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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-li

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.

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1. A liner system for repairing a failing culvert, comprising: a liner;an attachment mated to an inlet of the liner, said attachment defining a central fluid passageway extending from an inlet end to an outlet end, and said attachment having an inner wall surface that defines a sinusoidal waveform g

1. A liner system for repairing a failing culvert, comprising: a liner;an attachment mated to an inlet of the liner, said attachment defining a central fluid passageway extending from an inlet end to an outlet end, and said attachment having an inner wall surface that defines a sinusoidal waveform geometry near the inlet end and around a circumference of the inner wall surface for directing fluid into the liner, the sinusoidal waveform geometry consisting of a curvature beginning at the inlet end of the attachment where an inner diameter of the attachment is maximized and continuing until reaching a first predetermined location where the inner diameter of the attachment is minimized, the curvature then continuing with the inner diameter immediately increasing again to a second predetermined location, before the inner diameter again decreases to a third predetermined location, thus creating a single annular recess in the inner wall surface of the attachment, which, in cross-section, forms a continuous arc in the inner wall surface of the attachment extending from the first predetermined location to the second predetermined location to the third predetermined location. 2. The liner system as recited in claim 1, in which the annular recess has a maximum depth that is approximately equal to 1.0% of an inner diameter of the attachment. 3. The liner system as recited in claim 1, wherein, immediately after the third predetermined location, the inner diameter remains substantially constant along the remaining length of the attachment. 4. The liner system as recited in claim 1, wherein the inner diameter of the attachment at the first predetermined location is substantially identical to the inner diameter of the attachment at the third predetermined location. 5. An attachment for a pipe comprising a continuous wall defining an inner wall surface and an exterior wall surface, said attachment further defining a central fluid passageway extending from an inlet end to an outlet end, wherein the inner wall surface defines a sinusoidal waveform geometry near the inlet end and around a circumference of the inner wall surface, the sinusoidal waveform geometry consisting of a curvature beginning at the inlet end of the attachment where an inner diameter of the attachment is maximized and continuing until reaching a first predetermined location where the inner diameter of the attachment is minimized, the curvature then continuing with the inner diameter immediately increasing again to a second predetermined location, before the inner diameter again decreases to a third predetermined location, thus creating a single annular recess in the inner wall surface of the attachment, which, in cross-section, forms a continuous arc in the inner wall surface of the attachment extending from the first predetermined location to the second predetermined location to the third predetermined location. 6. The attachment as recited in claim 5, in which the annular recess has a maximum depth that is approximately equal to 1.0% of an inner diameter of the attachment. 7. The attachment as recited in claim 5, wherein, immediately after the third predetermined location, the inner diameter remains substantially constant along the remaining length of the attachment. 8. The attachment as recited in claim 5, wherein the inner diameter of the attachment at the first predetermined location is substantially identical to the inner diameter of the attachment at the third predetermined location. 9. A liner for repairing a failing culvert, comprising a continuous wall defining an inner wall surface and an exterior wall surface, said liner further defining a central fluid passageway extending from an inlet end to an outlet end, wherein the inner wall surface defines a sinusoidal waveform geometry near the inlet end and around a circumference of the inner wall surface, the sinusoidal waveform geometry consisting of a curvature beginning at the inlet end of the liner where an inner diameter of the liner is maximized and continuing until reaching a first predetermined location where the inner diameter of the liner is minimized, the curvature then continuing with the inner diameter immediately increasing again to a second predetermined location, before the inner diameter again decreases to a third predetermined location, thus creating a single annular recess in the inner wall surface of the liner, which, in cross-section, forms a continuous arc in the inner wall surface of the liner extending from the first predetermined location to the second predetermined location to the third predetermined location. 10. The liner as recited in claim 9, in which the annular recess has a maximum depth that is approximately equal to 1.0% of an inner diameter of the attachment. 11. The liner as recited in claim 9, wherein, immediately after the third predetermined location, the inner diameter remains substantially constant along the remaining length of the liner. 12. The liner as recited in claim 9, wherein the inner diameter of the liner at the first predetermined location is substantially identical to the inner diameter of the liner at the third predetermined location. 13. A pipe comprising a continuous wall defining an inner wall surface and an exterior wall surface, said pipe further defining a central fluid passageway extending from an inlet end to an outlet end, wherein the inner wall surface defines a sinusoidal waveform geometry near the inlet end and around a circumference of the inner wall surface, said sinusoidal waveform geometry consisting of a curvature beginning at the inlet end of the pipe where an inner diameter of the pipe is maximized and continuing until reaching a first predetermined location where the inner diameter of the pipe is minimized, the curvature then continuing with the inner diameter immediately increasing again to a second predetermined location, before the inner diameter again decreases to a third predetermined location, thus creating a single annular recess in the inner wall surface of the pipe, which, in cross-section, forms a continuous arc in the inner wall surface of the pipe extending from the first predetermined location to the second predetermined location to the third predetermined location. 14. The pipe as recited in claim 13, wherein, immediately after the third predetermined location, the inner diameter remains substantially constant along the remaining length of the pipe. 15. The pipe as recited in claim 13, wherein the inner diameter of the pipe at the first predetermined location is substantially identical to the inner diameter of the pipe at the third predetermined location.