# Development of Practical Design Approaches for Water Distribution Systems
## 2 Practical Design of Water Distribution Systems
### Pipe Continuity Search Approach  
The optimal design of WDSs using a metaheuristic algorithm resulted in low efficiency real-world WDSs construction, since the neighbor pipe diameter size had abnormal unevenness (e.g., concave-convex pattern) of flow direction. Therefore, a previous study proposed a pipe continuity search approach to improve the abnormal unevenness [10]. In the existing study, the pipe size continuity search algorithm searched all the possible flow paths in the distribution network, and the pipe size was gradually decreased on the basis of the flow direction of water, as shown in Figure 1. The existing approaches had a rule that the diameter of the downstream pipe should be equal or smaller than that of the upstream pipe. Therefore, Figure 1b will come up with the same diameter set, which is highlighted with the red dotted line in Figure 1.  
However, these approaches have limitations. When three or more pipes meet at a single node, the pipe path carrying the relatively larger flow meets the pipe with a smaller diameter. In other words, the flow and pipe size continuity cannot be reasonably determined. Figure 2 shows an example of the limitation for the existing pipe continuity search method. Based on the previous standard, the continuity of example network is that the pipe diameter of the route for Pipe 1-Pipe 3 and Pipe 2-Pipe 3 is smaller or the same as the one following the flow direction. However, this approach cannot be considered for the flow quantity of each pipe. In this case, since Pipe 3 has the largest flow, the size of Pipe 3 needs to larger than Pipe 2 at the confluence point.  
In addition, as existing pipe size continuity search algorithms search all flow paths in the distribution network, they takes relatively more time. Since the number of possible flow paths exponentially increases with the increasing size of water distribution network systems, the applicability in actual water distribution networks declines.  
The proposed approach addresses the disadvantages of existing continuity search algorithms to reduce computation time and to reasonably consider pipe size continuity based on flow at the confluence point where three or more pipes meet. Existing continuity search algorithms explore all the possible flow paths between two selected nodes within the WDSs, determine whether pipe size is gradually reduced on the basis of flow directions of water, and impose penalties on designs with increasing pipe sizes. Designs with penalties are replaced by other designs during the process of optimization.  
However, the proposed continuity search algorithm identifies two pipe paths connected at one selected node in the WDSs. From the node, pipes for water inflow and outflow are defined as upstream and downstream, respectively. It compares the flow rate of upstream and downstream pipes and determines whether pipe sizes are appropriate for the flow rates. If the pipe size is not appropriate for the flow rates, it is deemed to be an unsatisfactory design that does not satisfy pipe size continuity, and it is penalized. It will be eliminated during the process of optimization. The procedure can be detailed as shown in Figure 3.  
Figure 1: Existing pipe continuity search approach [10]. (**a**) abnormal pipe unevenness; (**b**) satisfy pipe continuity.  
Figure 2: Limitation of pipe continuity search at the confluence point.  
If the pipe size continuity is searched in the proposed approach, the areas that are redundantly searched by existing algorithms are substantially reduced; therefore, the time efficiency is improved. In addition, as pipe size and flow rate are simultaneously considered when the pipe size continuity is searched, the pipe size continuity can be reasonably searched in the relatively complex joint point. Table 1 itemizes the differences in the existing pipe size continuity search algorithm and the pipe size continuity search algorithm in this study.