The electrokinetic phenomena occurring in homogeneous cylindrical pores containing symmetric electrolytes are studied. The local relations for flow in the pores (Nernst-Planck and Navier-Stokes equations) are developed. The analysis includes a numerical solution of the nonlinear Poisson-Boltzmann equation. The integral expressions of the phenomenological coefficients coupling the solvent flow and the electrical current with the hydrostatic pressure and the electrical potential gradients are established and calculated numerically. The mobilities of anions and cations are individually specified and the electroviscous effects as well as the surface conductance are taken into account. Streaming potentials obtained from numerical calculations are compared with results given by classical relations in a range of zeta potentials and electrokinetic radii that may commonly occur in experimental investigation of micro- and ultrafiltration membranes. In this work, it is shown that classical approximated relations can give rise to very misleading conclusions and that the determination of the true zeta potential requires a full analysis (including numerical calculations) of the basic relations for flow and potential distribution in charged pores.