Liquid flow in pipeline branching

[fewnick]

As we know, when thinking Bernoulli´s equation in one horizontal pipeline, it is p + 0.5 * density * v^2 = Constant. But when thinking a branching of this pipe, then Bernoullis principle for one branch is p1+0.5*ro* v1^2 = C and p1+0.5*ro*v1^2 = C. We think that the two branches are the same, therefore there are the same velocities v1 = v/2 in each branch. But the problem is connected with the static pressure p1 (which is the pressure in the critical position - just in the junction). The pressure is actually always assumed the same, but in reality it is not, it oscillates. The consequence is that the mass flow is changing in each branch during time. I think it oscillates in certain accordance with fluctuating part of velocity. And I would like to ask you - do you know any empirical or theoretical integral relation for the oscillating static pressure value in dependence on Reynolds number?
I am probably wrong when thinking that static pressure is in accordance with fluctuating part of velocity. Nevertheless, I would be very grateful for any idea or link.

 

[Nate810]

Unfortunately, I am not aware of any empirical or theoretical relations that connect the oscillating static pressure with the Reynolds number. However, it is possible to calculate the static pressure in each branch of the branching pipe using the Bernoulli equation. The Bernoulli equation relates the total pressure of a fluid in a system to the velocity of the fluid, the density of the fluid, and the height of the fluid. The total pressure consists of the static pressure, which is the pressure of the fluid at rest, and the dynamic pressure, which is the pressure resulting from the movement of the fluid. Thus, by calculating the total pressure in each branch, you can determine the static pressure and the dynamic pressure in each branch.