Sorry, it seems like the answer to this question is just a quick google search away; but I have not found a page defining what the axis is.
My guess was that the axis of a piple is the imaginary line running down through the middle of the pipe. However, this doesn't make sense based on a question I am looking at in a calculus book. The question is "write the vector field describing the flow if the axis of the pipe is the unit circle in the $xy$ plane." This makes me think that the axis of a pipe is cross section of a pipe, but that doesn't really make sense either because usually an axis is a line, not a circle.