On the Eccentric Rotation of a Circular Cylinder in Fluid (1st Report)

Abstract

In the previous and another reports, we obtained the stream functions for the eccentric rotational motion of a cylinder in fluid. In this report, from these results we calculate the pressure distributions on the surface of the cylinder and the resultant force. The pressure distributions for the motion in the infinitely wide region (Case A) are expressed by Eq. (4) and for the motion in the cylindrical vessel (Case B), by Eq. (12), and some numerical examples are shown in Fig. 1 for Case A and in Fig. 5 and 6 for Case B. The resultant force PL' acting towards the direction that increases the eccentricity, is expressed by Eq. (8) for Case A and by Eq. (22) and (25) (when ri/r0 is nearly equal to 1) for Case B. Figs. 7 and 8 show the above results respectively for ω/Ω=1 (forward precession) and for ω/Ω=-1 (backward precession). Also we calculate the attached moment of inertia which is shown in Eqs. (30) and (31), and in Fig. 12.