I thought the OP wanted a solution that fades linearly across the entire pipe shape, regardless of its shape. Your solution works fine for nearly straight pipes, but it won’t work if the pipes start to loop back to the origin of the object, like this:
It’s great if the solution is only required for simple pipe shapes, because the simplest solution is definitely better. My solution is not that simple, but it works for any shape. If your solution works for the OP, I’m not sure if it makes sense to publish my complex one.