An Experimental Study of Flow Energy Loss in Trapezoidal Stepped Piano Key Weirs (PKWs)

Weir is a structure that is made in the body or in supports of a dam to safely discharge the excess volume of water from a reservoir. It is the main factor of safety for dams during floods. A Piano Key Weir (PKWs) is a modified type of labyrinth weir that is designed and built for increasing weir capacity at a specified water head on the weir crest compared to linear weirs. It can provide a specified discharge with a significantly lower upstream water depth. Considering that there is little information about energy loss in PKWs, this article dealt with the experimental study of energy loss in a type-A trapezoidal PKW. The experiments were conducted in a flume made from metal with a length, width, and height of respectively 10, 0.75, and 0.80 m in the hydraulic laboratory of the department of Water and Hydraulic Structures in the Faculty of Civil and Environmental Engineering, Tarbiat Modares University, Tehran. They were performed with weirs with and without steps in their outlet keys at the different flow rates of 30, 40, 50, and 60 L/s. The flow from the upstream tank of 2.05 m length was conducted by a guiding wall to enter the weirs after passing a distance of 1 m. A type-A trapezoidal PKW with 3 keys was utilized. The examined weir had an inlet key width of 0.175 m, outlet key width of 0.051 m, upstream and downstream overhang length of 0.125 m, lateral wall length of 0.5 m, weir height of 0.2 m, weir wall thickness of 0.012 m, and inlet and outlet key slope of 0.53. 3 weir models with different dimensions and number of steps were employed at the outlet keys. The first, second, and third weirs were investigated with 5, 10, and 15 steps, respectively. The PK weir geometry creates a 3D flow field that can be characterized by inclined jet and free fall jet exiting the inlet and outlet keys, respectively. to the downstream and into the outlet keys. The results showed that the energy loss was higher at lower flow rates. The average energy losses were 15.73, 24.93, and 18.52% in the 5-, 10-, and 15-step weirs compared to those without steps, respectively. The discharge coefficients were calculated and compared via two methods. The discharge coefficient calculated with an integral relation was 2.64% higher than that calculated with the general relation for weirs. In addition, this coefficient increased with an increase in the ratio of the weir crest length to its total width. The difference in energy loss measured before the hydraulic jump at a distance of 10 times the weir height was about 3%. The energy loss decreased with an increase in the flow rate and depth of the flow upstream of the weir. The presence of steps at the weir outlet keys had an increasing effect on the energy loss. The highest energy loss (24.93%) was observed in the 10-step weir. Some relations were presented for calculating the amount of energy loss in the type-A trapezoidal stepped PKW, as well as its amount on each step.