# Optimization of Water Pressure of a Distribution Network within the Water-Energy Nexus
## Materials and Methods
### Energy Consumption Simulation for Domestic Water Pressure Booster Systems  
WPBSs are used wherever there is a need to increase pressure and are responsible for supplying water and maintaining water pressure in the pipelines of a building [56]. WPBSs are widely installed in houses and apartments around the world to increase water pressure and provide the flow required by consumers (which the water company is not able to provide) on different floors throughout the day. Different designs for installing WPBSs have been proposed for domestic water supply systems, based on different local rules and standards. Figure 2 presents the design of a typical domestic water supply system proposed by booster pump producer companies [57]. In most designs, the water storage tank is located on the ground floor. Water can be stored in these tanks during off-peak hours, during which the water provided by water companies exceeds the level of consumption. The stored water can then be used during peak hours to meet the flow requirements of consumers using WPBSs. A WPBS  
Figure 1: The general relationship between pressure and leakage rate, based on the FAVAD equation for different values of N1. increases the pressure of the water stored in the tank through a conduit and includes one or more pumps that are designed and selected according to the height of the building, a booster pump controller, and a pressure sensor affixed to the exit side of the booster pump and connected to the control device. The controller switches off any number of pumps when they reach the predetermined upper-pressure limit and switches on when the lower pressure limit is reached. The pressure tank can be installed on the roof to satisfy the demands imposed on the system. Without the pressure tank, the booster would restart upon the slightest call for flow--for example, due to a small leak in the piping system. A typical energy-saving strategy is to install a bypass connection to use the pressure provided by the water company for the domestic water supply system that reduces the need to start the WPBS. The higher the supply of pressureed water from water companies is, the lower the energy consumption of the WPBS will be. The power required for the pump to lift an amount of liquid at a particular height is called hydraulic power and is calculated by Equation (5). \[\mathrm{P}=\left\{ \begin{array}{ll}0&\mathrm{h}\leq 0\\ \frac{\rho\mathrm{gh}\mathrm{Q}}{\eta}&\mathrm{h}>0\end{array} \right. \tag{5}\]  
In this equation, \(\mathrm{P}\) is the power consumption, \(\rho\) is the water density, \(\mathrm{g}\) is the acceleration of the gravity, \(\mathrm{Q}\) is the water discharge, \(\eta\) is the pump efficiency, and \(\mathrm{h}\) is the pumping head and it is calculated according to the Equation (6). \[\mathrm{h}=\mathrm{h}_{\mathrm{sup}}+\mathrm{h}_{\mathrm{elv}}+\mathrm{h}_{ \mathrm{loss}}-\mathrm{h}_{\mathrm{avl}} \tag{6}\]  
Figure 2: The domestic water supply system. In this formula, hsup is the head supplied to the faucet by the pump, hlev is the faucet elevation relative to the pump, hloss is the piping friction losses, and hav1 is the suction pressure. Suction pressure can be regarded as the water pressure supplied by the water company, which equals Hj and its calculation is shown in Section 2.1. The efficiency of the pump \(\eta\) can be calculated using Equation (7). \[\eta=\frac{\text{water energy}}{\text{electric energy}} \tag{7}\]  
When the pumping head h is negative, the pressure supplied by the water company is enough for the building's consumers. In this case, there is no need for the WPBS, and no additional energy is consumed. The energy efficiency varies according to the production or installation conditions [58]. Many researchers have focused on energy efficiency enhancement opportunities.