We study the process of charged polymer translocation, driven by an external electric potential, through a narrow pore in a membrane. We assume that the number of polymer segments, m, having passed the entrance pore mouth, is a slow variable governing the translocation process. Outside the pore the probability that there is an end segment at the entrance pore mouth, is taken as the relevant parameter. In particular we derive an expression for the free energy as a function of m, F(m). F(m) is used in the Smoluchowski equation in order to obtain the flux of polymers through the pore. In the low voltage regime we find a thresholdlike behavior and exponential dependence on voltage. Above this regime the flux depends linearly on the applied voltage. At very high voltages the process is diffusion limited and the flux saturates to a constant value. The model accounts for all features of the recent experiments by Henrickson [Phys. Rev. Lett. 85, 3057 (2000)] for the flux of DNA molecules through an alpha-hemolysin pore as a function of applied voltage.