Application of Pascal's Law (Questions)

Application of Law

When a force is applied to a contained, incompressible fluid, the pressure increases equally in all directions throughout the fluid. This fundamental characteristic of fluids provides the foundation for hydraulic systems found in barbershop chairs, construction equipment, and the brakes in your car.

Because the force applied to the contained fluid is distributed throughout the system, you can multiply the applied force through this application of Pascal’s Principle in the following manner. Assume you have a closed container filled with an incompressible fluid with two pistons of differing areas, A₁ and A₂. If you apply a force, F₁, to the piston of area A₁, you create a pressure in the fluid which you can call P₁.

Similarly, the pressure at the second piston, P₂, must be equal to F₂ divided by the area of the second piston, A₂.

Since the pressure is transmitted equally throughout the fluid in all directions according to Pascal’s Principle, P₁ must equal P₂.

Rearranging to solve for F₂, you find that F₂ is increased by the ratio of the areas A₂ over A₁.

Therefore, you have effectively increased the applied force F₁. Of course, the law of conservation of energy cannot be violated, so the work done on the system must balance the work done by the system. In the hydraulic lift diagram shown on the previous page, the distance over which F₁ is applied will be greater than the distance over which F₂ is applied, by the exact same ratio as the force multiplier!

Question: A barber raises his customer’s chair by applying a force of 150N to a hydraulic piston of area 0.01 m². If the chair is attached to a piston of area 0.1 m², how massive a customer can the chair raise? Assume the chair itself has a mass of 5 kg.

Answer: To solve this problem, first determine the force applied to the larger piston.

If the maximum force on the chair is 1500N, you can now determine the maximum mass which can be lifted by recognizing that the force that must be overcome to lift the customer is the force of gravity, therefore the applied force on the customer must equal the force of gravity on the customer.

If the chair has a mass of 5 kilograms, the maximum mass of a customer in the chair must be 148 kg.

Introduction

Introduction of Blaise Pascal

Pascal’s principle, also called Pascal’s law,  in fluid (gas or liquid) mechanics, statement that, in a fluid in an enclosed system, the pressure change in one part is transmitted without equally throughout the fluid in all directions. The principle was first enunciated by the French scientist Blaise Pascal.

Blaise Pascal, French philosopher, mathematician, and physicist, considered one of the great minds in Western intellectual history. Inventor of the first mechanical adding machine.

In 1642 he invented the first mechanical adding machine. Pascal proved by experimentation in 1648 that the level of the mercury column in a barometer is determined by an increase or decrease in the surrounding atmospheric pressure rather than by a vacuum, as previously believed. This discovery verified the hypothesis of the Italian physicist Evangelista Torricelli concerning the effect of atmospheric pressure on the equilibrium of liquids. Six years later, in conjunction with the French mathematician Pierre de Fermat, Pascal formulated the mathematical theory of probability, which has become important in such fields as actuarial, mathematical, and social statistics and as a fundamental element in the calculations of modern theoretical physics.Pascal's important scientific contributions include the derivation of Pascal's law or principle, which states that fluids transmit pressures equally in all directions

Video

                                           Albert Einstein Breifly Explains Pascal's Principle




Applications of Pascal's Principle in Everyday Life

.Hyraulic Jacks
Hydraulic jacks are used to lift a heavy load such as when changing a car tyre. When the handle is pressed down, a valve closes and the small piston forces hydraulic fluid through another valve to the larger cylinder. The pressure transmitted results in a large force on the load.


When the handle is raised, valve B closes and hydraulic fluid flows from the buffer tank through valve A into the small cylinder. The handle is moved up and down repeatedly until the load is sufficiently lifted up.

The large piston can be lowered at the end by opening the release valve to allow all the hydraulic fluid to flow back into the buffer tank.

Hydraulic Brakes

Hydraulic brakes are used in cars, lorries and motorcycles.

In a hydraulic brake system, a liquid, known as brake fluid,
is used to transmit pressure from the brake pedal to all the wheels of the vehicle.

When the brake pedal is pressed, the piston of the control cylinder applies a pressure on the brake fluid and this pressure is transmitted, via a system of pipes, to each cylinder at the wheels.

The cylinder at the wheels cause a pair of pistons to push a pair of friction pads to press against the surface of the brake discs or brake drums. The frictional forces between these brake components cause the vehicle to slow down and stop.

When the brake pedal is released, a spring restores the brake discs to their original positions.


Hydraulic Pumps

Hydraulic pumps are used to raise cars in a motor workshop.

The machine is equipped with a small cylinder connected to a large cylinder. Both cylinders are filled with oil.

Compressed air is introduced into the small cylinder in which the compressed air exerts a pressure on the surface of the oil.

This pressure is transmitted by the oil to the large cylinder where the pressure acts on a large piston to produce a force which is large enough to lift a car.