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

In summary, the conversation discusses how the addition of oil in a u-shaped tube filled with water disturbs the equilibrium and the effect of air flow on the water and oil levels. The equations used to calculate the pressure and velocity of the air are shown, and additional information such as the length and density of the oil is requested.
  • #1
faradayscat
57
8

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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  • #2
What does P(air) exactly stand for?
 
  • #3
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 ...
 
  • #4
Replusz said:
What does P(air) exactly stand for?
The air pressure
 
  • #5
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.
 
  • #6
Can you please provide a diagram?
 

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

1. What is a U-shaped tube used for in fluid dynamics?

A U-shaped tube is used to demonstrate the principles of fluid dynamics, specifically the behavior of fluids at rest and in motion. It is a simple yet effective tool for visualizing how fluids move and interact with each other.

2. How does a U-shaped tube demonstrate fluid pressure?

The U-shaped tube is filled with fluid, usually water or another liquid, and the fluid levels on either side of the tube are different. This difference in fluid levels is due to the pressure exerted by the fluid on each side. The higher fluid level indicates higher pressure, while the lower fluid level indicates lower pressure.

3. What is the significance of the shape of the U-shaped tube in fluid dynamics?

The shape of the U-shaped tube is important because it allows for the visualization of how fluids move and behave in different conditions. By changing the angle of the tube or altering the fluid levels, different effects such as laminar or turbulent flow can be observed.

4. How does the height of the fluid in the U-shaped tube affect fluid pressure?

The height of the fluid in the U-shaped tube directly affects fluid pressure. The higher the fluid level, the greater the pressure exerted by the fluid. This is due to the weight of the fluid above, which increases as the height increases.

5. Can a U-shaped tube be used to measure the density of a fluid?

Yes, a U-shaped tube can be used to indirectly measure the density of a fluid. By filling the tube with a known fluid and observing the fluid levels, the density of an unknown fluid can be calculated using the principles of fluid pressure and equilibrium.

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