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The container shown in (Figure 1) is filled with oil (ρ = 900 kg/m3 ). It is open to the atmosphere on the left. What is the pressure at point A? What is the pressure difference between points A and B? What is the pressure difference between points A and C?

The container shown in (Figure 1) is filled with oil (ρ = 900 kg/m3 ). It is open-example-1
User Jack Casas
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1 Answer

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The pressure at point A is equal to the atmospheric pressure, which is typically about 101.3 kPa.

The pressure difference between points A and B is equal to the hydrostatic pressure of the oil column between the two points, which is calculated to be 1764 Pa. Therefore, the pressure at point B is 103.064 kPa.

The pressure difference between points A and C is equal to the hydrostatic pressure of the entire oil column in the container, which is calculated to be 6562.5 Pa. Therefore, the pressure at point C is 6663.8 kPa.

Pressure at point A

The pressure at point A is equal to the atmospheric pressure, since the container is open to the atmosphere on the left. Atmospheric pressure is typically about 101.3 kPa, so the pressure at point A is 101.3 kPa.

Pressure difference between points A and B

The pressure difference between points A and B is equal to the hydrostatic pressure of the oil column between the two points. The hydrostatic pressure is calculated using the following equation:

P = ρgh

where:

P is the pressure in Pascals (Pa)

ρ is the density of the fluid in kilograms per cubic meter (kg/m³)

g is the acceleration due to gravity in meters per second squared (m/s²)

h is the height of the fluid column in meters (m)

In this case, the density of the oil is 900 kg/m³, the acceleration due to gravity is 9.81 m/s², and the height of the oil column between points A and B is 0.2 m. Therefore, the pressure difference between points A and B is calculated as follows:

P = (900 kg/m³)(9.81 m/s²)(0.2 m) = 1764 Pa

Therefore, the pressure at point B is 101.3 kPa + 1764 Pa = 103.064 kPa.

Pressure difference between points A and C

The pressure difference between points A and C is equal to the hydrostatic pressure of the entire oil column in the container. The hydrostatic pressure is calculated using the following equation:

P = ρgh

where:

P is the pressure in Pascals (Pa)

ρ is the density of the fluid in kilograms per cubic meter (kg/m³)

g is the acceleration due to gravity in meters per second squared (m/s²)

h is the height of the fluid column in meters (m)

In this case, the density of the oil is 900 kg/m³, the acceleration due to gravity is 9.81 m/s², and the height of the oil column between points A and C is 0.75 m. Therefore, the pressure difference between points A and C is calculated as follows:

P = (900 kg/m³)(9.81 m/s²)(0.75 m) = 6562.5 Pa

Therefore, the pressure at point C is 101.3 kPa + 6562.5 Pa = 6663.8 kPa.

User Ahasanul Haque
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