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Physics Lesson 9.3.2 - Pascal's Principle
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Welcome to our Physics lesson on Pascal's Principle, this is the second lesson of our suite of physics lessons covering the topic of Liquid Pressure. Pascal's Principle, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
Pascal's Principle
The way in which pressure acts inside a liquid, was first discovered and outlined by the famous French scientist Blaise Pascal. For this reason, the unit of pressure bears his name, i.e. Pascal. Thus, pressure in liquids obeys to a universal rule, known as "Pascal's Principle" which says:
"In a fluid at rest in a closed container, a pressure change in one part is transmitted without loss to every portion of the fluid and to the walls of the container."
This principle is particularly useful in communicating vessels, in which we can use a small force in a small area to transmit pressure in a larger area and in this way, to increase the value of force. Look at the figure below.
Thus, since liquid pressure is transmitted equally in all positions of the communicating vessel, we obtain
or
Pascal's principle is the operating principle of all hydraulic machines, i.e. in mechanisms that use the water pressure to lift heavy weights or in other words, to apply large forces as an output by applying a very small force at input, as the one shown in the above figure. As examples in this regard we can mention hydraulic lifts, hydraulic press machines, hydraulic steering wheels, etc.
Example 3
A hydraulic lift has a 4 cm2 area at the button side and it is used to lift a maximum load of 6 tons as shown in the figure.
What is the maximum force the user can apply on the button (left side) of this hydraulic lift if the wider area is 8 m2? For convenience, take g = 10 m/s2.
Solution 3
First, let's convert the units into the standard ones. We have:
A1 = 4 cm2 = 0.0004 m2 = 4 × 10-4 m2
A2 = 8 m2
F2 = m × g = 6 t × 10 m/s2 = 6000 kg 10 m/s2 = 60 000 N = 6 × 104 N
F1 = ?
Given that pressure is transmitted equally in all directions of a communicating system (based on Pascal's Principle), we can write for pressure at the positions where the two forces act:
and therefore,
Substituting the known values, we obtain
8 × F1 = 4 × 10-4 × 6 × 104
8 × F1 = 24
F1 = 3 N
Thus, by only 3 N of applied force, we can lift a 6 t object using this kind of hydraulic lift.
You have reached the end of Physics lesson 9.3.2 Pascal's Principle. There are 2 lessons in this physics tutorial covering Liquid Pressure. Pascal's Principle, you can access all the lessons from this tutorial below.
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