Some observations on energy loss and network entropy in water distribution networks

The design of water distribution networks has been extensively studied with the aid of computers, and the focus has shifted from merely satisfying the hydraulic requirements to fulfilling the need for reliability. One of the interesting research areas recently is the use of informational entropy as a surrogate measure for reliability. The actual meaning of the informational entropy for water distribution network has not been fully elucidated, and it was hypothesed that reliability is in some way proportional to the numerical value of network entropy. The purpose of this paper is to explore the relationship between energy loss and network entropy. The investigation approach used is to take a simple looped network and individually vary the pipe diameters from zero to infinity, and calculate the corresponding network entropy and energy loss for the water distribution network. The results revealed many interesting observations in the variation of network entropy with pipe resistance coefficient K_i, and the revelation of local maximum and minimum points.