Abstract
The effect of boundary proximity on the resistance to rotation of an axially symmetric body of otherwise arbitrary shape is theoretically calculated, at small angular Reynolds numbers, for the case in which it rotates symmetrically about the axis of a circular cylinder filled to a finite depth with viscous liquid. The body may occupy any position along the cylinder axis. Owing to the presence of the cylinder walls, the cylinder bottom and the free surface, the rotational resistance of the body is different than would obtain in an unbounded fluid medium. Results are expressed in terms of the ratio of torques experienced by the body in the bounded and unbounded fluids, respectively, when rotating at the same angular velocity. Numerical values are provided which enable this ratio to be computed from the fundamental parameters of the system.
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