Conceptual pressure question

[SaintJude]

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EK Can someone explain?

Edit: EK's explnation: The fluid at A, C, D is at atmospheric pressure. The fluid at B is at atmospheric pressure plus "pgh"[the elevation head].

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[MedPR]

Well, A and D are both just atmospheric pressure, so those are out. If I'm not mistaken, since fluids are incompressible, any fluid at a particular depth will have equivalent pressure as well. So, I don't know between B and C?

B seems like it would have higher pressure because there is taller column of water above it, but C is in a smaller volume (a little pipe vs the huge beaker). Although, according to my ruler, point C is actually slightly lower than point B. So C?

 

[SaintJude]

Yeah, I follow you: A& D are immediately out. I myself have trouble distinguishing between B& C.

 

[milski]

C is slightly lower. The shape of the container around it does not matter.

 

[SaintJude]

No, the answer is B. And I think point C and point B were intended to be shown at equal heights...

 

[MedPR]

No, the answer is B. And I think point C and point B were intended to be shown at equal heights...

If B is the answer then the only explanation I can think of (why it's not C) is that there is a taller column of water above B than C. Pressure = patm+pgh. hB is greater than hC.

 

[milski]

Or the pressure in the tube is lower since the water is moving there and the pressure is lower due to Bernoulli.

 

[MedPR]

Or the pressure in the tube is lower since the water is moving there and the pressure is lower due to Bernoulli.

Yea that too. I have a feeling I'm going to be wrong, but I'm going to say that velocity at C is higher than velocity at B (continuity) and higher velocity = lower pressure (bernoulli)?

 

[silverice]

Or the pressure in the tube is lower since the water is moving there and the pressure is lower due to Bernoulli.

can you please elaborate on this a little more?

 

[milski]

Yea that too. I have a feeling I'm going to be wrong, but I'm going to say that velocity at C is higher than velocity at B (continuity) and higher velocity = lower pressure (bernoulli)?

That would be it, you're correct this time.

To make that assessment, you want B and C to be equally high. If B is higher than C, you'll have to do the math with the exact pressures, velocities, fluid, etc. to determine which one is lower.

 

[milski]

can you please elaborate on this a little more?

You can consider the big reservoir as a very wide pipe and the syphon as a much smaller pipe. You have (supposedly) laminar flow and the points are at the same height. Apply Bernoulli's law and you'll have faster velocity of movement and lower pressure in the tube with lower area.

 

[TXKnight]

View attachment 18586

EK Can someone explain?

I go with B since it has both depth pressure and atm pressure on top. C is lower pressure due to faster speed. A and D are at atmospheric pressure. Whats the answer?

 

[ljc]

Hoppin' on board the "B" bandwagon here.

 

[MT Headed]

It's B, for the bernoulli reasons MedPR and others outlined above.

 

[dmf2682]

B has higher static pressure, b and c have the same total pressure.

 

[MedPR]

B has higher static pressure, b and c have the same total pressure.

What?

 

[dmf2682]

What?

Total pressure is static pressure plus dynamic head. Think of it as an analogy for total energy being the sum of your potential and kinetic energy.

 

[MedPR]

Total pressure is static pressure plus dynamic head. Think of it as an analogy for total energy being the sum of your potential and kinetic energy.

What is "dynamic head"?

 

[dmf2682]

.5*density *velocity^2

 

[MedPR]

.5*density *velocity^2

Oh, right. I remember reading about "heads" in EK. Better go back and take another look. I know what you're referring to, but I have no idea what it means.

 

[dmf2682]

.5*density *velocity^2

This is a way of expressing Bernoulli. Air over a wing flows faster than the air flowing on the bottom surface. So the dynamic head is higher on top than on the bottom. In an ideal situation the total pressure is constant, which means the top of the wing sees a lower static pressure than the bottom. So over the area of the wing the bottom gets pushed on more than the top, and lift is generated.