What is Pascal’s Law?

Pascal's law or Pascal’s principle, the backbone of fluid mechanics was discovered over 350 years by a French mathematician Blaise Pascal. It states that the pressure change occurring at any point in a confined fluid will be transmitted equally in all direction. When you apply pressure on an enclosed fluid, it will be distributed equally undiminished. That is, the pressure of the fluid at the bottom of the container will be equal to the pressure at top of the container.

Pascal Law Derivation

Pressure is the applied force over a surface. It is calculated as;

P=F/A

Where F is the applied force and A is the surface area.

Consider the image, there are two pistons on either side of the container and the container is filled with incompressible fluid like water or oil. According to Pascal’s law, the pressure applied will be transferred equally and undiminished to all parts of the system.

For the first piston, a force F1 is applied over a surface area A1. Then, the pressure P1 is calculated as;

P1=F1/A1

Similarly, the pressure P2 in the second cylinder with a force of F2 and surface area A2 will be;

P2=F2/A2

When you apply pressure(P1) in the first piston it will be equally transmitted through the confined incompressible fluid. So,

P1=P2

i.e;

F1/A1=F2/A2

Then, the force F2 on the second piston can be calculated as;

F2=(F1/A1)*A2

This is called multiplication of forces. That is when a force of 1N is applied over an area of 10cm. Then the force F2 over the area 100cm will be 10N. This is a common principle used in hydraulics for lifting heavy loads.

Pascal's Law and its Applications

Pascal’s law has a wide range of applications in most of the industries. Pascal’s law is related to fluids and gases. So, you can find most of its applications in hydraulic and pneumatic industry. Also, scuba drivers require knowledge of this principle. Some important applications are listed below.

Hydraulic System: The basic working principle of every hydraulic system is Pascal’s law. Hydraulic systems are used for lifting, holding or moving loads with a small applied force. It uses incompressible hydraulic fluids and works with the concept of force multiplication(discussed above). Few examples of hydraulic systems work using Pascal’s law is listed below.

Hydraulic Jack and Pascal’s Law

Hydraulic jacks are used for lifting heavy loads. They are commonly used in automobile workshops for lifting vehicles. Mechanics can lift heavy vehicles by applying a small force in one end.

Hydraulic Brake and Pascal’s Law

While applying a small force on the brake, the brake fluid is passed towards the wheels through the brake lines. This force helps the vehicle to stop or slow down immediately.

Hydraulic Lifts and Pascal’s Law

For lifting purpose, different types of hydraulic lifts are available. This application uses principles of force multiplication and with a small applied force, one can generate a higher force.

Unit: Pascal (Pa) or N/m²