Passing of Liquid from the Random Velocity Through Medium Filled by Particles-Granules

The article discusses in passing the particles generally inhomogeneous density fluid through the tube in which the particles are granules, the dimensions of which are much exceed size liquid particles. It is assumed that the liquid is exposed to external interference, which leads to the presence of the velocity fluctuations of liquid particles. The aim of this work is to statistical characteristics of liquid density in these conditions, including the power spectral densities of the density fluctuations, and to identify the statistical characteristics considered depending on the cross-sectional area of the tube. For this problem, we obtain an equation similar to diffusion. His solution for additional initial and boundary conditions led to a stochastic integral equation for the density of the liquid. Using the method of description of stochastic systems described by linear integral transforms it possible to obtain the necessary characteristics of the process. It turned out that the low-frequency fluctuations in the density of the liquid have the character of flicker noise (pink noise). Moreover, due to the strong dependence of the behavior of the fluid and the diffusivity ratio of the cross sectional area of the tube, the power spectral density of the density fluctuations are not dependent on the cross-sectional area continuously, but undergoes a kind of "oscillation". It is also shown that if the distribution of particle beads in an medium is not homogeneous and is weakly dependent on the distance along the tube axis, it is still possible to use the first approximation results for the homogeneous distribution of the particles of the granules. To do this, the formulas obtained granules distribution parameter should be replaced with the corresponding function. The results obtained can be used in problems of fluid flow in pipes and suspensions, as well as issues of hydraulic engineering