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 …show more content…
(4)
The balance of linear momentum for the viscous fluid through porous media according to Brinkman-Darcy equation is
, (5)
The basic assumptions that lead to the Brinkman-Darcy equation were illustrated by Rajagopal [23], and can be summarize in the following points:
1- The porous medium is a solid and thus the balance of linear momentum of the porous medium can be ignored.
2- The interactive force between the fluid and the porous medium is due to the frictional forces only and this force proportional to the flow velocity which represents by the term , where is the Darcy's coefficient, is the fluid viscosity and is the permeability of the porous medium.
3- The frictional effects due to viscosity were taken into account by the term , where is the effective viscosity of the fluid that flowing through the porous medium and is the porosity of the medium.
4- The flow is unsteady and sufficiently fast so that the inertial nonlinearities can not be ignored, thus the term needs to be retain.
According to the previous assumptions the balance of linear momentum can be written as in Eq.(5). Also, we want to confirm on the following
They just forgot to mention the other effects of fluids in nature. “The influence of the fluid on a body moving through it depends not only on the body’s velocity but also on the velocity of the fluid,” this is called relative velocity ( ). The relative velocity of a body in a fluid has an effect on the magnitude of the acting forces. For example, as a long distance runner is running into a head wind, the force of the fluid is very strong. If the runner is running with the help of a tail wind, the current’s force is reduced and may even be unnoticeable.
Aristotle, R. P. Hardie, and R. K. Gaye. Physics. Adelaide: The University of Adelaide Library, 2000. Print.
Ross, Danice, Re-Ann Sabubu, and Era Manitas. "Applications - Bernoulli's Principle." Bernoulli's Principle. N.p., n.d. Web. 26 Jan. 2014.
However, it is obvious that the tennis ball was most affected by friction, as it has the greatest difference between the theory and data. This was also visually apparent during the experiment. It was observed that the tennis ball slowed down considerably more that the other two balls. This is because the outer surface of a tennis ball is made from a furry cloth material, which generates more friction that a smooth surface, like the other two balls. (Bowden, 1951, pg. 302; Tremaine and Weinberg, 1984)
The biological universe is the idea that our solar system contains life other than ourselves.
(Misturelli, F. and Hefferman, C., 2008). I wrote this paper in a way that challenges you to put
A representation of the slow decrease in flux that can result from consolidation of the fouled layer is presented in figure 2.4.
Bernoulli’s principle is the concept that as the speed of a moving fluid (liquid or gas) increases, the pressure within that fluid decreases. This principle was originally formulated in 1738 by the Swiss mathematician and physicist Daniel Bernoulli, it states that the total energy in a steadily flowing ...
M.Mann. (2013). Momentum and Impulse. In M.Mann, Mind Action Series Physical Sciences 12 Textbook and Workbook (p. 9). Sanlamhof: Allcopy Publishers.
Purpose: To show that momentum is conserved in a closed system by illustrating the conservation of momentum in an elastic collision and an inelastic collision.
Renaissance theory of the open system where a flow occurs both in and out. A Midsummer
Table 3. 1 lists expressions for the resistance Coefficient and values for the flow exponent for each of the formulas
The effect of Temperature of liquid on flow rate. - the effect of Temperature on liquid flow (turbulent/laminar) 3) The effect of the Vertical height between source and destination of the fluid on flow rate. - the effect of Vertical height on liquid flow (turbulent/laminar) 4) The effect of the Liquid's Viscosity/Density on flow rate.
The solutions using in integro-differential equations have an important role in lots of engineering fields, also in financial problems, physics theories. The major area of integro-differential –equations are especially mechanical engineering, electric-electronic engineering, economics.[5] Boundary conditions are very important for Volterra equations in order to make them more visual. Furthermore the benefit working on boundary conditions is to see excellent satability properties and high accuracy for Volterra equations.[1] In addition, while evaluating integro differential equations, we should consider the situations about nonlinear integro-differential equations. Nonlinear integro differential equations are essential also in several fields. For instance, fluid dynamics, polymer science, population dynamics, thermoelasticity, chemical engineering can be researching area.[2]
As discussed in class, submission of your solutions to this exam will indicate that you have not communicated with others concerning this exam. You may use reference texts and other information at your disposal. Do all problems separately on clean white standard 8.5” X 11” photocopier paper (no notebook paper or scratch paper). Write on only one side of the paper (I don’t do double sided). Staple the entire solution set in the upper left hand corner (no binders or clips). Don’t turn in pages where you have scratched out or erased excessively, re-write the pages cleanly and neatly. All problems are equally weighted. Assume we are working with “normal” pressures and temperatures with ideal gases unless noted otherwise. Make sure you list all assumptions that you use (symmetry, isotropy, binomial expansion, etc.).