RESUMO
In this study, a theoretical framework is developed to predict the equilibrium conditions of a non-neutrally buoyant sphere placed in a vertical conical tube as encountered in liquid rotameters. The analysis presented herein is applicable for a sphere heavier than the surrounding fluid, situated on the axis of a slightly tapered tube. The sphere is subject to the laminar flow conditions with the Reynolds numbers ranging between the Stokes type regimes up to values corresponding to slightly inertial regimes. In this work, we assume that the aperture angle of the tube is small and that the drag force is mainly due to the dissipation located in the gap between the tube and the sphere. Under these conditions, it is possible to consider the tube as locally cylindrical and we can use the results previously obtained for the correction factor of the Stokes force on a sphere subject to a Poiseuille flow in a tube of constant cross-section. We obtain an equation relating the flow rate to the vertical position of the sphere in the tube and the validity of this analysis is demonstrated by applying it to a commercially available rotameter. The present study provides a simple but sound theoretical method to calibrate such flowmeters.
RESUMO
The continuity and momentum equations have been solved numerically for the two-dimensional steady flow of power law fluids over a thin circular disk oriented normal to the direction of flow. Extensive results on the individual and total drag coefficients are obtained as functions of the power law flow behavior index (0.4 < or = n < or = 1.0), Reynolds number (1 < or = Re < or = 100) and the blockage ratio, disk-to-cylinder diameter ratio (0.02 < or = e < or = 0.5), which can be used to estimate the settling velocity of a circular disk. The numerical predictions of drag are consistent with the scant experimental results available in the literature.
