Pascal’s Law of Hydraulics Is the Foundation for Hydraulic Systems

Pascal's law of hydraulics is effectively the foundation of all hydraulic systems, allowing small amounts of force to be amplified into much larger amounts of output force using a liquid medium. However, Pascal’s law is often misunderstood or misapplied by those unfamiliar with its details.

What Is Pascal’s Law of Hydraulics?

Pascal’s law of hydraulics defines the complex relationship between fluids and the containers they are held in when forces are applied to their surfaces.¹ By working out the way liquids interact with their environment while under pressure, it is possible to make use of them to amplify force considerably.

Pascal’s law states simply: “If a force acts via an area on an enclosed liquid, a pressure is generated and this same pressure is transmitted equally throughout all of the liquid.”

History

Despite living to be just 39 years old, Blaise Pascal managed to contribute many fascinating findings to the material sciences, including his famous eponymous law and other discoveries we make use of to this day.

Although Pascal was mostly concerned with geometrical mathematics and material sciences, he dabbled in interests as diverse as theology, economics, and machinery. Pascal left a lasting legacy in the field of physical and applied sciences. For this, a unit for pressure was named after him. Even today, the works he produced in the 1600s are actively used and followed with consistent results.

Formula and Explanation

The actual formula² for Pascal’s law is as follows: Δp=pg*Δh

This formula can be broken down into the following parts:

Δp = Hydrostatic pressure (typically measured in pascals)
p = Fluid density (normally measured in kilograms per cubic metre)
g = Gravitational acceleration (usually measured in metres per second squared)
Δh = Height of fluid past measurement point (measured in metres)

Per Pascal’s clearly defined law, pressure applied on any part of an enclosed liquid spreads to all parts of that fluid and to the walls, in every direction.

There are a few interesting details worth considering about Pascal’s law to fully grasp how it works. This is best done by visualising a theoretical device featuring a cross section U-shaped tube filled with fluid and two pistons in either end of it that fit snugly but can move freely within the tube. With this in mind, imagine a force has been applied to one of the pistons. This creates pressure, which is then transferred throughout the fluid within the tube, pushing up the other piston.

What makes Pascal’s law so useful is that the pressure at any point is consistent throughout the fluid and can be transferred, unchanged, from one moving part to another.³ However, because pressure and force are different from one another, pressure transferral works differently under these conditions than force generation.

If an initial force of merely 1N were applied on a piston at one end of our imaginary cross sectional area U-shaped tube, but the pressure built up in the fluid was transferred to a much larger piston at the other end, the pressure exerted would compound across the area of the larger piston, resulting in the initial input force being multiplied. Additionally, the distance moved by the smaller piston is further than the larger piston will move once the force has been generated.

This makes it possible for hydraulics systems to move incredible amounts of weight with relatively small amounts of force. This comes in handy for a great many things.

Applications

A variety of industries make use of Pascal’s law every day to move a, compress materials, operate hydraulic presses, and move objects with hydraulic jacks. Here are a few important applications of Pascal’s famous principle:

Transportation

In transportation, a hydraulic brake makes it possible for large, heavy vehicles moving at tremendous speeds to stop quickly. When you press your car’s brake pedal, fluid is compressed in hydraulic lines that lead to a calliper. This calliper grabs a brake disc and slows its motion through friction, effectively bringing your car to a stop when you want it to.

In aviation, hydraulic systems move flaps and activate landing gear. Boats of all sizes employ this principle too. In fact, Pascal’s law is the only reason a captain can turn around a small sailboat or a full-sized cargo ship with relative ease.

Manufacturing and Construction

In manufacturing, hydraulics systems are used for bending, moulding, and compressing materials to make complex shapes. In construction, hydraulics are employed to power big machines to move and support incredibly heavy loads safely.

Want to see Pascal’s law in action? Reach out to our team, here at White House Products, Ltd., to learn how we can help power your hydraulic system with custom parts.

Sources:

1. https://www.sciencedirect.com/topics/engineering/pascals-law
2. https://www.edinformatics.com/math_science/pascals-principle-and-hydraulics.html
3. https://openstax.org/books/university-physics-volume-1/pages/14-3-pascals-principle-and-hydraulics