Pressure not matching at same height in a U-tube

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    Height Pressure U-tube
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Discussion Overview

The discussion revolves around the pressure differences observed in a U-tube containing two immiscible fluids, water and oil. Participants explore the implications of fluid heights and densities on pressure readings at the same height in the tube, questioning the assumptions made in the analysis.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions why the pressures at the same height in the U-tube do not match, given the differing heights of water and oil.
  • Another participant critiques an equation presented, suggesting it leads to absurd conclusions and indicates a misunderstanding of pressure relationships in the system.
  • There is a mention of the unusual situation where a denser fluid (water) is floating on a less dense fluid (oil), raising questions about the conditions of the U-tube setup.
  • Some participants seek clarification on the purpose of the attached image, wondering if it is a real scenario or a problem designed to identify mistakes.
  • There is a focus on understanding the implications of pressure assumptions, particularly regarding the dashed line in the diagram and the equality of pressures on either side.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the pressure calculations and the physical setup of the U-tube. There is no consensus on the correct understanding of the pressure relationships or the validity of the assumptions made.

Contextual Notes

Limitations include potential misunderstandings of fluid dynamics principles, the dependence on the specific conditions of the U-tube, and unresolved questions about the nature of the fluids involved.

Who May Find This Useful

This discussion may be of interest to students and educators in fluid mechanics, physics enthusiasts exploring fluid dynamics concepts, and individuals analyzing practical applications of pressure in U-tube setups.

Avimanyu Ray
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Can we please look at the following attached file image?
It shows a utube filled with a little water and the rest is oil.
Thus, the height of oil in one arm will be more than the height of water in the other.
When we compare the pressure at the height of the surface of water with that corresponding height of the oil, the pressures don't match. Why? Please refer to the attached image file.
 

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  • Screenshot_2018-05-29-21-24-10-299-01.jpeg
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Let us examine the first equation in your picture:

$$P_0+(h_1-h_2)\ \rho_2\ g = P_0$$

The left hand side looks like a correct computation for the pressure at the oil-water interface in the right hand tube. You take the surface pressure and add the contribution of the column of water with density ##\rho_2##. But what leads you to assert that that pressure is equal to ##P_0##?

One could conclude from that equation that either ##h_1 = h_2##, that water has zero density or that we are working in zero g. All three are silly, so that equation is obviously incorrect.

Edit: We also have the curious situation that although ##\rho_2## is greater than ##\rho_1## (water is denser than oil), we nonetheless have the denser fluid floating on top of the less dense fluid. Possibly this is a capillary U-tube (without an accounting for surface tension).
 
Last edited:
Avimanyu Ray said:
Can we please look at the following attached file image?
Where did the image come from? Is it an exercise to spot what's wrong or a 'real situation?
 
What are you looking for, the difference in height of the two columns?
 
Consider this diagram
.
upload_2018-5-29_14-44-3.png
 

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Likes   Reactions: Richard Spiteri, sophiecentaur, Avimanyu Ray and 1 other person
sophiecentaur said:
Where did the image come from? Is it an exercise to spot what's wrong or a 'real situation?
It's an exercise to spot what's wrong.
 
gleem said:
What are you looking for, the difference in height of the two columns?
Precisely, I want to know what are we observing wrong when we concentrate on the dashed line XY. When we are showing both the pressures on either side on the line are equal, where are we wrong?

I want to know where this assumption is going wrong? Because we know, both the heights won't be equal.
 
gleem said:
Consider this diagram
.View attachment 226373
Wow, thanks a lot.
I got the answer by the diagram you indicated here :)
 

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