Pressure at the bottom of a cube immersed in two liquids

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SUMMARY

The calculation of hydrostatic pressure at the bottom of a cube immersed in two liquids, oil and water, requires accurate depth measurements. The correct formula is: hydrostatic pressure = ρoil . g . d + ρwater . g . h. The depth of oil should be calculated as d = 0.08 m, not 0.2 m, as the height of the cube submerged in oil is 0.1 m and the water depth is 0.02 m. The resulting pressure calculated is the gauge pressure, which is the pressure relative to the ambient air pressure above the oil.

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  • Familiarity with fluid density (ρ) and gravitational acceleration (g)
  • Knowledge of gauge pressure concepts
  • Basic skills in algebra for pressure calculations
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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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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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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
 
You are right and your teacher is wrong.
 
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Thank you very much jbriggs444 and Chestermiller
 
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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