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
Highlights
MATERIALS AND METHODSThe materials used include hydraulic calculation sheets, scientific calculator and C-Sharp programming language software
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
170.97m While the absolute cumulative value of the head loss divided by the flow rate (i.e. ) is Calculating the flow rate corrections, ∆1
Summary
The materials used include hydraulic calculation sheets, scientific calculator and C-Sharp programming language software. Three problems of pipe distribution network were identified and termed case study 1 which is a single closed loop, case study 2; a two closed loop and case study 3; a three closed loop. These network problems with their relevant information were extracted from different texts. User Interface Design: C# sharp programming software was used to write source code for solving all the three case studies identified. There are two major buttons named Hardy Cross and Newton Raphson based on the problem to be solved, the user will have to click on any of the two buttons depending on the method to be used. After writing the source code with C# in the Visual studio integrated development environment, the initiation phase began which is the phase that initiates the program developed and test for the ease and simplicity of the program
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