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Pressure is Force per Unit Area

by Ron Kurtus (revised 18 March 2006)

Pressure is the force on an object that is spread over a surface area. The equation for pressure is the force divided by the area where the force is applied. Although this measurement is straightforward when a solid is pushing on a solid, the case of a solid pushing on a liquid or gas requires that the fluid be confined in a container. The force can also be created by the weight of an object.

Questions you may have include:

• What is the pressure when a solid pushes on another solid?
• What happens when a solid pushes on a confined fluid?
• What happens when the force comes from gravity?

This lesson will answer those questions. There is a mini-quiz near the end of the lesson.

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Time = 4 min. 23 sec.

Pressure of solid on a solid

When you apply a force to a solid object, the pressure is defined as the force applied divided by the area of application. The equation for pressure is:

P = F/A

where

• P is the pressure
• F is the applied force
• A is the surface area where the force is applied
• F/A is F divided by A

For example, if you push on an object with your hand with a force of 20 pounds, and the area of your hand is 10 square inches, then the pressure you are exerting is 20 / 10 = 2 pounds per square inch.

Pressure equals Force divided by Area

You can see that for a given force, if the surface area is smaller, the pressure will be greater. If you use a larger area, you are spreading out the force, and the pressure (or force per unit area) becomes smaller.

Solid pressing on confined fluid

When a liquid or gas is confined in a container or cylinder, you can create a pressure by applying a force with a solid piston. The pressure created in the cylinder equals the force applied divided by the area of the piston: P = F/A.

In a confined fluid—neglecting the effect of gravity on the fluid—the pressure is the same throughout the container, pressing equally on all the walls. In the case of a bicycle pump, the pressure created inside the pump will be transmitted through the hose into the bicycle tire. But the air is still all confined.

Pressure is in all directions in a fluid

Increasing the force will increase the pressure inside the cylinder.

Caused by gravity

Since the weight of an object is a force caused by gravity, we can substitute weight in the pressure equation. Thus the pressure (P) caused by the weight (W) of an object is that weight divided by the area (A) where the weight is applied.

P = W/A

If you place a solid object on the floor, the pressure on the floor over the area of contact is the weight of the object divided by the area on the floor.

Pressure equals Weight divided by Area

Example with shoes

A good example of how a force on small area can result in a very high pressure is seen in women's shoes with high spiked heels. These types of shoes can cause damage to some floors due to the very high pressure on the floor at the heel.

An average shoe distributes the weight of the person over 20 square inches. Thus, a 100-pound person applies 100/20 = 5 pounds per square inch on the floor.

Since a spike-heel is only 0.25 square inches, the 100-pound person would be applying 100/0.25 = 400 pounds per square inch on the floor at the heel! In some cases, that is sufficient to damage the floor.

Fluid weight

If you put a liquid in a container, the weight of that liquid would be pressing on the bottom of the container similar to that of the weight of a solid object. The pressure on the bottom of the container would be the same as if the weight was from a solid: P = W/A.

The only difference is that pressure in a fluid goes in all directions. So the pressure on the sides at the bottom would be the same.

Gases and liquids exhibit pressure due to their weight at every point in the fluid.

Summary

Pressure is the force on an object that is spread over a surface area. The equation for pressure is P = F/A. Pressure can be measured for a solid is pushing on a solid, but the case of a solid pushing on a liquid or gas requires that the fluid be confined in a container. The force can also be created by the weight of an object.

Answers to Readers' Questions

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Resources

The following resources provide information on this subject:

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Books

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Miscellaneous

Mini-quiz to check your understanding

1. What is the pressure on 2 square meter surface where you push with a force of 6 Newtons?

2. Why must a liquid be confined when applying a force with a solid piston?

3. What is the pressure on the ground caused by a container of 2 pounds of water?

If you got all three correct, you are on your way to becoming a Champion in Physical Science. If you had problems, you had better look over the material again.

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Pressure is Force per Unit Area