pressure loss in a T fitting

Question

For weeks I have been searching internet , but still unable to find answer , so here it goes: I have to calculate pressure losses in heating circuit , and am stuck at calculating losses in T fittings. Here are some crude drawings of problem I know:

• diameters of each pipe leading to fitting (Da,Db,Dc)
• flow rates through these pipes (Qa , Qb , Qc)

What I need to know is Pressure drops:

• ∆Pc-a=Pc-Pa=?
• ∆Pb-a=Pb-Pa=?

I know of minor loss formula , but don't understand how to use if fitting has more than 2 ports.

Answer 1

I would recommend using Handbook of Hydraulic Resistance by I.E. Idelchik. This book is the literal bible for loss coefficient formulations. The book gives loss coefficient correlations based on test data. The image is an example of one chart provided for a tee configuration

Answer 2

I have two ways you could find a solution to that problem (actually 3 but the third is using a flow simulator :P)

Just assume that P2 and P3 are the same (or else you will find yourself in partial differential equation hell believe me been there and it isn't pretty)

1: Crane Flow of Fluids. Easy lazy, quick he gives you measured parameters for pressure loses and other things you just fit your numbers there http://www.waterlinefountains.com/wp-content/uploads/2017/09/Crane-410.pdf

Not the best method it has a lot of error. It is the first answer that comes up in google (though they do not provide you with the tables)

2: Bird transport phenomena:

Assume it is plug flow, define a three pipe system in which 1 is the feed and 2 and 3 are the exits, you calculate each exit with an equalized pressure (or so I remember). Just to be certain; I checked the book and problem 7Q4 can give you the answer, look up the solution and define n as 2.

So far I think this is the answer you want, you calculate everything by hand but it isn't a problem with an easy solution.

I recommend you checking if someone hasn't programmed it yet because you getting a short formula is a longshot the answer to 7Q4 is a differential equation.

3: Get a copy of EPAnet (free but works poorly), HYSYS (usually colleges with Chemical engineering majors have licences) or Olga, they do pressure drops though they use method 2 and 1 combined.

TLDR: To do it by hand is possible, has been done before and that is how most simulators work, though it is so hard to do that you use equivalent lengths instead.