Environmental Engineering Reference
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Numerical and Simplified Analytical
Solutions for Typical Spillways
F. Rojano, A. Rojano, W. Ojeda, R. Mercado, M. Iniguez
and T. Espinosa
Abstract
The present work compares the numerical solution and the simplified
analytical solution to describe behavior of spillways. Specifically, the study focuses
on the identification of the water fall profile formed at crossing a spillway. Both,
the numerical and simplified analytical solutions are derived from the Navier-Stokes
equations. The numerical solution can take into account information regarding the
velocities, pressure and sources distributed in space within the regime of turbulence.
However, numerical solutions provide detailed information that usually demand a
significant amount of time and computational resources. Alternatively, the simplified
analytical solution can be reduced to the most important variables such as the head
of water arrival and the slope of the facing. Such simplification can incorporate
additional information obtained from numerical solutions to improve the accuracy
of the predictions. The objective of this study is to show how the simplified analytical
solutions can better describe the water fall profiles due to a modification that takes into
account a limited number of numerical solutions. This modified analytical solution
uses the Reynolds number (Re) and the coefficient (a) associated to the turbulent
regime.
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