Can I apply Bernoulli's equation to this situation?

[Atouk]

TL;DR Summary

Necessary conditions for Bernoulli's theorem.

Can Bernoulli's equation be applied between points 1 and 2, ignoring the another tank ?

 

[Chestermiller]

Summary:: Necessary conditions for Bernoulli's theorem

https://www.physicsforums.com/attachments/263163
Can Bernoulli's equation be applied between points 1 and 2, ignoring the another tank ?

What do you think?

 

[Atouk]

I would say "of course not". But

What do you think?

I would say "of course not", but I can not explain what happens with the steamline between 1 and 2...

 

[Chestermiller]

All the water would flow from the upper reservoir to the lower reservoir on the right. There would be no flow from 2 to 1 unless a huge flow were forced by the pump. It would have to provide a pressure of at least 10 psi.

 

[Atouk]

All the water would flow from the upper reservoir to the lower reservoir on the right. There would be no flow from 2 to 1 unless a huge flow were forced by the pump. It would have to provide a pressure of at least 10 psi.

I see, but supposing that I have all the information about the points 1 and 2
(speed, pressure and height), could I be able to apply Bernoulli's equation and figure out Hp?
My question is conceptual, the values don't matter.

 

[Chestermiller]

I see, but supposing that I have all the information about the points 1 and 2
(speed, pressure and height), could I be able to apply Bernoulli's equation and figure out Hp?
My question is conceptual, the values don't matter.

I think that if you specify the flow at the pump, you can determine the pressure at the pump and the flows in the two arms using Bernoulli.

 

[Atouk]

I think that if you specify the flow at the pump, you can determine the pressure at the pump and the flows in the two arms using Bernoulli.

So, in an ideal situation (steady flow, without losses in pipes, etc.)
p1 / ρ + (v1^2) / 2 + g*h1 = p2 / ρ + (v2^2) / 2 + g*h2 - Hp ?

 

[Chestermiller]

So, in an ideal situation (steady flow, without losses in pipes, etc.)
p1 / ρ + (v1^2) / 2 + g*h1 = p2 / ρ + (v2^2) / 2 + g*h2 - Hp ?

To get your feet wet, start out by considering the problem where there is no flow from the pump.

 

[Lnewqban]

What does the red arrow mean?

 

[cjl]

All the water would flow from the upper reservoir to the lower reservoir on the right. There would be no flow from 2 to 1 unless a huge flow were forced by the pump. It would have to provide a pressure of at least 10 psi.

Where on Earth are you getting 10 psi from here?

 

[cjl]

Summary:: Necessary conditions for Bernoulli's theorem.

View attachment 263167
Can Bernoulli's equation be applied between points 1 and 2, ignoring the another tank ?

In general, this does not look like a situation where Bernoulli would apply because based on the diagram alone, I strongly suspect that there are significant viscous losses here, especially given that 2 is labeled as a river with what appears to be a free surface well below the surface of 1. Bernoulli applies to situations without significant viscous loss, and I don't see how that can be the case here.

 

[Chestermiller]

Where on Earth are you getting 10 psi from here?

If I remember correctly, the OP showed some dimensions on his original post (which was later edited).

 

[Chestermiller]

In general, this does not look like a situation where Bernoulli would apply because based on the diagram alone, I strongly suspect that there are significant viscous losses here, especially given that 2 is labeled as a river with what appears to be a free surface well below the surface of 1. Bernoulli applies to situations without significant viscous loss, and I don't see how that can be the case here.

After further consideration of this situation, I totally agree.

 

[cjl]

If I remember correctly, the OP showed some dimensions on his original post (which was later edited).

Ah, that would explain it. I first saw it with no dimensions, so your claim seemed totally arbitrary.

 

[boneh3ad]

You could apply Bernoulli with extra terms to account for losses.

 

[Joe591]

No, you cannot apply bernoulli between those two points and ignore the other tank. I vaguely remember these sorts of problems from technikon. You have to calculate the flows through multiple paths and then superimpose them on each other. You have to calculate how much flow there will be from the top tank to the river and then how much flow there will be from the top tank to the bottom tank etc and then the algebraic sum of the different flows will give you the actual flows. You could very well end up with net flow towards the bottom tank and towards the river simultaneously. You absolutely cannot ignore the bottom tank.

the fact that you have a pump in the mix is also another complication. You basically need to try and write a system curve up for this interconnection of tanks. This is a very difficult problem that I think you can only solve through making assumptions and then iterating until things work out. You are going to spend a lot of time on this...Do you have numbers for the different values like surface heights of the fluid and pipe diameters etc etc.
The pump curve would also help.