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I found this calculation here, which seems to be what I want..or at least a start:

https://www.pumpsandsystems.com/pumps/april-2015-calculating-head-loss-pipeline

My confusion/skepticism arises from the fact that the equations in the above link do not seem to take into account the orientation (ie, slope) of the pipe at all. It seems like slope should be very important in this calculation...if the pipe is horizontal then it's orthogonal to the force of gravity, causing a large amount of friction loss, but if the pipe is vertical then it aligns with gravity and friction of the pipe becomes almost irrelevant (ignoring other forms of attraction).

Can anyone provide insight as to:

1) why isn't slope included in the above equations? is it because these equations are only valid for horizontal pipes?

2) how can I properly take into account slope in my head loss calculations?

Thanks!