Pressure at the bottom of cylinder immersed in two liquids

In summary, a solid cylinder with base area A, height 20 cm and density 0.8 g/cm3 floats in a boundary of oil and water with a density of 0.6 g/cm3. To find the height of the cylinder immersed in each liquid, it is equal to 10 cm. The hydrostatic pressure at the bottom of the cylinder can be determined by adding the pressure due to 30 cm of oil and 10 cm of water.
  • #1
songoku
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Homework Statement


A solid cylinder has base area A, height 20 cm and density 0.8 g/cm3, floats in the boundary of oil and water. If the density of oil 0.6 g/cm3, find
a. the height of cylinder that immersed in oil and water
b. the hydrostatic pressure at the bottom of the cylinder if the height of oil = 3 times height of cylinder immersed in water


Homework Equations


P = ρgh
W = mg
Fa = ρgV


The Attempt at a Solution


a. I am able to do this one. I got the height that immersed in each liquid = 10 cm

b. So the height of oil = 30 cm. How to find the hydrostatic pressure at the bottom of cylinder? Does the oil give pressure for the bottom part?

Water will gives pressure at the bottom which is equal to ρgh = 1000 x 10 x 0.1 = 1000 Pa

I do not know what to do next...I even don't know whether 1000 Pa is the final answer or not...

Thanks
 
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  • #2
The oil pushes down on the top and also increases the pressure on the bottom pushing up. So if there is 30 cm of oil total, the pressure at the bottom can be determined by adding the pressure due to 30 cm of oil plus the 10 cm of water.
 
  • #3
LawrenceC said:
The oil pushes down on the top and also increases the pressure on the bottom pushing up. So if there is 30 cm of oil total, the pressure at the bottom can be determined by adding the pressure due to 30 cm of oil plus the 10 cm of water.

OK thanks :smile:
 

FAQ: Pressure at the bottom of cylinder immersed in two liquids

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

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

How does the density of the liquids affect the pressure at the bottom of the cylinder?

The density of the liquids has a direct impact on the pressure at the bottom of the cylinder. The higher the density of the liquid, the greater the pressure will be at the bottom of the cylinder.

What happens to the pressure at the bottom of the cylinder if the height of the liquids is increased?

If the height of the liquids is increased, the pressure at the bottom of the cylinder will also increase. This is because the weight of the liquid column above the bottom of the cylinder increases, resulting in a greater pressure being exerted on the bottom of the cylinder.

Does the surface tension between the two liquids affect the pressure at the bottom of the cylinder?

Yes, the surface tension between the two liquids does affect the pressure at the bottom of the cylinder. The surface tension adds an additional force that must be taken into account when calculating the pressure at the bottom of the cylinder.

How does the shape of the cylinder affect the pressure at the bottom?

The shape of the cylinder does not have a significant effect on the pressure at the bottom. As long as the height and radius of the cylinder are consistent, the pressure at the bottom will remain the same regardless of the shape.

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