The intense, super-Eddington, well-collimated radiation field generated by non-Keplerian accretion disks orbiting black holes can accelerate matter to high velocities. By using an energy balance argument which is both simple and physically appealing, we show that ordinary electron-proton plasmas can only reach relativistic gamma-factors up to 1.5. A light electron-positron plasma could be accelerated up to γ≲5. The approach is valid if the optical depth along the accelerating funnel is significant, and the optical depth across the funnel is negligible. It is, therefore, appropriate for long, narrow funnels. Our method could easily be generalized to disk geometries other than the examples we give.