Pascal’s Law and Its Applications

Pascal’s Law stipulates that pressure applied to any part of a liquid in a container can be transferable without loss to other liquid components. Hydraulic jack, hydraulic brake, and hydraulic press are just a few of the applications under Pascal law.

Pascal Law Formula

Blaise Pascal put forward this law when he discovered that in a liquid at rest, the force put on every point located at the exact height isn’t an inverse quantity. Therefore, one cannot assign it a direction. 

If the fluid has a vertical bar with an even cross-section and is in equilibrium, there is an equal force and balanced force applied at both ends. In contrast, if an unbalanced force is exerted on the horizontal bar, the liquid will be subject to a net force and will flow. 

Thus, we can state that because the liquid doesn’t flow, it certainly has the same pressure on it at all points.

Let us look at the mathematical representation of the law:

F = PA

Where 

F = applied force

P = pressure transmitted 

A = cross-sectional area

Application of Pascal’s Law

Pascal’s Law forms the basis of many devices such as hydraulic lifts and hydraulic brakes. All these devices use fluids to transmit pressure. Let us understand how they work.

Hydraulic Lift

Hydraulic lift is used in many ways throughout the day. 

Imagine a hydraulic lift with two pistons of different dimensions separated by a space filled with liquid. A is the smaller-sized piston, while B is the larger-sized one. 

Suppose we employ piston A to apply a force F directly onto the liquid. Then, it will transfer pressure P = F/A through the liquid to the larger piston B. This approach ultimately creates an upward force equal to B x P. Thus, the piston can support an enormous force (large weight, like the weight of a truck or car placed upon the plate). 

The platform moves upwards or downwards to alter the A force. We can multiply the force applied by B/A, which is the main advantage that the system offers.

Hydraulic Brake

In cars, the hydraulic brakes work using the same principles. If we apply a small force to the pedal using our feet, the main piston moves inside the main cylinder and transfers the pressure created through the brake oil to act on a piston having a bigger surface. 

The force multiplies as it travels through the piston, ultimately expanding the brake shoes and the brake lining. Therefore, a tiny push on the pedal can create an extremely slowing impact on the wheel. 

The force created by pressing the pedal transmits equally across all cylinders attached to four wheels. This aspect makes the braking force equal across all wheels, representing the primary advantage of the entire mechanism.

Pressure Variation with Depth

Visualise a container full of liquid at rest with two points 1 and 2. Point 1 is above point 2 at height h. P1 and P2 represent the pressure at points 1 and 2, respectively. 

Further, imagine a cylindrical component composed of fluid, with an area of base A and a height of h. The resultant forces should be zero because the fluid is still in the horizontal direction. Similarly, the vertical forces that result from that balance on the mass of the piece will also be zero.  

The forces exerted in the direction of the vertical result from the pressure of the fluid. This pressure on the highest point (P1A) acts downwards while moving upwards at the base (P2A). 

Since mg represents the mass of the fluid within the cylinder, we can conclude that:

(P2 −P1 ) A = mg                                                                              

Now, ρ represents the mass density of the fluid, the mass of fluid will be: 

m = ρV= ρhA 

so that    

(P2 −P1) = ρgh                                                                           

Pressure difference depends upon the vertical distance h between the points (1 and 2), 

P2 = P1 + ρgh

Hydraulic Pumps

Hydraulic pumps that transform electrical energy to hydraulic help in the flow of fluid. They aid in the dispensing of fluid. 

Hydraulic pumps have a smaller cylinder connected to a larger one, and both cylinders contain oil. Air compressed into the smaller cylinder creates a force on the underside of the oil. The pressure then transfers through the oil to a larger cylinder, where a piston absorbs it, generating an amount of force that is sufficient to raise a car. 

The automotive industry widely uses pumps with hydraulics.

Aircraft Hydraulic System

Hydraulic power systems aid in reducing aeroplane runway speed and help manage the flight control surface, landing gears and flaps.

A system of hydraulics for aircraft comprises three essential mechanical elements and hydraulic fluid. Even a small volume of the hydraulic fluid aids in transmitting large amounts of force. 

The hydraulic fluid in contact with the cylinders/pistons is at different pressures. One can pump the oil at a higher pressure to one side or the other of the head. The selector valve assists in directing the flow of fluid.

Hydraulic Jack

The principles outlined in Pascal’s Law are also the foundation for Hydraulic Jacks, which fall in the category of a closed container. They are used to lift large objects.

The hydraulic jack consists of two linked cylinders, one bigger and the other smaller. When one pulls the handle downwards, it closes the valve. The piston can then force the fluid through a valve to the bigger cylinder, generating a huge force that will transfer into the load. Thus, the moment force is applied, the pressure transmits throughout the entire surface and its volume.

One must frequently move the handle upwards and downwards until the load is lifted sufficiently by the hydraulic fluid flowing into the tank that buffers the cylindrical. Hydraulic jacks can be highly beneficial in the automobile industry and frequently raise automobiles above the surface for repairs and maintenance.

Conclusion

This article delves into the applications of Pascal’s Law after giving a brief introduction to the law itself.

Unlike other forms of stress, the pressure under Pascal’s Law is not a vector value. It is impossible to assign a direction to it. The force applied to any region within an area of fluid in a state of rest remains normal regardless of the region’s direction.