COMPARATIVE ANALYSIS OF THE NUMERICAL METHODS OF SOLUTION INVOLVED IN PIPE NETWORK DISTRIBUTION SYSTEM

Abstract

Water distribution is an important factor in the development of a community. Increase in population growth and Industrial development tends to influence the flow rates and other hydraulic supplies associated with water distribution systems which might lead to inadequate water supply. This research makes a comparative analysis of pipe network distribution system for three different case studies that comprise of one, two and three looped systems. Already existing mathematical expression of Hardy Cross and Newton Raphson methods of solution were used to evaluate for the flow rate correction and ultimately the approximate flow rates in the loops while the Darcy Weisbach head loss equation was also used to account for the major losses in the networks. The calculation analysis was first carried out manually for each case study before a C-Sharp computer programming software was developed to confirm the former calculation done. The results showed that for the one looped network using both methods, head loss around the loop converged from 25.60m to 0.13m at the third iteration. Also, for the two looped network, the head loss around each loop converged from 170.97m and 8.92m to 0.05 and 0.06m at the sixth iteration using the Hardy Cross method whereas the Newton Raphson method has the head losses to converge to 0.88m and 0.24m at the fourth iteration. The three looped network had the head losses around the three loops converged after the fourth iteration from 0.26, 1.36 and 18.32 metres to 0.13, 0.11 and 0.10 metres respectively when Hardy Cross was used but converged at the third iteration where the head losses were calculated to be 0.03, 0.00 and 0.05 metres using Newton Raphson method. Newton Raphson method was found to have a better convergence pattern in that its convergence is uniform unlike the Hardy Cross method. It was also observed that the computer program developed gave almost but more accurate results as compared to that of the manual calculations with the agreement between them rated at 98%. Some slightly differences encountered in the mathematical terms calculated was as a result of some accumulated approximation errors. It is noteworthy to know that the more complex the network system, the more prone to error the analysis might be when solved manually. Hence, the use of the computer programming software developed is highly recommended due to its ease, speed and error-free in network analysis.