Abstract: During hydraulic transition, the highest water level in a pump station forebay determines its design top elevation, and the lowest determines its design bottom elevation. If the designs are not correct, it will overflow or be empty. Determining its extreme water levels is crucial to ensuring the station’s safe operation for the water supply project. Based on the KBM method, this paper derives explicit formulas for calculating the forebay’s extreme water levels through solving a nonlinear dynamic equation that describes the variations in its water level in a long-distance water supply system. We verify the accuracy of these formulas using numerical calculations, and conduct a sensitivity analysis. The results show that relative to the MOC numerical simulations, the error is less than 1.0% for the highest level formula, and less than 2.5% for the lowest level formula. These formulas have simple forms and are convenient for engineering design.

Key words: high water pool, pump station forebay, KBM asymptotic method, extreme water levels, water supply system