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

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SUMMARY

The discussion focuses on the impact of air pressure on fluid levels in a U-shaped tube, specifically when oil is introduced to one end. The key equations derived include P1 + ρwatergL = Pair + ρoilgL and 0.5ρairvair² = gL(ρfluid - ρoil), which relate the pressures and velocities of the fluids involved. The participant seeks validation of their calculations and clarification on the meaning of P(air) and the necessary parameters such as the size of the oil column and its density. A diagram is requested to enhance understanding.

PREREQUISITES
  • Understanding of fluid dynamics principles, particularly Bernoulli's equation.
  • Knowledge of pressure concepts in fluid mechanics.
  • Familiarity with the properties of fluids, including density and gravitational effects.
  • Ability to interpret and create diagrams representing fluid systems.
NEXT STEPS
  • Study Bernoulli's equation and its applications in fluid dynamics.
  • Research the effects of air pressure on fluid equilibrium in U-shaped tubes.
  • Learn about the properties of different fluids, focusing on density and viscosity.
  • Explore how to create and interpret fluid diagrams for complex systems.
USEFUL FOR

Students in physics or engineering, educators teaching fluid dynamics, and anyone interested in understanding the principles of fluid behavior in response to pressure changes.

faradayscat
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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+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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