Scale effects related to the rating curve of cylindrically crested Piano Key weirs

Hydraulic scale effects on physical Piano Key weir (PKW) models were so far rarely discussed in literature, even though almost all prototypes are model-tested before construction. In parallel, physical weir models are generally known to include significant scale effects if operated under small heads, so that an up-scaling of the results derived from the latter is unreliable regarding the discharge-head function (rating curve). This comes from the fact that viscosity and surface tension of water are fluid properties which cannot be scaled simultaneously, whereas both affect the flow in models. Thus, scale effects occur particularly for small overflow heads. Literature mentions limiting heads to respect in the order of 0.03 to 0.05 m. Furthermore, a specific ‘low-head behavior’ regarding the transition from the clinging to the leaping nappe has been reported, which is different in a prototype and its scaled model. The latter is linked to the teapot effect and to air-water flow features. To derive general equations for the head-discharge relationship of PKWs, researchers thus have to exclude data which could be subjected to scale effects, without knowing the precise limit so far. However, the tests to be excluded are of specific interest to develop the aforementioned relationship, as PKWs are particularly efficient for these conditions. The paper discusses scale effects related to PKWs, based on an analogy considering cylindrical weirs.