Hydraulic Analysis of Water Distribution Networks Based on the Gradient Matrix Form and Comparing it with Other Conventional Methods

Subject Areas : Subjects

M. حیدری ¹ (عضو هیات علمی گروه مهندسی آب دانشکده کشاورزی دانشگاه بوعلی سینا)
S. رضویان ² (دانشجوی مقطع کارشناسی ارشد رشته آبیاری و زهکشی گروه مهندسی آب دانشکده کشاورزی دانشگاه بوعلی سینا)
S.M نبوی همدانی ³ (دانشجوی کارشناسی ارشد سازه های آبی دانشگاه آزاد اسلامی واحد علوم و تحقیقات تهران)

Received: 2014-10-01 Accepted : 2014-10-01 Published : 2014-11-22

Keywords: Gradient method, Hydraulic analysis, Water distribution network, conventional method, Hardy Cross,

Abstract :

Hydraulic analysis of water networks consists of determination of the discharge rate in each pipe and the piezometric head at nodes. Benefiting from the matrices algebra, and developing equations following the Taylor series, the gradient method numerically solves the continuity equation determining simultaneously the flow rate in nodes and energy dissipation in loops. The objective of this study was the hydraulic analysis of water distribution networks based on the matrix form of the Gradient method, comparing the results with the statistical indices, namely: NS, CRM, R² and RMSE with Hardy Cross, Newton Raphson and Linear theory methods. The indices Values were NS=1, CRM=0, R2=1 and RMSE=0; very close to the ideal values. Following the same reasoning, the gradient method is reliable in predicting the head in unknown nodes and the flow through pipes. Accordingly performance of Gradient was proved in computing head of unknown nodes and discharge through pipes. The obtained results indicated that the Gradient method delivers accurate and reliable output. This ability highly facilitates the design and hydraulic analysis of wide spread networks.