Choi and Kim [J. Colloid Interface Sci. 333 (2009) 672] proposed a new wall boundary condition for zeta-potential and surface charge density to describe the electrokinetic flow-induced currents in silica nanofluidic channels using the Poisson-Boltzmann (PB) model and the Poisson-Nernst-Planck (PNP) model. They showed that the results from the PNP model are in close agreement with the experimental data reported by van der Heyden et al. [Phys. Rev. Lett. 95 (2005) 116104]. In this paper, a theoretical model based on the PB model incorporating their proposed boundary condition is presented, which does not necessitate highly expensive computational effort. The results from our proposed model are shown to be in agreement with their numerical results of the PNP model. The present model also addresses the importance of the electrical resistance of reservoirs or the position of the electrodes for the measurement of the streaming current. Further, we point out that there is a misinterpretation in a comparison between their numerical results and those of van der Heyden et al.'s experiments. Finally, we conclude that the experimental data still cannot be predicted accurately by their proposed boundary condition and model, especially for the electrolyte concentration C(0)<10(-3)M.