Gröbner bases for solving ΔQ-equations in water distribution networks

The analysis of water distribution network is of great interest to hydraulic engineers. Although the water distribution network has been extensively studied for the last decades, there are still many unsolved problems awaiting clarification. In this paper, an algorithm is presented that describes a computationally efficient technique for water distribution networks based on Gröbner basis method. Gröbner basis algorithm provides the exact algorithmic solutions for solving the system of equations. However, Gröbner algorithm works only for polynomials and moreover for a large scale network, it takes a long CPU time. Hence, we present two other algorithms that work for non-polynomials and large scale problems. Three examples are presented to show the effectiveness of Gröbner basis method compared with Hardy Cross method, linear theory and Gradient method.