How Does Air Pressure Affect Fluid Levels in a U-Shaped Tube?

AI Thread Summary
The discussion revolves around the effects of air pressure on fluid levels in a U-shaped tube filled with water and oil. The user attempts to derive the velocity of air above the open end of the tube using pressure equations and Bernoulli's principle. Key equations relate the pressures at the bottom of the oil column and the air flow, indicating that the velocity of air can be calculated based on the difference in densities and the height of the fluid columns. Clarifications are sought regarding the meaning of air pressure (P(air)) and the need for specific values like the density of oil and the size of the oil column. The user is looking for validation of their calculations and a diagram to aid understanding.
faradayscat
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Homework Statement

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Suppose we have a u-shaped tube filled with water, with oil added at one end which disturbs the equilibrium. Now say one end is blocked off and the other is exposed to air flow which reduces the pressure above the water and causes the water to climb back to equilibrium with the top of the oil. What would be the velocity of the wind above the open end?

Homework Equations

The Attempt at a Solution


If the column of oil has a length 'L', then the pressures at the bottom level of the oil are the same:

P1+ρwatergL = Pair+ρoilgL
P1 = Pair + gL(ρoil-ρwater) (1)

Where P1 is the pressure due to the air flow
Using Bernoulli's equation at the top of the tube as the reference point yields:

P1+0.5ρairvair2 = Pair (2)

Substituting equation (1) into (2) gives

0.5ρairvair2=gL(ρfluid-ρoil)

And then the velocity of air can be found... Is my work good? Thanks!
 
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What does P(air) exactly stand for?
 
I would think we'd have to know the size of the column of oil ...

... and the density of the oil while you're at it ...
 
Replusz said:
What does P(air) exactly stand for?
The air pressure
 
rude man said:
I would think we'd have to know the size of the column of oil ...

... and the density of the oil while you're at it ...

It has length 'L' and density ρoil

I'm not asking for a specific solution, just wanted to see if my work checks out.
 
Can you please provide a diagram?
 
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