

Introduction Pressure is defined as a force per unit area. In an equation, that's That's the mathematical definition, but what does it mean? Here are some examples from everyday life:
What causes pressure? It's just atoms and molecules bashing into each other. Water molecules at the bottom of the swimming pool bouncing off the molecules of your head, air molecules bouncing off the rubber of a tire's inner tube, shoe molecules bouncing off the water molecules of snow, iron atoms of a knife bouncing off chicken molecules. It is the normal force — our old frind F_{N} — divided by area. The pressure of a fluid operates normal (perpendicular) to the surface, regardless of the surface's orientation. This is called Pascal's Principle, after its discoverer Blaise Pascal (French, 16231662). The atoms bang against each other because either

Activities & Practice
1. Women wearing high heels have a difficult time walking across lawns. Why?
2. Here's a video mystery: can you explain why the balloon is so hard to pop? 
Atmospheric Pressure At the bottom of a swimming pool, the pressure is equal to the weight of the overlying water divided by the area that weight is pressing against. The same idea applies in the atmosphere. For every square meter of the surface of the Earth, the full weight of all the air above that square meter, extending all the way up to space, is pressing down. This is called atmospheric pressure. Atmospheric pressure is less when you go up a mountain, because the higher you go the less air is above you. This is why air is denser at lower altitudes; the greater pressure squeezes more air molecules into each cubic centimeter. In class we recreate the 1650 Magdeburg experiment, in which Otto von Guericke demonstrated the existence of air pressure and his invention of the air pump. Two hemispheres are joined together and the air between them removed, creating a vacuum inside. Atmospheric pressure on the outside presses the two hemispheres tightly together, making them very difficult to separate. Read more about the Magdeburg experiment in the Wikipedia article "Magdeburg Hemispheres." When you go flying, or drive up a mountain road, it feels like your head is going to pop. There is some air inside your head, in the sinuses and inner ear. On the ground, the air pressure inside those cavities is equal to the atmospheric pressure outside your head. The net force is zero and you feel fine. But when you suddenly gain altitude, the outside air pressure decreases rapidly. The pressure inside your head is greater than outside, creating a net force outwards that can be painful. Eustachian tubes connect your mouth (and the atmosphere) to the inside of your head, allowing air molecules to flow from high pressure to low pressure, equalizing the pressure. That's why you feel OK after a while. You can speed up that process by chewing gum: the movement of the jaws flexes the Eustachian tubes, helping the air bubbles work their way through. Far outside the Earth's atmosphere, space itself is essentially a vacuum, with almost no pressure because there are almost no gas atoms.


Units Pressure is measured in a variety of units. In SI, the standard unit is the N/m², which is also called the Pascal (abbreviated Pa) in honor of Blaise Pascal. A bar is equal to 100,000 Pa; a millibar is more commonly used, and is equal to 100 Pa. The usual English unit for pressure is the pound/inch², commonly abbreviated psi. Atmospheric pressure is measured with barometers, of which there are two types: liquidcolumn and anaeroid. Pressure can be indicated by the height of a mercury (Hg) column in a liquidcolumn barometer (see diagram, below left), in either millimeters or inches. Liquidcolumn barometers are not terribly common, because they are large and inconvenient, not to mention that the mercury is toxic. Instead, you are more likely to own or see an aneroid barometer (see photo, above right). Here's a diagram showing how an aneroid barometer works. The average atmospheric pressure at sea level is
The decrease of air pressure with increasing altitude is used in aircraft altimeters. They are essentially aneroid barometers, only instead of reading one of the standard pressure units above, display altitude.

2. A standardsize brick is 2.25" x 3.5" x 8" and weighs 3.5 pounds. (a) What is the pressure exerted, in psi, by a brick laying flat on a table? (b) What is the pressure it exerts if standing up on one end? (c) Convert both previous answers into Pascals.

Example A standard "twobyfour" is actually 1.5" x 3.5". An eightfoot length of this wood weighs about 9 pounds. (a) How much pressure, in psi, is it exerting on the ground, if stood on end? (b) Convert your answer to Pascals. (a) The area of the end of the board is 1.5 inch x 3.5 inch = 5.25 inch².
(b) Use the factorlabel method, and don't forget to square the inchestometers conversion factor. 

Example How much force does the atmosphere exert on the outside surface of a square window, 2.0 feet on a side. Since P = F/A, then F = P·A. We'll use barbaric units, since that's what we were given. Atmospheric pressure is 14.7 lb/in^{2}, so we need to know the area in square inches. The side of the window is 24 inches, so the area is (24 inches)^{2} = 576 in^{2}.

3. If the atmosphere is pressing in on this averagesize window with 8500 pounds of force, how come windows don't break from the pressure. 
Fluid Pressure For a fluid of constant density ρ on a planet with gravitational field strength g, the pressure at a depth h is equal to Proof: Pressure is the weight of fluid pressing down on every unit of area at depth h. Consider a horizontal area A, and we'll calculate the weight of the fluid in the column above that area.

4. How deep do you have to go in a swimming pool in order for there to be one atmosphere's worth of pressure due to the water? 
Additional Activities & Practice 6. How deep would you have to dive into a pool of mercury, in order for the added pressure to equal one atmosphere? 7. The deepest point of Earth's oceans, the bottom of the Mariana Trench, is 10,923m deep! The US Navy research submersible Trieste was the first vessel to reach this point, in 1960. What pressure did the Trieste have to withstand? Give your answer in psi, Pa, and atmospheres. (NOTE: the density of seawater is about 1025 kg/m³.) 8. Which one of these locations has the greatest pressure? (A) ten meters below the surface of Lake Brandt, (B) ten meters below the surface of Lake Michigan, (C) ten meters below the surface of a deep swimming pool? 9. A cube, one meter on a side, is located with its top 20 meters below the surface of a freshwater lake. (a) What is the pressure at the top of the cube? (b) What is the force pressing down on the top of the cube? (c) What is the pressure at the bottom of the cube? (d) What is the force pressing up on the bottom of the cube? (e) What is the net force of forces (b) and (d)? 10. This suctioncup ball is stuck on a window. Can you explain how suction cups work? 11. The density of air near the surface of Earth, on a typical day at 20°C, is about 1.2 kg/m^{3}. How much height do you need to rise, in order for the air pressure to decrease by 1.0 Pa? 12. Write a paragraph explaining in detail why this happens? Here's a larger event, same idea. 
