But there is another component to the cost of supplying fluid to \\(x\\), which is the additional work that needs to be done when there are changes of direction in at the junctures in piping chain from the root to \\(x\\).

In other words, this model also gives a cost for the turning of fluid around bends.

Note: each pipe is modeled as a straight line; a bend here is a change in angle between one pipe and the next.