# Optimization of Water Pressure of a Distribution Network within the Water-Energy Nexus
## 4 Results and Discussion  
### Daily Pressure Optimization  
In order to manage the pressure for achieving daily optimum results, the mechanical control method was used in this section. Because there is no need to consider continuous alterations of pressure in this mode and the optimum results are required on daily basis, the mechanical control method was applied to PRV. The results of the attempt to find an optimum water network pressure value are presented in Figure 6. According to this figure, as the average water pressure of the network increases, the energy consumed by the WPBSs decreases, while leakage and burst frequencies increase. According to the model, the optimum average daily water pressure of the WDN in the city of Baharestan is 47.6 mH\({}_{2}\)O. By adopting this pressure, the daily energy-consumption cost of the WPBS, combined with the operation and maintenance costs of the WDN, would total USD 1009. If the pressure adopted were lower, the operating and maintenance costs would decrease, while the energy consumed by the WPBSs would significantly increase. This shows the importance of using an integrated approach towards water and energy regarding the average pressure of the water network. The determined optimum pressure level is highly dependent on local conditions. The degradation of water pipes results in a reduction of the optimum pressure of a WDN. Managing water pressure becomes increasingly important as pipes age. In addition, over time, existing slums will be replaced by multi-story buildings, which will increase the optimum average pressure. Clearly, the complicated impact of any change in local  
Figure 5: The share of people living on different floors of the buildings for the city of Baharestan. Figure 6: Model results for calculating the optimized average pressure of the network. conditions on water and energy price on the optimum pressure requires policymakers to employ a dynamic approach to the challenge. The sensitivity analysis was used in this study to assess the influence of input variables uncertainties on the daily optimized pressure and daily optimized cost. Water and energy price, leakage exponent, WPBSs efficiency, the height of buildings, and leakage were the selected parameters to be analyzed. The range of each parameter was defined based on price policy, historical data, and physical attributes of the water distribution network and WPBSs. Once the parameters were set, the model was run, and the optimized cost and optimized average water pressure of the WDN were calculated. Figure 7 depicts the sensitivity of optimized cost and pressure to the changes in energy and water prices. Water and energy prices are determined by policymakers at the macro level and are generally dependent on economic, social, and political conditions. These two factors were imposed into the developed model. Considering the implantation of price adjustment policies to cut the water and electricity subsidies, it is likely that water and electricity prices will rise in the years to come. The increase in water and energy prices will decrease and increase optimized pressure, respectively. Moreover, as it is shown in the figure, the sensitivity of the optimized cost to the increase of energy is higher in comparison to the water price increase. As it is illustrated in Figure 8, with a simultaneous increase of water and energy prices, the minimum price will be in the first optimized pressure and does not change. In addition, it can be expressed that 50% and 100% simultaneous increase in water and energy prices will result in a 46% and 92% increase in optimized cost, respectively. Figure 8: Sensitivity of optimized cost to simultaneous increase of water and energy price. Figure 7: Sensitivity of optimized pressure and cost to water and energy price increase. In the FAVAD equation, the leakage exponent has a remarkable impact on determining leakage amount considering pressure alterations and is particularly calculated empirically.