Video: Calculating the Upward Pressure on a Mercury Column

The apparatus shown in the diagram is used to measure atmospheric pressure. Find the upward pressure on the mercury column. Use a value of 13,595 kg/m³ for the density of mercury.

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Video Transcript

The apparatus shown in the diagram is used to measure atmospheric pressure. Find the upward pressure on the mercury column. Use a value of 13,595 kilograms per meters cubed for the density of mercury.

In the diagram, we have an apparatus which is filled with liquid mercury. The apparatus contains a test tube that is filled with mercury as well as a dish that’s filled with mercury. The dish is open to the atmosphere such that the atmosphere applies a pressure as represented by the blue arrows onto the liquid mercury. This atmospheric pressure provides the upward pressure on the mercury column inside the test tube.

How do we find this pressure? Well, we know that the atmospheric pressure is equal to the pressure of the liquid column of mercury inside the test tube. And we know that the pressure of a fluid 𝑃 is equal to the density of the fluid 𝜌 times the acceleration due to gravity 𝑔 times the height of the fluid ℎ. So if we calculate the pressure of the liquid column of mercury based on the density of mercury, acceleration due to gravity, and height of the column, we will therefore know the atmospheric pressure.

The pressure of our column liquid mercury is equal to the density of mercury, 13,595 kilograms per meter cubed, times the acceleration due to gravity, 9.81 meters per second squared, times the height of the liquid mercury, 0.760 meters. When we multiply out these three values, we get a pressure of 101,358.88 pascals.

Looking at our values, we can see that the acceleration due to gravity and the height of our liquid column are reported to three significant figures. Therefore, we must report our answer to three significant figures, which rounds our pressure to 101,000 pascals. When dealing with such large numbers, we typically use a prefix to make the numbers more manageable. In this case, we can use the prefix kilo-, which means 1,000. So one kilopascal is the same thing as 1,000 pascals. So 101,000 pascals becomes 101 kilopascals. Our final answer for the upward pressure on the mercury column is 101 kilopascals.

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