Numerical simulations of the pulsating flow in a pipe of circular cross-section characterized by small imperfections are carried out to determine the conditions leading to the appearance of turbulence. The results show that in the oscillatory case (no steady velocity component of the basic flow), the critical value of the Reynolds number Rδ depends on the Womersley parameter α and, in particular, Rδ increases as α decreases. The critical value of Rδ of the plane wall case is recovered when α is larger than about 10. For moderate values of the Reynolds numbers but larger than the critical one, turbulence appears around flow reversal and breaks the symmetry of the flow, originating a steady velocity component. Moreover, turbulence is not present throughout the whole cycle and there are phases during which the flow relaminarizes. The presence of a steady pressure gradient tends to destabilize the flow and this destabilizing effect becomes larger as the steady velocity component is increased. When turbulence is present, its dynamics is similar to that of the steady case and a log-law layer can be identified both in the oscillatory and the pulsating case.