# Optimization of Water Pressure of a Distribution Network within the Water-Energy Nexus
## 4 Results and Discussion
### Daily Pressure Optimization
The influence of this parameter generally is not taken into account in the evaluations of pressure management impact. The value of this parameter is reported between 0.5 and 2.5 in different studies. As it is described in Table 3, the value of this parameter was considered 1.4 in the present study. Figure 9A shows the investigation of the sensitivity of optimized results on this parameter. It was deduced that the sensitivity of optimized pressure to the alterations of this parameter is low, but the remarkable point is the sensitivity of optimized cost. The sensitivity of optimized cost to this parameter was more than any other five parameters assessed in this study. This shows the importance of precise calculation of this parameter using empirical data. WPBS efficiency is a parameter that policymakers can use to decrease costs by providing necessary education and investments. Different operating circumstances will result in booster pumps to get out of their designed performance conditions. This will lead to a considerable decrease in the efficiency of this system. Therefore, the appropriate and comprehensive design of WPBSs will likely have a major impact on the system's efficiency improvement. Figure 9B shows the sensitivity of optimized results on WPBSs efficiency. An increase in WPBSs efficiency can lead to a decrease in optimized pressure, and therefore in water section costs, and as a result, the optimized cost will decrease. If the WPBSs' efficiency increases by 20%, optimized pressure and cost will decrease by 17% and 16%, respectively. Considering the limitations and price of land in recent years, investors and policymakers have focused on increasing the number of high buildings. The increase in the number of building floors means an increase in \(\mathrm{h_{elv}}\) and \(\mathrm{h_{loss}}\), which results in an increase in energy consumption for supplying water for higher floors. Figure 9C illustrates the impact of this phenomenon on optimized cost and pressure. The horizontal axis shows the percent of  
Figure 9: Sensitivity of optimized pressure and optimized cost to the (**A**) leakage exponent, (**B**) WPBS efficiency, (**C**) parameter F, and (**D**) physical water loss. families that will go from a floor to a higher floor and is expressed with the F parameter (e.g., when F = 5%, 5% of the families living on floor 1 will go to floor 2, 5% of the families living in floor 2 will go to floor 3 and... ). According to the results, when F is equal to 50%, the value of optimized cost and pressure will increase by 30% and 31%, respectively. Aging and exhaustion of pipes can lead to leakage in both pipes and pipes connections, resulting in physical water loss and an increase in maintenance costs. Establishing the necessary infrastructure for replacing exhausted pipes imposes enormous amounts of costs on water supply companies. If these companies cannot fund these costs, they will decrease the water pressure, therefore ignoring costs imposed on the energy sector. Figure 9D shows the sensitivity of optimized pressure and cost regarding physical water loss. Decreasing the physical water loss will enable us to lower the costs of the energy sector by increasing optimized pressure. If physical water loss reaches 4%, the optimized cost will decrease by 42%, which is an indicator of this parameter impact. Moreover, increasing the water pressure will increase the satisfaction of water supply companies' subscribers. In contrast, ignoring real water loss and the absence of investment in this field would necessitate a decrease in water pressure of WDN. As a result, energy costs would increase, and the optimized cost would increase in advance. If the physical water loss reaches 40%, the optimized cost will increase by 14% and optimized pressure will drop 14%.