Zhou and Adewumi proposed an analytical flow equation (ZA model) for steady-state flow through pipelines without neglecting any terms in the momentum equation. In the present study, the linear theory method (LTM) is utilized to solve the network equations based on the ZA model. Some programming strategies are also addressed. A field network with 21 pipes and 16 nodes is simulated using the model. and the simulation results are compared with the field data as well as those obtained using Weymouth equation, Panhandle-A and Panhandle-B equations, respectively.