Predicting the Discharge Coefficient of Arched Piano Key with a Trapezoidal Cross Section

In this research, a special form of nonlinear weirs called piano key overflows has been studied. In this type of weirs, unlike congressional weirs, the openings are sloping inwards and outwards one by one.so this study was conducted with the aim of laboratory study of the discharge coefficient of the arched piano key in the plan in free flow conditions. In this research, 27 models of arched piano key overflow structures with three arc lengths of 1.20, 1.40, 1.60 m, three crown lengths of 5.10, 4.30, 3.20 m and three crown heights of 0.30, Made 0.20, P = 0.15 m. All models were made of glass with a thickness of 10 mm.The models were compared in terms of height effect, key width ratio and arc effect under the same effective length conditions. The results showed that increasing the flow rate and consequently increasing the dimensionless ratio, leads to a decrease in watering coefficient and in fact has the opposite effect on the permeability coefficient of piano switch weir in free flow. Also, by increasing the dimensionless ratio, the flow currents from the output switch interfere with each other, and as a result, due to the local immersion, the overflow coefficient of the overflow of the arched piano switch in the free flow decreases. The arc model with an arc length of 1.40 m with 1.27 had the highest and the arc model with 1.20 m and 1.22 had the lowest permeability coefficient in free flow. Finally, it was found that the arc model has a higher permeability coefficient than the direct model, which indicates the positive effect of the arc. Also, in order to estimate the permeability coefficient of free flow and Q flow rate, relationships were provided for the overflow of the piano switch in the arc position.