Semi-analytical approximations of the laminar friction coefficients for flow in conduits with polygonal cross-section
[ 1 ] Instytut Mechaniki Stosowanej, Wydział Budowy Maszyn i Zarządzania, Politechnika Poznańska | [ 2 ] Katedra Techniki Cieplnej, Wydział Maszyn Roboczych i Transportu, Politechnika Poznańska | [ P ] pracownik
2002
artykuł naukowy
angielski
EN The steady laminar flow in conduits whose cross-section has an inner or an outer contour in the form of a regular polygon or a circle, is considered. To calculate the laminar friction, coefficient the velocity field is determined. Four cases are considered: (a) laminar flow in regular polygonal conduits, (b) laminar flow in regular polygonal conduits having circular cores, (c) laminar flow in cylindrical conduits having regular polygonal cores, (d) laminar flow in regular polygonal conduits having regular polygonal cores. The boundary collocation method in the least squares sense for solving appropriate boundary value problems for the velocity field is used. By means of analytical integration of the velocity field, for the four considered cases the analytical formulae for the laminar friction coefficients are obtained. Some coefficients in these formulas are determined numerically. By means of nonlinear approximation (Marquardt method), for the first considered geometry case, the simple analytical formula for the laminar friction coefficients is proposed.
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