The Saint-Venant shallow water equations are commonly used to model river hydraulics. The equations utilize a hydrostatic assumption with a recommendation to limit use to a bed slope less than 1:10, vertical to horizontal. This recommended limit was made in an era when calculations were performed by hand and therefore minimized by performing a one-dimensional analysis with the distance between river stations maximized. Current technology makes a more detailed analysis accessible.
This study investigates the effects of applying a two-dimensional hydraulic model that utilizes the Saint-Venant shallow water equations without correction for non-hydrostatic conditions to a bed slope of 1:8. By doing so it was hoped to show that there exists an effective and economical method for engineers to analyze hydraulic effects in these conditions.
A comparative analysis of the results from the 2D model and a 3D non-hydrostatic model was utilized to investigate the theoretical limit of slope on the hydrostatic assumption. The models consisted of an existing 2D model previously developed for an engineering study and a 3D model developed for this study, which employed a novel approach to approximate the effects of surface roughness. The analysis compared model results for depth, velocity, and flow rate at nine cross sections on the study reach. While the findings from the research are not conclusive they do illustrate that a well resolved 2D model is able to push the 1:10 slope limit on the hydrostatic assumption for the shallow water equations. It was found that a uniform flow applied to the 2D model and allowed to come to steady state maintained a relatively consistent flow rate throughout the length of the reach. This demonstrates that the model did not produce any artificial gains or losses. Surprisingly, the 2D model accomplished this while the 3D model did not.
These findings are important in locations where the accepted methods of 3D non-hydrostatic modeling would be computationally cumbersome and cost prohibitive. The lack of efficient and affordable analysis tools rated for steep slopes leads to the construction of facilities with unknown hydraulic risk to life and property. Fully verifying the methods of this study would provide needed support to hydraulic engineers for these conditions.
Concurrent to the research for this thesis, was the development of a series of lessons on introductory hydraulic engineering for middle school students. Engineering is characterized by its hands on, real world application of science and math and is rooted in a tradition of disseminating knowledge through mentorship. Many engineering topics provide opportunity to spark the minds of our youth. The final chapter of this paper is a summary of this work. It is included it here to encourage more engineers to share their work with the next generation.
|Advisor:||Bombardelli, Fabian A.|
|Commitee:||Bronner, Colleen E., Fleenor, William E.|
|School:||University of California, Davis|
|Department:||Civil and Environmental Engineering|
|School Location:||United States -- California|
|Source:||MAI 57/05M(E), Masters Abstracts International|
|Subjects:||Hydraulic engineering, Civil engineering, Water Resource Management|
|Keywords:||Education outreach, Hec-ras, Hydraulic engineering, Hydrostatic, Steep slope, Terrain roughness|
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