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.
Ross, Danice, Re-Ann Sabubu, and Era Manitas. "Applications - Bernoulli's Principle." Bernoulli's Principle. N.p., n.d. Web. 26 Jan. 2014.
The biological universe is the idea that our solar system contains life other than ourselves.
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 ...
Osmosis Theory [IMAGE] [IMAGE][IMAGE]Solution A
A representation of the slow decrease in flux that can result from consolidation of the fouled layer is presented in figure 2.4.
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M.Mann. (2013). Momentum and Impulse. In M.Mann, Mind Action Series Physical Sciences 12 Textbook and Workbook (p. 9). Sanlamhof: Allcopy Publishers.
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The objective of this lab is to determine the coefficients of static and kinetic friction between a block of wood and wooden table. It was hypothesized that the mass of the object would not impact the coefficient of friction. It was also hypothesized that the coefficient of static friction would be larger than the coefficient of kinetic friction.
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
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.
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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.).