André Luiz Andrade Simões

Stepped and smooth spillways: resistance effects on stilling basin lengths

The Darcy–Weisbach equation was used in the analysis of flow over spillways, furnishing theoretical tools to design stilling basins. Predictions for the length of hydraulic jump stilling basins downstream of stepped and smooth spillways are presented, together with ranges of values for the Darcy–Weisbach friction factor of both spillways. The experimental data were compared with results of the theoretical solution of the gradually varied flow equation. All comparisons were made in non-dimensional form. The values of the Darcy–Weisbach friction factor were roughly five times smaller for smooth spillways than for stepped spillways. The theoretical predictions and the experimental data allow to present approximate equations for a preliminary evaluation of the length and the bed level of hydraulic jump stilling basins. In the same way, approximate equations were presented for the evaluation of the friction factor in smooth and stepped spillways, as a function of the Froude number at the downstream cross-section.

Transition length between water and air-water flows on stepped chutes

This study presents the steps followed to obtain mathematical models for the length of the transition region between the “full-water” and “full-mixed” flows in stepped spillways. This transition length is defined here as the distance along the flow, parallel to the pseudo-bottom, starting at the end of the “full-water” region and ending at the beginning of the “full-mixed” region. The definition is proposed based on experimental profiles of the surface obtained with an acoustic sensor in a stepped chute, which allows one to locate adequately the minima and maxima of the profile. A set of profiles obtained for different flow conditions is shown, and a comparison between predicted and calculated transition lengths is made. Experimental data and theoretical predictions superpose adequately for the present set of data.

Efeito da Turbulência na Determinação da Superfície Livre para o Cálculo da Resistência aos Escoamentos em Canais com Fundo em Degraus

The use of the Darcy-Weisbach equation involving research on smooth and stepped chutes developed over decades is presented in this work, looking at the wide variety of data and forecasts for the friction factor. The variations found for this dimensionless quantity are discussed with the help of experimental data measured in the physical model with 45o and step height of 5.0 cm. The results show that the turbulence near the free surface that prevents an accurate determination of the depth to be used, may be responsible for the dispersion in evaluating the resistance factor found in the literature. In addition, equations are presented that can help develop projects involving similar structures to those adopted in the tests performed.