Avaliação de equações para cálculo do escoamento uniforme em canais lisos e rugosos

Abstract

Since the pioneering equation, developed by Chézy in the 18th century, there has been a search for new formulations to represent the uniform open-channel flow. Thus, until the 20th century, several researchers introduced new parameters related to the roughness of the walls and the shape fator of the channel to this equation. From the concepts of turbulent flow, in the first decades of the 20th century, new equations emerged with other parameters, seeking to improve the flow calculation performance. The present work aimed to assess the performance of classical and contemporary explicit equations for the calculation of the flow rate for uniform flow in channels of varied cross-sections. It also aimed to assess the best performance when considering equations for flows classified as relatively shallow or deep, hydraulically smooth or rough, and in subcritical or supercritical regimes. An extensive set of experimental data was used for the evaluations. The methodology consisted of comparing measured and calculated flow rates using the classical equations developed by Ganguillet and Kutter, Manning, and Bazin on the nineteenth century, and on the twentieth century by Pimenta, all based on the Chézy formula. Additionally, the calculations were performed using the equations developed in the current decade by Cheng and by Cabral da Silva, both based on the Darcy-Weisbach friction factor and on the Prandtl turbulence theory. The performance of each equation was determined using indicators, the frequency of smallest deviations, gradients and coefficients of determination of the linear regressions of the calculated flows and the Mean Absolute Relative Error (MARE). The results indicate that the most recent equations, which are Cheng for smooth rectangular channels and Cabral da Silva for the remaining cross-sections, presented the best performance indicators, highlighting the lowest MARE values of 0.83% and 2.66%, respectively.