Minimum pumping energy of tree-shaped water supply networks for probabilistic demands in built environment

Minimization of pumping energy is a major concern for designing sustainable water supply in buildings. Modular designs of tree-shaped water supply piping system, such as 2 by N array include water cisterns of water closet in public toilets, washbasin taps in schools are commonly found in building complexes. Potable water demands in water systems serving built environment are unsteady, random and intermittent. However, the existing statistical Hunter-based probabilistic approaches to pipe sizing, however, do not consider the minimization of pumping energy for water distribution through proper selection of pipe radii. This paper demonstrates a pipe sizing method with probabilistic demands for optimizing pipe friction energy loss constrained by the fixed pipeline volume. A mathematical model for pumping energy optimization in infinite tree-shape water supply piping networks for probabilistic demands is proposed. Compared with the Hunter's based probabilistic approach in sizing an 8- section tree-shape water supply network for demand of probabilities 0.1 and 0.2, the proposed method offers reduction potentials of pipe friction energy loss of 12% and 43% respectively. With piping systems of pipe radius ratios, the optimal tree-shape networks are also determined.