Introduction

The stationary pressure acts perpendicular to any surface which is in contact with fluid. Pascal found that the pressure at a point for a stationary fluid is the same across all planes which passes through that point in that fluid. Pascal’s law is considered as Pascal’s principle or principle of transmission of fluid pressure. Pascal law was coined in 1653 by a French mathematician Blaise Pascal.

According to Pascal Law external static pressure which is applied to a confined liquid is distributed or transmitted evenly in all directions throughout the liquid.

Pascal Law Formula

The formula for Pascal Law is given as

F=PA

Here, 

F = force 

P = pressure

A = area of cross section

Blaise Pascal, a French scientist found that the pressure in a static fluid is similar at every point as long as they are at the same height.

The pressure exerted in all directions is the same in the static fluid. We can say that pressure is not a vector quantity because no direction is assigned to it. The force against any area inside a static fluid and under pressure is perpendicular to the area.

Let, three forces Fa,Fb,F cacted on a static fluid having area of cross section Aa,Ab,Ac . Now, we know from the Pascal law that the pressure of static fluid in any direction is the same.

Hence, we get

FaAa=FbAb=FcAc

Pascal Law Application

There are many applications of Pascal’s Law. We will discuss some of the Pascal law applications here.

Aircraft Hydraulic System

Three important mechanical pieces and hydraulic fluid make up an aeroplane hydraulic system. A small volume of hydraulic fluid allows a large amount of force to be transmitted. The hydraulic fluid has a different pressure when it comes into contact with the pistons. Oil can be pumped to either side of the piston head since it is under a higher pressure. The selector valve aids in fluid direction control.

Hydraulic Pump

Fluid is released with the use of hydraulic pumps. It comes with a small cylinder that is connected to a larger cylinder, both of which are filled with oil. The oil surface is squeezed by the compressed air injected into the tiny cylinder. This pressure is carried to the huge cylinder via the oil, where it acts on a giant piston to provide enough force to raise a car.

Hydraulic Jack

The hydraulic jack is made up of two cylinders, one larger and one smaller, which are coupled to one another. When the handle is depressed, one valve closes, and the small piston drives fluid through another valve into a larger cylinder, resulting in a large force that is imparted to the load. As a result, we can deduce that when force is applied, pressure is applied to the cylinder’s whole volume and surface.

The handle is moved up and down until the load is lifted onto the little cylinder by hydraulic fluid coming from the reservoir. Hydraulic jacks are extremely useful in the automobile sector, and they’re commonly used to lift cars off the ground for repairs and maintenance.

Variation of Pressure with Depth

Let us consider a stationary fluid in a container. Let point 1 is at a height of h from point 2. P1 and P2 are the pressure at point 1 and point 2. Consider a cylindrical fluid element with base area A and height h. Because the fluid is static, the resultant horizontal forces must be zero along with the resultant vertical forces that balance the element’s weight. The forces acting in the vertical direction are due to fluid pressure at top acts (P1A) down and at bottom (P2A) it acts upward. If mg is the weight of the liquid in the cylinder, we can say that

(P2–P1)A=mg

Now, let be the mass density then mass of fluid is

m=V=hA

Hence

(P2–P1)=gh

The pressure difference depends on

Mass density of fluid

Gravitational Acceleration g.

Conclusion

According to Pascal Law external static pressure which is applied to a confined liquid is distributed or transmitted evenly in all directions throughout the liquid.

Blaise Pascal, a French scientist found that the pressure in a static fluid is similar at every point as long as they are at the same height.

There are many applications of Pascal’s Law. We will discuss some of the Pascal law applications here.

1. Hydraulic Lift
2. Hydraulic jack
3. Hydraulic Brake

Hydraulic Jack is almost similar to hydraulic lift but Hydraulic Jack is smaller than Hydraulic lift. The small cylinder can be pressed by pressing the foot pedal.

Pascal’s Law is also applicable for gases. The law is given for fluid and fluid also include gases.