A Newton–Raphson analysis of urban water systems based on nodal head-driven outflow

Abstract

The urban water distribution systems are conventionally analysed using iterative methods such as Cross, Linear, Newton–Raphson and Gradient algorithm. The basic assumption of those methods is that the outflow is concentrated at the nodes and it is always known and constant. However, the outflow at each node is dependent on the pressure at the node. The paper presents a new methodology for analysing looped water distribution systems, incorporating the pressure-dependent outflow at each node using the h-Newton–Raphson method as it was modified recently by using a direct and exact equation to calculate the flow of each branch with respect to the corresponding hydraulic heads. The resulted algorithm is simpler and more accurate compared to the other head-driven h-Newton–Raphson methods, while it avoids the use of the hydraulic resistance. A numerical example is presented to illustrate the proposed methodology and its performance.