Author(s): Mauricio Romero
Linked Author(s):
Keywords: Flow resistance; Steep slope rivers; Darcy-Weisbach roughness coefficient; Average flow velocity; Levenberg-Marquard iterative algorithm
Abstract: The aim of the present research work is the development of new flow resistance equations for steep slope rivers, in order to assess the Darcy-Weisbach friction factor coefficient f and the average flow velocity V in a studied reach. These new-found relationships are based upon extensive field work at five torrents from the Northern Mountain Range of the City of Cochabamba, Bolivia. Basic hydraulic data from the five studied rivers were collected at representative cross-sections through 120 liquid discharge measurements, 15 river sampling campaigns and 30 topographic surveys. The measurements were carried out during the dry season in order to achieve large scale roughness conditions at all the considered reaches. Eighteen empirical models from the scientific literature were initially assessed in order to estimate their precision and accuracy in the prediction of the Darcy-Weisbach roughness coefficient f and the average flow velocity V. For the development of new own flow resistance equations, semi-logarithmic and linear and non linear power relationships were explored. Eight models were initially considered where relevant variables playing a key role were the relative submergence d/D84, the ratio D84/D50, the standard geometric deviation σ = (D84/D16) 0. 5, the bed slope Sf and the Froude number of flow Fr. Software SPSS Statistics 17. 0 was used for linear and non-linear regression purposes, the latest based upon the Levenberg-Marquardt iterative algorithm (LMA). During the calibration phase, 102 data were randomly chosen through SPSS, leaving the remaining 18 data (15 % of total data) for models’ validation. The obtained results for most of the applied models from the scientific literature show a remarkable dispersion between calculated and observed values of the Darcy-Weisbach roughness coefficient f and the average flow velocity V in the studied reaches. From the eight tested own models, two formulas provided very satisfactory estimated values of the Darcy-Weisbach roughness coefficient f and the average flow velocity V for the studied cross-sections, when compared to the accuracy of the assessed literature models. However, It is observed that in spite of both models accurately predicting values of f and V, it is still a great deal of a challenge that those models fulfil the expected physical behavior of f vs. flow depth d due to the very complex existing flow patterns in steep slope torrents, flow regime, the uncertainty and accuracy in the data collection of hydraulic and geometric variables, suitable methods of bed particles areal sampling and other factors to be taken into account, being the skills and expertise of the user a fundamental aspect for a reliable interpretation of those results.
Year: 2013