- #1
Solving Pressure Puzzle: Find P1 in Diagram
- Thread starter goldfish9776
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SUMMARY
The pressure P1 at the water/air interface in a sealed tank is calculated using the formula P1 = Patm - ρ(water)gh1 - ρ(oil)gh2 + ρ(mercury)gh3. This equation accounts for the atmospheric pressure (Patm) and the hydrostatic pressures exerted by water, oil, and mercury at their respective heights (h1, h2, h3). The discussion clarifies that the pressure at P1 is not equal to atmospheric pressure due to the sealed nature of the tank, which allows for different internal pressures.
PREREQUISITES- Understanding of hydrostatic pressure principles
- Familiarity with fluid density (ρ) and gravitational acceleration (g)
- Knowledge of pressure measurement in sealed systems
- Ability to interpret fluid diagrams and pressure paths
- Study hydrostatic pressure calculations in fluid mechanics
- Learn about pressure differences in sealed versus open systems
- Explore the implications of fluid density on pressure calculations
- Investigate the use of pressure measurement devices in various applications
Students studying fluid mechanics, engineers working with fluid systems, and anyone involved in pressure measurement and analysis in sealed environments.
- #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.
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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.
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If looks to me like they have the h2 and the h1 incorrectly switched in the equation.
Chet
Chet
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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.
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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 ?
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Yes. That's correct.goldfish9776 said:
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