy dissipation and mitigate scour in the downstream beds of rectangular piano key weirs (RPKWs) and trapezoidal piano key weirs (TPKWs). By leveraging three state-of-the-art supervised machine learning algorithms—multi-layer perceptron (MLP), extreme gradient boosting (XGBoost), and support vector regression (SVR)—to estimate scour hole parameters, this research showcases significant advancements in predictive modeling for scour analysis. Experimental results reveal that the incorporation of baffles leads to a remarkable 18–22% increase in energy dissipation and an 11–14% reduction in scour depth for both RPKWs and TPKWs. Specifically, introducing baffles in RPKWs resulted in a noteworthy 26.7% reduction in scour hole area and a 30.3% decrease in scour volume compared to RPKWs without baffles. Moreover, novel empirical equations were developed to estimate scour parameters, achieving impressive performance metrics with an average R2 = 0.951, RMSE = 0.145, and MRPE = 4.429%. The MLP models demonstrate superior performance in predicting maximum scour depth across all scenarios with an average R2 = 0.988, RMSE = 0.035, and MRPE = 1.036%. However, the predictive capabilities varied when estimating weir toe scour depth under diverse circumstances, with the XGBoost model proving more accurate in scenarios involving baffled TPKWs with R2 = 0.965, RMSE = 0.048, and MRPE = 2.798% than the MLP and SVR models. This research underscores the significant role of baffles in minimizing scouring effects in TPKWs compared to RPKWs, showcasing the potential for improved design and efficiency in water-management systems. [ABSTRACT FROM AUTHOR]

The piano key weir (PKW) is an evolution with more hydraulic efficiency, compared to labyrinth weir. The studies on this type of weir have shown a significant increase in its discharge efficiency, especially at low heads. In this study, discharge coefficient of various shapes of piano key weir (i.e. rectangular, trapezoidal, and triangular) is investigated experimentally. Also, the aeration process of the studied weirs is described. According to the results, it was found that the discharge coefficient of the triangular PKW is about 28.2% more than the discharge coefficient of the rectangular PKW, and the discharge coefficient of the trapezoidal PKW is about 12.9% more than the discharge coefficient of the rectangular PKW. Also, the discharge capacity of the rectangular, triangular, and trapezoidal PKWs are 3.8, 3.96, and 3.96 times the sharp crest weir, respectively. The equations introduced for the discharge coefficient show good agreement (with R2 from 0.968 to 0.988 and average percentage error from 0.82 to 2.6%) between the actual and calculated values. [ABSTRACT FROM AUTHOR]

AbstractThe understanding of scouring around piers is crucial for ensuring the safety of bridges. However, the effects of bridge pier inclination angle and pier inclination direction on river bed topography have not been extensively explored. In this article, the effects of pier inclination angle and direction on local scouring were experimentally studied for both rectangular and circular bridge piers. Three pier inclination directions (upstream, downstream, and laterally inclined) were investigated, along with various pier inclination angles and flow intensities. Eighty-seven experiments were conducted on a uniform sand bed. It was observed that the relative scour depth was highest for upstream-inclined piers and lowest for downstream-inclined ones, with intermediate values for vertically and laterally inclined piers. Moreover, the scour depth decreased significantly for downstream-inclined piers with increasing pier inclination angle, while it increased for upstream-inclined piers. The relative scour depth increased with higher flow intensity, ranging from 1.2 to 3.7 for rectangular piers and 1.3 to 2.45 for circular piers. Approximately 72.5%, 74.5%, 72%, and 75% of the equilibrium scour depth were reached after about 10% of the experimental duration for flow intensities of V/Vc = 0.75, 0.85, 0.95, and 0.98, respectively. Rectangular piers exhibited higher scour depths compared to circular piers. Furthermore, relative scour depths for downstream-inclined rectangular and circular piers were reduced by approximately 34% and 15%, respectively, relative to vertical piers, while for upstream-inclined piers, they increased by about 9% and 7.5%, respectively. The corresponding reductions for laterally inclined rectangular and circular piers were 4% and 3%, respectively. Several available predictive equations for scour depth were compared, and the one that correlated best with the data was introduced. Additionally, new equations were developed to predict maximum scour depth, considering pier inclination angle and direction, which showed good agreement with previous data. [ABSTRACT FROM AUTHOR]

Soil fluidisation around buried pipes is one of the water leakage effects that has a direct influence on the ultimate failure of pipelines. In this research, using a laboratory model, the fluidisation caused by water leakage from three cracks with three lengths (14, 17, and 20 mm) and a 3 mm diameter hole for five pressures (1.5–5.5 bar) in non-uniform soils has been evaluated. The experiments were carried out both for pipes buried in soil, as well as exposed pipes. In the buried pipe tests, leakage flow rate, fluidisation, and mobile bed zone dimensions were investigated. The results showed that the increase in leakage flow rate due to an increase in pressure and crack length in exposed pipes is higher than in buried pipes. The exponent of the leakage–pressure relationship was obtained between 0.40 and 0.47 for the hole and between 0.8 and 1.9 in the crack. Observing different development patterns for fluidisation and mobile bed zones in cracks and holes, new relationships are presented for the height, width, and cross-sectional area of the leakage zones. [ABSTRACT FROM AUTHOR]

In this paper, a straightforward approach was applied for estimating the discharge of sharp-crested rectangular and triangular side weirs. The extensive experimental data (356 for rectangular side weir and 362 for triangular side weir) and the available data from other sources (171 for rectangular side weir and 145 for triangular side weir) were used for the analysis. The effects of approach Froude number Fr1, ratio of weir height to upstream flow depth p/y1, ratio of effective weir length to main channel width L/B, and ratio of effective weir length to upstream flow depth L/y1 were studied. It was found that the parameters p/y1, Fr1, and L/B have a reciprocal effect on each other. Sensitivity analysis performed by using ANFIS model, showed that the relative discharge of the rectangular side weir is influenced by Fr1, p/y1, L/B, and L/y1. Moreover, Fr1 for triangular side weir and p/y1 for rectangular side weir are the most effective parameters influencing the relative discharge. Meanwhile, L/y1 has a secondary effect on the relative discharge of side weir. Based on dimensional analysis, new explicit equations for estimating the relative discharge for rectangular and triangular side weirs were presented. The results were also compared with previous studies. The capability of ANN, ANFIS, SVR, and GBRT methods was also evaluated in estimating the side weir relative discharge. The ANFIS model for rectangular side weir with MSE = 0.0011 and CP10% = 85.09, and SVR model for triangular side weir with MSE = 0.0011 and CP10% = 87.25 were found to be the superior models in estimating the relative discharge. [ABSTRACT FROM AUTHOR]

In this paper, a fluidized granular sand bed by a vertically upward water leak jet was studied experimentally. It was found that an increase in the size of sand particles decreases the height of the fluidized zone, and vice versa. By increasing the cover depth, the height and area of the fluidized and mobilized bed zones are reduced. Dimensions of the fluidized zone increase as the pressure increases. As the pressure inside the pipe increases 5-fold, the relative area of the fluidized zone increases approximately 3.5-fold, and the relative height increases 12-fold. By increasing ratio of the cover depth to mean particle size, the relative area and relative height of fluidization increases. New equations were obtained to determine the relative area and the relative height of the fluidized zone. [ABSTRACT FROM AUTHOR]

The hydraulic characteristics of a side sluice gate were studied experimentally. It was found that the specific energy remains constant along the side sluice gate. The coefficient of discharge for the side sluice gate is related to the main channel Froude number and the ratio of upstream depth of flow to sluice gate opening for free flow. It also depends on an additional parameter: the ratio of tailwater depth to the gate opening for submerged flow. Suitable equations for discharge coefficient are obtained. DOI: 10.1061/(ASCE)0733-9437(2003)129:6(458) CE Database subject headings: Discharge coefficients; Gates; Free flow; Submerged flow.

In this paper, the effects of the nondimensional parameters influencing the discharge coefficient of a side-combined structure located in a channel bend were studied using 288 experimental data. Experiments were conducted in a rectangular recirculating U-shaped channel (0.6 m width and 0.7 m height) for different discharges and depths of flow in the channel. The effects of approach Froude number Fr, the ratio of the gate height to gate opening d/a, the ratio of the approach flow depth to gate opening h1/a, and angle of the bend curvature α on the discharge coefficient under subcritical flow conditions are investigated. It was found that the flow diversion by a side-combined structure leads to a reverse flow, two separation zones, and a stagnation zone in the main channel. The specific energy remains constant along with the side-combined structure. It was found that the discharge coefficient is a decreasing function of Fr and d/a. Moreover, the discharge coefficient increases by increasing h1/a. By changing the location of the side-combined structure along the channel bend, the discharge coefficient reduces from upstream, reach to a minimum value at α= 90ᵒ, and increase further downstream. The discharge coefficient of a side-combined structure is maximums when it is located at section 115° of the bend. New equations for the discharge coefficient of a side-combined structure under subcritical flow conditions were obtained. [ABSTRACT FROM AUTHOR]