A pipe, such as a liner for repairing a failing culvert, comprises a continuous wall defining an inner wall surface and an exterior wall surface. The pipe further defines a central fluid passageway extending from an inlet end to an outlet end. The inner wall surface of the pipe defines a waveform-like geometry near the inlet end, said waveform-like geometry including an initial curvature beginning at the inlet end of the pipe and continuing until reaching a predetermined location where an inner diameter of the pipe is minimized, the curvature then continuing with the inner diameter increasing again to a second predetermined location, before the inner diameter again decreases to a third predetermined location and then remains substantially constant along the remaining length of the pipe, thus creating an annular recess in the inner wall surface of the pipe.