Here is the illustration:
1. Now, to calculate flow in pipe A-B you need to know pressure on point B. I would make assumption as it is 5 bar.
Flow rate Q1 can be calculated now.
2. Calculate flow in B-C and B-D based on the same pressure of 5 bar in B. Flow Q2 and Q3 can be calculated.
3. Now calculate new value of Q1=Q2+Q3.
4. Calculate pressure in B based on Q1 in 4.
5. This new pressure in B should be used for step 2. - calculate flow in Q2 and Q3 ... etc.
Hope this helps