Simple Differential Manometer Question

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aoifaosf24
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Q)Pipe A contains a liquid of specific gravityPipe A contains a liquid of specific gravityPipe A contains a liquid of specific gravityPipe A contains a liquid of specific gravityPipe A contains a liquid of specific gravityPipe A contains a liquid of specific gravityPipe A contains a liquid of specific gravityPipe A contains a liquid of specific gravityPipe A contains a liquid of specific gravity
Last edited by aoifaosf24; 1 month ago
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0le
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I don't follow your diagram. Assuming the pipes are connected and we have a manometer, I only see one liquid there, not two. The two liquids should be water and an unnamed liquid. Make an assumption that the liquids are immiscible. Then label the diagram properly, making three points, the interface between the liquids, and the other two points where atmospheric pressure is applied at the surface of each liquid. It also is not clear to me where or how you got the heights.
Last edited by 0le; 1 month ago
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Eimmanuel
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(Original post by aoifaosf24)
Q)Pipe A contains a liquid of specific gravity 7.8, pipe B contains water (density = 1000kgm^-3) and the specific gravity of mercury is 13.6.

Calculate the difference between the pressures and conclude whether pressure A or pressure B is greater and if you could have come to this conclusion directly by the level of the mercury.

(Ive attached my working and sketch of the diagram provided.)

Can someone help me with where i've gone wrong. Ive tried calculating it out but I seem to end up with the pressure B being greater than pressure A whereas I know from analysis of the diagram and the mercury level that the pressure A should be greater.

https://pasteboard.co/JBzRLLx.jpg
Maybe you want to upload the actual given diagram.
Based on your “diagram that you have drawn”, how do you reach the conclusion of “I know from analysis of the diagram and the mercury level that the pressure A should be greater”.
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aoifaosf24
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(Original post by 0le)
I don't follow your diagram. Assuming the pipes are connected and we have a manometer, I only see one liquid there, not two. The two liquids should be water and an unnamed liquid. Make an assumption that the liquids are immiscible. Then label the diagram properly, making three points, the interface between the liquids, and the other two points where atmospheric pressure is applied at the surface of each liquid. It also is not clear to me where or how you got the heights.
There are 3 liquids in total. The left one (above mercury) labeled ρA, the right one labeled ρB (above mercury) and the bottom one labeled ρM (mercury). I wrote the densities of each liquid underneath. The heights are from the diagram, i didn't calculate them. But I think i've solved my issue, it was that I thought that as the height of the left fluid, ρA, was greater than the height of the right fluid, ρB, therefore Pa > Pb (just like a standard manometer) but I think the change in height is due to the density ρA>ρB and not because of the pressure. So my analysis was wrong and you cant see whether Pa or Pb is greater just by looking at the manometer.
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aoifaosf24
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(Original post by Eimmanuel)
Maybe you want to upload the actual given diagram.
Based on your “diagram that you have drawn”, how do you reach the conclusion of “I know from analysis of the diagram and the mercury level that the pressure A should be greater”.
Sorry but I lost the diagram as the question was from a while ago, I was just doing revision from questions I didnt fully understand earlier on in the semester. But I think my analysis was wrong, it was that I thought that as the height of the left fluid, ρA, was greater than the height of the right fluid, ρB, therefore Pa > Pb (just like a standard U-tube manometer) but I think the change in height is due to the density ρA>ρB and not because of the pressure. Therefore you cant see whether Pa or Pb is greater just by looking at the manometer in this instance. So Pb can be > Pa
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Eimmanuel
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(Original post by aoifaosf24)
Sorry but I lost the diagram as the question was from a while ago, I was just doing revision from questions I didnt fully understand earlier on in the semester. But I think my analysis was wrong, it was that I thought that as the height of the left fluid, ρA, was greater than the height of the right fluid, ρB, therefore Pa > Pb (just like a standard U-tube manometer) but I think the change in height is due to the density ρA>ρB and not because of the pressure. Therefore you cant see whether Pa or Pb is greater just by looking at the manometer in this instance. So Pb can be > Pa
A video that may help your revision.
https://www.youtube.com/watch?v=6MOXwxbLvls

A lot of people has commented that the answer is incorrect. Try and see whether you can get the correct answer.
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aoifaosf24
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(Original post by Eimmanuel)
A video that may help your revision.
https://www.youtube.com/watch?v=6MOXwxbLvls

A lot of people has commented that the answer is incorrect. Try and see whether you can get the correct answer.
I've already seen that video, and at 6mins40 in he says "according to the analysis Pb is greater than Pb" but that analysis is done because of the difference in heights of the 2 fluids. So he goes to do Pb-Pa and it gives him a positive answer. Whereas in my question if I go about the same logic I get a negative answer hence indicating that the opposite of his analysis is correct for my situation.
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Eimmanuel
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(Original post by aoifaosf24)
I've already seen that video, and at 6mins40 in he says "according to the analysis Pb is greater than Pb" but that analysis is done because of the difference in heights of the 2 fluids. So he goes to do Pb-Pa and it gives him a positive answer. Whereas in my question if I go about the same logic I get a negative answer hence indicating that the opposite of his analysis is correct for my situation.
I think you misunderstand my asking.
I was asking you if you can find the numerical answer. I believe you can find based your explanation.
No need to show me.
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