This paper presents a formalization of the notion of function as operation on flows as advanced in the Functional Basis approach of Stone and Wood. We first analyze the modeling of functions in this approach and identify the notions that are ontological significant for their formalization within the foundational ontology DOLCE. Then, we build the logical system in which this engineering notion of function is formally translated and connected to the ontology. Furthermore, we posit a number of constraints for a correct interpretation of the formal system and also provide a web ontology language version. We conclude with an assessment of our results and a discussion of our larger project aimed at analysing functional descriptions of technical artifacts, and at translating functional descriptions using different engineering notions of function.