The article solves the motion of a spherical solid particle in plane coquette fluid flow by using the HPM-Padé technique which is a combination of the Homotopy Perturbation method and Padé approximation. The series solutions of the couple equations are developed. Generally, the truncated series solution is adequately in a small region and to overcome this limitation the Padé techniques, which have the advantage in turning the polynomial approximation into a rational function, are applied to the series solution to improve the accuracy and enlarge the convergence domain. The current results compared with those derived from HPM and the established fourth order Runge–Kutta method in order to ascertain the accuracy of the proposed method. It is found that this method can achieve more suitable results in comparison to HPM.
In the heart of all the different engineering sciences, everything shows itself in the mathematical relation that most of these problems and phenomena are modeled by linear and nonlinear equations. Therefore, many different methods have recently introduced some ways to solve these equations. Analytical methods have made a comeback in research methodology after taking a backseat to the numerical techniques for the latter half of the preceding century. One of the analytical methods of recent vintage, namely, the Homotopy Perturbation Method (HPM) which was firstly proposed by Chinese mathematician Ji-Huan He [1–8] has attracted special attention from researchers as it is flexible in applying and gives sufficiently accurate results with modest effort. This method as a powerful series-based analytical tool has been used by many authors [9–14]. But, the convergence region of the obtained truncated series app...
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Job's method is ordinarily applicable to system in which only one complex is present. Robert Gould and Vosburgh [12] have applied above method to system where second equilibrium exists and showed that it also obey's Beer'slaw.
Also, the equations for Potential energy and Kinetic energy are stated to get the Total Energy. They are respectively:
Well it's quite simple actually. Spudguns use some of the same principles as internal combustion engines. Just as burning gas forces a piston out of a cylinder it can also force out a potato. A spudgun is a device that uses some form of propellant to project a potato across the sky. Usually these devices are made of ABS plastic sewer pipe. There are several major parts of the spud gun that these pages will refer to. These parts are the firing chamber, the igniter, and the barrel.
Serway, Jewett. Physics for Scientists and Engineers 6th Edition. Pomona: California State Polytechnic University. 2004.
Some presumptions were included in academic sources upon which we relied. The theoretical coefficient of drag for a three-dimensional flat-faced circular cylinder was written to have a relation to the length to diameter. The length of the Kinder egg container is measured to be 3.5±0.1 cm, while the diameter is 1.7±0.1 cm. Therefore the length to diameter ratio is 2.05. Now referring to the graph of the l/d ratio relation to Cd the theoretical drag coefficient could be deduced. The approximate value varies between 0.8 and 0.9. However, it should be pointed out that the Kinder egg container is less of a cylinder as its edges are cut. Therefore, the theoretical drag coefficient is expected to approach the lowest value, i.e. 0.8.
The evolution of a fluid (gas) can also be described by the exact dynamics of the individual particles that constitutes the fluid (gas) in terms of Newton equations. However, this is complicated in the sense that in order to compute the time evolution of the fluid, one will have to solve a system of 6N first order differential equations with 6N unknowns constituting the position and velocity vectors. A perquisite for this computation is the knowledge of 6N initial
Ordinary fluid flow is different from granular flow so study of every particle’s behavior is necessary. Different physical phenomena, like interaction between particles and
Consider the parallel flow of two viscous fluids in an infinite, fully saturated, uniform, homogeneous and isotropic two porous media with the Darcy's coefficients and . The statically stable situation was considered, so the upper fluid is assumed the lighter (vapor) while the lower one is assumed to be the heaver (liquid). The two fluids are incompressible and have uniform densities and viscosities for the liquid and for the vapor. The interface between the two fluids is assumed to be well defined and is initially flat to form the plane y = 0. Also, we consider that the two fluids are streaming with uniform horizontal velocities and throughout the two superposed porous media. The subscripts (1) and (2) refer to the lower and upper fluid, respectively. The acceleration due to gravity
Swameer, P. K. and Jain, A. K., “Explicit equation for pipe flow problems”, Journal on Hydr.Divi., ASCE, 102 (5), 657-664, 1976.
1 David Halliday, Robert Resnick, and Jearl Walker, Fundamentals of Physics, Extended, 5th ed. (NewYork:Wiley, 1997) 361
On a more scientific note I am interested in mechanics of fluids. This interest was enforced last year when I had the opportunity to attend a lecture on fluid mechanics at P&G. At the conference I greatly expanded my knowledge regarding the physical aspect of fluids and their properties. In last year's AS course we have met a topic in this field. I will be applying ideas and knowledge gathered from last year for this investigation.
Because to solve a problem analytically can be very hard and spend a lot of time, global, polynomial and numerical methods can be very useful. However, in last decades, numerical methods have been used by many scientists. These numerical methods can be listed like The Taylor-series expansion method, the hybrid function method, Adomian decomposition method, The Legendre wavelets method, The Tau method, The finite difference method, The Haar function method, The...
Trask, J. Chapter 8 Alternative Methods [Power Point slides]. Retrieved from Lecture Notes Online Website: https://compass.illinois.edu/webct/urw/lc5116011.tp0/cobaltMainFrame.dowebct
Projectile motion is used in our daily lives, from war, to the path of the water in the water fountain, to sports. When using a water fountain or hose, projectile motion can be used to describe the path and motion of the water. This technology was created by finding the angle at which the water would come out at a maximum height and the person using it would be able to drink it without leaning over too much. These types of projectile motion will be further explored and analyzed in this assessment.