The inviscid evolution along a pipe of two families of inlet cylindrical swirling flows is analysed using the Bragg-Hawthorne equation. The first flow corresponds to exact solutions of the axisymmetric Euler equations near the axis, at which the velocity field is singular. The quasi-cylindrical problem is reduced to solving a phase-plane first order differential equation. It is found that, for both converging and diverging pipes, cylindrical solutions for the downstream flow determined by the inlet flow exist even for very high values of the swirl parameter (L). The second family of inlet flows coincides with the first except inside an axial core of radius rc, where the flow now has constant axial velocity and rotates as a rigid body. For diverging or straight pipes, this regularised family exhibits the usual behaviour, with a maximum value of L = Lf above which one-cell cylindrical solutions for the downstream flow fail to exist, even for very small rc. The downstream flow may also stagnate at the axis above another value Lo < Lf. Thus, there is no inviscid breakdown unless the vortex core is (arbitrarily) regularised. Since regularization of singular inviscid flows is actually carried out by viscosity, it follows that, within the limitations of the present simple model, the presence of viscosity is essential to describe the phenomenon of vortex breakdown in pipes from the inviscid equations, regularising the usually singular inlet inviscid flow. The jet-like radial decay of the axial and swirl velocities in the present inlet model flows leads also to values of Lf closer to those observed experimentally than those found in some previous models.