Optimization of AIr Volume in Water Hammer: Pump Shutdown in Single-Characteristic Pipeline

Protection against water hammer, a common phenomenon in water pumping stations and hydroelectric power stations, requires the installation of appropriate equipment to mitigate over- and under-pressures resulting from sudden or accidental pump operation (instantaneous stops or starts) that can cause pipes to burst or flatten. In this article, an air reservoir is proposed as a solution to limit these pressures to levels compatible with the strength of the materials. The solution of the governing equations corresponding to this phenomenon was obtained by the characteristic method, which gave an optimal air volume of 4.5 m³, in perfect agreement with the volume obtained by Bergeron's graphical method from an initial volume of 3.0 m³. The pressure in the discharge pipe drops to -32.59 m at the end of the first phase, then reaches 66.59 m in the fourteenth phase before stabilizing at 60 m. The recommended standard capacity for this air tank is approximately 6 m³, considering a water volume representing 32% of the air volume.