Abstract: Based on the Poisson’s equation and the biharmonic equation, the fluid velocity distribution in the fan-shaped channel with different angle are studied analytically. The analytic expressions of axial velocity and stream function are obtained in the sectorial channel with different angle by the method of separation of variables, and the distributions of the circumferential and radial velocity components in the cross section of the channel are determined by the method collocation points. By numerical simulation method, the relative deviations between analytic solutions of Stokes equation and simulated solutions of N-S equation are analyzed at different Reynolds number. The conclusion indicates that the 3D Stokes flow at low Reynolds number within the fan-shaped channel can be decomposed into two 2D flows, namely the axial flow in the straight duct driven by pressure drop and the sectional flow in the fan-shaped cavity induced by circular wall rotation. In the condition of Re<1, the relative deviations between analytic solutions and simulated solutions are all less than 2%. The deviations increase greatly with Reynolds number enhancing，but maximum deviations of three velocity components are not larger than 10% as Re<100, which implies the analytic solutions can not only be used in Stokes flow at very low Reynolds number, but also be applied in laminar flow at lower Reynolds number.

Key words: fan-shaped section;separation of variables;Stokes flow;analytical solution;numerical simulation, Identification, Magnetic bearing, Rotordynamic stability, Bearing parameter