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In the long-distance water supply system, the air tank can effectively protect the water hammer when the pump stops, and the shape parameters of the air tank determine the protective effect. Based on the theory of rigid water body and harmonic vibration, this paper derived the calculation formulas for the surge and bottom pressure changing process of the air tank in the system with and without friction and impedance and put forward the theoretical method to estimate the air tank volume and established the relationship between the operating parameters and the volume. Combined with the actual water supply project, under different working conditions, the theoretical calculation results and numerical simulation results were compared and analyzed. The results showed that the theoretical calculation results of the system with friction and impedance had a better fitting performance than the numerical simulation results, and the operating parameters of the air tank derived after considering the influence of friction and impedance were accurate. This method can simplify the selection process of air tank body parameters. At the same time, the shape optimization of the air tank considering friction and impedance can be improved by 40–50% compared with the results of ignoring friction and impedance.

Formula for determining the size of the air tank in the long-distance water supply system