Why is the pressure of two different liquids in a manometer the same?

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SUMMARY

The pressure in a manometer remains equal for two different liquids due to the principle of hydrostatic equilibrium. In the discussed scenario, the pressure exerted by water and oil is calculated using the formula P(water) = P(oil), represented as (ϱwater)gh = (ϱoil)gh. This equality holds because, at the bottom of the U-tube, the pressures must balance; any difference would cause fluid movement until equilibrium is restored. Understanding this concept is crucial for solving problems involving manometers and fluid statics.

PREREQUISITES
  • Understanding of hydrostatic pressure principles
  • Familiarity with the U-tube manometer design
  • Knowledge of fluid density (ϱ) and gravitational acceleration (g)
  • Basic algebra for manipulating pressure equations
NEXT STEPS
  • Study the concept of hydrostatic equilibrium in fluid mechanics
  • Learn about different types of manometers and their applications
  • Explore the effects of fluid density on pressure calculations
  • Investigate real-world applications of manometers in measuring pressure
USEFUL FOR

Students in physics or engineering, educators teaching fluid mechanics, and professionals involved in pressure measurement and analysis.

cherryrocket
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I just finished a question in which a u-shaped tube (manometer) is filled with water to a certain height. Another substance, in this instance, oil, is added to one side of the manometer. I was asked to find the height of the new substance. I used the formula P(water) = P(oil), or
(ϱwater)gh = (ϱoil)gh. So, I know how to solve it, but I don't really understand it. Why is the pressure of both substances the same? Thanks for your replies.
 
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Think about what happens at the bottom of the U-tube. What happens if the pressure on one side is greater than the pressure on the other at the bottom?
 

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