Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

Version 1 : Received: 25 January 2020 / Approved: 26 January 2020 / Online: 26 January 2020 (07:32:50 CET)

A peer-reviewed article of this Preprint also exists.

Mousavi, S.N.; Júnior, R.S.; Teixeira, E.D.; Bocchiola, D.; Nabipour, N.; Mosavi, A.; Shamshirband, S. Predictive Modeling the Free Hydraulic Jumps Pressure through Advanced Statistical Methods. Mathematics 2020, 8, 323. Mousavi, S.N.; Júnior, R.S.; Teixeira, E.D.; Bocchiola, D.; Nabipour, N.; Mosavi, A.; Shamshirband, S. Predictive Modeling the Free Hydraulic Jumps Pressure through Advanced Statistical Methods. Mathematics 2020, 8, 323.

## Abstract

Pressure fluctuations beneath hydraulic jumps downstream of Ogee spillways potentially damage stilling basin beds. This paper deals with the extreme pressures underneath free hydraulic jumps along a smooth stilling basin. The experiments were conducted in a laboratory flume. From the probability distribution of measured instantaneous pressures, the pressures with different non-exceedance probabilities (P*a%) could be determined. It was verified that the maximum pressure fluctuations, as well as the negative pressures, are located at the positions closest to the spillway toe. The minimum pressure fluctuations are located at the downstream of hydraulic jumps. It was possible to assess the cumulative curves of P*a% related to the characteristic points along the basin, and different Froude numbers. To benchmark, the results, the dimensionless forms of mean pressures, standard deviations, and pressures with different non-exceedance probabilities were assessed. It was found that an existing methodology can be used to interpret the present data, and pressure distribution in similar conditions, by using a new third-order polynomial relationship for the standard deviation (σ*X) with the determination coefficient (R2) equal to 0.717. It was verified that the new optimized adjustment gives more accurate results for the estimation of the maximum extreme pressures than the minimum extreme pressures.

## Keywords

mathematical modeling; characteristic points; extreme pressure; hydraulic jump; pressure fluctuations; standard deviation; stilling basin

## Subject

Computer Science and Mathematics, Applied Mathematics