Demosponges possess a leucon-type canal system which is characterized by a highly complex network of canal segments and choanocyte chambers. As sponges are sessile filter feeders, their aquiferous system plays an essential role in various fundamental physiological processes. Due to the morphological and architectural complexity of the canal system and the strong interdependence between flow conditions and anatomy, our understanding of fluid dynamics throughout leuconoid systems is patchy. This paper provides comprehensive morphometric data on the general architecture of the canal system, flow measurements and detailed cellular anatomical information to help fill in the gaps. We focus on the functional cellular anatomy of the aquiferous system and discuss all relevant cell types in the context of hydrodynamic and evolutionary constraints. Our analysis is based on the canal system of the tropical demosponge Tethya wilhelma, which we studied using scanning electron microscopy. We found a hitherto undescribed cell type, the reticuloapopylocyte, which is involved in flow regulation in the choanocyte chambers. It has a highly fenestrated, grid-like morphology and covers the apopylar opening. The minute opening of the reticuloapopylocyte occurs in an opened, intermediate and closed state. These states permit a gradual regulation of the total apopylar opening area. In this paper the three states are included in a theoretical study into flow conditions which aims to draw a link between functional cellular anatomy, the hydrodynamic situation and the regular body contractions seen in T. wilhelma. This provides a basis for new hypotheses regarding the function of bypass elements and the role of hydrostatic pressure in body contractions. Our study provides insights into the local and global flow conditions in the sponge canal system and thus enhances current understanding of related physiological processes.