GENERAL EQUATION OF THE HYDRAULIC FRICTION LAW FOR HINDERED FALLING OF AN INDIVIDUAL BALL AND FLUID MOTION IN GRANULAR LAYERS

The article presents the results of a research into various hydromechanical processes such as hindered falling of an individual ball in a liquid; suspension of a homogeneous monodispersed granular layer with ascending fluid flow; homogeneous liquid filtration in a porous granular layer. The authors generalize the results of theoretical and experimental studies, employ the theory of similarity, and establish that the laws of hydraulic friction for the mentioned hydromechanical processes share the common ground described by one general equation that provides basis for obtaining the individual formulae computing the studied hydromechanical processes. The formulae appear in dimensionless similitude parameters that reflect correlation of the essential action forces.

The presented scientific results contribute to the theory development of the applied hydromechanical phenomena and the new obtained formulae enable enhancement of the calculation procedures for structures and installations that realize the studied hydraumechanical processes. Thus, the research results for the hindered falling of an individual ball in a liquid can apply in viscosimetry techniques and in handling the problems related to calculations of various movement types and separate units in technologies realizing the hydraulic processes of hindered falling of individual balls in liquids.

Fluidization processes (pseudo-liquefaction) of the granular layers enjoy wide application in various segments of industry for instance in chemical engineering at adsorption, desorption, dissolution, dealkalization, ablution. A new general calculating formula incipiency provides a possibility for technological computations realization under any operational mode. The filtration process is used in industry as well as occurs in nature, for example, in movement of the ground water. At present, the basis for calculating techniques is the monomial Darcy formula defining the filtering rate as function of the hydraulic gradient with bringing in the filtration coefficient. Thereat, the problems appear with determination of the filtration regime and the validity limits for the Darcy’s equation. The incipiency of the proposed in the article new general formula resolves this problem and allows estimating with high accuracy in a wide range of changing conditions.

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