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.