STUDY OF LAMINAR FLOW IN PRISMATIC CHANNELS OF RECTANGULAR AND ELLIPTICAL SECTION
Abstract
The main attention in this work is paid to the disadvantages of using in chemical technology, in power engineering and other applications such a concept as the equivalent diameter introduced for channels of complex shape (not circular cross-section) when describing liquid and gas flows in them. For the detailed examples, for illustrative purposes, prismatic channels in the form of a cross-section of an ellipse, a rectangle, and an equilateral triangle have been used. Such a channel characteristic as an equivalent diameter is also used in educational disciplines related to the flow of a continuous phase in chemical technology. For these cross sections, exact solutions of the hydrodynamic problem are known for a laminar steady flow of Newtonian fluids and weakly compressible gases. A good example is also a variant of fluid flow in a channel with an equilateral triangle-shaped cross section, which also has an exact solution to the hydrodynamics problem. In the case of a channel with a rectangular cross-section, the efficiency of using variational and related methods (Ritz and Kantorovich) for the analysis of flow problems in a prismatic channel at small values of the Reynolds number is shown. Analytical relationships are obtained, which are illustrated in the graphs for the dependence of the volumetric flow rate of liquid through the cross section of the considered channels on the main parameters of the process. Illustrating the problem, that is, evaluating the range of suitability of describing the flow of Newtonian fluids in the considered prismatic channels when using the concept of "equivalent diameter", in addition to the formula relations, graphical data are given. The results obtained were compared with those known from the literature.
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