1. Introduction

2. Material and methods

2.1. Description of the study area

Sekota town is located in Amhara region at 720km from Addis Ababa via the road of Addis Abeba-Weldiya-Alamata, or from regional state of Bahir Dar via Lalibela at approximately 440km (source from www.distancesto.com). It is a zonal state of Wag-Himra and lies between 12°33′30′′-12°41′00′′N and 38°58′00′′-39°06′00′′E.

Figure 5. Map of the study area.

Figure 5. Map of the study area.

2.2. Materials used

The materials used in this research to achieve the research goal. Because of materials are key elements to facilitate the research work. Materials, which were used in this research topographical map, computer, Mobile camera, and GPS.

Table 1. Material used and their functions.

Table 1. Material used and their functions.

No	Material used	Function
1	Water GEMS for ArcMap	Use to extracted elevation of junctions, prepare the map of the study area, make shapefiles
2	Gauge pressure	Used to measure the pressure for the selected sample points
3	Water GEMS	To analyze the hydraulic and optimize the hydraulic parameters like pressure, velocity and from the beginning to the end design water distribution network.
4	GPS	Used to find the x and y coordinate of the storage tank, sources (reservoirs), and collection chambers.
5	AutoCAD LT 2016-English	Used for convert for the layout from “dwg” format to DXF format
6	Google Earth pro	Used for connect the source and collection chamber with the distribution network

2.3. Methods of data analysis

2.3.1. Hydraulic modeling

Using physical characteristics and equations, a pipe network is represented through the process of hydraulics modeling. In a hydraulic model, the fluid or water is moved through the network by gravity or pressure difference. The SWSDS model has 63 demand nodes, 98 pipe links from the source to distribution network, 1 storage tank, 2 collection chambers, 3 sources (reservoir), 3 submersible pumps and 2 booster pumps. Water GEMS Connected Edition V10.02.03.06 is a hydraulic software, which was used for water distribution modeling and optimization, and made it simple to design and optimization a distribution network for continuous and intermittent water supply.

Nodal elevation extraction

The elevation of each junction was extracted using TRex in Water GEMS and it is integrated with ArcMap. Using the following steps extract the elevation of each node.

Figure 8. Extraction of nodal elevation.

Figure 8. Extraction of nodal elevation.

2.3.2. Calibration and Validation

A model's reliability is ensured if its output or simulated value is accurately corresponding to the values observed in the field. Therefore, a model needs to be calibrated in order to have confidence in its results. Calibration was implemented using Darwin Calibrator for the measured pressure value.

Coefficient of determination (R²): -The degree of the association between the observed and simulated values is indicated by the coefficient of determination (R²). R² 's description of the linear relationship between the two data sets is one of its main limitations, therefore using a faulty model that continually overestimates or underestimates the observations may result in a high R² value (Dufour, 2011).

$${\mathrm{R}}^2=\frac{({\sum }_{i=1}^n(\mathrm{P}\mathrm{o}\mathrm{b},\mathrm{i}-\mathcal{P}\mathrm{o}\mathrm{b})(\mathrm{P}\mathrm{s}\mathrm{i}\mathrm{m},\mathrm{i}-\mathcal{P}\mathrm{s}\mathrm{i}\mathrm{m}))}{\sqrt{{\sum }_{i=1}^n(\mathrm{P}\mathrm{o}\mathrm{b},\mathrm{i}-\mathcal{P}\mathrm{o}\mathrm{b})^2({\sum }_{i=1}^n(\mathrm{P}\mathrm{s}\mathrm{i}\mathrm{m},\mathrm{i}-\mathcal{P}\mathrm{s}\mathrm{i}\mathrm{m})^2)^2}}$$

Where: - 𝑃𝑜𝑏, 𝑖= observed pressure for junction i

$𝒫$𝑜𝑏= mean observed pressure for sample junction

𝑃𝑠𝑖𝑚, 𝑖= simulated pressure for junction i

$𝒫$𝑠𝑖𝑚= mean simulated pressure for sample junction

Mean error (ME): The difference between the measured and computed pressures is the mean error. Values closer to zero demonstrate better agreement between simulated and observed values, and the ranges from -∞ to +∞ (ATSDR, 2000).

$$\mathrm{M}E=\frac{{\sum }_{i=1}^n(\mathrm{ǀ}\mathrm{P}\mathrm{o}\mathrm{b},\mathrm{i}-\mathrm{P}\mathrm{s}\mathrm{i}\mathrm{m},\mathrm{i}\mathrm{ǀ})}{n}$$

Pob,i = observed pressure for junction i

Psim,i = simulated pressure for junction i

n = number of sample points

Root means square error (RMSE): The difference between observed and simulated values is measured on an individual basis using the simulation error's standard deviation (RMSE) (based on individual residues). Its values vary from 0 to +∞, with values nearer zero indicating better agreement between simulated and actual values. More values of RMSE imply poorer model performance, whereas lower values show higher accuracy of the model performance (Chai & Draxler, 2014).

$$\mathrm{R}\mathrm{M}\mathrm{S}E=\sqrt{\frac{{\sum }_{i=1}^n(\mathrm{P}\mathrm{o}\mathrm{b},\mathrm{i}-\mathrm{P}\mathrm{s}\mathrm{i}\mathrm{m},\mathrm{i})2}{n}}$$

Pob,i = observed pressure for junction i

Psim,i = simulated pressure for junction i

n = number of sample points

As Hunter, (2002) explained a good data set should have a pressure average difference of ±1.5m to a maximum of ±5.0m, and a poor data set should have a pressure average difference of ±3.0m to a maximum difference of ±10m

The sample points for the study area are listed in Table 3.

3. Result and Discussion

3.1. Hydraulic modeling

Due to rapid population growth and high-water losses from the distribution network, the system’s total water demand in Sekota Town exceeds the water supply at the moment. Higher pressure systems, that are regularly employed to limit overall demand and encourage unequitable distribution of the water supply.

Demand pattern

As SWSSO yearly reported, the hourly water demand pattern in the existing WDS as shown Figure 12. Examining the present water demand pattern in the area is critical for simulating and optimizing the WDS in Water GEMS using EPS.

Figure 12. Hourly demand factor for Sekota town.

Figure 12. Hourly demand factor for Sekota town.

Calibration and validation

Figure 13 shows a strong correlation between the simulated pressure values using Bentley Water GEMS with measured values obtained from the sample points using pressure gauge.

And the fitness value of this graph is 1.96, thus it indicates the model is best and accurate to run hydraulic model and got ready to analysis.

Figure 13. Calibration of hydraulic model using Darwin Calibrator.

Figure 13. Calibration of hydraulic model using Darwin Calibrator.

Model performance evaluation criteria

The Water GEMS model performance was evaluated using statistical evaluation methods such as R², ME, and RSME, the obtained results are presented in Table 10. Table 11 Summery of performance criteria.

Performance criteria	Results
R2	0.988
ME	0.0175
RSME	2.79

The performance evaluation results revealed that the Water GEMS has a promising approach to simulate the water pressure at nodes in the WDS. As explained in ATSDR (2000) an ME of pressure difference of ± 15.2kPa (± 1.52 m) with a maximum difference of ± 50.3 kPa (± 5.03 m) characterizes a good performance set. The ME of the Sekota, on the case, is 0.0175. As a result of these calculated pressures, the Water GEMS model has a very good pressure performance in the research area.

3.1.1. Pressure analysis

For water supply distribution network's minimum and maximum operating pressures are 10 m and 70 m respectively with regard to MoWR, (2006) guideline.

Figure 16. Existing SWDN pressure analysis.

Figure 16. Existing SWDN pressure analysis.

This result indicates 100% of the system is under risks, therefore it should be improved for good performance and to get permissible pressure using Water GEMS.

3.1.2. Velocity analysis

In order to prevent structural problems or undesirable hydraulic regimes brought on by high flow rates or to lessen the detrimental impact of extremely low flow rates on delivered water quality, it is required to control flow velocities in water distribution networks.

3.3. Optimized pipe diameter

Based on objective function and commercially available pipe sizes, the WDS's pipe diameter optimization was completed.

Figure 18. Pressure value for optimized water distribution system.

Figure 18. Pressure value for optimized water distribution system.

Figure 19. pressure before and after optimized using scatter graph.

Figure 19. pressure before and after optimized using scatter graph.

Velocity analysis after optimization

Making sure that water flow velocity is appropriate in water distribution system for its functioning correctly.

Figure 21. velocity after and before optimization using scatter graph.

Figure 21. velocity after and before optimization using scatter graph.

Pipe cost

The total pipe length of existing and optimized of Sekota water supply distribution system is the same, which is 30,229m. When decreasing pipe diameter during optimization, its unit cost also decreasing with somehow proportion at the same time. Pipe cost and pipe diameter haven’t directed proportion but have positive relationship. The optimized was accomplished only for the existing one not added any system.

Table 14. Unit and total cost for existing pipe diameter.

Table 14. Unit and total cost for existing pipe diameter.

Diameter (mm)	Length (m)	Cost per unitlength (Birr/m)	Total cost (Birr)
HDPE Pipes
37	635	39.29875	24954.70625
50	335	69.37	23238.95
80	2281	178.86	407979.66
100	6330	286.49	1813469.04
DCI Pipes
150	4111	2915	11983565
200	15886	3922	62304892
250	651	5088	3312288
Total length (m)	30229	Total cost (Birr)	79,870,387.36

Table 15. Total cost of optimized pipe diameter.

Table 15. Total cost of optimized pipe diameter.

Diameter (mm)	Material	Total length each diameter (m)	Cost per unit length (Birr/m)	Total cost (Birr)
32	HDPE	5780	29.73	171,839.4
40	HDPE	1562	45.04	70,352.48
50	HDPE	1295	69.37	89,834.15
63	HDPE	190	110.59	21,012.1
75	HDPE	653	156.09	101,926.8
80	HDPE	197	178.86	35,235.42
100	HDPE	134	286.488	38,389.39
140	HDPE	100	534.84	53,484
150	HDPE	88	616.48	54,250.24
100	DCI	19813	1939.8	38,433,257
125	DCI	126	283.29	35,694.54
150	DCI	15	2915	43,725
160	DCI	85	698.12	59,340.2
180	DCI	161	883.11	142,180.7
200	DCI	30	3922	117,660
	Grand length (m)	30,229	Grand cost(Birr)	39,335,188

The total cost of the existing and optimized system is 79,870,387.36 Birr and 39,335,187.56 Birr respectively.

$$Decreasepipecostinpercent=\mathrm{79,870,387.36}-\frac{\mathrm{39,335,187.56}}{\mathrm{79,870,387.36}}*100$$

Decrease in pipe cost = 50.75%

This result indicated the optimized pipe is decreased its total cost by 50.75% that approximately half of the existing pipe cost.

4. Conclusion

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