Numerical and Simplified Analytical Solutions for Typical Spillways

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.