The energy balance calculation for pressurized water networks is an important step in assessing the energy efficiency of water distribution systems. However, the calculation generally requires mathematical modelling of the water networks to estimate three important energy components: outgoing energy through water loss (), friction energy loss () and energy associated with water loss (). Based on a theoretical energy balance analysis of simplified pipe networks, a simple method is proposed to estimate , and with minimum data requirements: input energy, water loss (WL) and head loss between the source and the minimum energy point (ΔH). By inclusion of the head loss in water networks into the estimation, the percentages of and are lower and higher, respectively, than using only the percentage of WL. The percentage of can be a function of the percentage of ΔH. By demonstrating our analysis with the simulation results from the mathematical models of 20 real water networks, the proposed method can be used to effectively estimate , and as a top-down energy balance approach.

The water quality audit concept is an important feature in assessing the loss of disinfectant mass in drinking water distribution systems. Based on this concept, the loss can be divided into the loss of disinfectant mass through water losses (Ml) and the decay of disinfectant mass due to chemical reactions (Mr). When an audit focuses on the effect of water losses on the loss of disinfectant mass, the decay of disinfectant mass by chemical reactions with the ideal condition of no water losses (Mro) has to be estimated; thus, the disinfectant mass associated with water losses (MWL=Ml+Mr−Mro) can be assessed. Generally, the computation of these components (Ml, Mr, and MWL) needs hydraulic and water quality modeling. In this study, we propose a novel method based on a simple theoretical analysis to evaluate these components using only two parameters: the ratio of water losses (p) and the ratio of disinfectant concentrations at the critical pressure point and the network inlet (Cp*). The coefficients of our theoretical Ml, Mr, and MWL were estimated using 20 real network models, with p between 2.8% and 54.9% and Cp* between 18.4% and 91.9%. The results showed that our equations were effective at assessing the loss of disinfectant mass in drinking water distribution networks for the top-down auditing approach.