# Predictive Modeling the Free Hydraulic Jumps Pressure through Advanced Statistical Methods

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Department of Water Engineering, University of Tabriz, Tabriz 5166616471, Iran

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Departamento de Obras Hidráulicas, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS 91.501-970, Brazil

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Department of Civil and Environmental Engineering, Politecnico di Milano, L. da Vinci, 32, 20133 Milano, Italy

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Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam

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Institute of Structural Mechanics, Bauhaus Universität Weimar, 99423 Weimar, Germany

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Department of Mathematics and Informatics, J. Selye University, 94501 Komarno, Slovakia

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Faculty of Health, Queensland University of Technology, 130 Victoria Park Road, Brisbane, QLD 4059, Australia

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Kalman Kando Faculty of Electrical Engineering, Obuda University, 1034 Budapest, Hungary

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Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam

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Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City, Vietnam

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Author to whom correspondence should be addressed.

Received: 25 January 2020 / Revised: 22 February 2020 / Accepted: 26 February 2020 / Published: 2 March 2020

(This article belongs to the Section Engineering Mathematics)

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.