permeability coefficient in Darcy’s filtration law

Using the equation of living forces averaged over the volume of the filter and obtained from the Navier-Stokes equations of an incompressible fluid, an analytical formula for the permeability coefficient in the classical Darcy problem is derived to within the principal terms of the Poiseuille number...

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Bibliographic Details
Published in:Journal of applied mechanics and technical physics 2013-07, Vol.54 (4), p.608-611
Main Authors: Bushlanov, V. P., Bushlanov, I. V., Sentyakova, E. N.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Classical and Continuum Physics
Classical Mechanics
Fluid- and Aerodynamics
Mathematical Modeling and Industrial Mathematics
Mechanical Engineering
Physics
Physics and Astronomy
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Summary:Using the equation of living forces averaged over the volume of the filter and obtained from the Navier-Stokes equations of an incompressible fluid, an analytical formula for the permeability coefficient in the classical Darcy problem is derived to within the principal terms of the Poiseuille number. It is shown that the resulting permeability coefficient is inversely proportional to the square of the specific surface area and the dimensionless average dissipation rate of the kinetic fluid energy in the filter.
ISSN:0021-8944
1573-8620
DOI:10.1134/S0021894413040111