Definition, Formulas, Example Problems and Application of Pascal’s Law

Pascal’s Law – Definition, Formulas, Example Problems and Applications – What if a vessel U is filled with a homogeneous fluid and one of the pipes is compressed with a force of F? The physical processes occurring in such a U vessel were investigated by Blaise Pascal.

Pascal's Law - Definition, Formulas, Example Problems and Applications

Through his research, Pascal concluded that if pressure is applied to a fluid that fills an enclosed space, the pressure will be transmitted by the fluid in all directions with the same magnitude without decreasing. This statement is known as Pascal’s Law, which was proposed by Pascal in 1653. Based on Pascal’s law, it is obtained the principle that a small force can produce a larger force.

A. Definition and sound of Pascal’s Law

Pascal’s law was stated by the French mathematician and physicist Blaise Pascal (1623 – 1662). This law was born from an experiment conducted by Pascal using a sprayer or Pascal’s plane.

From the experimental results, when the suction rod is pressed, the water in the tube is compressed in all directions so that the water gushes out through the holes in the tube. The jet of water that comes out of the holes has the same pressure.

The pressure F1 in pipe one is equal to the lift force in pipe two

The picture above can be explained using Pascal’s law which reads:

The pressure exerted on a liquid in an enclosed space will be transmitted in all directions and all parts of the space are equally large.

This principle of Pascal’s law is widely used to manufacture hydraulic equipment, such as hydraulic jacks, hydraulic pumps, hydraulic brakes and hydraulic presses. This principle is used because it can provide a small force to produce a large force.

B. Pascal’s Law Formulas

In a simple analysis, Pascal’s Law can be described as in Figure above. Pressure by a force of F1 on pipe 1 which has a cross-sectional area of ​​pipe A1, will be transmitted by the fluid to a lifting force of F2 on pipe 2 which has a cross-sectional area of ​​pipe A2 with the same pressure. Therefore, mathematically Pascal’s Law is written as follows.

P1 = P2

(F1/A1) = (F2/A2)

Where :

  • F1 = force on pipe sucker 1,
  • A1 = cross-sectional area of ​​pipe sucker 1,
  • F2 = force on pipe sucker 2, and
  • A2 = cross-sectional area of ​​pipe sucker 2.

The hydraulic brake working system above is an example of the application of Pascal’s law. In addition, Pascal’s law can also be found in water lifting systems, presses, hydraulic jacks, and hydraulic drums.

C. Examples of Pascal’s Law Questions and Answers

1. A car lift having a suction area of ​​0.10 m2 and 4 × 10–4 m2, respectively, is used to lift a car weighing 2 × 104 N. How much force must be applied to the small sucker?

Answer:

Is known:

A1 = 4 × 10–4 m2

A2 = 0.1 m2, and

F2 = 2 × 104 N.

Based on Pascal’s Law then:

Pascal law question number 1

2. A cylindrical hydraulic pump has radii 4 cm and 20 cm. If the small plunger is pressed with a force of 200 N, how much force is produced on the large plunger?

Answer:

Is known:

r2 = 20 cm

r1 = 4 cm, and

F1 = 200 N

Based on Pascal’s Law, then:

Pascal's law question number 2

3. A car is about to be lifted using a hydraulic jack. If the large pipe has a radius of 25 cm and the small pipe has a radius of 2 cm. How much force must be applied to the small pipe if the weight of the car is 15,000 N?

Answer:

Is known :

R1 = 2 cm,

R2= 25 cm,

F2 = 15,000 N

Based on Pascal’s Law, then:

Pascal law question number 3

D. Application of Pascal’s Law in Daily Life

The above statement was first put forward by Blaise Pascal. After experimenting with a sprayer (Pascal’s spray), he stated that the pressure exerted on a liquid in an enclosed space is transmitted equally in all directions. Furthermore, this statement is known as Pascal’s law. Some of its applications in everyday life technology are as follows:

Hydraulic jack

Hydraulic jacks are used to lift heavy loads with small force. In the hydraulic jack there are two tubes of different sizes. Tube one is small in diameter and tube two is large in diameter. Each tube is equipped with a suction. The pressure applied to the small suction is transmitted to the large suction. The large suction produces an upward lifting force that is much greater than the compressive force on the small suction. That is why hydraulic jacks can be used to lift very heavy loads such as; hold the car at the time of tire change.

Application of Pascal's Law in Daily Life

Car Lift Tool

We find a lot of car lifters in large car repair shops. High-pressure air is introduced through one of the two taps on the car lifter. The air is then compressed in a room. The compressed air produces enormous pressure. The enormous pressure is transmitted by the oil to the large suction. This pressure is what produces a very large lifting force that can lift the car. Furthermore, to lower the car, it is done by expelling compressed air through another faucet, namely the exhaust valve.

Application of Pascal's Law in Daily Life

Hydraulic Brake

The main parts of a hydraulic brake are the brake pedal, master cylinder, clamp shoe, and brake fluid. When the brake pedal is pressed with the foot, the pressure is transmitted by the brake fluid to the clamp shoes through the brake cylinder (there are 4 brake cylinders, two in front and two in the back). On the flip-flops, a very large frictional force (resistance) is produced so that it can stop the rotation of the car wheels. This is because the suction area of ​​the brake cylinder is much larger than the suction area of ​​the master cylinder.

Application of Pascal's Law in Daily Life
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