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I have been trying to model a complex pipe network recently and have come across something I can't find any information on. In my model, I have been assigning equivalent lengths of pipe to various fittings, but I commonly encounter fittings such as this: 

Inlet to T: 10mm diameter pipe
t-through: 10mm diameter pipe
t-branch: 1mm diameter pipe

enter image description here

Essentially I have a T junction where the branch is also a sudden contraction, but the dominant flow direction is perpendicular to the branch. Does anybody know a method of calculating equivalent length of pipe in a case like this?

I don't think a regular vena contracta, as described by normal theory for sudden contractions, would occur in the 1mm branch, since it is perpendicular to the main flow and not coaxial with the main 10mm pipe.

But I have various instances where this occurs, and the amount of the contraction varies (e.g. the branch pipes can be 1,2 or 5mm) but the normal method of equivalent pipe length for a t-junction does not account for the changing area. I need something that will account for it.

Petrichor
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  • Bernoulli? This is basically the venturi used in early carburettors to "mix" fuel with air... – Solar Mike Jan 30 '18 at 14:20
  • If I knew the flow conditions, which I don't. Ideally, I need to represent the interface with an equivalent length of pipe that represents the 'resistance' to flow travelling down the branch. Typically for a T junction in steel pipes the coefficients are 20 for the thru flow and 60 for the branch... but the theory doesn't account for area change. I think my best chance is looking at flow through a hole drilled in a pipe. – Petrichor Jan 30 '18 at 14:23
  • How can you make any decision for an equivalent length if you don't know the conditions for the situation? Are you assuming the fluid flows into the smaller pipe or from the smaller pipe? – Solar Mike Jan 30 '18 at 14:25
  • @SolarMike - This doesn't seem to be a venturi, since there is no reduction in cross-section of the main pipe. – Jonathan R Swift Jan 30 '18 at 15:22
  • @JonathanRSwift so no change in diameter between pipe and the Tee then? ie those pipes that connect to the head of the Tee... – Solar Mike Jan 30 '18 at 16:39
  • @SolarMike - Possibly, - and if it's a female tee, then perhaps the venturi equations could be used to calculate the positive pressure, and consequential outflow? I was going off the supplied diagram, however... – Jonathan R Swift Jan 30 '18 at 18:45
  • There is a worked example of this type of problem [here](http://opac.vimaru.edu.vn/edata/EBook/Hydraulics_of%20pipeline%20systems.pdf) from page 35 onwards (page 42 using the PDF page numbers) - it seems solutions can be fairly complex. – Petrichor Feb 07 '18 at 13:36

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