Is it correct to apply two separate Bernoullis equation - for sections 1-3 and for 2-3? Why/why not?

I ve seen such solution to this problem on the internet but I have some doubts.

I think that energy between sections 1 and 3 is not conserved because of energy exchange with the other stream.

Energy conservation for the whole system

Q1(v1^2/2 +p1/rho)+Q2(v2^2/2 +p2/rho)=(Q1+Q2)(v3^2/2 +p3/rho)

is not enough to determine (p3-p2) needed for Y momentum conservation.

system of:

v1^2/2 +p1/rho +deltaE=v3^2/2 +p3/rho

v1^2/2 +p1/rho -deltaE=v3^2/2 +p3/rho

needs an additional equation as well

I would be thankful for every help