Complex Rating Curves for Sharp Crested Orifices and Rectangular or Triangular Weirs under Unsteady Flow Conditions

The importance of discharge measurements is fully acknowledged in many research fields, mostly in hydrology. Numerous measurement devices and various overflow structures have been proposed for discharge measurements; however, their use is based on calibrated simple stage discharge relationships that may cause significant errors when unsteady flow conditions occur. This issue is quite common because of rainfall and runoff temporal variability that inhibits the achievement of the steady state. Although this issue has already been experimentally investigated, it seems that a physically based line of approach has not been attempted before. In this paper, unsteady stage discharge relationships on a theoretical basis are derived for the most common shapes of weirs. According to previous experimental investigations, a transposition of the simple (steady-state) rating curve occurs, with higher input discharges than those under steady state, when the water level rises, and with lower input discharges, when the water level falls. The corresponding time to equilibrium is also studied and two different applications are performed. Finally, when the outflow process is unsteady, an error analysis quantitatively shows that using simple rating curves may determine high errors in discharge measurements, which decrease more and more at the attaining of the steady state, where no transposition of the rating curve occurs. Triangular weirs result more sensitive to the unsteadiness than rectangular weirs, which in turn result more sensitive than the sharp crested orifices. The suggested procedure could be relevant to improve the accuracy in the discharge estimate, as it could be demonstrated by comparing the discharges derived by the proposed procedure and the ones provided by the application of hydrodynamic and rainfall-runoff models.