Split Pipe Flow: Multiple Inlets and Outlets (Bernoulli's)

[CollegeCourt]

http://tinypic.com/view.php?pic=mhvarc&s=9#.WD__u_mLTIU Hey guys,
So, I've got this problem, attached.
I've used Bernoulli's to produce P1 + (1/2)p(u1)^2 +P2 + (1/2)p(u2)^2 = P3+ (1/2)p(u3)^2 +P4 + (1/2)p(u4)^2 +P5 + (1/2)p(u5)^2,
Plugging in the values you get 82500 + P2 + 500(u2)^2 = P3 + 60000 + 500(u4)^2 + P5 + 500(u5)^2
Replacing velocity with volumetric flow/area,
82500 + P2 + 500(Q2/A2)^2 = P3 + 500(Q4/0.03)^2 + P5 + 500(0.74/(A5)^2
Now I know Q1 + Q2 = Q3 +Q4 + Q5, but I have come to a dead end. Is this just numerous simultaneous equations or is there another way about this?
https://postimg.org/image/gqfk1aukn/

Thanks!

 

[Illmatic1]

Yes, this is a system of simultaneous equations. You will need to use the equation for conservation of mass to determine the unknown volumetric flows (Q2, Q4, and Q5). This equation states that the sum of all volumetric flows at any given point in the system must equal the volumetric flow at the next point. From this, you can solve for Q2, Q4, and Q5. Once you have these values, you can then plug them into your Bernoulli equation and solve for the pressures.