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

[faradayscat]

Homework Statement

[/B]
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+ρ_watergL = P_air+ρ_oilgL
P₁ = P_air + gL(ρ_oil-ρ_water) (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+0.5ρ_airv_air² = P_air (2)

Substituting equation (1) into (2) gives

0.5ρ_airv_air²=gL(ρ_fluid-ρ_oil)

And then the velocity of air can be found... Is my work good? Thanks!

 

[Replusz]

What does P(air) exactly stand for?

 

[rude man]

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 ...

 

[faradayscat]

What does P(air) exactly stand for?

The air pressure

 

[faradayscat]

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 ρ_oil

I'm not asking for a specific solution, just wanted to see if my work checks out.

 

[Chestermiller]

Can you please provide a diagram?