Calculating Atmospheric Pressure
As we’ve discussed (and illustrated in Slide Show 6.1.1–8), Earth’s atmospheric pressure at sea level is about the same as the pressure created by the weight of water in a 10-meter tall column. But how much is that? Let’s figure it out.
Step 1: Understand the problem. We know that we can measure atmospheric pressure in units of kilograms per square centimeter, representing the weight of the atmosphere above each square centimeter of surface. We also know that this must be the same as the pressure created by the weight of a 10-meter tall column of water. Therefore, we can answer this question by figuring out the weight of the water in a 10-meter tall column that sits above each square centimeter of the bottom. This will be easy if you remember that water has a density of 1 gram per cubic centimeter (1 g/cm3).
Step 2: Solve the problem. The 1 g/cm3 density of water tells us that if the water in any cup or vat were just 1 centimeter deep, then the weight of the water above each square centimeter would be 1 gram, creating a pressure of 1 gram per square centimeter. We can now find the pressure exerted by the 10-meter column of water as follows:
- Recall that 1 meter = 100 centimeters, which means that 10 meters =
- Therefore, water that is 10 meters deep must exert a pressure 1,000 times as much as water that is 1 centimeter deep.
- So because the 1-centimeter deep water exerts a pressure of 1 gram per square centimeter, the 10-meter column of water exerts a pressure of 1,000 grams per square centimeter.
- Recall that 1,000 grams is the same as 1 kilogram, so the water weight in the 10-meter tall column would exert a pressure of 1 kilogram per square centimeter.
Step 3: Explain your result. We’ve found that 10-meter tall column of water exerts a pressure due to its weight of 1 kilogram per square centimeter. We also know 10 meters is about the highest that a column of water will rise (at sea level), even in a tube with a perfect vacuum at the top, telling us that atmospheric pressure must equal the pressure of the water. We conclude that atmospheric pressure must be about 1 kilogram per square centimeter.
Check Your Skills
Suppose you try to pump water at a location high in the mountains, and you find that even with a perfect vacuum at the top, the water will rise no higher than 8 meters. What is the atmospheric pressure at your mountain location?
There are several ways students can answer the “check your skills” question, but the simplest is to note that the water weight in an 8-meter depth of water would exert 0.8 times as much pressure as that in a 10-meter depth. Therefore, the pressure due to the water weight is 0.8 kilograms per square centimeter, so this would be the atmospheric pressure at this altitude.
- Note that doing this example will help prepare students for understanding how atmospheric pressure declines with altitude.