This paper presents a general two-dimensional model for rotating barotropic flows over topography. The model incorporates in a vorticity–stream function formulation both inviscid topography effects, associated with stretching and squeezing of fluid columns enforced by their motion over variable topography, and viscous effects, due to the Ekman boundary layer at the solid bottom. From the present formulation, conventional two-dimensional models can be recovered. The model is tested by means of laboratory experiments on homogeneous vortices encountering irregular topographies. The experimental observations are then compared with the corresponding numerical simulations based on the general model. The results suggest that such a formulation incorporates both inviscid and viscous topography effects correctly.