Pascal's Law

A change in pressure at any point in an enclosed fluid is transmitted equally throughout the fluid.

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Pascal's Law

Did you ever watch someone make balloon animals like this turkey? 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:

\begin{align*}\mathrm{Pressure=\frac{Force}{Area}}\end{align*}

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 × 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.

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 × 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.

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.

Review

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

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