Physical and Numerical Analysis of Outflow Discharge from Type-A Piano Key Weirs Under Steady and Unsteady Flow Conditions

The accurate estimation of outflow discharge from Piano Key Weirs (PKWs) under unsteady flow conditions is critical for effective flood management and the safety of dams. While extensive research exists on PKWs under steady flow, their hydraulic behavior during unsteady flow remains poorly understood. This study addresses this gap by investigating a Type-A PKW using combined physical and numerical modeling. A total of eight steady-flow and fifty-three unsteady-flow experiments were conducted. The steady flow experiments covered a range of Q = 5.13–40.76 L/s (H = 1.29–10.45 cm), while the unsteady experiments employed hydrographs with peak discharges up to ~68 L/s. Outflow was estimated via the Modified Puls method (hydrological routing) and a validated 3D numerical model (hydraulic routing). The results revealed significant discrepancies between steady and unsteady stage-discharge relationships, with a mean relative error of up to 41.37% and instantaneous errors exceeding 150% during the rising limbs of hydrographs with high rates of change in discharge, associated with intensified unsteady flow effects. A validated looped stage-discharge curve was observed under unsteady conditions, showing lower discharge on the rising limb for the same head. The Modified Puls method exhibited high accuracy, with relative errors below 5% when compared to hydraulic routing results. Additionally, three comparative indices were proposed and used to evaluate the performance of outflow estimation methods. The findings underscore the importance of incorporating unsteady flow conditions in the design and analysis of PKWs, particularly in the context of climate change and increasing flood uncertainties.