The single-node flow problem, which is also known as the single-sink fixed-charge transportation problem, consists in finding a minimum cost flow from a number of nodes to a single sink. The flow cost comprise an amount proportional to the quantity shipped as well as a fixed charge. In this note, some structural properties of Fenchel cutting planes for this problem are described. Such cuts might then be applied for solving, e.g., fixed-charge transportation problems and more general fixed-charge network flow problems.