### Summary

Air pressure is pushing on us all the time although we do not usually notice it. In this activity, students learn about the units of pressure and get a sense of just how much air pressure is pushing on them.### Engineering Connection

Engineers take into consideration the existence of ambient air pressure in the design of everything from airplanes to chemicals. The weight of air is an important factor when developing the structure of aircraft and spacecraft. Environmental engineers pay careful attention to air pressure when designing wind turbines. Chemical engineers need to know how a chemical reacts in different air pressures. When designing anything that moves through the air, engineers analyze it to see how it reacts to air pressure.

###
Educational Standards
Each *TeachEngineering* lesson or activity is correlated to one or more K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in *TeachEngineering* are collected, maintained and packaged by the *Achievement Standards Network (ASN)*,
a project of *D2L* (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; *e.g.*, by state; within source by type; *e.g.*, science or mathematics;
within type by subtype, then by grade, *etc*.

Each *TeachEngineering* lesson or activity is correlated to one or more K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in *TeachEngineering* are collected, maintained and packaged by the *Achievement Standards Network (ASN)*,
a project of *D2L* (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; *e.g.*, by state; within source by type; *e.g.*, science or mathematics;
within type by subtype, then by grade, *etc*.

###### Next Generation Science Standards: Science

- Plan an investigation to provide evidence that the change in an object's motion depends on the sum of the forces on the object and the mass of the object. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?

###### Common Core State Standards: Math

- Fluently divide multi-digit numbers using the standard algorithm. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?

###### International Technology and Engineering Educators Association: Technology

- Knowledge gained from other fields of study has a direct effect on the development of technological products and systems. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?

###### Colorado: Math

- Graph points on the coordinate plane to solve real-world and mathematical problems. (Grade 5) Details... View more aligned curriculum... Do you agree with this alignment?
- Solve real-world and mathematical problems involving the four operations with rational numbers. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?

###### Colorado: Science

- Use the particle model of matter to illustrate characteristics of different substances (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Explain that the mass of an object does not change, but its weight changes based on the gravitational forces acting upon it (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?

### Learning Objectives

After this activity, students should be able to:

- Explain that the atmosphere exerts a pressure on objects.
- Describe how the pressure of the atmosphere changes depending on where it is being measured (e.g., Denver or Boston), due to differences in altitude.
- Use algebraic methods to explore values of air pressure.
- Describe how engineers, when designing anything that moves through the air, must analyze it to see how it reacts to the air pressure.

### Materials List

Each student needs:

- 1 piece of paper
- pencil
- ruler
- Air Pressure Worksheet
- (optional) 1 gallon water

### Introduction/Motivation

Have you ever felt the pressure on your ears when you dive to the bottom of a swimming pool? The pressure in a pool increases with depth just as air pressure increases as you go deeper into the* sea of air* (atmosphere).The bottom of the *sea of air* is represented by sea level, while higher elevations represent shallower parts of the atmosphere. As you move to shallower parts of the atmosphere, such as the top of Mount Everest, the pressure decreases.

*Pressure* is measured in different units. Scientists and engineers typically use the metric unit Pascal (Pa). A Pascal is defined as the pressure exerted by 1 Newton weight (1 kg under the Earth's force of gravity) resting on an area of 1 square meter. Let's go through some of the common units used to measure* pressure *and their equivalents. I'll write out four different units, but many additional units exist to describe the amount of pressure.

At sea level, the atmospheric *air pressure* can be represented as any of the following: (*Write the units on the classroom board.*)

- 1.013 x 10
^{5}Pa (Pascal or N/m^{2}) - 1 atm (atmosphere)
- 760 mm Hg (millimeters of mercury)
- 14.7 lb/in
^{2}(psi – pounds force per square inch) (if 1-pound weight rests on 1-square inch of surface area, the pressure is 1 psi)

### Procedure

Background

*Pressure (P)* is defined as the amount of force (F) applied per unit area (A) or as the ratio of force to area:

**P= F/A** (equation 1)

The pressure an object exerts can be calculated if its weight (the force of gravity on an object) and the contact surface area are known. For a given force (or weight), the pressure it applies increases as the contact area decreases. (To better understand this, hold a large book flat on your outstretched hand and notice how much pressure the book puts on it. Next, try to balance the book on the tip of your index finger. How much pressure does it seem to exert now?) It is also important to note that** air pressure** decreases with increasing altitude. It is helpful to think of the atmosphere as a swimming pool, with the water representing the air.

Before the Activity

Gather materials and make copies of the Air Pressure Worksheet (1 per student) and the Pressure vs. Altitude Graph (a few to share).

With the Students

- In Denver, CO, the Earth's atmosphere has a force of about 12 pounds per square inch (psi). For reference, a gallon of milk or water weighs about 8 pounds. Have students make a 1-inch by 1-inch square with their hands. Now ask the students what a 2 x 2 square looks like, and ask them how many pounds would be pressing down on that square. Solving for the force in equation 1, students can see that by multiplying the area (4 in
^{2}) by the pressure gives 48 pounds as an answer.*(Note: multiply the length times the width to get the area of the square.)* - Ask students how many pounds would be pressing on a 3 x 3 square? (Answer: 108 lbs for an area of 9 in
^{2}.) A 4 x 4? (Answer: 192 lbs for an area of 16 in^{2}.) - Have students complete the Air Pressure Worksheet.
- Do the students see a pattern? What happens every time the area of the square increases by 1 in
^{2}? (Answer: The pounds of force increase by 12 for every 1 square inch increase in area. This is called a linear relationship. Linear means line; have students make a line graph plotting the area vs. the force so they see that it makes a straight line. See the worksheet for an example of the relationship between area and force.)

What happens every time the sides of the square are increased by 1 inch? (Answer: This is harder since the relationship is not linear. Every time you increase the length of the sides by one inch the force increases by more than 12 lbs. In fact, as the length of each side gets longer the increase in the force gets larger as well. When the length of the sides are 1 inch, the force is 12 lbs. If we increase the sides to 2 inches, the force becomes 48 lbs. This is an increase of 36 lbs. If we add another inch and make each side 3 inches, the force becomes 108 lbs, which is an increase of 60 lbs. If we plot the length of each side vs. the force, we see that the relationship is not linear. The line curves up, which is known as an* exponential relationship*.)

- The average pressure on a middle school student is 24,000 pounds! Ask the students why they do not feel the 24,000 pounds, and why they are not crushed. (Answer: The air inside the body [from breathing, through the skin, ears, etc.] balances out the pressure on the outside of the body.)
- The average force of the atmosphere at sea level is 15 lbs per square inch (almost two gallons of milk). Have students repeat their calculations for the sea level pressure. (Cities to use: New York City, 87ft; San Diego, 3 ft; and Boston, 10ft. All are very close to sea level.)
- Have students look at the Pressure vs. Altitude Graph and make pressure predictions for several places based on different altitudes. (For example: Chicago, IL [580 ft], Las Vegas, NV [2,030 ft], Leadville, CO [10,177 ft], Mt. Whitney, CA [14,495 ft], Mt. Everest [29,035 ft], airliner cruising at 30,000 ft.) Have students estimate the air pressure at 1 mile below sea level if no ocean water was present (this number is not on the graph, which means students must extend the line below the zero altitude line to estimate it).

### Attachments

### Assessment

Pre-Activity Assessment

*Discussion Question:* Solicit, integrate and summarize student responses.

- Review Bernoulli's principle. Make sure everyone understands how Bernoulli's principle relates to pressure. (The faster a fluid moves, the less pressure it exerts.)
- Think about an airplane in motion. Is the air pressure only acting on the top of the plane? (Answer: No, it is acting on the entire surface of the plane.) Does this air pressure affect the speed of the plane? (Answer: Yes, at higher pressures, air is denser, and more air molecules exist to run into, and thus slow the plane down. This is a primary reason that planes fly at such high altitudes, even though ozone can be a problem for those inside the plane, compared to flying at 25,000 ft.)

Activity Embedded Assessment

*Worksheet:* Have students use the Air Pressure Worksheet to record measurements and follow along with the activity. After students have finished their worksheets, have them compare answers with their peers.

Post-Activity Assessment

*Graphing:* Have students use the information from their worksheets to create line graphs of the relationship between area and force. Plot area (in^{2}) on the x-axis and force (ponds) on the y axis. Ask students or teams to explain what is happening in their graphs in their own words.

### Activity Extensions

Have students complete an Air Pressure Worksheet for planets where the air pressure is different than on Earth. Examples are Jupiter (735,000,000 psi), Venus (1,325 psi), Mars (0.25 psi), Pluto (0.000147 psi). Have students discuss what kinds of challenges these pressures might impose on manned and unmanned missions to these planets.

### Activity Scaling

For older students:

- Rather than telling students that the amount of air pressure pushing on them is about 24,000 lbs, tell them the average surface area for an elementary school student is about 2000 in
^{2}and have them calculate the pressure themselves. - Have students calculate the force for other areas such as 1 square foot (144 in
^{2}), a football field (approximately 8,000,000 in^{2}). - Have students plot square inches vs. force on a graph.

### References

### Contributors

Tom Rutkowski; Alex Conner; Geoffrey Hill; Malinda Schaefer Zarske; Janet Yowell### Copyright

© 2004 by Regents of the University of Colorado### Supporting Program

Integrated Teaching and Learning Program, College of Engineering, University of Colorado Boulder### Acknowledgements

The contents of this digital library curriculum were developed under grants from the Fund for the Improvement of Postsecondary Education (FIPSE), U.S. Department of Education and the National Science Foundation (GK-12 grant no. 0338326). However, these contents do not necessarily represent the policies of the DOE or NSF, and you should not assume endorsement by the federal government.