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I'm trying to understand how to apply the energy equation at a junction of 3 pipes. For example, when we are considering points A and D, should we consider that velocity at point D just before the fluid entres the junction (that is, there are 3 different values for V_D, one for each branch? Or it should be zero, as the sum of flow rates is zero? The energy should be almost the same inside the junction and at the end / begining of the branches (around point D). I know i can apply it between A and B, etc., but I would like to know how to apply it for point D.

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    $\begingroup$ why do you want this? Apply a pressure drop for the junction and go back to straight pipe losses. The velocity at the Y isn't important, use empirical methods. The reality is that you won't have uniform flow in that area. $\endgroup$
    – Tiger Guy
    Dec 1, 2023 at 18:04

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Velocity at $D$ should definitely not be zero, because you would have to apply the same logic to other points, which would mean zero velocity everywhere. The energy equation does not use local velocity, but mean velocity through a section. So "velocity at $D$" depends on which section you consider there.

A simplified version of the problem dealing just with a section change would be a straight pipe with abrupt change of section in the middle. In such case you could also ask what is the velocity at the middle. I think it is more clear in that case, that while local velocities might be very diverse, mean velocity will change just as abruptly as the section.

Also a more general point regarding energy equations is that you only need to consider conditions at some (boundary) points to be able to use them (and avoid hard to describe conditions at internal points). In your case, you would have input at $A$ and two outputs at $B$ and $C$. For these, the energy equation will describe the relation between velocities, sections, elevations and pressures. There is no point in considering point $D$ in the equation (or any other "internal" point of the system). Very simple example of this is change of potential energy of an object due to change of its elevation. Only important information is start and end elevation (boundary points), no one cares if took the object using elevator or crane, or if you first went 20 m down and 25 meters up.

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