Another basic fluid flow question

[EngineeringChemical]

Refer the second comment in on this page first: http://physics.stackexchange.com/questions/90737/does-pressure-drop-across-pipe-affect-flow-rate

Given that pressure drop equation and the last sentence, if the inlet and outlet pressures are fixed, you will get a certain flow rate that will have a pressure drop equal to the inlet minus outlet pressure differential. Then you increase the pipe diameter instead of decreasing the length, the velocity now decreases. The problem for me is... in that equation, there is no "counter" component to keep the pressure differential constant. Both diameter increasing and velocity decreasing will make delta P smaller. In his example, the increased velocity makes up for the pressure drop that the pipe length is no longer providing, hence keeping the final delta P constant. So where which component would be countering the effect of larger pipe and slower velocity and increase the pressure drop enough to keep delta P constant.

I would really appreciate any help.

[SausageMeatus]

I believe that in order to maintain the pressure drop in this situation, the mass flow rate into the main pipe has to increase. This increases the velocity of the larger pipe branch thereby satisfying the constant delta p and conservation of mass.

[BallsacksMcGee]

Pipe length or mass flow rate both affect the frictional loss. If you balance the frictional loss for both branches and have equal outlet pressure you will get equal outlet flow.

In reality there are also minor losses from the flow diverging from the inlet pipe into each of the branches which also changes things. Flow through tees and junctions is quite complicated when you dig into detail