Water dynamics in aluminum pipeline for dummies

This topic is totally alien to me, so I may be asking something very obvious.

I am designing a cooling system. In the bulk of aluminum, I drill 3mm holes and then I connect them one to another to create a long path for the stream.

The question is now, how long can this maze be? What I am trying to figure out to answer this question is first of all, what pressure is required to drive water into this pipeline. And to determine that, I believe, somewhere should be a coefficient of friction between water and aluminum. Though I can't seem to find a useful chart, it's all about solid bodies friction. Is it because the coefficient might in fact depend on the pipe diameter?

• It is a beam of segments, you need to provide regularly spaced supports to prevent sagging. Slopping the pipe to utilize gravity flow, unless you need a higher flow rate, no pressure is required. Using the friction coefficient for corrugate metals should be giving you a close enough estimate.
– r13
Oct 20 '21 at 1:49
• It actually should flow regardless orientation. Oct 20 '21 at 3:40
• Why not a parallel path? Oct 20 '21 at 4:10
• This is an ok approach. Might be a pain to maintain long term but sometimes that's not a problem. For rough approximation, use any "pipe flow" calculator on the web, with the total length of the 3mm diameters. Assuming that is the smallest diameter, and the connections between the holes are less restrictive. Also for this purpose, if you want to just build it, it's super easy to measure with a cup.... Oct 20 '21 at 8:57
• Yes, I would expect a very large pressure drop (mainly friction loss) due to the size of the pipe.
– r13
Oct 20 '21 at 13:04

$$\Delta P = 0.5 k\rho Q^2/A^2$$
$$\rho$$ density, $$Q$$ volumetric flow rate, $$A$$ cross sectional area. $$k$$ is a factor you can look up in a table for Minor losses. Valves and filters also have published $$C_V$$ values, which are used in a different formula to relate pressure drop to flow rate. Major losses are the friction in a straight pipe, and $$k=(f*L/D)$$ is expressed as a function of friction factor (very conservatively $$f=0.1$$), length, and diameter. For non-civil engineering flow systems, major losses are often negligible.