In this paper, we used a computational model to estimate the clearance of a tracer driven by the circulation of cerebrospinal fluid (CSF) produced in the choroid plexus (CP) located within the lateral ventricles. CSF was assumed to exit the subarachnoid space (SAS) via different outflow routes such as the parasagittal dura, cribriform plate, and/or meningeal lymphatics. We also modelled a reverse case where fluid was produced within the spinal canal and absorbed in the choroid plexus in line with observations on certain iNPH patients. No directional interstitial fluid flow was assumed within the brain parenchyma. Tracers were injected into the foramen magnum. The models demonstrate that convection in the subarachnoid space yields rapid clearance from both the SAS and the brain interstitial fluid and can speed up intracranial clearance from years, as would be the case for purely diffusive transport, to days.