Abstract
Minimizing water delivery costs and increasing water supply dependability are the two key objectives in designing and operating of water distribution systems. An analytical solution for the best pipe diameters of a water distribution pipe network was created in this study. The raw water was collected from a water canal and transported to a treatment plant (WTP). The cleansed water was pushed into the water distribution network via the pumping station. The derivative approach was used in the optimization process, and the cost functions incorporating the various capital and operating expenses were used. The initial diameters were adjusted to reach the least-cost diameters. The study shows that the optimum design of a pipe network (PNW) achieves saving a total cost of about 12.3% after utilizing our unique method. The optimal pumping rate in the PNW can also be determined using an analytical approach that considers the optimum value that occurs when the minor and friction losses in the entire network are at their lowest. The analytical solution for the optimum pumping rate shows a rigid value of optimum pumping rate (Qopt) which is 5296.32 m3/day. On comparative estimates, this figure is very close to that of 5,300 m3/day interpreted from the graphical solution, with negligible deviation. The total cost and optimum pumping rate results for the analyzed PNW example demonstrate the correctness of the analytical solutions, reliability, and dependability of the assumptions.
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Abbreviations
- a :
-
Pipe cost coefficient
- A 1 :
-
Unit cost of pumping
- A 2 :
-
Unit cost of pump
- B :
-
Unit water return
- b :
-
Price of water/m3
- C :
-
Loss coefficient due to fittings in main
- C p :
-
Total pipe cost
- C es :
-
Cost of elevated storage
- C Lm :
-
Labor and maintenance cost
- C Tr :
-
Treatment cost
- C T :
-
Total cost
- d :
-
Diameter of pipe
- f i :
-
Friction factor in pipe
- g :
-
Gravitational acceleration
- H :
-
Operating head of pump
- h r :
-
Residual pressure in the PNW
- h LT :
-
Head loss in main
- K m :
-
Loss coefficient in main
- K i :
-
Loss coefficient of minor losses
- L :
-
Length of pipe
- L e :
-
Equivalent length of pipe
- L r :
-
Shortest length of path between inlet and point of low pressure in PNW
- M i :
-
fraction on individual to total discharge in PNW
- N :
-
Average pumping hours per day
- P :
-
pump cost/KWh
- PNW:
-
Pipe network
- P i :
-
Pipe number
- Q :
-
Pumping rate
- Q i :
-
Individual discharge in pipe
- Q opt :
-
Optimum pumping rate
- S :
-
Hydraulic gradient
- w :
-
Specific weight of water
- x :
-
Pipe cost exponent
- Y :
-
Life period of scheme
- Z :
-
Depth of water in the canal from ground level
- η :
-
Pump efficiency
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ElZahar, M.M.H., Amin, M.M.M. Optimization of Water Pipe Network and Formulation of Pumping Rate. KSCE J Civ Eng 27, 2882–2890 (2023). https://doi.org/10.1007/s12205-023-0872-8
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DOI: https://doi.org/10.1007/s12205-023-0872-8