PASCAL’S LAW

Introduction

Blaise Pascal, a well-known French mathematician, physicist, and philosopher, stated this law in 1647.

This law asserts that the pressure exerted on a stationary liquid is the same in all directions.

OR

When external pressure is applied to any section of a fluid enclosed in a vessel, it is transmitted in all directions undiminished and evenly.

Hydraulic Machines work over This Principle

Formula for Pascal’s Law

Pascal’s Law demonstrates the link between pressure, applied force, and contact area, i.e.

FA = P

PA = F

Where P denotes pressure, F denotes force, and A is the area of contact.

Let us use an example to better comprehend the working principle of Pascal’s law.

By exerting force on a piston, a pressure of 2000 Pa is transmitted throughout a liquid column. What is the force applied if the piston has an area of 0.1 m2?

Pascal’s Law can be used to calculate the value of force.

PA = F

Here,

P = 2000 Pa = N/m2

A = 0.1 m2 

We get Force = 20N or F = 200 N after substituting the data.

Pascal’s Law in Practice

1)Hydraulic Lift 

It has a wide range of uses in everyday life. Pascal’s law is used in a variety of systems, including hydraulic lifts and hydraulic brakes. All of these technologies rely on fluids to transmit pressure. Two pistons are separated by a gap filled with liquid in a hydraulic lift, as indicated in the diagram above. To exert a force F directly on the liquid, a piston with a tiny cross-section A is used. The pressure P =F/A is passed via the liquid to the larger cylinder, which is connected to a larger piston with an area B, resulting in an upward force of P * B. As a result, the piston can withstand a significant amount of force (large weight of, say a car or a truck placed on the platform). The platform can be moved up or down by altering the force at A. As a result, the applied force has been enhanced by a factor of B/A, which is the device’s mechanical advantage.

2)Hydraulic Brake

Hydraulic brakes on autos work on the same basis. When we press down on the pedal with our foot, the master piston inside the master cylinder rotates, and the resulting pressure is conveyed through the brake oil to work on a piston with a greater surface area. The piston is then driven down by a large force, expanding the brake shoes against the brake lining. As a result, a slight effort on the pedal causes the wheel to slow down dramatically. The system’s main advantage is that the pressure created by pushing the pedal is distributed evenly among all four cylinders, ensuring that the braking effort is equal on all four wheels.

3. Pressure Change with Depth

Consider a fluid in a container that is at rest. Point 1 is at a height of h from point 2 in the diagram above. The pressures at sites 1 and 2 are denoted by P1 and P2, respectively. Consider a fluid-filled cylindrical device with a base area of A and a height of h. Because the fluid is at rest, the consequent horizontal forces, as well as the corresponding vertical forces, should be zero, balancing the element’s weight. The forces operating in the vertical direction are caused by fluid pressure acting downward at the top (P1A) and upward at the bottom (P2A). We can say that, if mg is the weight of the fluid in the cylinder, A = mg (P2 P1)

Now the mass of the fluid will be.:-

(P2 −P1) = ρgh 

The difference in pressure is determined by

The h between the points is the vertical distance between them (1 and 2),

The mass density of the fluid ρ

Gravitational acceleration is measured in g.

If the   point 1  which is discussed above is moved to the top of the fluid (say, water), which is open to the atmosphere, we can replace P1 with atmospheric pressure (Pa) and P2 with P. As a result of the earlier equation,

P = Pa + ρgh

Frequently Asked Question (FAQ) 

1)Is Pascal’s Law applicable to both solids and gases?

Pascal’s Law is most commonly used with incompressible fluids. It could be used on gas, but it wouldn’t be as effective as it would be on liquid. Solids are unable to do so because fluids assist in determining pressure through flow resistance. This is why hydraulic systems such as hydraulic brakes, hydraulic jacks, hydraulic presses, and so on are employed for such tasks. The air from the air pressure is applied to the top of the oil container in one common form found in vehicle repair shops with a lift. This causes the oil to exert pressure on the gun, which lifts the vehicle. However, if a solid object is dropped into a fluid within an enclosed container, the solid object will feel the pressure as well when force is applied to it.

• Who Proposed Pascal’s Law:-

Blaise Pascal, a French scientist, was the first to propose the principle.

• Write Pascal’s Law Formula

PA = F

Where P denotes pressure, F denotes force, and A is the area of contact.

CONCLUSION:

A change in pressure imparted to a contained fluid is transferred unequally to all parts of the fluid and the container’s walls. The importance of pressure in fluids is due to Pascal’s principle, which is a scientifically proven truth.