Comparison between the time evolution of the shell radius (top panel), velocity (middle), and acceleration (bottom) for an outflow produced by an exponentially growing BH in the energy-driven (black curves) and momentum-driven (red curves) limits. The source input parameters are as in Figs. 2 and 5. The ratio between the two radii is plotted as a dashed curve in the top panel. The vertical dotted lines are as in Fig. 2. At any given time, the energy-driven outflow is about two times more extended and faster than the momentum-driven outflow (apart from very late times, t> 1 Gyr, where the ejected wind mass becomes comparable with the shell mass and our treatment is inaccurate).