<abstract xmlns="http://www.w3.org/1999/xhtml"><p> To find the steady flow water surface profile, it is possible to use Bernoulli’s equation, which is a discrete form of the differential energy equation. Such an approach requires the average energy slope between cross-sections to be estimated. In the literature, many methods are proposed for estimating the average energy slope in this case, such as the arithmetic mean, resulting in the standard step method, the harmonic mean and the geometric mean. Also hydraulic averaging by means of conveyance is commonly used. In this study, water surface profiles numerically computed using different formulas for expressing the average slope were compared with exact analytical solutions of the differential energy equation. Maximum relative and mean square errors between numerical and analytical solutions were used as measures of the quality of numerical models. Experiments showed that all methods gave solutions useful for practical engineering purposes. For every method, the numerical solution was very close to the analytical one. However, from the numerical viewpoint, the differences between the methods were significant, as the errors differed up to two orders of magnitude.</p></abstract>

To find the steady flow water surface profile, it is possible to use Bernoulli’s equation, which is a discrete form of the differential energy equation. Such an approach requires the average energy slope between cross-sections to be estimated. In the literature, many methods are proposed for estimating the average energy slope in this case, such as the arithmetic mean, resulting in the standard step method, the harmonic mean and the geometric mean. Also hydraulic averaging by means of conveyance is commonly used. In this study, water surface profiles numerically computed using different formulas for expressing the average slope were compared with exact analytical solutions of the differential energy equation. Maximum relative and mean square errors between numerical and analytical solutions were used as measures of the quality of numerical models. Experiments showed that all methods gave solutions useful for practical engineering purposes. For every method, the numerical solution was very close to the analytical one. However, from the numerical viewpoint, the differences between the methods were significant, as the errors differed up to two orders of magnitude.

Comparison of Average Energy Slope Estimation Formulas for One-dimensional Steady Gradually Varied Flow

Gdańsk University of Technology, Faculty of Civil and Environmental Engineering, ul. G. Narutowicza 11/12, 80-233 Gdańsk, Poland

Archives of Hydro-Engineering and Environmental Mechanics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

To find the steady flow water surface profile, it is possible to use Bernoulli’s equation, which is a discrete form of the differential energy equation. Such...

Comparison of Average Energy Slope Estimation Formulas for One-dimensional Steady Gradually Varied Flow

Published Online: Oct 07, 2015

Page range: 89 - 109

Received: Oct 09, 2014

DOI: https://doi.org/10.1515/heem-2015-0006

Keywords
open channel, steady flow, gradually varied flow, standard step method, energy slope

© by Wojciech Artichowicz

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Comparison of Average Energy Slope Estimation Formulas for One-dimensional Steady Gradually Varied Flow

Published Online: Oct 07, 2015

Page range: 89 - 109

Received: Oct 09, 2014

DOI: https://doi.org/10.1515/heem-2015-0006

Keywordsopen channel, steady flow, gradually varied flow, standard step method, energy slope

© by Wojciech Artichowicz

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
open channel, steady flow, gradually varied flow, standard step method, energy slope