In the present work, we obtained explicit formulas that relate permeability to porosity and specific surface area of pores and cracks. We show that Darcy's law is not an obligatory condition for the determination of fluid flow velocity; this empirical law may be true for some geometry of grains and pores, and maybe not valid for another geometry with flowing conditions. The role of permeability is played by the ratio of porosity (to the third power) to the specific surface area (to the second power) of pores or cracks. Fluid flow velocity depends on porosity, specific surface area, viscosity, and borehole radius. The analog of Darcy's law can be calculated using integral geometry parameters and boundary conditions; i. e., it does not have to be only empirical, but it is also an analytical law. The dependence of permeability on porosity differs significantly from enough big to small porous media. The fluid flow can be calculated using the elastic equilibrium equations and the incompressibility of viscous fluid without any phenomenological parameters.