Bernoulli's

[chiddler]

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So tell me if I got this right. Flow under "3" is the fastest, creating the lowest pressure and therefore the highest pressure difference allowing fluid to get out of 3 faster.

Yes?

If so, then my question is then: Beyond intuition, how do I know that there will be the greatest flow speed under tube 3?

Thank you.

 

[milski]

The flow is volume over time. As you go further along the tube (A, B, C, D) you have to carry the output volume from more columns. You cannot compress the fluid and the cross-sections stays the same, so the only other way is to increase the flow.

 

[SaintJude]

I thought the fluid would flow fastest at point A,

According to Bernoulli's equation (or Toricelli's law)

Column 1 has the highest h, so the fluid flow should be fastest at point A.

Is that right or wrong?

 

[milski]

I thought the fluid would flow fastest at point A,

According to Bernoulli's equation (or Toricelli's law)

Column 1 has the highest h, so the fluid flow should be fastest at point A.

Is that right or wrong?

You cannot apply Toricelli's law here - it is about flow out of a container directly into open air. Toricelly's law is a simplified version of Bernoulli's law which has a few assumptions. One of them is that the pressure on top of the fluid and the pressure of where the fluid flows out are the same. That's certainly not the case for point A, so you cannot apply the formula for v.

 

[SaintJude]

Ah, I see. Thanks Milski!! I didn't realize that Bernoulli's law included an assumption that ΔP=0.

 

[milski]

Ah, I see. Thanks Milski!! I didn't realize that Bernoulli's law included an assumption that ΔP=0.

Sorry, what I wrote turned out a bit ambiguous. Bernoulli is valid for any P. Toricelli makes a few assumptions, including ΔP=0, and gives you v=sqrt(2gh).