Valves are installed at the end of each branch pipeline in a tree-type long distance gravitational water supply system to regulate flow. However, the sequential closing of all valves may cause a tremendous superposed pressure rise, even larger than the pressure rise under simultaneous valve closure. In this paper, the effects of sequential valves closure on the superposed maximum water hammer pressure rise in a pipeline were investigated. By using the wave superposition principle, a sequential valves closure formula leading to maximum water hammer was proposed and verified using numerical simulation based on a practical project. In addition, the superposed maximum pressure rises in the pipeline were compared under single, simultaneous and sequential valves closure, respectively. The results show that the sequential valves closure formula agrees well with the numerical results and the pressure rise in the pipeline under the sequential closing was the largest. Moreover, compared with the superposed maximum pressure rises at the main pipeline, the effect of sequential valves closure on superposed maximum pressure rise at the branch pipeline is more sensitive.

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