The student will know:
- How atmospheric pressure is measured.
- How gauge pressure is defined.
atmospheric pressure: The pressure from the Earth's atmosphere.
barometer: The oldest design for scientifically measuring pressure.
gauge pressure: The pressure above the current atmospheric pressure.
Calculating pressure from gas is different than pressure from fluids, because gases change their density easily. The Earth's atmosphere is denser close to sea level, and gets less dense the higher you go. Thus, there is no simple relationship between the height of air and pressure. Indeed, the actual pressure at sea level often changes with the location, climate, and current weather. Human beings can detect the differences in air pressure when our altitude changes a few hundred feet. This is most noticeable when your ears pop when driving up or down a mountain, or taking a plane flight.
The oldest design for scientifically measuring pressure is the barometer, invented in 1643. The main part of it is just a glass tube closed at one end and open on the other, filled with liquid and put open side down in a dish. The closed end can hold liquid up, just like when you put your finger on the end of a straw, it lets you hold water in the straw. The open end has full atmospheric pressure pressing on it, while the sealed side has no pressure. The Figure below shows a mercury-filled barometer.
If the tube is filled with mercury and has no air, then the atmospheric pressure pushes on the top of the dish, lifting up the mercury in the tube that has no air pushing down on it from above. All suction works this way – it is really atmospheric pressure pushing, rather than the vacuum pulling. The mercury is stable when the atmospheric pressure on the mercury in the dish is equal to the hydrostatic pressure which the column of mercury exerts at the bottom of the tube.
Illustrative Example 1
So the pressure of one standard atmosphere hold a column of mercury with a height of 0.76 meters. As the atmospheric pressure changes, the height of the column of mercury changes.
Check Your Understanding
In the above experiment, if water had been used rather than mercury what would the height of the column of water have been?
Answer: Mercury is 13.6 times denser than water. So the atmosphere can support a column of water 13.6 times higher than a column of mercury.
A column of water 10.3 m high has the same weight as a column of mercury 0.76 m. Mercury barometers are therefore much more practical than water barometers.
In practice, most examples of pressure happen inside atmospheric pressure. When a faucet pushes out water, that water is pressing out against atmospheric pressure. The gauge pressure is the pressure above the current atmospheric pressure. For example, a completely deflated tire still has pressure on it. Atmospheric pressure is pushing on both the inside and outside of the tire. What matters is how much additional pressure we put in when the tire is inflated.
Check Your Understanding
1. A tire pressure gauge reads 32 pounds per square inch (psi) when measuring tire pressure. What is the total pressure in pounds per square inch?
Answer: Atmospheric pressure is 101,325 Newtons per square meter. To convert, we use:
- 1 pound = 4.45 newtons
- 1 inch = 0.0254 meters