Energy loss prediction and analysis for rectangular, triangular, and trapezoidal piano key weirs

ABSTRACT This study evaluates and compares the energy dissipation of piano key weirs (PKWs) with different shapes in plan view (rectangular, triangular, and trapezoidal plans). To achieve this goal, a series of laboratory experiments was conducted using a straight flume with dimensions of 10 × 0.75 × 0.9 m and a deep rectangular flume using physical models of PKWs under varying flow conditions. The findings revealed a steady reduction in relative energy dissipation (ΔEr) as the head above the weir increased. Among the different shapes, rectangular PKWs presented the highest energy dissipation across various flow conditions, whereas triangular PKWs presented the lowest dissipation, particularly at higher flow rates. Trapezoidal PKWs demonstrated superior efficiency at lower flow conditions, outperforming triangular PKWs but falling short of rectangular PKWs under similar circumstances. The average energy dissipation was 81.41, 79.03, and 79.67% for trapezoidal, rectangular, and triangular PKWs, respectively, indicating superior performance of trapezoidal PKWs at high heads and better performance of rectangular PKWs at low heads. The discharge coefficient (Cd) was highest for the rectangular PKW in lower discharge scenarios, whereas the highest average coefficient was observed for triangular PKW.