This study mainly aims to investigate and quantify the influence of piano key weir (PKW) characteristics on its discharge coefficient. Accordingly, based on dimensional analysis, seventy-two experimental runs were carried out using sixteen PKW physical models of various geometric characteristics as well as different flow rates too to develop the target empirical discharge coefficient formula.
The analysis highlights that relative length (𝐿/𝑊) and alveoli width (𝑊i/𝑊o) are the most studied effective PKW dimensionless ratios that significantly influence the discharge coefficient. Increasing 𝐿/𝑊 from 1 to 7 leads to noted discharge coefficient values increasing up to 27.15%. While variation Wi/Wo ratio from 0.5 to 2 can cause the discharge coefficient to increase up to 25.28%.
The study results were statistically compared with the previously developed models and it has shown good agreement with their outcomes. Considering the proposed discharge coefficient formula, the optimum hydraulic design of the new PKW model can be successfully facilitated by the extrapolation of characteristics of the idealized scale.