# Flow in a T-Junction with pipes of different diameters

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


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.

• Bernoulli? This is basically the venturi used in early carburettors to "mix" fuel with air... Jan 30, 2018 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. Jan 30, 2018 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? Jan 30, 2018 at 14:25
• @SolarMike - This doesn't seem to be a venturi, since there is no reduction in cross-section of the main pipe. Jan 30, 2018 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... Jan 30, 2018 at 16:39