Analitical study of the velocities relation in the laminar flow of rectangular, square and elliptical shaped section ducts

Edgar Paz Pérez, Luiz Robert Carroccí, João Andrade de Carvalho Jr., José Marques Neto

Resumen


In the present study takes into account an analytical deduction of the relation between the maximum and average velocities of the flow in ducts or pipes of rectangular and elliptical shaped section, with the purpose of getting an expression to enable simple and fast calculation of the flow rate in ducts. Starting from the equation that models the flowing fields in rectangular and elliptical pipes, expressions to calculate the maximum and average velocities of the flow are obtained; dividing them the relation between them is obtained. From the result, it may be observed that in rectangular tube, the relation between maximum and average velocities depends only on the aspect ratio. This relation assumes its biggest value when the transversal section of the tube is a square. In elliptical tube the relation between maximum and average is equal to 2 in all case, incusing circular tube. On the other hand in rectangular and elliptical tube, the viscosity of the fluid, the variation of the linear pressure, and the measurements of the transversal section of the tube influence the maximum and also the average velocities.

Keywords: No circular pipe, maximum and average velocities of draining, no conventional flow


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