Predictive Modeling the Free Hydraulic Jumps Pressure through Advanced Statistical Methods

Seyed Nasrollah Mousavi, Renato Steinke Júnior, Eder Daniel Teixeira, Daniele Bocchiola, Narjes Nabipour, Amir Mosavi and Shahabodin Shamshirband
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Seyed Nasrollah Mousavi: Department of Water Engineering, University of Tabriz, Tabriz 5166616471, Iran
Renato Steinke Júnior: Departamento de Obras Hidráulicas, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS 91.501-970, Brazil
Eder Daniel Teixeira: Departamento de Obras Hidráulicas, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS 91.501-970, Brazil
Daniele Bocchiola: Department of Civil and Environmental Engineering, Politecnico di Milano, L. da Vinci, 32, 20133 Milano, Italy
Narjes Nabipour: Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam
Amir Mosavi: Institute of Structural Mechanics, Bauhaus Universität Weimar, 99423 Weimar, Germany
Shahabodin Shamshirband: Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam

Mathematics, 2020, vol. 8, issue 3, 1-16

Abstract: Pressure fluctuations beneath hydraulic jumps potentially endanger the stability of stilling basins. This paper deals with the mathematical modeling of the results of laboratory-scale experiments to estimate the extreme pressures. Experiments were carried out on a smooth stilling basin underneath free hydraulic jumps downstream of an Ogee spillway. From the probability distribution of measured instantaneous pressures, pressures with different probabilities could be determined. It was verified that maximum pressure fluctuations, and the negative pressures, are located at the positions near the spillway toe. Also, minimum pressure fluctuations are located at the downstream of hydraulic jumps. It was possible to assess the cumulative curves of pressure data related to the characteristic points along the basin, and different Froude numbers. To benchmark the results, the dimensionless forms of statistical parameters include mean pressures ( P* m ), the standard deviations of pressure fluctuations ( σ* X ), pressures with different non-exceedance probabilities ( P* k% ), and the statistical coefficient of the probability distribution ( N k% ) were assessed. It was found that an existing method can be used to interpret the present data, and pressure distribution in similar conditions, by using a new second-order fractional relationships for σ* X , and N k% . The values of the N k% coefficient indicated a single mean value for each probability.

Keywords: mathematical modeling; extreme pressure; hydraulic jump; stilling basin; standard deviation of pressure fluctuations; statistical coefficient of the probability distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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