scholarly journals Predictive Modeling the Free Hydraulic Jumps Pressure through Advanced Statistical Methods

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 323
Author(s):  
Seyed Nasrollah Mousavi ◽  
Renato Steinke Júnior ◽  
Eder Daniel Teixeira ◽  
Daniele Bocchiola ◽  
Narjes Nabipour ◽  
...  
Keyword(s):  
Probability Distribution ◽  
Pressure Fluctuations ◽  
Mean Value ◽  
Maximum Pressure ◽  
Hydraulic Jumps ◽  
Statistical Parameters ◽  
Characteristic Points ◽  
Stilling Basins ◽  
The Stability ◽  
Cumulative Curves

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 (Nk%) 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 Nk%. The values of the Nk% coefficient indicated a single mean value for each probability.

scholarly journals Predictive Modeling the Free Hydraulic Jumps Pressure through Advanced Statistical Methods

2020 ◽  
Author(s):  
Seyed Nasrollah Mousavi ◽  
Renato Steinke Júnior ◽  
Eder Daniel Teixeira ◽  
Daniele Bocchiola ◽  
Narjes Nabipour ◽  
...  
Keyword(s):  
Pressure Fluctuations ◽  
Maximum Pressure ◽  
Hydraulic Jumps ◽  
Third Order ◽  
Stilling Basin ◽  
Laboratory Flume ◽  
Order Polynomial ◽  
Characteristic Points ◽  
Negative Pressures ◽  
Cumulative Curves

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.

scholarly journals Analysis of minimal and maximal pressures, uncertainty and spectral density of fluctuating pressures beneath classical hydraulic jumps

2020 ◽  
Vol 20 (5) ◽  
pp. 1909-1921
Author(s):  
Seyed Nasrollah Mousavi ◽  
Davood Farsadizadeh ◽  
Farzin Salmasi ◽  
Ali Hosseinzadeh Dalir ◽  
Daniele Bocchiola
Keyword(s):  
Spectral Density ◽  
Large Scale ◽  
Pressure Fluctuations ◽  
Low Frequency ◽  
Dominant Frequency ◽  
Standard Uncertainty ◽  
Hydraulic Jumps ◽  
Stilling Basins ◽  
Density Analysis ◽  
Real Scale

Abstract Knowledge of extreme pressures and fluctuations within stilling basins is of the utmost importance, as they may cause potential severe damages. It is complicated to measure the fluctuating pressures of hydraulic jumps in real-scale structures. Therefore, little information is available about the pressure fluctuations in the literature. In this paper, minimal and maximal pressures were analyzed on the flat bed of a stilling basin downstream of an Ogee spillway. Attention has been focused on dimensionless pressures related to the low and high cumulative probabilities of occurrence (P*0.1% and P*99.9%), respectively. The results were presented based on the laboratory-scale experiments. These parameters for the relatively high Froude numbers have not been investigated. The total standard uncertainty for the dimensionless mean pressures (P*m) was obtained around 1.87%. Spectral density analysis showed that the dominant frequency in the classical hydraulic jumps was about 4 HZ. Low-frequency of pressure fluctuations indicated the existence of large-scale vortices. In the zone near the spillway toe, P*0.1% reached negative values of around −0.3. The maximum values of pressure coefficients, namely |CP0.1%|max and CP99.9%max, were achieved around 0.19 and 0.24, respectively. New original expressions were proposed for P*0.1% and P*99.9%, which are useful for estimating extreme pressures.

scholarly journals Pressure Fluctuations in the Spatial Hydraulic Jump in Stilling Basins with Different Expansion Ratio

Water ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 60
Author(s):  
Nasrin Hassanpour ◽  
Ali Hosseinzadeh Dalir ◽  
Arnau Bayon ◽  
Milad Abdollahpour
Keyword(s):  
Hydraulic Jump ◽  
Laboratory Tests ◽  
Pressure Fluctuations ◽  
Expansion Ratio ◽  
Hydraulic Jumps ◽  
Extreme Pressure ◽  
Flow Conditions ◽  
Stilling Basins ◽  
Channel Expansion ◽  
Shed Light

Pressure fluctuations are a key issue in hydraulic engineering. However, despite the large number of studies on the topic, their role in spatial hydraulic jumps is not yet fully understood. The results herein shed light on the formation of eddies and the derived pressure fluctuations in stilling basins with different expansion ratios. Laboratory tests are conducted in a horizontal rectangular flume with 0.5 m width and 10 m length. The range of approaching Froude numbers spans from 6.4 to 12.5 and the channel expansion ratios are 0.4, 0.6, 0.8, and 1. The effects of approaching flow conditions and expansion ratios are thoroughly analyzed, focusing on the dimensionless standard deviation of pressure fluctuations and extreme pressure fluctuations. The results reveal that these variables show a clear dependence on the Froude number and the distance to the hydraulic jump toe. The maximum values of extreme pressure fluctuations occur in the range 0.609<X<3.385, where X is dimensionless distance from the toe of the hydraulic jump, which makes it highly advisable to reinforce the bed of stilling basins within this range.

Determination of the Probability Distribution of the Mean Sound Level

2010 ◽  
Vol 35 (4) ◽  
pp. 543-550 ◽  
Author(s):  
Wojciech Batko ◽  
Bartosz Przysucha
Keyword(s):  
Probability Distribution ◽  
Probability Distribution Function ◽  
Mean Value ◽  
Sound Level ◽  
Function Form ◽  
Noise Levels ◽  
Logarithmic Mean ◽  
The Mean ◽  
Estimation Of Uncertainty

AbstractAssessment of several noise indicators are determined by the logarithmic mean <img src="/fulltext-image.asp?format=htmlnonpaginated&src=P42524002G141TV8_html\05_paper.gif" alt=""/>, from the sum of independent random resultsL1;L2; : : : ;Lnof the sound level, being under testing. The estimation of uncertainty of such averaging requires knowledge of probability distribution of the function form of their calculations. The developed solution, leading to the recurrent determination of the probability distribution function for the estimation of the mean value of noise levels and its variance, is shown in this paper.

scholarly journals Inlay-Retained Dental Bridges—A Finite Element Analysis

2021 ◽  
Vol 11 (9) ◽  
pp. 3770
Author(s):  
Monica Tatarciuc ◽  
George Alexandru Maftei ◽  
Anca Vitalariu ◽  
Ionut Luchian ◽  
Ioana Martu ◽  
...  
Keyword(s):  
Finite Element ◽  
Young Patients ◽  
Maximum Pressure ◽  
Class Iii ◽  
Element Analysis ◽  
Dental Prostheses ◽  
Abutment Teeth ◽  
Fixed Dental Prostheses ◽  
Implant Therapy ◽  
The Stability

Inlay-retained dental bridges can be a viable minimally invasive alternative when patients reject the idea of implant therapy or conventional retained full-coverage fixed dental prostheses, which require more tooth preparation. Inlay-retained dental bridges are indicated in patients with good oral hygiene, low susceptibility to caries, and a minimum coronal tooth height of 5 mm. The present study aims to evaluate, through the finite element method (FEM), the stability of these types of dental bridges and the stresses on the supporting teeth, under the action of masticatory forces. The analysis revealed the distribution of the load on the bridge elements and on the retainers, highlighting the areas of maximum pressure. The results of our study demonstrate that the stress determined by the loading force cannot cause damage to the prosthetic device or to abutment teeth. Thus, it can be considered an optimal economical solution for treating class III Kennedy edentation in young patients or as a provisional pre-implant rehabilitation option. However, special attention must be paid to its design, especially in the connection area between the bridge elements, because the connectors and the retainers represent the weakest parts.

scholarly journals Parametric and Internal Resonances of an Axially Moving Beam with Time-Dependent Velocity

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Bamadev Sahoo ◽  
L. N. Panda ◽  
G. Pohit
Keyword(s):  
Internal Resonance ◽  
Multiple Scales ◽  
Time History ◽  
Mean Value ◽  
Phase Portraits ◽  
Axially Moving Beam ◽  
Internal Resonances ◽  
Moving Beam ◽  
Axially Moving ◽  
The Stability

The nonlinear vibration of a travelling beam subjected to principal parametric resonance in presence of internal resonance is investigated. The beam velocity is assumed to be comprised of a constant mean value along with a harmonically varying component. The stretching of neutral axis introduces geometric cubic nonlinearity in the equation of motion of the beam. The natural frequency of second mode is approximately three times that of first mode; a three-to-one internal resonance is possible. The method of multiple scales (MMS) is directly applied to the governing nonlinear equations and the associated boundary conditions. The nonlinear steady state response along with the stability and bifurcation of the beam is investigated. The system exhibits pitchfork, Hopf, and saddle node bifurcations under different control parameters. The dynamic solutions in the periodic, quasiperiodic, and chaotic forms are captured with the help of time history, phase portraits, and Poincare maps showing the influence of internal resonance.

scholarly journals Lattice Distortion and Phase Stability of Pd-Doped NiCoFeCr Solid-Solution Alloys

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 900 ◽  
Author(s):  
Fuxiang Zhang ◽  
Yang Tong ◽  
Ke Jin ◽  
Hongbin Bei ◽  
William Weber ◽  
...  
Keyword(s):  
Long Range ◽  
Lattice Distortion ◽  
Maximum Pressure ◽  
Local Lattice Distortion ◽  
X Ray ◽  
High Entropy ◽  
Local Lattice ◽  
Pd Doping ◽  
Fcc Phase ◽  
The Stability

In the present study, we have revealed that (NiCoFeCr)100−xPdx (x= 1, 3, 5, 20 atom%) high-entropy alloys (HEAs) have both local- and long-range lattice distortions by utilizing X-ray total scattering, X-ray diffraction, and extended X-ray absorption fine structure methods. The local lattice distortion determined by the lattice constant difference between the local and average structures was found to be proportional to the Pd content. A small amount of Pd-doping (1 atom%) yields long-range lattice distortion, which is demonstrated by a larger (200) lattice plane spacing than the expected value from an average structure, however, the degree of long-range lattice distortion is not sensitive to the Pd concentration. The structural stability of these distorted HEAs under high-pressure was also examined. The experimental results indicate that doping with a small amount of Pd significantly enhances the stability of the fcc phase by increasing the fcc-to-hcp transformation pressure from ~13.0 GPa in NiCoFeCr to 20–26 GPa in the Pd-doped HEAs and NiCoFeCrPd maintains its fcc lattice up to 74 GPa, the maximum pressure that the current experiments have reached.

Nycthemeral Rhythm of the Frequency and Biomechanical Energy of High Frequency Intraocular Pressure Fluctuations

2013 ◽  
Author(s):  
Vincent Libertiaux ◽  
William P. Seigfreid ◽  
Massimo A. Fazio ◽  
Juan F. Reynaud ◽  
Claude F. Burgoyne ◽  
...  
Keyword(s):  
Intraocular Pressure ◽  
High Frequency ◽  
Pressure Fluctuations ◽  
Low Frequency ◽  
Pulse Amplitude ◽  
Mean Value ◽  
Multiple Time Scales ◽  
Dynamic Contour Tonometry ◽  
Multiple Time ◽  
Ocular Pulse

The optic nerve head (ONH) is the site of insult in glaucoma, the second leading cause of blindness worldwide. Intraocular pressure (IOP) is commonly regarded as a major factor in the onset and progression of the disease1 and lowering IOP is the only clinical treatment that has been shown to retard the onset and progression of glaucoma2. However, many patients continue to progress even at an epidemiologically-determined normal level of IOP3. This suggests that in addition to the mean value of IOP, IOP fluctuations could be a factor in glaucomatous pathophysiology. The importance of low frequency fluctuations of clinically-measured mean IOP remains controversial. These studies all rely on snapshot measurements of mean IOP at each time point, and those measurements are taken at relatively infrequent intervals (hourly at the most frequent, but usually monthly or longer). Recently however, there has been some interest in ocular pulse amplitude, or the fluctuation in IOP associated with the cardiac cycle, which can be measured by Dynamic Contour Tonometry (DCT). DCT provides continuous measurement of IOP, but only for a period of tens of seconds in which a patient can tolerate corneal contact without blinking or eye movement, which ironically are two of the most common sources of large high frequency IOP fluctuations according to our telemetric data collected from monkeys4 and previous human studies. In a recent report, continuous IOP telemetry was used in three nonhuman primates to characterize IOP dynamics at multiple time scales for multiple 24-hour periods5.

Coating of Particles in Spouted Bed: Flow Regime and Stability

2010 ◽  
Vol 660-661 ◽  
pp. 573-579
Author(s):  
J.L. Vieira Neto ◽  
J.E. Borges ◽  
Claudio Roberto Duarte ◽  
Marcos A.S. Barrozo
Keyword(s):  
Power Spectrum ◽  
Pressure Fluctuations ◽  
Flow Regimes ◽  
Main Flow ◽  
Agricultural Products ◽  
Soybean Seeds ◽  
Spouted Bed ◽  
Cyclical Motion ◽  
The Stability ◽  
The Many

The coating and encapsulating of particles presents many applications in the chemical, pharmaceutical, food and agricultural products industries. Among the many applications of seeds coating, the enlargement of small seeds is included in order to facilitate the planting, the addition of herbicides, fungicides, fertilizers, micronutrients and inoculation. The spouted bed has often been used in studies related to the coating of particles, due to the cyclical motion of the material, which promotes a fast axial mixture of particles and an excellent gas-particle contact. In this work, the coating of soybean seeds with inoculum and micronutrients in spouted bed has been studied. The different flow regimes were investigated using the pressure fluctuations and power spectrum. The results of the present work showed that it was possible to identify the main flow regimes and to analyze the influence of the coating in the stability of those regimes.

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