A constant flow down a circular bend in a rotating open channel of rectangular cross section is considered. By using the eddy viscosity concept combined with a finite slip velocity at the bed, simple analytical solutions of the problem are obtained. They show a helical motion induced by the combined effects of channel curvature and Coriolis force. For values of the inverse Rossby number close to zero we have the well known secondary flow away from the centre of curvature near the surface and towards it near the bottom. As the inverse Rossby number increases the secondary flow is strengthened or weakened depending on the relative direction of rotation of the basic flow. The basic flow is also shown to be strongly influenced by the inverse Rossby number.