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

[Gear2d]

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 ?

 

[mgb_phys]

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.

 

[baba89]

I would like to clarify that the pressure of a fluid is not solely dependent on its density, but also on the depth or height of the fluid column. In this case, the pressure of water and mercury cannot be compared directly without taking into account the height of the fluid column.

To accurately compare the pressure of water and mercury, we need to use the equation P = pgh, where P is pressure, p is density, g is the acceleration due to gravity, and h is the height of the fluid column.

Using this equation, we can calculate the pressure of water and mercury as follows:

Pwater = (1)(9.8)(10) = 98 Pa

Pmercury = (14)(9.8)(5) = 686 Pa

Therefore, the pressure of mercury is approximately 7 times greater than the pressure of water. This is because mercury is a denser fluid and has a greater height in the container compared to water.

In conclusion, the correct answer would be: Pmercury = 7*Pwater. It is important to consider the height of the fluid column when comparing the pressures of different fluids.