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The flow rate of each branch would be proportional to the area of the pipe correct? flow = Vel. * Area. Or would they all have an equal flow rate and just vary in the velocity? How would friction losses play a part in determining the flow rate of each branch? I feel like we need to use Bernoulli's/Darcy-Weisbach equations.

If we close a valve on one of the branches, how does that affect the flow rate of each of the other branches? Would the flow rate increase equally amongst all the other branches? or would it be proportional to their area's? If it is proportional, would we be able to do a sort of weighted average to determine how much more flow one branch would receive vs another? Also again how would viscous/friction losses play a roll in determining this?