We have proposed a new system for an accurate wet-type centrifugal classification to which an almost rigidly rotating through-flow is applied. This flow can be produced within a highly rotating double-walled container, without any turbulent fluctuation. In the present paper, we have employed the batch-type classification with a cylinder-sphere-shaped container in classification experiments, theoretical and numerical flow analyses, and flow-visualization measurements. Consequently, we have obtained the following main conclusions: (i) with decreasing Ekman number (i.e. increasing rotation rate) at a constant Rossby number or with decreasing Rossby number (decreasing throughflow rate) at a constant Ekman number, the cut size and fine yield decrease and the classification accuracy increases, and (ii) for the occurrence of the rigid-rotation region which is indispensable to collect the coarse product, it is necessary to make the flow field inverse-C-shaped towards the rotation axis.