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Question

The container shown is filled with oil. It is open to the atmosphere on the left.
a. What is the pressure at point A?
b. What is the pressure difference between points A and B? Between points A and C?

Answer “The container shown is filled with oil. It is open to the atmosphere on the left.”.

Pascal’s Law:

For fluids that are in a container at rest the pressure of the liquid is determined through Pascal’s Law. In accordance with Pascal’s law that the pressure of the fluid rises with depth. Pressure at the base of the vessel caused by the fluid is thus higher than the pressure in the middle of the liquid.

Answer

Relevant knowledge

Question:

The axis of a cylindrical container is vertical. The container is filled with an equal mass of water and oil. The oil floats on top of the water, and the open surface of the oil is at a height h above the bottom of the container. What is the height, h, if the pressure at the bottom of the water is 11 kPa greater than the pressure at the top of the oil? Assume the oil density is 875 kg/m³.

Answer:

Given Data:

• mass of water = mass of oil in the container

• Density of oil, ρ_o =875 kg/m³
• Pressure difference between the bottom of the water and the top of the oil, P_bottom −P_top =11 kPa =11×10³ Pa

Taking the density of water as ρ_w =1000 kg/m³

The cross-sectional area of the cylindrical container to be A

Finding the height (h) of the top surface of the oil from the bottom of the container

Consider the hights of the water columns and oil columns to be h_w and h_o respectively.

Now, Applying Pascal’s law:

The difference in pressure between the bottom of the container and the top of the oil surface:

Thus, the height of the water column is determined as:

The height of top surface of the oil from the bottom of the container is:

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