Tree networks for minimal pumping power

In this paper the optimization of fluid networks is based on the minimization of pumping power requirement. The total pipe network volume is constrained. It is shown that only in special cases the minimization of pumping power leads to the same architecture as the minimization of pressure drop or flow resistance. Fundamentals of fluid network optimization are developed for both spanning networks and networks where new non-consumer points are added (Gilbert-Steiner points). It is shown that networks with minimum pumping power must not contain loops. The influence of gravity on the optimization of flow configuration is also addressed. The principles developed in the paper are illustrated with an example representing a set of ten vertices to be connected with pipes. The paper provides designers with more effective basic tools for the conceptual design of fluid networks.