# Simplifying head loss across a piping network

I am tasked with designing a compressed air piping network,with and would like to determine the pressure loss across the different layers of instruments

-now here is the 3D layout of the network. The blue circles are instruments I want to deliver air to. They are in parallel with each other and connected in rows parallel to each other. L connotes pipe length (and in some contexts also the vertical elevation) while d is the diameter.

-I would like to find the maximum possible head loss (from point 1 to point 2) given that a proportion of the flow is teed off at each branch. I would also like to find consequently the proportion of flow teed off in each branch.

Am I correct in assuming points 1 and 2 (below) and going about the normal head loss calculation? How do I account for the tees and wyes branching off?

Assumptions

Flow is turbulent

The pressure drop across each brand is designed to be constant (with regulator valves -otherwise they differ due to elevation - maximum between the bottom and the top being 35 meters).

• Heavily related to : engineering.stackexchange.com/q/21920/10902 Commented Jun 7, 2018 at 18:45
• You'll want to use the Hardy-Cross Method here. (en.wikipedia.org/wiki/Hardy_Cross_method). A generalized version, using simple friction factors, would be best, so long as you don't approach within 50% of the speed of sound of air in the piping (epublications.bond.edu.au/cgi/…). You'll need to recognize that all air flowing out of the instruments is in fact going to a common outlet (the building), and will have a common pressure value (the building's air pressure), so you will have a fully connected network.
– Mark
Commented Jun 7, 2018 at 19:21
• Potentially relevant previous question: engineering.stackexchange.com/questions/18840/… Commented Jun 7, 2018 at 21:56
• @SolarMike apologies, how is it related? it's another question posted by myself but I am still looking for an answer Commented Jun 7, 2018 at 23:58
• Each branch off the main line has a regulator valve? How's the control scheme? What pressure & flow rates are we talking about (approx!)? Pressure required at the demand points? I find it confusing that your main pipe and branches are desigated d1 except the main line near pint 2 is designated d2. Can you draw a proper P&ID with all the information you have now?
– mart
Commented Jun 8, 2018 at 9:20