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Pascals Principle Formula

In any fluid, the static pressure is exerted on the walls of the container and in the fluid. These forces act perpendicular to the walls of the container. When an external pressure is applied to the fluid, the pressure is distributed uniformly in all parts of the fluid and this is known as Pascal’s principle named after the Physicist Blaise Pascal.The Pascal’s principle refers to only the external pressure and within the fluid the pressure at the bottom is greater than the top.

According to Pascal’s principle, the force per unit area describes an external pressure which is transmitted through fluid and the formula is written as,

 

Example 1:

In a hydraulic system, a piston has a cross-sectional area of 20 square centimeters pushes on an incompressible liquid with a force of 30 newtons. The other end of the hydraulic pipe connects to the second piston with a cross-sectional surface area of 100 square centimeters. Calculate the force on the second piston.

Solution:

Pascal’s principle is given by,

We know that,

F1 = 30 newtons,

A1 = 20 square centimeters

A2 = 100 square centimeters

Insert the given values to calculate the force on the second piston:

F2 = A2 x F1/A1

= 100 x 30 / 20

  = 150 N

 

Example 2:

A piston has a cross-sectional area of 40 square centimeters in a hydraulic system and pushes an incompressible liquid with a force of 50 newtons. The other end of the hydraulic pipe is connected to a second piston with a cross-sectional surface area of 50 square centimeters. Determine the force on the second piston.

Solution:

Pascal’s principle is given by,

We know that,

F1 = 50 newtons,

A1 = 40 square centimeters

A2 = 50 square centimeters

Insert the given values to calculate the force on the second piston:

F2 = A2 x F1/A1

= 50 x 50 / 40

  = 62.5 N

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