Valve Stroking to Control Water Hammer

Equations are developed for the closing of a valve at the downstream end of a pipeline leading from a reservoir so that a maximum permitted pipe stress is not exceeded and pressures remain above their steady state values at all times. By allowing the unit of time to be the round-trip travel time of the pressure wave, the hydraulic grade line is established in the first unit of time that is linear and yields the maximum permitted pipe stress. In addition, uniform flow is established in the pipeline. The hydraulic grade line is maintained constant while the flow decelerates uniformly throughout the pipe. During the last unit of time before complete closure, the hydraulic gradeline is brought down to the level of the reservoir and the flow is brought to rest. Turbulent frictional effects are included. These equations may be applied to digital-computer solutions. Valve opening equations are also developed to avoid pressures in excess of steady state values.