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Pascal's law

physical science Maturity 11-13 Next article →

Pascal's law is a fundamental principle in fluid mechanics. It describes how pressure behaves within a confined, incompressible fluid. An incompressible fluid is a substance that does not change its volume easily. This law states that a pressure change at any point in such a fluid is transmitted throughout the entire fluid. This means the same change in pressure occurs everywhere within that closed space. This principle is essential for understanding how machines use liquids and gases to perform work.

Pressure water air (en)
Pressure water air (en)

To understand the mechanism, imagine a U-shaped tube filled with a liquid like water. This tube has pistons, which are sliding plugs, at each end. If you apply pressure to the left piston, that pressure travels through the liquid. It moves through the fluid to the bottom of the right piston. The pressure exerted by the left piston is exactly equal to the pressure exerted against the right piston. This happens because the fluid transmits the force undiminished to every part of the container.

Working principle of a hydraulic jack
Working principle of a hydraulic jack

This law allows us to multiply forces using different piston sizes. Suppose the right side of the tube is 50 times wider than the left side. If you place a 1 Newton load on the small left piston, it creates a specific pressure. This pressure is transmitted to the larger piston on the right. Because the right piston has 50 times more surface area, the resulting upward force is 50 times larger. Thus, a 1 Newton input can produce a 50 Newton output. By changing the ratio of the piston areas, you can multiply forces by almost any amount.

Working principle of a hydraulic jack
Working principle of a hydraulic jack

While force is multiplied, we must also consider the distance moved. This process does not violate the law of energy conservation. A decrease in distance moved compensates for the increase in force. For example, if the small piston moves downward 100 centimeters, the large piston will only rise 2 centimeters. This is a one-fiftieth ratio, matching the force increase. The input force multiplied by the distance moved equals the output force multiplied by its distance. This makes the hydraulic press a simple machine, much like a mechanical lever.

Working principle of a hydraulic jack
Working principle of a hydraulic jack

The law was established by the French mathematician Blaise Pascal. He formulated these ideas in 1653 and published them in 1663. His work was titled "Traitez de l'Equilibre des Liqueurs," or "Treatise on the Equilibrium of Fluids." A famous story associated with him is the "barrel-buster" experiment, or "crève-tonneau." It is said that Pascal poured water into a tube inside a sealed barrel. The resulting hydrostatic pressure allegedly caused the barrel to burst. Although this story might be apocryphal, it remains a common example in physics textbooks.

Pascal's Barrel
Pascal's Barrel

We see Pascal's principle in many modern technologies. Automobile lifts in service stations are common examples of hydraulic jacks. These devices often use an air compressor to create pressure. This air pressure is transmitted to the surface of an oil reservoir. The oil then transmits that pressure to a piston to lift the vehicle. The pressure used to lift the car is often similar to the air pressure found in automobile tires.

Working principle of a hydraulic jack
Working principle of a hydraulic jack

Hydraulics are used in devices ranging from tiny tools to enormous construction machines. Most motor vehicles use hydraulic systems for their braking mechanisms to amplify force. The principle also applies to water towers, dams, and artesian wells. Even scuba divers must account for these pressure changes in the ocean. At the surface, atmospheric pressure is about 100 kilopascals. As a diver descends, the pressure increases by about 100 kilopascals for every 10 meters of depth.

Pressure water air (en)
Pressure water air (en)
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File:Working principle of a hydraulic jack.svg
Working principle of a hydraulic jack.svg
File:Pressure water air (en).svg
Pressure water air (en).svg
File:Pascal's Barrel.png
Pascal's Barrel.png
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