Fluids: Liquids and Gases

Pressure in Liquids

Pascal’s Principle and Hydraulic Lifts

Liquids transmit pressure equally in all directions. This means that an increase in pressure at any point in a confined fluid causes an equal increase in pressure at every point within the container. This only works because liquids are incompressible – they can’t be squeezed to fit into smaller volumes. This was first realized by our friend Pascal, and is known as Pascal’s Principle.

The fact that pressure is applied equally within a uniform fluid comes in very handy when you need to lift something that is very heavy – like an automobile that needs to be repaired. Car repair garages typically have a hydraulic lift based on Pascal’s Principle.

The lift has two cylinders of different diameters, connected at their bottoms. Any pressure applied to the either side will be equally distributed throughout the liquid. So if a piston on one side is pushed down, the piston on the other side rises.

It is easy to calculate how a hydraulic lift works using the original equation for pressure, P = F/A. Pascal’s Principle tells us that the pressure on the right side equals that on the left, so we have

P1 = P2F1/A1 = F2/A2

If A1 = 10 cm2 and A2 = 100 cm2, then the force F2 will be 10 times the force F1

So pushing down the piston on the small, left side with a force, F1 of 100 N will cause a force, F2, on the right side piston’s surface of 1000 N, enough to lift a car.

Of course pushing down a distance of one meter on the left, doesn’t raise the car a meter on the right. The work (W=Fd) done on one side has to equal what is done on the other:

W = F1*d1 = F2*d2

so the distance piston 2 moves up is

d2 = (F1/ F2)*d1

In the example above, a force of 100 N for F1, 1000 N for F2 and a distance, d1, of 1 m means the piston on the right moves up only 10 cm! This means a lot more force will be necessary to push the small piston down to make the right side go up high enough for the mechanic to get underneath the car to do repairs.