9.2.1 – Transmission of Pressure (Hydraulic Systems)

Pascal’s Law

Definition: Pascal’s Law
Pascal’s Law states that pressure exerted anywhere in a confined incompressible fluid is transmitted equally in all directions throughout the fluid.

Blaise Pascal (1623 – 1662)
French mathematician, physicist, inventor & philosopher. Aside from his work in pressure and fluid dynamics (the unit of pressure is named after him), he contributed much towards the field of modern economics and developed one of the earliest mechanical calculating machines. https://en.wikipedia.org/wiki/Blaise_Pascal

Blaise Pascal (1623 – 1662)

French mathematician, physicist, inventor & philosopher. Aside from his work in pressure and fluid dynamics (the unit of pressure is named after him), he contributed much towards the field of modern economics and developed one of the earliest mechanical calculating machines.

https://en.wikipedia.org/wiki/Blaise_Pascal

If we consider a sphere with holes around it connected to a syringe like this:

If we fill this with a liquid and press in the piston we will observe liquid squirting out in all directions.

The liquid will be leaving each of the holes at the same speed. This is because in pressing the piston we increased the pressure in the liquid and that pressure increase is transmitted throughout the whole liquid.

Hydraulic Systems

Hydraulic systems are used to transmit pressure from one point to another.

Hydraulic systems work because liquids are almost incompressible and they transmit pressure equally in all directions (Pascal’s Law).

Example
What is the maximum load that can be lifted by an effort of 20 N applied to the left-hand piston? Pushing down on the left-hand piston with a force of 20 N will compress the liquid below it. The pressure exerted on the left-hand side piston will be given by: P = F / A P = 20 / 5.0 P = 4.0 N/cm² According to Pascal’s Law the pressure will be transmitted equally throughout the liquid and so this will be the pressure acting on the right-hand side piston. The force on the right-hand piston (exerted by the liquid) is thus: F = P × A F = 4.0 × 100 F = 400 N So the right-hand piston is able to lift a load with a weight of up to 400 N.

Example

What is the maximum load that can be lifted by an effort of 20 N applied to the left-hand piston?

Pushing down on the left-hand piston with a force of 20 N will compress the liquid below it.

The pressure exerted on the left-hand side piston will be given by:

P = F / A

P = 20 / 5.0

P = 4.0 N/cm²

According to Pascal’s Law the pressure will be transmitted equally throughout the liquid and so this will be the pressure acting on the right-hand side piston.

The force on the right-hand piston (exerted by the liquid) is thus:

F = P × A

F = 4.0 × 100

F = 400 N

So the right-hand piston is able to lift a load with a weight of up to 400 N.

Example
The following shows a hydraulic system consisting of two pistons having areas 5 cm² and 20 cm². If the left-hand piston is pushed down 10 cm, what is the distanced the right-hand piston moves up? The left-hand piston moving down displaces a volume given by: V = area × distance moved V = 5 × 10 V = 50 cm³ As the liquid is incompressible, the 50 cm³ of liquid displaced from the left-hand piston must have moved into the right-hand piston. The right hand piston is thus pushed upwards by a distance X, where: V = area × distance moved 50 = 20 × X X = 2.5 cm

Example

The following shows a hydraulic system consisting of two pistons having areas 5 cm² and 20 cm².

If the left-hand piston is pushed down 10 cm, what is the distanced the right-hand piston moves up?

The left-hand piston moving down displaces a volume given by:

V = area × distance moved

V = 5 × 10

V = 50 cm³

As the liquid is incompressible, the 50 cm³ of liquid displaced from the left-hand piston must have moved into the right-hand piston.

The right hand piston is thus pushed upwards by a distance X, where:

V = area × distance moved

50 = 20 × X

X = 2.5 cm

Conservation of Energy
We are not getting an increased force for nothing. In the above example the force becomes 4 times larger, however the distance the load moves will only be ¼ times the distance. This means that the Law of Conservation of Energy is not violated.

Conservation of Energy

We are not getting an increased force for nothing. In the above example the force becomes 4 times larger, however the distance the load moves will only be ¼ times the distance.

This means that the Law of Conservation of Energy is not violated.

Example
The diagram below shows the structure of a simple hydraulic lift. When a force F is applied at A, a force is set up at B to lift a load. Calculate the magnitude of force F required to lift a load of 80 N at B. Since pressure in a liquid is equally transmitted in all directions, P₁ = P₂ ➔ F₁ / A₁ = F₂ / A₂ F / 2.0 = 80 / 40.0 therefore F = 4.0 N

Example

The diagram below shows the structure of a simple hydraulic lift. When a force F is applied at A, a force is set up at B to lift a load.

Calculate the magnitude of force F required to lift a load of 80 N at B.

Since pressure in a liquid is equally transmitted in all directions,

P₁ = P₂ ➔ F₁ / A₁ = F₂ / A₂

F / 2.0 = 80 / 40.0

therefore F = 4.0 N

Example
The diagram below shows a simple hydraulic system. Piston P has a diameter of 1.0 cm and piston Q has a diameter of 2.5 cm.Calculate the magnitude of the force F on piston P to exert a force of 200 N on piston Q. P_P= P_Q➔ F_P/ A_P= F_Q/ A_Q F_P / (π × 0.5²) = 200 / (π × 1.25²) therefore F_P = 32 N

Applications Of Hydraulic Systems

Car Brakes
Hydraulic systems form an important part of vehicle brake systems.

Operating Machinery
Many machines are powered by hydraulic systems.

hydraulic pistons can clearly be seen on this digger

Links

Pascal’s Law & Hydraulic Brake System
Properties of brake fluids
Advantages & Disadvantages of Hydraulic Systems

Physics with Mr Shone

9.2.1 – Transmission of Pressure (Hydraulic Systems)

Pascal’s Law

Hydraulic Systems

Applications Of Hydraulic Systems

2025 Physics Lessons