# Pipe flow

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 eqution flow chart we will get for each pipe a different head loss "slope"
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.

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