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BACKGROUNDPump failures induce rapid changes in the flow rate, which causes extremely high-pressure water hammer surges in the water supply system, including extremely high-and low-pressure water hammer surges. Extreme water hammer pressure damages pipes and hydraulic equipment and results in water supply service interruptions. To eliminate or reduce the impact of extreme water hammer pressure on water delivery systems, water hammer prevention measures are normally implemented; these include bypass pipes, air valves, check valves, air tanks, pressure regulating chambers, unidirectional pressure regulating chambers, pressure discharge valves, water hammer prevention valves, etc.[1] to [3]. An air valve is a common, economical, and effective piece of water hammer prevention equipment that is normally installed at the local peak of a pipe. When negative pressure occurs inside the pipe, the air valve opens to allow air in; when the pressure inside the pipe increases, the air valve releases it by discharging air [4] and [5]. A check valve is an economical and reasonable water hammer prevention measure that is widely used in pumping stations [6]. Check valves can prevent water pumps from rotating in reverse due to liquid backflow and thus prevent damage to the motor. However, instant check valve closure results in a catastrophically high pressure [7] and [8]. Therefore, when a check valve is installed in a pumping station to control transients, an air tank should also be installed near the pumping station to prevent the increase in pressure that results from closing the check valve [9]. However, air tanks have drawbacks that include their large volume, high maintenance cost and complex operation (the gas in the tank should be replenished). A pressure discharge valve with the proper parameters can prevent a water delivery system from generating excessively high or low pressures; otherwise, the negative impact of water hammer surges on the water delivery system is exacerbated [10]. To ensure proper protection of a water delivery system by a pressure discharge valve, the pressure discharge valve should have so little inertia that it can be opened promptly in response to a rapid change in the pressure to prevent delays in its opening [11]. A water hammer