  We use numerical modelling to study the flow patterns of an active nematic
confined in a cylindrical capillary, considering both planar and homeotropic
boundary conditions. We find that active flow emerges not only along the
capillary axis but also within the plane of the capillary, where radial
vortices are formed. If topological defects are imposed by the boundary
conditions, they act as local pumps driving the flow. At higher activity we
demonstrate escape of the active defects and flow into the third dimension,
indicating the importance of dimensionality in active materials. We argue that
measuring the magnitude of the active flow as a function of the capillary
radius allows determination of a value for the activity coefficient.
