Pressure at the bottom of a cube immersed in two liquids

In summary, the conversation discusses the correct values to use in calculating hydrostatic pressure at the bottom of a cube submerged in oil and water. The correct approach is to use a - h = 0.1 - 0.02 = 0.08 m as the depth of oil, rather than d = 0.2 m. This is because the height of the cube in the oil should be included in the calculation. The resulting pressure is the "gauge" pressure relative to the ambient pressure in the air above the oil layer.
  • #1
songoku
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Homework Statement
Please see the diagram below

A cube with side a = 0.1 m is immersed in 2 liquids as shown (upper liquid is oil and lower liquid is water). The value of h is 0.02 m and the value of d is 0.2 m

Find the hydrostatic pressure at the bottom of the cube
Relevant Equations
Hydrostatic pressure = ρ . g . h
1602848978219.png


I am not sure about value of depth I need to use. What I did:

Hydrostatic pressure at bottom of cube = hydrostatic pressure by oil + hydrostatic pressure by water

= ρoil . g . d + ρwater . g . h

Is it correct I use value d = 0.2 m for depth of oil and value of h = 0.02 m for depth of water to calculate the pressure?

Thanks
 
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  • #2
songoku said:
Is it correct I use value d = 0.2 m for depth of oil and value of h = 0.02 m for depth of water to calculate the pressure?
Yes. That is the correct approach and the correct values to use.
 
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  • #3
jbriggs444 said:
Yes. That is the correct approach and the correct values to use.

Just now the teacher said my answer is wrong, h = 0.02 m is correct but it is wrong to use d = 0.2 m as the depth of oil. Instead, I should use a - h = 0.1 - 0.02 = 0.08 m as the depth of oil because that is the height of the cube in the oil.

I don't understand why I should use a - h , I think all height of oil should be included in calculating the pressure at bottom of the cube because all height of oil exerts pressure?

Thanks
 
  • #4
You are right and your teacher is wrong.
 
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  • #5
Thank you very much jbriggs444 and Chestermiller
 
  • #6
And that calculated pressure is the "gauge" pressure, that is, the pressure relative to the ambient pressure in the air located above the layer of oil.
 
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Related to Pressure at the bottom of a cube immersed in two liquids

1. What is the formula for calculating the pressure at the bottom of a cube immersed in two liquids?

The formula for calculating the pressure at the bottom of a cube immersed in two liquids is P = ρgh, where P is the pressure, ρ is the density of the liquid, g is the acceleration due to gravity, and h is the height of the liquid column.

2. How does the pressure at the bottom of a cube immersed in two liquids compare to the pressure at the top?

The pressure at the bottom of a cube immersed in two liquids is greater than the pressure at the top. This is because the pressure at any point in a fluid is directly proportional to the depth of the fluid above it.

3. Does the density of the liquids affect the pressure at the bottom of the cube?

Yes, the density of the liquids does affect the pressure at the bottom of the cube. The greater the density of the liquid, the greater the pressure at the bottom of the cube.

4. How does the height of the liquid column affect the pressure at the bottom of the cube?

The height of the liquid column directly affects the pressure at the bottom of the cube. The higher the liquid column, the greater the pressure at the bottom of the cube.

5. Can the pressure at the bottom of the cube be negative?

No, the pressure at the bottom of the cube cannot be negative. Pressure is a scalar quantity and can only have positive values. However, it can be lower than the pressure at the top of the cube if the density or height of the liquid column is lower.

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