# Applying Bernoulli's Principle after pipe branching (flow separates)

When I have a pipe (1) that branched into 2 pipes (2 and 3). I noticed that Bernoulli's equation can be applied between point 1 and 2 or 1 and 3. So my question is how is this valid? Isn't Bernoulli just an energy balance so the energy at point 1 in the the original pipe should be equal to the sum of energies at point 2 and 3? I tried starting with this equation and dividing by the mass flow rate at each point (taking into consideration the continuity equation) and ended up with this $$\dot{m_2}e_1+\dot{m_3}e_1 = \dot{m_2}e_2+\dot{m_3}e_3$$where e is the energy per mass passing in the pipe per second. But this doesn't strictly imply that $$e_1 = e_2$$ or $$e_1 = e_3$$.

Also can Bernoulli's equation be applied on points 2 and 3 (between the 2 branched pipes)?

• Could you spell check the name? Commented Nov 13, 2019 at 0:51
• But the equation is consistent with the latter two conditions. You can apply the Bernoulli equation separately to the portion of the flow between points 1 and 2 and to the portion of the flow between points 1 and 3. It is not valid to apply the Bernoulli equation to points 2 and 3, because the represent different flows. Commented Nov 15, 2019 at 15:38
• Okay, but why is it possible to apply Bernoulli's principle after the flow separates into 2? Am I mistaken about Bernoulli's principle being an energy balance? Commented Nov 18, 2019 at 14:32