In recent years, the protein nanopore cytolysin A (ClyA) has become a valuable tool for the detection, characterization and quantification of biomarkers, proteins and nucleic acids at the single-molecule level. Despite this extensive experimental utilization, a comprehensive computational study of ion and water transport through ClyA is currently lacking. Such a study yields a wealth of information on the electrolytic conditions inside the pore and on the scale the electrophoretic forces that drive molecular transport. To this end we have built a computationally efficient continuum model of ClyA which, together with an extended version of Poison-Nernst-Planck-Navier-Stokes (ePNP-NS) equations, faithfully reproduces its ionic conductance over a wide range of salt concentrations. These ePNP-NS equations aim to tackle the shortcomings of the traditional PNP-NS models by self-consistently taking into account the influence of both the ionic strength and the nanoscopic scale of the pore on all relevant electrolyte properties. In this study, we give both a detailed description of our ePNP-NS 1 model and apply it to the ClyA nanopore. This enabled us to gain a deeper insight into the influence of ionic strength and applied voltage on the ionic conductance through ClyA and a plethora of quantities difficult to assess experimentally. The latter includes the cation and anion concentrations inside the pore, the shape of the electrostatic potential landscape and the magnitude of the electro-osmotic flow. Our work shows that continuum models of biological nanopores-if the appropriate corrections are applied-can make both qualitatively and quantitatively meaningful predictions that could be valuable tool to aid in both the design and interpretation of nanopore experiments.