Extended Use of Linear Graph Theory for Analysis of Pipe Networks

Linear graph theory used for pipe network analysis is to make the method systematic. A numerical method that uses linear graph theory is presented for the steady-state analysis of flow and pressure in a pipe network including its hydraulic components (pumps, valves, junctions, etc.). The proposed method differs from other linear graph methods in terms of the linear graph and the selection of its tree. The solution algorithm uses a function that depends on a power law to update the pipe flows in successive iterations. The exponents of this function are chosen to obtain a fast convergence rate even for large errors in the assumption of initial pipe flows. The convergence rate of the proposed method is validated using an error function and is compared to those of other methods. Some typical networks are analyzed to check the reliability of the proposed method. The results demonstrate the superior conditioning of the proposed method.