How Do Water and Mercury Pressures Compare in Different Height Containers?

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SUMMARY

The discussion focuses on comparing the pressures exerted by water and mercury in two different height containers. Using the formula P = pgh, the pressure of water at 10 cm is calculated to be 10 g/cm², while the pressure of mercury at 5 cm is 70 g/cm². The conclusion drawn is that the ratio of pressures is 7:1, indicating that mercury exerts significantly more pressure than water at the specified heights. Additionally, the discussion clarifies that when considering total pressure, atmospheric pressure must be factored in for a complete comparison.

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  • Understanding of fluid mechanics principles
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  • Knowledge of the densities of water and mercury
  • Basic concepts of atmospheric pressure
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Homework Statement


If you have two containers one with water (filled to 10cm) and one with mercury (5cm), how do the pressure of water and mercury compare?

p of water = 1 gm/cm^3
p of mercury = 14 gm/cm^3

Homework Equations



P = pgh where p is density, and h is height

The Attempt at a Solution



P water = (1)(10) = 10 (I am not include gravity since its the same for both and they are only looking for a ratio)

P mercury = (14)(5) = 70

Would the correct answer be: 7*Pwater = Pmercury ?
 
Last edited:
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Correct, although if they were looking for the RATIO of total pressure at the bottom of the two containers then you do have to consider the air pressure.
70 / 10 is not quite the same as 70+atm / 10+atm (ps. 1 atm is roughly 1000g/cm^2)
The DIFFERENCE between the pressures doesn't depend on the atmosphere.
 

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