Pressure and Height in Liquids: A Container with Different Diameter Tubes

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SUMMARY

The discussion centers on a physics problem involving a container with two tubes of different diameters, specifically tube A (wider) and tube B (narrower), where the diameter of tube A is four times that of tube B. The problem requires calculating the rise of mercury in tube A and the fall in tube B after water is added to tube B to a depth of 70 cm. The key equation used is P = hρg, which relates pressure, height, density, and gravitational acceleration. Participants clarify that while the pressure remains constant across both tubes, the heights of the liquid columns will differ due to the diameter variation.

PREREQUISITES
  • Understanding of hydrostatic pressure principles
  • Familiarity with the equation P = hρg
  • Knowledge of fluid mechanics concepts, particularly in U-tube manometers
  • Basic algebra for solving height and pressure equations
NEXT STEPS
  • Study the principles of hydrostatics in fluid mechanics
  • Learn about U-tube manometers and their applications
  • Explore the effects of fluid density on pressure calculations
  • Practice solving problems involving pressure differences in fluids of varying diameters
USEFUL FOR

This discussion is beneficial for physics students preparing for exams, particularly those studying fluid mechanics and hydrostatics, as well as educators seeking to clarify concepts related to pressure in liquids.

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Homework Statement


A container consists of two tubes, tube A which is wider and tube B which is narrower. The diameter of a tube A is four times that of tube B. Some mercury is poured into the container first and then water is added into the thin tube until it reaches a depth of 70 cm.

a) By how much does the mercury in the big tube rise?

b) By how much does the mercury in the thin tube fall?

c) If the water is poured into the wide tube, what is the difference in height of the mercury level between the narrow tube and the wide tube?



Homework Equations


P=hρg
(though I think no calculations are needed)


The Attempt at a Solution


I really have no idea on how to do this, but I'm guessing that the heights are the same since the pressure is the same?
Please help! This is my own revision and not a homework because my physics paper for my o-level is coming next week.
 
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Is the situation a U-tube manometer with a diameter change?
 
It's as stated a container with diameter change.
What I understand is that the pressure is not affected by shape.
So the heights should be equal, right?
The problem is I don't know how to get the length.
 

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