# How to use General Energy Equation in parallel pipes?

My question comes from exercises with parallel pipes such as this.

I know that to analyse internal flow, we use general energy equation which origins from the 1st law so each time we apply it we are using a Control Volume. However for this type of question, if I apply a CV that goes from 1 to 2, part of the mass flows toward C and so starting from the 1st law the equation should become like this:

However the solution tells me that it is:

I dont understand why you can procede as the solution. It ignores the mass flow toward 3, almost as if there is only mass flow from 1 to 2 which permits it to cancel out completely the mass flow.

EDIT: Equations from 1 to J and from J to 2. The velocity heads still remains. Have I done anything wrong?

• There is pressure drop in the piping and in the valve going to tank 3 that is not accounted for in your Bernoulli equation approach. – David White Dec 13 '18 at 1:58
• Yeah i didnt account for that because my CV only goes from 1 to 2. My confusion is basically that the solution treats the energy equation as if it is bernoulli by following the same streamline. But we take a CV, no matter how,for example from 1 to 2 or the covering the whole fluid, it is inevitable to consider the energy that carries the mass in 3, which isnt in the solution. – Richard Dec 13 '18 at 16:11
• Questions: 1) Are the levels in the 3 tanks constant? 2) Are you open to a somewhat different approach to solving this problem? 3) Do you have a way to estimate pressure drop in piping and the valve as a function of flow rate? 4) Are there elevation differences between the tanks? – David White Dec 13 '18 at 16:16

The term involving $$V_B$$ takes into account the fact that it doesn't involve the full flow. You also need to include the continuity equation which helps to establish the flow rate split between branches B and C. Also, the pressure at junction J has to be the same for the entrance to branches B and C, and this too helps to constrain the split.