Evaluation of Flow Rate Correction in Water Pipeline Distribution Network by Two Numerical Methods of Solution

Abstract

This study evaluates flow rate correction and approximate flow rates in  loops for three different case studies of closed looped pipe distribution network systems using Hardy Cross and Newton Raphson. Darcy Weisbach head loss equation was also used to account for major losses. Manual calculation was initially done for each case study followed by a C-Sharp programming software which was developed to affirm the manual  calculation. For one looped network, head loss around the loop converged from 25.60 m to 0.13 m at the third iteration. The two looped network head loss around each loop converged from 170.97 m and 8.92 m to 0.05 and 0.06 m for Hardy Cross at the sixth iteration while the head loss are 0.88 m and 0.24 m at the fourth iteration for both Hardy Cross and Newton Raphson method while for the three looped network, it has head losses around the three loops converged after the fourth iteration from 0.26, 1.36 and 18.32 m to 0.13, 0.11 and 0.10 m respectively for Hardy Cross at third
iteration while the head losses are 0.03, 0.00 and 0.05 m for Newton  Raphson method. Newton Raphson method was found to have a better convergence pattern because it convergences in a uniform manner unlike Hardy Cross method. Also, the program developed gave almost but more accurate results as compared to that of manual calculations with the agreement between them rated at 98%. Some slight differences encountered in the mathematical terms calculated were as a result of some accumulated approximation errors.

Keywords: Pipe Distribution Network, Head loss, Convergence, Iteration