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# 4.32: Pascal's Law

Difficulty Level: At Grade Created by: CK-12
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Did you ever watch someone make balloon animals like this poodle? When you blow up a balloon, you force air inside the balloon through a small opening. The air spreads out and presses against the inside of the balloon, forcing it to expand. Pressure always spreads throughout a contained fluid like air in a balloon.

### Pressure and Force

Pressure is the amount of force acting on a given area. It is represented by the equation:

$\mathrm{Pressure=\frac{Force}{Area}}$

The pressure exerted by a fluid increases if more force is applied or if the same force is applied over a smaller area. The equation for pressure can be rewritten as:

Force = Pressure x Area

This equation shows that the same pressure applied to a greater area increases the force.

### Pascal and His Law

Some of the earliest scientific research on pressure in fluids was conducted by a French mathematician and physicist named Blaise Pascal (1623–1662). The SI unit of pressure, the Pascal (Pa), is named for him because of his important research. One of Pascal’s major contributions is known as Pascal’s law . This law states that a change in pressure at any point in an enclosed fluid is transmitted equally throughout the fluid. To see a video about Pascal’s law, go to this URL:

### A Simple Example

A simple example may help you understand Pascal’s law. Toothpaste is a fluid that is enclosed in a tube with a small opening at one end. Look at the toothpaste tube in the Figure below . When any part of the tube is squeezed, toothpaste squirts out the open end. The pressure applied to the tube is transmitted equally throughout the toothpaste. When the pressure reaches the open end, it forces toothpaste out through the opening.

### Using Fluid Pressure

The ability of fluids to transmit pressure in this way can be very useful—besides getting toothpaste out of a tube! For example, hydraulic brakes in a car use fluid to transmit pressure, and when they do, they also increase force. You can see how hydraulic brakes work in the Figure below .

Hydraulic Brakes

Q : In this diagram, how can you tell that the force applied by the brake cylinder is greater than the force applied by the brake pedal mechanism?

A : The arrows representing the force applied by the break cylinder are larger than the arrow representing the force applied by the brake pedal mechanism. A larger arrow indicates greater force.

Q : How do hydraulic brakes increase the force that is applied to the brake shoes?

A : The pressure exerted by the fluid on the brake shoes is applied over a larger area. When pressure acts over a larger area, it increases the force (Force = Pressure x Area).

Hydraulic car lifts also use fluid to transmit pressure and increase force. The lifts are used to raise cars, which are very heavy, so mechanics can work on them from underneath. Controls in airplanes use fluids to transmit pressure and increase force so a flick of a switch can raise or lower heavy landing gear. To see animations of hydraulic systems such as these, go to URLs:

For a dramatic demonstration of the use of hydraulics to increase force, watch Bill Nye the Science Guy at this URL:

### Summary

• Pascal’s law states that a change in pressure at any point in an enclosed fluid is transmitted equally throughout the fluid.
• The ability of fluids to transmit pressure in this way can be very useful—from getting toothpaste out of a tube to applying the brakes on a car.

### Vocabulary

• Pascal’s law : SI unit for pressure, equal to 1 Newton per square meter (N/m 2 ).

### Practice

At the following URL, read how a hydraulic car lift works and do the animation. Then answer the questions below.

1. How does force change in a hydraulic lift?
2. In the animation of the lift, what happens when you add mass to the small cylinder?
3. Explain how a hydraulic lift can raise an object as heavy as a car.

### Review

1. What is Pascal’s law?
2. Apply Pascal’s law to the ketchup packets seen below . Explain what will happen if you tear a small hole in one corner of a packet and then squeeze the packet.

### Vocabulary Language: English

Pascal’s law

Pascal’s law

Law stating that a change in pressure at any point in an enclosed fluid is transmitted equally throughout the fluid.

7 , 8

## Date Created:

Nov 01, 2012

Sep 11, 2015
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