No. That equation is available for one way between a and b. If you have bifurcated zones, the formula is not available...

Please, lets see:

https://www.sciencedirect.com/topics/engineering/bernoullis-equation

Dear

You have to have continued flow to apply this equation

Very good question and thank you for asking it: Bernoulli's theorem is written along a streamline or a stream-tube and relates velocity to pressure (including the weight of the column) in saying that the total energy (kinetic and potential) is conserved. By definition of the current tube, the mass flux is preserved along the tube. You put an opening between point A and point B: if there is no flow through the opening (a pressure tap for example); well you can apply Bernoulli. If there is flow in the opening, you no longer have conservation of the mass in the current tube A-B and Bernoulli no longer applies.

Thank you for answering this jamel. If there is a flow in between stream tube. How to calculate the pressure at the point c? By doing a momentum balance in x and y direction over the control volume? In the figure attached you can find the drawing.

You are Welcome,

Sorry, Vivek, that is not correct.

To calculate the pressure at point C you can apply Bernoulli on a current tube between A and C (there is still conservation of the mass flux). Now, if you want to calculate the pressure at point B you have to know the mass flux taken at point C, say Qc. Consider then the current tube C-B, the mass flux (constant) which circulates is Qa-Qc. Qa being the initial mass flux from A. Knowing the pressure in C calculated previously, you can then calculate the pressure in B by applying Bernouilli again between C and B with the mass flux Qa-Qc.

Sorry, that is not correct! To calculate the pressure at point C you can apply Bernoulli on a current tube between A and C (there is still conservation of the mass flow). Now if you want to calculate the pressure at point B you will know the flow rate taken at point c, say qc. Consider then the current tube C-B, the flow (constant) which circulates there is qa-qc. qa being the initial flow in A. Knowing the pressure in C calculated previously, you can then calculate the pressure in B by applying Bernouilli again between C and B

if you follow the image attached herewith, you will find that flow is begging decides ar the AC plane. is not it ? So Bernoulli can be applied betwee A and AC plane and BC and B. mass flow dies not remain conserved between A and C. Mass flow at A is higher than at C or B.

i was watching an example in you tube fir T section flow. They are using brenoulli between entrance and the any of the two exits . How they are using Bernoulli in that case? Mass flow does not remain conserved there also

You have to know the flux through the opening. Then calculate the new flux between C and B

Otherwise, you have to know the outlet from the opening: this will give rise to a two-equation system the resolution of which will give a solution to your problem

Hi,

My question is how can you apply Bernoulli at the point C, where the flow is being divided? I don't know the outlet flow.

you write Bernouilli between C and the outlet where P and Z should be known -> Calculate V in this vein -> you have then an expression for QC-Outlet

You do the same between C and B -> you have then an expression for Qc-B

With : QC-Outlet+QC-B=QA

Then resolve the equation system

Try and say to me

Pressure at the point c (which is just at the entrance to the outlet) is given by

Pc=rho*(Poutlet/rho+gz +Voutlet^2/2) - rho*Vc^2/2

In this case, Voutlet=0, Z(suppose)=1 m, Vc is known from continuity equation. So one can calculate the pressure at C.

Now I can apply Bernouli between C and B.

But my question is how can you apply Bernoulli between C and B or C and A? C is the point where flow is getting divide. If you look at the image that I shared with you there is a plane AC, where flow is getting divided, before the point C.

Is Mass flow between A and C or C and B conserved?

I would like you to do it on yourself.

Let's start from the beginning: you have 4 points: A (entry); C (bifurcation); B (output 2) and let's say D (output 1)

I know QA, PA, ZA, ZB, ZC and the pressures at the outputs (PB and PD) as well as the sections (S) in A, B, and D. We shall know also the sections in C1 (upstream section of the current tube C-D) and in C2 (section upstream of the current tube C-B)

1. I consider the current tube A-C; Q = QA -> I apply Bernoulli -> I get PC

2. I consider the current tube C1-D; Q = QD (QD is unknown) -> I apply Bernoulli -> I get QD = f (ZC, ZD, PC, PD and sections SC1 and SD)

3. I consider the C2-B current tube; Q = QA-QD (QD = f (ZC, ZD, PC, PD and sections SC1 and SD)) -> I apply Bernoulli -> and I calculate QD

4. QB = QA-QD

Very interesting point, Vivek. I would appreciate your and Professor Jamel's opinion, if possible, with comments please on the following. In the situation where the kinetic energy (V^2 / 2*g) can be neglected (e.g. in water supply systems, where velocities are quite limited), I believe that the relationship (piezometric head upstream = piezometric head downstream + head loss) can be kept valid, right? Am I correct? If so (or if not), what is the theoretical explanation for this? Thanks.