Sizing Open Pipe System for Equal Head Losses

[firavia]

If we have an open pipe system that will deliver in total 200 gpm divided in 2 pipes
the first pipe is 50 gpm and the second is 150 gpm , the 2 pipes have the same length , if we want to size the pipes where both pipes will have the same diameter , if we do that through william hazen equation flow chart we will get for each pipe a different head loss "slope"
m/100m head loss.
my question is first , how does water chose between the 2 pipes that have the same diameter and length to go in the fist 150 gpm and the second 50 gpm ?

my 2nd question is : according to bernoulli energy balance the head loss between "o &a" and "o&b" should be equal the same because

Po/guamma +Va square /2g -hl =0+vasquare/2.g
and po/guamma +vbsqaure/2g - hl =0 +vbsquare/2g
p.s: check the picture below for more explanation.

so the head loss must be the same , but using hazen william equation show us that they are not the same.?
p.s:the system is open to the atmosphere.
p.s:a pump is used to deliver the 200 gpm.

 

[maxx_payne]

water takes the easiest path or the path with minimum losses
so here in your case your desired flow rates may be acheived by the means of valves
because if the system is only constructed of pipes water discharges via pipes will be approximatly the same
if you study the case of branched pipes systems the discharge will be always same
there is something missing in the system