Pascal's Law


Learning Objectives

1. Defining Pascal's Law

2. Understand what is Pascal's Law

3. Understand the applications of Pascal's Law

4. Deriving the formula and applying it

5. Learning how to applied Pascal's Law everyday life


Defining Pascal's Law

    • Pressure exerted anywhere in a mass of confined liquid is transmitted undiminished in all directions throughout the liquid

This means that when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container


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Take this set up for example. This set up is two syringes connected by a tube. The tube is filled with an incompressible liquid such as water. When a downward force is exerted on one of the syringe, The piston on the other syringe is pushed up. This is easily explained by Pascal's Law. A downward force on the piston of the syringe adds pressure to the incompressible liquid. As such, this liquid also exert the same pressure on the piston on the other syringe. If one syringe is pushed down with a force of 20N, the force exerted by the liquid on the piston will be the same at the other end.


Who discovered It?


As the name suggests, this principle was established by a French Mathematician Blaise Pascal. He was the one who came up with the Pascal's triangle too!.


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File:Principe de Pascal.jpg

Pascal's Barrel.

Blaise Pascal conducted this test on 1646 using a 10 metre long vertical tube and a wine barrel. He filled the barrel with water to the brim and inserted the tube into the barrel before pouring more water down the tube. As he poured more water down the tube, suddenly, the barrel exploded. This also can be explained by the law he established. Firstly, water has weight. As more water is poured down the tube, the water exert a greater pressure on the water below such as the water in the barrel. The water presses against the walls of the barrel in all directions and when the water pressure is too great, the barrel burst. This showed that pressure exerted on a incompressible liquid exert a pressure in all directions which caused the barrel to burst instead of creating a hole in the barrel that releases the pressure.


Formula


The principle is stated mathematically as:

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where

external image 8eb1e9faae697fe28511ee1cf58208b2.png is the hydrostatic pressure, or the difference in pressure at two points, due to the weight of the fluid;

ρ is the fluid density (in kilograms per cubic meter);

g is acceleration due to gravity;

external image 9f3c301fac67211fdde50417bb758907.pngis the height of fluid above the point of measurement, or the difference in elevation between the two points (in metres).


The formula shows that the change in pressure between two elevations is due to the weight of the fluid between the elevations.


Applications



One very significant way the Pascal's Law comes into practical use is in the hydraulics system.The hydraulic brakes in cars, hydraulic lifts in car service shops to lift up cars and the landing system and hydraulics in airplanes are all based on this law. One advantage is that this system is very efficient as the liquid is incompressible and pressure is transferred almost immediately. This allows car to brake suddenly to avoid accidents. Also, in hydraulic systems, the force exerted by your foot on the brake can be multiplied many times to effectively stop the car.



Fun Time


Experiment we conducted ourselves( Very simple demonstration)

Materials

1.Cotton swab/Matchsticks

2. Plastic bottle

3.Scissors

4.Water

Procedure

1. Using a scissors, cut the ends of the cotton swab ( The part with the cotton)

2. Fill a plastic bottle to the brim with water

3. Place the end of cotton swab on the water( It should float)

4.Close the bottle with the cap

5. Squeeze the bottle by exerting force on it sides

6. See what happens !

Here is the video! Enjoy!



Explanation


Firstly, there is an air bubble trapped in the small end of the cotton swab causing it to float initially. However, when we squeeze the bottle. The force exerted on the hand cause the pressure on the water in the bottle to distribute equally evenly throughout the liquid. This actually compress the air bubble inside the cotton swab. With water going into the cotton swab, the cotton swab sinks. Also, note that due to the equal pressure from all directions acting on the cotton swab, the air bubble does not escape but rather compresses. When the force exerted on the bottle is released, pressure is released, water leaves the cotton swab which become less dense and thus rises again.