Acceleration effects in dissipative flows

Based on the comparison of the obtained non-stationary equation for filtration rates with the classical Darcy's law, the dependence of the dissipative force on the viscosity of the filtered liquid and the permeability of the porous medium is found, and the relationship between the main component of the dissipative force tensor and these quantities is established. It is shown that the contribution of the acceleration component of the pressure gradient during radial flow is proportional to the square of the filtration rate and does not depend on the permeability. A refined expression for Darcy's law is obtained for radial filtration in a highly dissipative medium taking into account the acceleration component. It is established that at small pressure gradients, the refined Darcy's law agrees well with its classical expression.

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