Hydrodynamics (Physics)

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Merupakan susunan murni dari penulis, untuk pembaca yang masih awam dengan mekanika fluida dan sebagai pengantar untuk ilmu hidrodinamika dasar.

Minus Bernoulli dan Navier-Stokes Equations. Akan diterangkan pada bagian 3.

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Merupakan susunan murni dari penulis mengenai pembahasan mengenai dasar-dasar dari aliran fluida dan macam-macam aliran fluida. Sebagai pengantar untuk ilmu mekanika fluida dan ilmu hidrodinamika dasar.

A superluminal quantum-vortex model of the electron and the positron is produced from a superluminal double-helix model of the photon during electron-positron pair production. The two oppositely-charged (with Q = ±e sqrt (2/α) = 16.6e) open-helix spin-½ half-photons compose the double-helix photon. These half-photons separate and curl up their separated superluminal single-helical trajectories to form an electrically-charged superluminal closed-helix spin-½ quantum-vortex electron model and a corresponding positron model. The helical radius and the Dirac equation's zitterbewegung angular frequency of the quantum vortex electron and positron models equal the helical radius and zitterbewegung angular frequency of the two spin-½ half-photons, each of energy E = mc^2 , that composed the double-helix photon model of energy E = 2mc^2 from which the electron and positron models were produced. The photon and electron models are also compatible when a photon of energy E > 2mc^2 produces a relativistic electron-positron pair. Implications of the quantum vortex electron model for electron stability are discussed.

This report describes the modelling of an appended yacht hull that is free to heave and pitch with CFX v15.0, a finite volume Reynolds Averaged Navier-Stokes (RANS) code developed by ANSYS. The model is validated against experimental towing tank data, and is compared with predictions made using the Delft Systematic Yacht Hull Series (DSYHS) regression equations, and the results of a panel code.

We consider the Universe deep inside the cell of uniformity. At these scales, the Universe is filled with inhomogeneously distributed discrete structures (galaxies, groups and clusters of galaxies), which perturb the background Friedmann model. Here, the mechanical approach (Eingorn & Zhuk, 2012) is the most appropriate to describe the dynamics of the inhomogeneities which is defined, on the one hand, by gravitational potentials of inhomogeneities and, on the other hand, by the cosmological expansion of the Universe. In this paper, we present additional arguments in favor of this approach. First, we estimate the size of the cell of uniformity. With the help of the standard methods of statistical physics and for the galaxies of the type of the Milky Way and Andromeda, we get that it is of the order of 190 Mpc which is rather close to observations. Then, we show that the nonrelativistic approximation (with respect to the peculiar velocities) is valid for $z \lesssim 10$, i.e. approximately for 13 billion years from the present moment. We consider scalar perturbations and, within the $\Lambda$CDM model, justify the main equations. Moreover, we demonstrate that radiation can be naturally incorporated into our scheme. This emphasizes the viability of our approach. This approach gives a possibility to analyze different cosmological models and compare them with the observable Universe. For example, we indicate some problematic aspects of the spatially flat models. Such models require a rather specific distribution of the inhomogeneities to get a finite potential at any points outside gravitating masses. We also criticize the application of the Schwarzschild-de Sitter solution to the description of the motion of test bodies on the cosmological background.

- The Solar Planets order proves that, the planet orbital distance is defined based on his Diameter and NOT his Mass, which disproves the Gravity Theory..

But
- Planet Diameter and Orbital Distance Relationship Equation is so hard to define…! Why?

Because
- The solar Group has 2 Heads (The Sun and Earth).
The Solar Group is A Dipole….

We need to modify the Solar Group Basic Description to be " A Dipole System"… 
 
- This paper also discusses the Sun nature and Origin…

Nowadays, several stern devices are attracting a great deal of attention. The control surface is an effective apparatus for improving
the hydrodynamic performance of planing hulls and is considered an important element in the design of planing hulls. Control
surfaces produce forces and a pitching moment due to the pressure distribution that they cause, which can be used to change the
running state of high-speed marine boats. This work elaborates a new study to evaluate the hydrodynamic performance of a
planing boat with a trim tab and an interceptor, and optimizes them by using an optimization algorithm. The trim tab and the
interceptor have been used to optimize the running trim and motion control of semi-planing and planing boats at various speeds
and sea conditions for many years. In this paper, the usage of trim tab is mathematically verified and experimental equations are
utilized to optimize the performance of a planing boat at a specificd trim angle by using an optimization algorithm. The genetic
algorithm (GA) is one of the most useful optimizing methods and is used in this study. The planing boat equations were
programmed according to Savitsky’s equations and then analyzed in the framework of the GA-based optimization for performance
improvement of theplaning hull. The optimal design of trim tab and interceptor for planing boat can be considered a multiobjective
problem. The input data of GA include different parameters, such as speed, longitudinal center of gravity, and deadrise
angle. We can extract the best range of forecasting the planing boat longitudinal center of gravity, the angle of the trim, and the
least drag force at the best trim angle of the boat.

Membrane bioreactor (MBR) is a reliable and promising technology for wastewater treatment and reclamation applications. In spite of more than a decade of significant advances in developing fouling mitigation methods, different physical and cleaning protocols are still necessary to be developed to limit the membrane fouling. The use of scouring agents in MBR applications has been paid attention as a new approach as an energy-efficient way to control membrane fouling. Recently, mechanical cleaning by scouring agents is becoming as intense research area considering high efficiency of fouling reduction while requiring low energy consumption. In this review, fundamental and comprehensive assessments of the mechanical cleaning concepts and their applications with porous and nonporous scouring agents for MBR system are critically reviewed. The existing challenges and future research prospects on the mechanical cleaning technology associated with scouring agents for the MBR applications are also discussed.

Energy is unarguably the key factor for today's economic and social development within nations. Electricity as one of many energy forms is a critical input to developing countries in the struggle to the national self-satisfaction in all domains. Rural electricity supply involved institutions have recently recommended the pump as turbine (PAT)-based micro hydropower plant (MHP) schemes for remote off-grid electrification, mostly from their economic advantages. However, from different published research findings, PAT-based MHP is not only simple and economically feasible, but has presented bottlenecks in the move to its full understanding. Moreover, compared to other clean energy technologies, PAT technology has not found much literature in academic published researches, thus contributing to its limited understanding within the community. Therefore, the PAT literature availability is one way to level up its understanding, which can be helpful to academic and professional communities. In the present study, a literature review on the two most challenging PAT aspects, namely pump-turbine selection and performance prediction, is presented; where a summary about energy sources history leading to the actual MHP global

The Earth moves with C velocity (light velocity) relative to the Sun
i.e.
The light is produced by The Earth Motion, where
The Earth transforms her motion mechanical waves into light waves, producing the light beams   
These light beams travel to the sun and reflect on her where the sun is just a mirror. 

The Earth Motion = The Solar Planets Daily Velocities Total based on new time rate defined by the Earth.

We make use of an effective field-theoretical approach to derive post-Newtonian equations of motion of hydrodynamical inhomogeneities in cos-mology. The matter Lagrangian for the perturbed cosmological model includes dark matter, dark energy, and ordinary baryonic matter. The Lagrangian is expanded in an asymptotic Taylor series around a Friedmann-Lemeître-Robertson-Walker background. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the expansion series is gauge-invariant and all of them together form a basis for the successive post-Newtonian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Newtonian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background metric. Temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large-scale inhomogeneities of matter as those generated by the primordial cos-mological perturbations in these two components with δρ/ρ ≤ 1. The small scale inhomogeneities are generated by the baryonic matter which is considered as a bare perturbation of the background gravitational field, dark matter and energy. Mathematically , the large scale structure inhomogeneities are given by the homogeneous solution of the post-Newtonian equations while the small scale inhomogeneities are described by a particular solution of these equations with the stress-energy tensor of the baryonic matter that admits δρ/ρ 1. We explicitly work out the field equations of the first post-Newtonian approximation in cosmology and derive the

Why there's No velocity higher than Light Velocity C =300000 km/sec? Because • The Matter is created from light beams coherence (according to Young Experiment-The Main Hypothesis) • The Time is created as the Matter Changing measurement • Our body (matter) is produced by the same method, from this light beams coherence • Our bodies are connected with specific Light velocity and specific time rate because our bodies are produced by specific Light Beams coherence

This review evaluates computational fluid dynamic applications to analyze solid suspension quality in stirred vessels. Most researchers typically employ either Eulerian-Eulerian or Eulerian-Lagrangian approach to investigate multiphase flow in stirred vessels. With sufficient computational resources, the E-L approach simulates flow structures with higher spatial resolution for dispersed multiphase flows. Common turbulence models such as the two-equation eddy-viscosity models (k-ε), Reynolds stress model, direct numerical simulation, and large eddy simulation are described and compared for their respective limitations and advantages. Literature confirms that k-ε is the most widely used turbulence model, but it suffers from some inherent shortcomings due to assumption of isotropy of turbulence and homogenous mixing. Subsequently, the importance of different forces concerning solid particle flotation is concluded. Studies on dilute systems take into account only drag and turbulence forces while other forces have always been ignored. The simulations of off-bottom solid suspension, solid drawdown, solid cloud height, solid concentration distribution, and particle collision are considered for studies involving solid suspension. Different models and methods applied to investigate the abovementioned phenomena are also discussed in this review.

This paper explores an alternative to the metaphysically barren traditional view of electromagnetism we have inherited, by hydrodynamically explaining magnetic and electric fields in terms of vacuum fluid flow. Once the vacuum is taken to be a real physical medium composed of interacting and dynamically fluid quanta (like a superfluid), electromagnetism can be naturally derived from well-known principles. Through this lens, a vector field, representing the positions and velocities of all quanta within the vacuum fluid, becomes ontologically prior to electromagnetism and the Helmholtz theorem can be used to generally characterize the fluid flow of that flux vector field. Decomposing that characterization into independent expressions for curl and divergence automatically maps out the magnetic and electric fields; providing a physical model for electromagnetism in which magnetic flux is interpreted as the curl of the quantum vector field and the electric field is interpreted as divergence in that vector field.

FOR CITATIONS:
Salem, Hilmi S. "A Budget of the Surface and Underground Water in Northern Jordan (Pages: 135-162)" in "Water and Peace in the Middle East", Studies in Environmental Science 58., J. Isaac & H. Shuval (Eds.), 1992, Elsevier.

ABSTRACT:
The motivation for this study is the great requirement for water expected in the future to satisfy the increasing demands of accelerated growth, and development programs in Jordan. This fact, in addition to the recent migration of hundreds of thousands of people after the Gulf War, should encourage more intensive studies of the quality and quantity of water
resources in Jordan. The aim of this study is to carry out a comprehensive assessment and evaluation of the water resources-potential of the northern area of Jordan. This work required hydrological,
hydrogeological, hydrodynamical and hydrochemical analyses and interpretations. The rates of precipitation, evaporation, surface runoff and infiltration were calculated. The regional recharge sources and directions of the groundwater movements were mapped. The recharge-discharge mechanisms should provide an improved understanding of the water resources in the study area, which covers about 6,000 km of northern Jordan.

The mechanism of wake-induced vibrations (WIV) of a pair of cylinders in a tandem arrangement is investigated by experiments. A typical WIV response is characterised by a build up of amplitude persisting to high reduced velocities; this is different from a typical vortex-induced vibrations (VIV) response that occurs in a limited resonance range.
We suggest that WIV of the downstream cylinder is excited by the unsteady vortex-structure interactions between the body and the upstream wake. Coherent vortices interfering with the second cylinder induce fluctuations in the fluid force that are not synchronised with the motion. A favourable phase lag between the displacement and the fluid force guarantees that a positive energy transfer from the flow to the structure sustains the oscillations. If the unsteady vortices are removed from the wake of the upstream body then WIV will not be excited.
We introduce the concept of wake stiffness, a fluid dynamic effect able to sustain a body without any structural stiffness into oscillatory motion. The role played by the unsteady wake is central to this idea and contributes to the understanding of WIV as a wake-excited and wake-sustained mechanism. A simple analytical model predicts the frequency of response rather well, but fails to model the displacement because important nonlinear effects are not taken into account. We conclude that while unsteady vortex-structure interactions provide the energy input to sustain WIV, it is the wake stiffness effect that defines the character of the response.
Suppression of cross-flow and in-line VIV, with resulting drag coefficients less than that for a static plain cylinder, is achieved using two-dimensional control plates free to rotate around the body. Devices based on parallel plates show great potential to suppress VIV and WIV of offshore structures with considerable reduction in drag.

This thesis deals with the dynamics of irreversible processes within the context of the general theory of relativity. In particular, we address the problem of the 'infinite' speed of propagation of thermal disturbances in a dissipative fluid. The present work builds on the multi-fluid variational approach to relativistic dissipation, pioneered by Carter, and provides a dynamical theory of heat conduction. The novel property of such approach is the thermodynamic interpretation associated with a two-fluid system whose constituents are matter and entropy. The dynamics of this model leads to a relativistic generalisation of the Cattaneo equation; the constitutive relation for causal heat transport. A comparison with the Israel and Stewart model is presented and its equivalence is shown. This discussion provides new insights into the not-well understood definition of a non-equilibrium temperature. The variational approach to heat conduction presented in this thesis constitutes a mathematically promising formalism to explore the relativistic evolution towards equilibrium of dissipative fluids in a dynamical manner and to get a deeper conceptual understanding of non-equilibrium thermodynamic quantities. Moreover, it might also be useful to explore the more fundamental issues of the irreversible dynamics of relativity and its connections with the time asymmetry of nature.

Finding solutions to farm problems and issues is a painstaking process which requires acceptance of new body of knowledge that may disprove and invalidate some long held theories and "truth". Poor and small (landowners of 3 has. and below) veteran Filipino farmers refrained from use while newly-bred farmers are reluctant to use the farm-machine---2WT, due to high-cost of fuel and or rental fee for the tractor which usually owned by merchants engaged in usurious cash-lending and rice trading. They prefer the hard way of farming to save a little amount for the socio-economically struggling family from tractor expenses contribution. The researcher-proponents, Automotive Technology students from College of Technology, Eastern Visayas State University, coached by Rannie C. Agustin, are investigating for the feasibility of manufacturing cost-efficient solar-powered 2WT to help the poor Filipino farmers increase their farm productivity, easing the hard-way of farming with efficient and effective farm technology as tools for strategic and engineered timely land preparation and sowing, harvesting, threshing, processing and  transporting. All of which, according to Biggs & Justice (2015)  lead to productivity gains and increases in cropping intensification through quicker and higher turn-around or turn-overs of production cycles.

In accordance to studies by G.S.Hawkins, the author of this paper continued decoding of ancient monument Stonehenge in Great Britain. The method of decoding by J.-F.Champollion was used with success. The author discovered mathematical code and several images which look like Egyptian hieroglyphs. The author worked out the vocabulary of Stonehenge. It became possible to decode several words and short message with the help of the vocabulary. Mathematical theory of Hydrogen atom and atomic mass (1.0079...) were coded in Stonehenge. A part of message looks like the phrase: "Eternally living Atom". Where Atom (or Atum) is well-known name of Egyptian solar god. Also knowledge of partial differential equations is demonstrated by builders of Stonehenge. The author considers that Stonehenge was distant Egyptian solar temple and ancient center of science and higher education simultaneously. Probably Stonehenge was used for military purposes and for forecasting of results of wars with the help of mathematical modeling too. It explains military power of ancient Egypt. Also the author describes process of building of Stonehenge with the method of hydraulics.

Prinsip Bernoulli adalah sebuah istilah di dalam mekanika fluida yang menyatakan bahwa pada suatu aliran fluida, peningkatan pada kecepatan fluida akan menimbulkan penurunan tekanan pada aliran tersebut. Prinsip ini sebenarnya merupakan penyederhanaan dari Persamaan Bernoulli yang menyatakan bahwa jumlah energi pada suatu titik di dalam suatu aliran tertutup sama besarnya dengan jumlah energi di titik lain pada jalur aliran yang sama. Prinsip ini diambil dari nama ilmuwan Belanda/Swiss yang bernama Daniel Bernoulli.

In this paper we consider dynamical behavior of astrophysical objects (galaxies and dwarf galaxies) taking into account both gravitational attraction between them and cosmological expansion of the Universe. First, we obtain the general system of equations and apply them to some abstract systems of galaxies. Then we investigate the collision between the Milky Way and Andromeda in future. We distinguish two models. For the first one, we do not take into account the influence of Intra-Group Matter (IGrM). In this case we demonstrate that for currently known parameters of this system the collision is hardly plausible because of the angular momentum. These galaxies will approach the minimum distance of about 290 Kpc in 4.44 Gyr from present and then begin to run away irreversibly from each other. For the second model, we take into account dynamical friction due to IGrM. We find a characteristic value of the IGrM particle velocity dispersion $\tilde\sigma=2.306$. For $\tilde\sigma\leq2.306$ the merger will take place, but for the bigger values of $\tilde\sigma$ the merger can be problematic. If the temperature of the IGrM particles is $10^5$ K, this characteristic value of $\tilde\sigma$ corresponds to the IGrM particle mass 17 MeV. Therefore, for the IGrM particles with masses less than 17 MeV the merger becomes problematic. We also define the region in the vicinity of our Local Group where the formation of Hubble flows starts. For such processes the zero-acceleration surface (where gravitational attraction is balanced by cosmological accelerated expansion) plays the crucial role. We show that such surface is absent for the Local Group. Instead, we find two points and one circle with zero acceleration. Nevertheless, there is a nearly closed area around the MW and M31 where the absolute value of the acceleration is approximately equal to zero. Hubble flows are formed outside of this area.

Several advantages such as good gas and solids dispersion have been associated with triple-impeller system for three phase mixing processes. In this work, minimum impeller speed required for achieving just suspended condition was studied with gassing using three Rushton turbines as agitators. The effects of sparger location and gas flow rate on the just suspension speed, gas holdup , gas–liquid mass transfer coefficient and power consumption were discussed. Sparger placed above the bottom impeller showed the highest gas holdup at just suspended condition with the same total power consumption as the other two sparger locations. The highest gas holdup value achieved was 12% at total power consumption of 370 W. The data obtained fitted well into ΔN js = kQ g with k = 3.67 when the sparger is located below the bottom impeller. Significantly lower k values can be obtained when the sparger is shifted above the bottom impeller. The sparger location above the bottom-most impeller is proposed to be superior for industrial application of aerated solid suspensions where at least 8% saving on power consumption can be achieved.

Fluidized bed gasifiers have been adopted for gasification of solid fuels like coal and biomass along with other gasification technologies like moving bed and entrained flow gasifiers. Fluidized bed gasifiers offers better mixing, uniform temperature and have ability to handle low quality fuels. Such units are industrially proven for combustion of solid fuels. Bubbling fluidized beds are commonly used for small to medium scale capacities. Gasification being order of magnitude slower than combustion process, handling it in fluidized bed gasifier pose many challenges as it may lead to loss of efficiency, unburnt carbon and so on. Hence study of fluidized bed gasifier is important from aspects like gas-solid hydrodynamics, reaction kinetics and inter-phase mass transfer that control the overall performance of the gasifier unit. In this paper, the objective of the study is to develop method for predicting the performance of the bubbling fluidized bed gasifier. This will critically evaluate the various correlations/methods available in literature which enables the research/ process designer to predict the performance of bubbling fluidized bed gasifier.

El-Burullus Lake is affected by increasing and extensive human activities, rapid social-economic
development and the construction of fish ponds nearby. This has significantly impacted the health of the
lake eco-system. On the foundation of the two-dimensional depth averaged hydrodynamic model,
distributions of the salinity, Dissolved Oxygen (DO), Biochemical Oxygen Demand (BOD), Chemical
Oxygen Demand (COD) and Ammonium (NH4) were modeled. The heat flux model was also utilized
to enhance the accuracy of the calculations in the water quality modeling stage. The calibration and the
verification of this model were based on spatially distributed water quality measurements during the
period 2010-2011. The correlation coefficients between measured and simulated salinity was found to
be 0.79 in January 2011 and 0.84 in August 2010 with a mean errors of 1.3407 and 2.0727 ppt in
August 2010 and January 2011 respectively. The results generally agree with the observations, but this
indicates that more measurements are needed to verify the predictability of the simulations. In
addition, Delft-3D model has been applied in evaluating the feasibility of adding a new artificial inlet
or diversion of some drains. The model proved to be an effective tool for the water dynamics, water
quality simulation and evaluating different scenarios of such shallow Lake.

For Citations:
Salem, H.S., 2001. Determination of the acoustic coupling factor of Biot's theory of elasticity, using in situ seismic measurements. Energy Sources, 23(10) December: 917-936. (A Scholarly Paper Published in an International Journal).

Abstract:
Besides other elastic, petrophysical, and hydrophysical parameters, the acoustic coupling factor (coupling factor or structure factor, μ) is a critical micro-geometrical parameter in the Biot’s theory of elasticity. The coupling factor exerts a
speci®c in¯uence on the mechanisms of propagation and attenuation of vibrations (seismic waves and acoustic signals) in porous media. It is a measure of the internal structure (geometry and shape of pores and pore tubes) of a porous medium, and
thus it is a good indicator of the degree of coupling between pore ¯uid and solid grains. It is unity for no coupling and in®nity for perfect coupling. In this study, the coupling factor is obtained for surface soils and shallow sediments, using compressional
wave velocity (¸p) determined from in situ seismic refraction measurements. The investigated soils and underlying sediments (aeration zone and aquifer) exhibit a general μ range of 1.22±3.19 (average = 1.82), corresponding to a general ¸f range of 134±2060 m/s (average = 1134m/s). The μ values are correlated to the
bulk modulus-shear modulus ratio (K/·) and the porosity (¿). A direct linear correlation between μ and K/· and an inverse polynomial correlation between μ and ¿ are obtained, with
coefficients of correlation of 0.91 and 0.98, respectively.
Also, various items related to the coupling factor, Biot’s theory, attenuation mechanisms, fast and slow compressional waves (®rst and second kinds), and shear waves are discussed.

Keywords:
Acoustic coupling factor (structure factor), attenuation mechanisms, Biot’s theory, compressibility, compressional and shear wave velocities, fast and slow compressional waves, frequency, in situ seismic refraction measurements,
permeability, porosity, rigidity, shallow sediments (aeration zone and aquifer), surface soils, tortuosity, viscosity.

The present study was carried out in order to study the textural characteristics of sediments and their seasonal changes along with the Coleroon estuary. Sediment samples were collected at different stations in monsoon, postmonsoon, summer and premonsoon seasons from 2009 to 2010. Spatial variations in grain-size parameters (i.e. grain-size trends) contain information on sediment transport patterns. Analytical procedures have been proposed using the grain-size trends to determine sediment transport pathways. Spatial distribution of sediments clearly indicated more finer particles deposited at mid estuarine region compared to at mouth and freshwater region. Hydrodynamic condition of Coleroon estuarine sediments indicates moderate to high energy condition. The grain size trend analysis indicates the estuarine sediments belong to type-1 trend F, B (finer, better sorted more negative skewed). Clay mineral studies exhibit the observed order of abundance minerals are illite followed by the kaolinite+chlorite, montmorillonite and gibssite. The higher percentage of clay minerals was present at estuary and mouth regions when compared to the freshwater region.

In a previous paper we outlined a series of historical touchpoints between classical aether theories and modern theoretical physics which showed a shared conceptual lineage for the modern tools and methods of the most common interpretations and fluid based "Hydrodynamic" treatments of an electromagnetic medium. It was proposed that, though the weight of modern experimentation leaves an extremely narrow and convoluted window for even a reconceptualization of a medium, all of modern physics recognizes a plethora of behaviors and attributes for free space and these physics are interchangeable with modern methods for treating superfluid-like continuums. Thus the mathematical equivalence of the methods do not comprise alternative physics but an alternative​ interpretation​ of the same physics. Though many individual components describing a "neo-aether" are available, an overarching structural outline of how these tools can work together to provide an alternative working overview of modern physics has remained undefined. This paper will propose a set of introductory concepts in the first outline of a toy model which will later connect the alternative tools and conceptualizations with their modern counterparts. This introductory paper provides the simpler "100-miles out" overview of the whole of physics from this perspective, in an easily comprehensible, familiar and intuitive, and informal dialog fashion. While this paper grants the largest and loosest introductory overview, subsequent papers in this series will address the finite connections between modern physics and this hydrodynamic view.

In this study, a high-order compact scheme for 2D Laplace and Poisson equations under a non-uniform grid setting is developed. Based on the optimal difference method, a nine-point compact difference scheme is generated. Difference coefficients at each grid point and source term are derived. This is accomplished through the consideration of compatibility between the partial differential equation and its difference discretization. Theoretically, the proposed scheme has third-to fourth-order accuracy; its fourth-order accuracy is achieved under uniform grid settings. Two examples are provided to examine performance of the proposed scheme. Compared with the traditional five-point difference scheme, the proposed scheme can produce more accurate results with faster convergence. Another reference scheme with the same nine-point grid stencil is derived based on the five-point scheme. The two nine-point schemes have the same coefficients for each grid points; however, their coefficients for the source term are different. The overall accuracy level of the solution resulting from the proposed scheme is higher than that of the nine-point reference scheme. It is also indicated that the smoothness of grids has significant effects on accuracy and convergence of the solutions; efforts in optimizing the grid configuration and allocation can improve solution accuracy and efficiency. Consequently, with the proposed method, solution under the non-uniform grid setting with appropriate grid allocation would be more accurate than that under the uniform-grid manipulation, with the same number of grid points.

Abstract
Details are given of the development of a two-dimensional vertical numerical model for simulating unsteady free-surface flows, using a non-hydrostatic pressure distribution. In this model, the Reynolds equations and the kinematic free-surface boundary condition are solved simultaneously, so that the water surface elevation can be integrated into the solution and solved for, together with the velocity and pressure fields. An efficient numerical algorithm has been developed, deploying implicit parameters similar to those used in the Crank–Nicholson method, and generating a block tri-diagonal algebraic system of equations. The model has been applied to simulate a range of unsteady flow problems involving relatively strong vertical accelerations. The results show that the numerical algorithm described is able to produce accurate predictions and is also easy to apply.

Hydraulischer Widerstand ist der vierte Baustein zum Lehrwerk Systemphysik für Fachhochschulen.  In der Einführungsphase werden Systeme mit einem systemdynamischen Tool (System Dynamics) modelliert, simuliert und validiert. Diese Methode fördert das saubere Analysieren und das strukturierte Denken. Nach einer intensiven Lern- und Erfahrungsphase werden die ausgereiften Modelle auf Modelica umgeschrieben und in einer speziell dafür geschriebenen Bibliothek hinterlegt.

Inverse fluidization is a technique in which solid particles having lower density
than that of the liquid are kept in suspension by the downward flow of continuous liquid
phase. Inverse fluidization has several advantages such as high mass transfer rates due to
reduced film thickness resulting from rotation due to low inertia, minimum carry over of
coated microorganisms due to less solids attrition, efficient control of bio-film thickness
and ease of re-fluidization in case of power failure. These significant advantages found
many applications of inverse fluidized beds in biochemical processes like ferrous iron
oxidation and aerobic and anaerobic biological wastewater treatment like treatment of
wine distillery wastewater. Even though, the applications of the inverse fluidized bed
technique to industrial processes are fast growing, much information on hydrodynamics,
mass transfer and chemical reaction is not yet available. Two phase (liquid – solid)
inverse fluidized beds are used for anaerobic biological processes due to their high mass
transfer potential.
The studies on the hydrodynamics and mass transfer of two-phase inverse
fluidization were performed only in the last few decades one of the most important recent
applications of inverse fluidized beds is in the field of bioreactor engineering. Inverse
fluidization is used in biotechnology as the basics of a new type of bioreactor, the so
called inverse fluidized bed bioreactor are among the most efficient application for
aerobic and anaerobic wastewater treatment Penicillin Production and Phenol
degradation.
The inverse fluidization system gained significant importance during the last few
decades in the field of environmental, biochemical engineering, and oil water separation.
The hydrodynamics of the inverse fluidization have been studies by Karamanev
and Nikolov (1996), Ulaganathan and Krishnaiah (1996), Ramos et al. (1998), Banerjee
et al. (1999), Vijaya Lakshmi et al. (2000), and Renganathan and Krishnaiah (2003, 2004,
2007) using water-solid system. They proposed empirical correlations to predict the
minimum inverse fluidization velocity. Fan et al. (1982), Karamanev and Nikolov (1992),
Biswas and Ganguly (1997), Bendict (1998), Lee (2001), Renganathan and Krishnaiah
(2005) reported the bed expansion characteristics in two phase downward fluidization
and predicted their bed expansion data in terms of Richardson and Zaki equation.
It is very much essential to study on hydrodynamic characteristics such as
pressure drop and minimum inverse fluidization velocity for successful analysis, design
and operation of inverse fluidization bed.
Experiments will be carried out using four polyethylene particles having different
densities, different diameter and sphericity with different concentrated aqueous solutions
of SCMC as fluidizing liquid. Minimum fluidization velocity will be estimated from the
experimental data. An empirical correlation will be developed for the minimum
fluidization velocity as a function of physical and dynamic variables of the system.