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Mr. Otim Brian

*Brian Otim is a practicing water resources engineer currently working with National Water and Sewerage Corporation. He has over six years of experience in whole-of-cycle drinking water infrastructure development and management. He has supervised the construction of sanitation facilities and water mains. He graduated from Ndejje University in 2013 with a Bachelor of Science in Civil Engineering.*

**ABSTRACT**

This project aims to model water distribution networks in four villages of Uganda to determine if they can meet projected water demands for the next ten years. The study found that the networks had sufficient pressures to meet water demands and be commercially viable. The intermittent water supply experienced by over 1.3 billion people worldwide, including in Uganda, affects water utilities’ commercial viability and customer satisfaction. To achieve the study’s objectives, network profiling, water demand forecasting, and numerical modeling of water distribution networks were conducted using Microsoft Excel. The profiling exercise involved using a tape measure and GPS to establish network distance along supply routes and take elevation profiles. Water demand modeling projected future populations geometrically and multiplied the per capita consumption obtained from the Ugandan WSD manual with the populations to get the demands. Numerical modeling calculated various factors to determine water supply pressures. In conclusion, this study demonstrates that with adequate profiling, water demand forecasting, and numerical modeling, water distribution networks can meet projected water demands for supply continuity in the next ten years.

**Keywords:***Hydraulic modeling, Numerical modeling, Water distribution networks, Water supply intermittence, Water demand forecasting.*

**1.0 INTRODUCTION**** **

Well-modeled water distribution networks that meet projected water demands in a specific geographical location and design period, instill customer trust and therefore make water utilities commercially viable and profitable. However, over 1.3 billion people worldwide are supplied with water intermittently (Charalambous, 2019). This supply regime should be temporary, maybe due to technical faults in an existing water system that should always be addressed promptly. In the case of Uganda, NWSC which is the sole designated government agency mandated to provide potable water and sewerage services face the IWS syndrome in the majority of over 258 operational towns (Lutaaya & Echelai, 2021); furthermore, climate change, leaks/bursts contributing to NRW, exponential population growth, and inadequately designed water distribution networks are amongst the major contributors to IWS. Hydraulically sound water distribution networks that are in sync with projected water demands and supply pressures within a given timeframe are highly serviceable (Abu-Mahfouz et al., 2019),and consequently meet customer interests.

The issue discovered in the case study area was the perennial intermittence of piped water supplies leads to uncollected revenues and customer dissatisfaction. This later informed the objectives of the study with the main objective being to continuously and timely avail sufficient water supplies to the delight of all stakeholders. Some of the other specific objectives included;

- Profiling of water distribution networks
- Water demand forecasting
- Numerical modeling of water distribution networks

The existence of a few disgruntled customers in several NWSC supply towns that intermittently receive water results in uncollected revenues and a low customer satisfaction index in such areas. This, therefore, prompts people to search for alternative unsustainable communal sources that not only provide unsafe water but also time-consume due to the long lines as shown in *Image** 1*, leading to low household productivity.

Image 1: Crowded alternative water point-Kampala City

The project was limited to the establishment of network profiles in designated supply routes using the hand-held GPS, forecasting of water demand, and application of numerical models using Microsoft Excel in selected water distribution networks.

**2.0 METHODOLOGY**

The methodology for this study involves three main components: network profiling, water demand modeling, and network numerical modeling. Firstly, network profiling was conducted by using a tape measure to establish the network distance along the designated supply routes in the villages, followed by taking elevation profiles at intervals of 100m of the proposed water distribution networks using a hand-held GPS. Secondly, water demand modeling was performed by obtaining present and future populations, calculating per capita consumption, incorporating appropriate tariffs, and applying a peak factor of two to obtain design demands for the entire project lifecycle of ten years. Lastly, network numerical modeling involved calculating flow velocity, dynamic viscosity, Reynolds number, relative pipe roughness, frictional factor, and computing the dH losses and h losses in the water distribution networks over given specified lengths using various equations. Empirical Head/Pressure was also obtained by installing pressure gauges on identified sample points of the existing pressurized water distribution networks in different villages and obtaining corresponding pressure readings after 24 hours. The modeling was performed using MS Excel.

**2.1 Network Profiling**

A 100m tape measure was used as shown in *Image 2* to establish network distance along the designated supply routes in the villages, and a hand-held GPS was then used to take elevation profiles at intervals of 100m of the proposed water distribution networks.

Image 2:Measuring pipe length using a Tape-measure

**2.2 Water Demand Modelling**

The present populations in the year 2022 were obtained from interviews conducted with the LC I chairpersons of the villages by multiplying the households with the existing average number of people, and the future population in ten (10) years up to 2032 was projected geometrically using *equation 1*; the per capita consumption obtained from the Ugandan WSD manual with appropriate tariffs incorporated was multiplied with the populations to get the demands. The design demands for the entire project lifecycle of ten (10) years were obtained by applying a peak factor of two (2); and the modeling was done using MS Excel.

**2.3 Network Numerical Modelling**

The section discusses the process of obtaining both Numerical Head/Pressure and Empirical Head/Pressure in a water distribution network. In order to obtain Numerical Head/Pressure, the design demand was used to calculate flow velocity and determine dynamic viscosity. Reynolds number (Re) and Relative Pipe Roughness (RPR) were calculated to obtain the frictional factor/constant value from the Moody chart. Darcy Weisbach formula and elevation profiles were used to compute dH and h losses, respectively. The ultimate modeling was done using MS Excel. On the other hand, Empirical Head/Pressure was obtained by installing pressure gauges on identified sample points of existing pressurized water distribution networks in various villages, followed by obtaining corresponding pressure readings after 24 hours.

**2.3.1 Numerical Head/Pressure**

The obtained design demand in ten (10) years was used to calculate flow velocity using equation 2 and the dynamic viscosity was determined from the viscosity chart using the average ambient Kitgum temperature of 30 ; the Re was then calculated using equation 3 and the RPR using equation 4. Using both the Re and RPR, the Moody chart was used to obtain the frictional factor/constant value. The dH losses in the water distribution networks over given specified lengths were computed using the Darcy Weisbach formula using equation 5, whereas the h losses were computed from the earlier determined elevation profiles. The H was then computed using *equation 6*, and the eventual modeling was done using MS Excel.

**2.3.2: Empirical Head/Pressure**

This was obtained by installing pressure gauges like the one shown in *Figure 4* on identified sample points of the existing pressurized water distribution networks in the different villages, after which the corresponding pressure readings were obtained after 24 hours.

Image 3: Installed Pressure-gauge on a WDN

**3.****0**** RESULTS AND ANALYSIS**

This chapter presents the results and analysis of network profiling, water demand modeling, and network numerical modeling for four selected villages under the SCAP100 project. Profiles were established for a total length of 3km of 2’’ HDPE PN10 distribution mains, and water demand modeling was conducted based on current and projected population with different water usage rates. Network numerical modeling was also performed to determine the Head/Pressure of the water distribution system. The data collected is illustrated in figures for each village. The results of this study can help improve the design and management of the water distribution systems in the selected villages, ensuring sufficient water supply for domestic and institutional use.

**3.1 Network Profiling**

Profiles were established for a total length of 3km of 2’’ HDPE PN10 distribution mains in four (4) selected villages under the SCAP100 project as highlighted below;

**Oryang-Ojuma**

The start elevation was 933m asl and falls by 2m to 931m asl after 100m, and there was a further fall from 931m asl by 5m to 926m asl for 100m-water flow at this section is counteracted by solely frictional force. The elevation then rises exponentially from 926m asl by 9m to 935m asl for 400m-and water flow at this section is counteracted by both frictional and static forces, and the profiling was done for 600m pipe length. This data was collected and illustrated in *Figure **1**.*

Figure 1:Network Profile of Oryang-Ojuma A North

**Pagen**

The start elevation was 946m asl and rises by 2m to 948m asl for 100m, and there was a further rise from 948m asl by 2m to 950m asl for 100m-water flow at this section is counteracted by both frictional and static forces. The elevation of 950m asl remains constant for 600m-water flow at this section is solely counteracted by frictional force; and after which there is an exponential increase from the 950m asl by 1m to 951m asl for 100m, and then from 951m asl by 1m to 952m asl for 100m-and similarly, water flow at this section is counteracted by both frictional and static forces; and the profiling was done for 1km pipelength. This data was collected and illustrated in *Figure **2**.*

Figure 2: Network Profile of Pagen

**Lemo-East**

The start elevation was 947m asl and this remains constant for 100m-water flow at this section is counteracted solely by frictional force; the elevation then increases from 947m asl by 1m to 948m asl for 100m, and from 948m asl by 1m to 949m asl for 100m-water flow at this section is counteracted by both frictional and static forces; and the profiling was done for 300m pipe length. This data was collected and illustrated in *Figure **3**.*

Figure 3: Network Profile of Lemo-East

**3.2 Water Demand Modelling**

**Oryang-Ojuma**

In the year 2022, it had a current population of 400 people with a 40l per person daily domestic water usage with a design demand of 1.3m^{3}/h; after five (5) and ten (10) years, the population increased to 470 and 554 people with design demands of 1.5m^{3}/h and 1.8m^{3}/h respectively.

**Oryang-Ojuma A North**

In the year 2022, it had a current population of 1160 people with a 40l per person daily domestic water usage with a design demand of 3.8m^{3}/h; after five (5) and ten (10) years, the population increased to 1365 and 1608 people with design demands of 4.5m^{3}/h and 5.3m^{3}/h respectively**.**

**Pagen**

In the year 2022, it had a current population of 820 people with a 40l and 1l per person daily domestic and institutional-St. John Church of Uganda and NAMU, water usage respectively with a design demand of 1.6m^{3}/h; after five (5) and ten (10) years, the population increased to 908 and 1013 people with design demands of 1.9m^{3}/h and 2.3m^{3}/hrespectively.

**Lemo-East**

In the year 2022, it had a current population of 2640 people with a 40l and 10l per person daily domestic and institutional-Aninelia Senior Academy, Friendship Nur. & Pri. Sch. and Pager Div., water usage respectively with a design demand of 7.2m^{3}/h; after five (5) and ten (10) years, the population increased to 2994 and 3412 people with design demands of 8.3m^{3}/h and 9.7m^{3}/h respectively.

**3.3 Numerical Head/Pressure**

This section discusses the water usage and design demands of four communities in Uganda: Oryang-Ojuma, Oryang-Ojuma A North, Pagen, and Lemo-East. In 2022, Oryang-Ojuma had a population of 400 people with a daily domestic water usage of 40 liters per person and a design demand of 1.3m3/h. After five and ten years, the population increased to 470 and 554 people with design demands of 1.5m3/h and 1.8m3/h. Similarly, Oryang-Ojuma A North had a population of 1160 people with a daily domestic water usage of 40 liters per person and a design demand of 3.8m3/h. After five and ten years, the population increased to 1365 and 1608 people with design demands of 4.5m3/h and 5.3m3/h, respectively. Pagen had a population of 820 people in 2022 with a daily domestic water usage of 40 liters per person and a daily institutional water usage of 1 liter per person, and a design demand of 1.6m3/h. After five and ten years, the population increased to 908 and 1013 people, respectively, with design demands of 1.9m3/h and 2.3m3/h. Finally, Lemo-East had a population of 2640 people in 2022 with a daily domestic water usage of 40 liters per person and a daily institutional water usage of 10 liters per person, and a design demand of 7.2m3/h. After five and ten years, the population increased to 2994 and 3412 people, respectively, with design demands of 8.3m3/h and 9.7m3/h.

**Oryang-Ojuma**

Using Q of 0.00513429m^{3}/s, ρ of 1000kg/m^{3}, V of 0.26148713m/s, d of 0.05m, and μ of 0.0008Pa*s; Re was found to be 16,342.94572≈10^4. Similarly, using ε of 0.0025mm and d of 50mm; RPR was found to be 0.0005≈5^-5. Using the obtained Re and RPR values, an approximate λ of 0.011 was obtained. And using L of 600m and g of 9.81m/s^{2}, dH of 0.460018788m was obtained; h of 2m was also obtained from the end and start point elevations. Therefore, H was found to be 2.460018788m or 0.246001879 bars.

**Oryang-Ojuma A North**

Using Q of 0.001488943m^{3}/s, ρ of 1000kg/m^{3}, V of 0.758312681m/s, d of 0.05m, and μ of 0.0008Pa*s; Re was found to be 47,394.54257≈10^4. Similarly, using ε of 0.0025mm and d of 50mm; RPR was found to be 0.0005≈5^-5. Using the obtained Re and RPR values, an approximate λ of 0.011 was obtained. And using L of 1100m and g of 9.81m/s^{2}, dH of 7.092723019m was obtained; h of -10m was also obtained from the end and start point elevations. Therefore, H was found to be -2.907276981m or -0.290727698 bars.

**Pagen**

Using Q of 0.000649193m^{3}/s, ρ of 1000kg/m^{3}, V of 0.330631476m/s, d of 0.05m, and μ of 0.0008Pa*s; Re was found to be 20,664.46725≈10^4. Similarly, using ε of 0.0025mm and d of 50mm; RPR was found to be 0.0005≈5^-5. Using the obtained Re and RPR values, an approximate λ of 0.011 was obtained. And using L of 1000m and g of 9.81m/s^{2}, dH of 1.225778697m was obtained; h of 6m was also obtained from the end and start point elevations. Therefore, H was found to be 7.22578697m or 0.72257787 bars.

**Lemo-East**

Using Q of 0.002715292m^{3}/s, ρ of 1000kg/m^{3}, V of 1.38288689m/s, d of 0.05m, and μ of 0.0008Pa*s; Re was found to be 86,430.43059≈10^4. Similarly, using ε of 0.0025mm and d of 50mm; RPR was found to be 0.0005≈5^-5. Using the obtained Re and RPR values, an approximate λ of 0.011 was obtained. And using L of 300m and g of 9.81m/s^{2}, dH of 6.433069615m was obtained; h of 2m was also obtained from the end and start point elevations. Therefore, H was found to be 8.433069615m or 0.843306961 bars.

**3.****4**** Empirical Head/Pressure**

For Oryang-Ojuma, the installed pressure gauge reading was found to be 1.1 bars; and since this is greater than the H of 0.246001879 bars, there will be sufficient pressure for water supply and meeting water demand for the next ten (10) years till the year 2032.

For Oryang-Ojuma A North, the installed pressure gauge reading was found to be 2.3 bars; and since this is greater than the H of -2.290727698 bars, there will be sufficient pressure for water supply and meeting water demand for the next ten (10) years till the year 2032.

For Pagen, the installed pressure gauge reading was found to be 1.8 bars; and since this is greater than the H of 0.72257787 bars, there will be sufficient pressure for water supply and meeting water demand for the next ten (10) years till the year 2032.

For Lemo-East, the installed pressure gauge reading was found to be 2.4 bars; and since this is greater than the H of 0.843306961 bars, there will be sufficient pressure for water supply and meeting water demand for the next ten (10) years till the year 2032.

**4.0 CONCLUSION**

Since the Ugandan WSD has no per capita demand for church-goers, one (1) liter consumption for basically hand-washing was taken for the two (2) churches of St. John Church of Uganda and NAMU in Pagen. In ten (10) years, the project has a payback period of **1.041** (3dp.) VAT exclusive, assuming domestic consumption, 85% connection efficiency, and coupled with the current NWSC tariff indexation.

**5.0 RECOMMENDATIONS**

For NWSC and associate partners to phase off water supply intermittence, I would recommend;

- ERB and/or UIPE should continue fostering the already ongoing industrial-institutional synergies to train the next generation of water experts in the design, construction, and maintenance of water infrastructure systems for resilience.
- NWSC should continue with the already ongoing professional development of her engineers through themed training in the hydraulic design of water-waste water systems.
- NWSC monitoring and evaluation department should yearly carry-out a cost-benefit analysis on water infrastructure projects to determine the rate of return on capital investment.

**REFERENCES**

Abu-Mahfouz, A. M., Hamam,Y., Page, P. R., Adedeji, K. B., Anele, A. O., & Todini, E. (2019). Real-Time Dynamic Hydraulic Model of Water Distribution Networks. MDPI. Retrieved from https://www.mdpi.com/2073-4441/11/3/470

Charalambous, B. (2019). Intermittent Water Supply-A Paradigm Shift is Imperative. IWA Publishing. Retrieved from https://iwa-network.org/intermittent-water-supply-a-paradigm-shift-is-imperative/

Kasozi, E. (2020, November 9th). Kampala residents risk a water crisis due to climate change effects. The Daily Monitor. Retrieved from https://www.monitor.co.ug/uganda/news/national/kampala-residents-risk-water-crisis-due-to-climate-change-effects-report-3016158

Lutaaya, M. H., & Echelai, G. A. (2021). Intermittent supply in a rapidly growing city: the case of Kampala. IWA Publishing. Retrieved from https://www.thesourcemagazine.org/intermittent-supply-in-a-rapidly-growing-city-the-case-of-kampala/

MWE. (2013). Water Supply Design Manual (2nd edn.). MWE, Kampala.

NWSC. (2022). Tariff Guide. NWSC. Retrieved from https://www.nwsc.co.ug/tariff-guide/

Weather Spark. (2022). Climate and Average Weather Year Round in Kitgum. Weather Spark. Retrieved from https://weatherspark.com/y/97237/Average-Weather-in-Kitgum-Uganda-Year-Round

World Population Review. (2022). Uganda Population. World Population Review. Retrieved from https://worldpopulationreview.com/countries/uganda-population

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