Pressure at the bottom of a cube immersed in two liquids

[songoku]

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

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

= ρ_oil . g . d + ρ_water . 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

 

[jbriggs444]

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.

 

[songoku]

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

 

[Chestermiller]

You are right and your teacher is wrong.

 

[songoku]

Thank you very much jbriggs444 and Chestermiller

 

[gmax137]

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.