Stepped and smooth spillways: resistance effects on stilling basin lengths

Abstract

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.

Keywords:

• Darcy–Weisbach equation
• hydraulic jump
• preliminary design
• spillway
• stilling basin

Acknowledgements

The authors thank the Brazilian institutions FAPESP, CNPq and CAPES (process 2201/06-2) for financial support of this research.