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Saint-Venant Fractional Equation and hydraulic gradient

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Journal of Mathematics and System Science 2012年第8期2卷 494-503页

The overall objectives to support analytically the mathematical background of hydraulics, linking the Navier-Stokes with hydraulic formulas, which origin is experimental but have wide and varied application. This, leads us study the inverse problem of the coefficients of differential equations, such as equations of the porous medium, Saint-Venant, and Reynolds, and accordingly with the order of derivatives. The research led us to see that the classic version suffers from a parameter that reflects the fractal and non-local character of the viscous interaction. Motivated by the concept of spatial occupancy rate, the authors set forth Navier-Stokes＇s fractional equation and the authors obtain the fractional Saint-Venant. In particular, the hydraulic gradient, or friction, is conceived as a fractional derivative of velocity. The friction factor is described as a linear operator acting on speed, so that the information it contains is transferred to the order of the derivative, so that the same is linearly related to the exponent of the friction factor. It states Darcy＇s non-linear law. The authors take a previous result that describes the nonlinear flow law with a leading term that contains a hyper-geometric function, whose parameters depend on the exponent of the friction factor and the exponent of the hydraulic radius. It searches the various laws of flow according to the best known laws of hydraulic resistance, such as Chezy and Manning.

关键词： Fractional derivative hydraulic gradient Navier-Stokes fractional equation Saint-Venant fractional equation Darcy'snonlinear law.

Performance between the hydraulic gradient Method and the Perturbation Method for the Analysis of Water Supply Networks

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Journal of Environmental Science and Engineering(A) 2020年第6期9卷 217-226页

作者： Iván Ayala Bizarro Elviz Quispe García Marco Lopez Barrantes Freddy Marrero Saucedo Omar CaballeroSanchez Hugo Lujan Jeri Carlos Gaspar Paco Jorge Ortega Vargas Department of Civil Engineering National University of HuancavelicaHuancavelica 09001Peru

The HGM(hydraulic gradient Method),it is used in most of the current commercial software,such as EPANET,WaterCAD,MikeNet,among others,the same that corresponds to an iterative method that depends on initial estimated parameters and programming structures that ensure convergence to obtain results with the highest precision,in addition to this the method makes use of non-linear equation ***,the execution time for large extensions of water distribution networks is considerably *** the other hand,the PM(Perturbation Method),is a new direct solution method,which makes use of principles of quantum mechanics to transform nonlinear equations into simpler linear *** a simple and robust optimization method that only requires simple and direct mathematical *** the MathCad and Python programming languages as a verification tool,multiple tests were carried out,the results for the hydraulic parameters showing that the flow rates and pressures obtained by the HGM and the PM are extremely similar,in the same way the execution time(time run)have been 77.09%favorable to the *** other words,the PM presents efficiency to estimate the hydraulic characteristics such as the pressures at the nodes and the velocities in the pipes of the drinking water distribution networks.

关键词： Perturbation method quantum mechanics hydraulic gradient

Experimental study on the effects of big particles physical characteristics on the hydraulic transport inside a horizontal pipe

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Chinese Journal of Chemical Engineering 2016年第2期24卷 317-322页

作者： Salah Zouaoui Hassane Djebouri Kamal Mohammedi Sofiane Khelladi Aomar Ait Aidelr LMSE Laboratory Mouloud Mammeri University of Tizi-OuzouP.O.Box 17 RPI 5000Algeria LEMI Laboratory MESO M'Hamed Bougara University of Boumerdes35000Algeria DynFluid Laboratory Arts et Metiers Paris Tech151 boulevard de PHOpital75013 ParisFrance

This paper presents an experimental study of the physical characteristic effects of large particles on hydraulic transport in a horizontal *** particles are spherical and are large with respect to the diameter of the pipe(8%,10%,16% and 25%).Experiments were done to test the important parameters in solid transport(pressure,velocity,etc.).As a result,the relationship between the pressure gradient forces and the mixture velocity was substantially different from the pure liquid ***,in a single-phase flow a monotonous behavior of the pressure drop curve is observed,and the curve of the solid particle flow attains its minimum at the critical *** regimes are characterized with differential pressure measurements and visualizations.

关键词： Solid transport Two-phase flow hydraulic gradient Flow regime

Three-Gorge Dam influences wetland macrophytes in middle and lower reaches of Yangtze

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Progress in Natural Science:Materials International 2007年第9期17卷 1035-1041页

作者： Wang Lingling1,Zeng Guangming1,Li Zhongwu1,Su Xiaokang1,Li Jianbing1,2 and Huang Guohe1(1.College of Environmental Science & Engineering,Hunan University,Changsha 410082,China 2.Environmental Engineering Program,University of Northern British Columbia,Prince George,British Columbia V2N 4Z9,Canada) College of Environmental Science and Engineering Hunan University Changsha 410082 China Environmental Engineering Program University of Northern British Columbia British Columbia V2N 4Z9 Prince George Canada

Dongting Lake,located in the middle and lower reaches of Yangtze,is regarded as a lake during the water swelling period and a continent in the ebbing *** construction of the Three-Gorge Dam has influenced the water level of Dongting Lake and the growth of wetland macrophytes in the *** this study,the growth of main species of wetland macrophytes,such as Carex and Phragmites at Dongting Lake,was observed,and the hydraulic gradient,one of the main factors dominating the abundance and distribution of wetland macrophytes,was also studied at six stations in Dongting Lake area and the effect of the Three-Gorge Dam construction on the growth of wetland macrophytes was observed.

关键词： Three-Gorge Dam Dongting Lake wetland macrophytes hydraulic gradient

On the Influence of Vortex-Induced Resistance on Oil-Shale Particle-Slurry Flow in Vertical Pipes

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Fluid Dynamics & Materials Processing 2021年第2期17卷 413-426页

作者： Li-an Zhao Tieli Wang College of Mining Liaoning Technical UniversityFuxin123000China Pipeline Engineering Institute Wuhan Design and Research Institute of China Coal Technology and Engineering GroupWuhan430064China

The transportation in vertical pipelines of particle slurry of oil shale has important applications in several fields(marine mining,hydraulic mining,dredging of river reservoir,etc.).However,there is still a lack of information about the behavior of coarse particles in comparison to that of fine *** this reason,experiments on the fluidization and hydraulic lifting of coarse oil shale particles have been carried *** experimental data for three kinds of particles with an average size of 5 mm,15 mm and 25 mm clearly demonstrate that vortices can be formed behind the *** this basis,a vortex resistance factor K is proposed here to describe this effect.A possible correlation law is defined by means of a data fitting method *** law is validated by an experiment employing particles with an average size of 3.4 *** vortex resistance factor K results in a reduction of the speed of solid particles and an increase in the sliding speed as well as a decrease in the hydraulic *** a result,using this factor,the calculation of the solid particle speed and hydraulic gradient can be made more accurate with respect to measured values.

关键词： Coarse particle hydraulic gradient vertical pipe fluidization

Groundwater Waves in a Coastal Fractured Aquifer of the Third Phase Qinshan Nuclear Power Engineering Field

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Journal of Shanghai Jiaotong university(Science) 2005年第4期10卷 441-445页

作者：周念清唐益群唐和平 Dept. of Geotechnical Eng. Tongji Univ. Shanghai 200092 China No.4 Research and Design Inst. of Nuclear Industry Shijiazhuang 050021

Tidal fluctuations of Hangzhou Bay produce progressive pressure waves in adjacent field fractured aquifers, as the pressure waves propagate, groundwater levels and hydraulic gradients continuously fluctuate. The effect of tidal fluctuations on groundwater flow can be determined using the mean hydraulic gradient that can be calculated by comparing mean ground and surface water *** fluctuation is shown to affect the piezometer readings taken in a nearshore fractured aquifer around the nuclear power engineering field. Continuous monitoring of a network of seven piezometers provided relations between the tidal cycle and the piezometer readings. The relations can be expressed in times of a time and amplitude scaling factor. The time lag and the tidal efficiency factor and wavelength are calculated using these parameters. It provides significant scientific basis to prevent tide and groundwater for the nuclear power engineering construction and safety run of nuclear power station in the future.

关键词： tidal fluctuation fractured aquifer hydraulic gradient time lag tidal efficiency factor nuclear power engineering

Development of a simple method for determining the influence radius of a pumping well in steady-state condition

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Journal of Groundwater Science and Engineering 2020年第2期8卷 97-107页

作者： A S El-Hames Saudi Geological Survey PO Box 54141Jeddah 21514Saudi Arabia

Influence radius of a pumping well is a crucial parameter for hydrogeologists and engineers. Knowing the radius of influence for a designed drawdown enables one to calculate the pumping rate required to layout a project foundation that may need lowering of groundwater level to a certain depth due to dewatering operation. In addition, this is important for hydrogeologists to determine ground water contamination flow paths and contributing recharge area for domestic water supply and aquifer management purposes. Empirical formulas that usually neglect vital parameters to determine the influence radius accurately have been traditionally utilized due to lack of adequate methods. In this study, a physically based method, which incorporates aquifer hydraulic gradient for determining the influence radius of a pumping well in steady-state flow condition, was developed. It utilizes Darcy and Dupuit laws to calculate the influence radius, where Darcy’s law and Dupuit equation, in steady-state condition, represent the inflow and the outflow of the pumping well, respectively. In an untraditional manner, this method can be also used to determine aquifer hydraulic conductivity as an alternative to other pumping test methods with high degree of accuracy. The developed method is easy to use;where a simple mathematical calculator may be used to calculate the influence radius and the pumping rate or hydraulic conductivity. By comparing the results from this method with the MODFLOW numerical model outputs with different simulated scenarios, it is realized that this method is much superior and more advantageous than other commonly used empirical methods.

关键词： Radius of influence Dewatering hydraulic gradient hydraulic conductivity Pumping rate Aquifer management

Properties of Bentonite Enhanced Loess and Laterite

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Chinese Journal of Chemical Engineering 2004年第1期12卷 37-41页

作者：刘阳生白庆中聂永丰 Department of Environmental Engineering Peking University Beijing 100871 China Department of Environmental Science and Engineering Tsinghua University Beijing 100084 China

Loess and laterite distributed widely in the northern and southern China cannot be directly used as the natural barrier to isolate the solid waste because of their high hydraulic conductivity. In this paper, they are enhanced by bentonite to improve their hydraulic performance. The impact of bentonite content and water content on compressive strength of the compacted soil was investigated. The effects of bentonite content, water content, dry density and hydraulic gradient on the hydraulic conductivity were studied in detail. For the laterite and the laterite with 8% of bentonite, the experimental results of hydraulic conductivity can be applied in the engineering design. However, for the loess and the bentonite enhanced loess, those of hydraulic conductivity can not be directly applied in the engineering design because their hydraulic performance does not comply with the Darcy's law. These experimental results have to be carefully modified before application.

关键词： bentonite loess laterite hydraulic conductivity compressive strength hydraulic gradient

Experimental and Numerical Investigation of Stress Condition in Unstable Soil

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Open Journal of Civil Engineering 2016年第3期6卷 370-380页

作者： Marx Ferdinand Ahlinhan Emmanuel Kokou Wouya Yvette Kiki Tankpinou Marius Bocco Koube Codjo Edmond Adjovi School of Sciences and Technologies for Building and Road (ESTBR) Polytechnic University of Abomey (UPA) Abomey Benin Institute University of Technology Lokossa (IUT) University of Lokossa Lokossa Benin

In unstable soils, a special erosion process termed suffusion can occur under the effect of relatively low hydraulic gradient. The critical hydraulic gradient of an unstable soil is smaller than in stable soils, which is described by a reduction factor α. According to a theory of Skempton and Brogan (1994) [1], this reduction factor is related to the stress conditions in the soil. In an unstable soil, the average stresses acting in the fine portion are believed to be smaller than the average stresses in the coarse portion. It is assumed that the stress ratio and the reduction factor for the hydraulic gradient are almost equal. In order to prove this theory, laboratory tests and discrete element modelings are carried out. Models of stable and unstable soils are established, and the stresses inside the sample are analysed. It is found that indeed in unstable soils the coarse grains are subject to larger stresses. The stress ratios in stable soils are almost unity, whereas in unstable soils smaller stress ratios, which are dependent on the soil composition and on the relative density of the soil, are obtained. A comparison between the results of erosion tests and numerical modeling shows that the stress ratios and the reduction factors are strongly related, as assumed by Skempton and Brogan (1994) [1].

关键词： Unstable Soil Suffusion hydraulic gradient Stress Reduction Factor Laboratory Tests Discrete Element Modeling