- #1
Solving Pressure Puzzle: Find P1 in Diagram
- Thread starter goldfish9776
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- Pressure
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Homework Help Overview
The discussion revolves around understanding the pressure P1 in a fluid mechanics context, specifically related to a sealed tank containing water, oil, and mercury. Participants are trying to clarify the relationship between various pressures and fluid heights in the system.
Discussion Character
- Exploratory, Conceptual clarification, Assumption checking
Approaches and Questions Raised
- Participants are examining the definition and location of pressure P1, questioning its relationship to atmospheric pressure and the pressures exerted by different fluids in the tank. There are discussions about the correct interpretation of the pressure equation and the significance of fluid heights in determining P1.
Discussion Status
Some participants have provided insights into the pressure calculation process and the reasoning behind the equation used for P1. There is an ongoing exploration of the implications of moving between different fluid levels and how that affects pressure. Multiple interpretations of the pressure relationships are being discussed.
Contextual Notes
Participants are addressing potential confusion regarding the atmospheric pressure and the pressure within the sealed tank, as well as the specific heights of the fluids involved in the calculations. There is an acknowledgment of the need for clarity on how pressure changes with fluid movement.
- #2
gneill
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It looks like P1 is meant to be the pressure at the water/air interface in the tank. So, it's the same as the air pressure in the tank.
- #3
goldfish9776
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isn't the air pressure at water surface = atmospheric pressure , which is 85.6Pa ?gneill said:
- #4
gneill
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Nope. That would be the pressure at the open end of the "S" tube.goldfish9776 said:
The tank is a sealed enclosure except for the tube, and the enclosed air can have a different pressure than atmospheric.
- #5
goldfish9776
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ok , can you explain why the pressure at P1 is found by subtracting the ρ water (gh2) and ρ(oil)(gh1) and plus ρ(mercury)(gh3) ??gneill said:
- #6
gneill
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Sure. The calculation follows a path from the open air at the open end of the S-tube to a point where the pressure is that of the water/air interface. In the system, horizontal lines through the fluids are lines of equal pressure. Look at the path described in orange:
Edit: Modified picture to describe a pressure change path from atmosphere to tank water surface with labels so points with equal pressures can be seen.
Edit: Modified picture to describe a pressure change path from atmosphere to tank water surface with labels so points with equal pressures can be seen.
Last edited:
- #7
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If looks to me like they have the h2 and the h1 incorrectly switched in the equation.
Chet
Chet
- #8
gneill
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I think you are right. I hadn't written out and simplified the full path equation before, now I have and I agree with you. Thanks for catching that.Chestermiller said:
I've modified the diagram in my previous post to reflect the full path. Points with the same letter labels are at the same pressure. The OP should be able to follow the path summing the pressure changes, then simplify the result.
- #9
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He also needs to recognize that moving upward lowers the pressure and moving downward increases the pressure. I'm wondering if he is aware of this.
- #10
goldfish9776
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so P1 = Patm +ρ (water)gh2 - ρ(oil)g(h1+h2) + ρ(oil)gh1 - ρ(water)g(h1+h2) + ρ(mercury)gh3gneill said:
P1 = Patm - ρ(water)gh1 - ρ(oil)gh2 + ρ(mercury)gh3 ?
- #11
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Yes. That's correct.goldfish9776 said:
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