Pressure Calculations at Points A and B using Pascal's Paradox

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SUMMARY

This discussion focuses on calculating pressures at points A and B using Pascal's Paradox, specifically in the context of gage pressure where atmospheric pressure is ignored. The relevant equations include P = pgh and P = sg x specific weight of water x height. The user initially calculates the pressure at point A as 0 and seeks assistance for point B, assuming equilibrium and equal surface areas in the tanks. The conversation emphasizes the need to equate the weights of oil and atmospheric pressure to derive the pressure at point B.

PREREQUISITES
  • Understanding of gage pressure and its implications in fluid mechanics.
  • Familiarity with Pascal's Paradox and its applications in pressure calculations.
  • Knowledge of hydrostatic pressure equations, specifically P = pgh.
  • Basic principles of fluid equilibrium and weight balance in connected tanks.
NEXT STEPS
  • Study the applications of Pascal's Paradox in various fluid systems.
  • Learn about hydrostatic pressure calculations in different fluid scenarios.
  • Explore the implications of gage pressure versus absolute pressure in fluid mechanics.
  • Investigate the effects of surface area on pressure distribution in connected tanks.
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Students and professionals in fluid mechanics, engineers working with hydraulic systems, and anyone involved in pressure calculations in fluid dynamics.

Brownie
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Homework Statement


The points of interest are at point A and B, I want to calculate the pressures at that point. I am working in gage pressure so we can ignore atmospheric pressure.

Homework Equations


P = pgh
P = sg x specific weight of water x height

The Attempt at a Solution


Attempting a first because I am stuck at a.
I used Pascal paradox. The level I am using is at the level of the open tank oil level. Left side is p1 and right is p2.

Pressure at point 1 is = 0 (as I’m working in gage pressure)

I’m stuck at point 2.

I think I would need a to solve b
 

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Brownie said:

Homework Statement


The points of interest are at point A and B, I want to calculate the pressures at that point. I am working in gage pressure so we can ignore atmospheric pressure.

Homework Equations


P = pgh
P = sg x specific weight of water x height

The Attempt at a Solution


Attempting a first because I am stuck at a.
I used Pascal paradox. The level I am using is at the level of the open tank oil level. Left side is p1 and right is p2.

Pressure at point 1 is = 0 (as I’m working in gage pressure)

I’m stuck at point 2.

I think I would need a to solve b
You have left out a lot here, so I am going to make some assumptions:
1) The system is in equilibrium
2) The pipe is full of oil
3) The surface area in the two tanks is the same

Please let me know if those assumptions are not correct. I am not sure how you plan to use the hydrostatic paradox here because the levels in the two tanks are not equal. Let's talk about the pressure at point B. If we assume that the two tanks have the same area, then you can equate the weight of the oil in the tank on the left plus the weight of the entire atmosphere above it with the weight of the oil and air in the tank on the right. You should be able to solve for the pressure at point B.
 

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