http://www.ck12.org Chapter 12. Fluid Mechanics
12.3 Pascal’s Law
Objective
The student will:
- Understand and be able to solve problems using Pascal’s Principle.
Vocabulary
- Pascal’s Law:Increasing the pressure of fluid anywhere in a system increases the pressure everywhere in the
system.
Introduction
Pressure is defined as force divided by area, but this does not explain in itself how pressure transfers. Blaise Pascal,
after whom the metric unit of pressure is named, also clarified a useful physical principle that is now named after him.
Pascal’s Lawstates that any confined incompressible fluid under pressure will transmit pressure equally throughout
the system. In other words, increasing the pressure of the fluid anywhere increases the pressure everywhere.
If you have ever been to an auto repair shop, you’ve probably seen cars raised high enough above the ground so that
the mechanics can perform their repairs. The device that raises the car is called a hydraulic lift (Figure12.12). A
hydraulic lift can create a very large force to lift the car with only a small force.
How does it work? The diagram in the Figure12.12 shows a cross-section of a hydraulic lift with square pistons.
The pressure applied at the narrow piston of surfaceAis transmitted to the bottom of the wide piston of surface area
A′= 9 A. If, for example, the pressure isPat the narrow piston is 1000mN 2 , the bottom of the wide piston will have
the same pressure applied to it, but over nine times the area. The total force on the wide piston will be nine times
greater, for a total ofF′=PA′=P( 9 A) =9000 N.
The force is multiplied in proportion to the ratioAAnarrowwide.
More formally, we can writePnarrow=Pwide→AFnarrownarrow=FAwidewide→AAnarrowwide =FFnarrowwide; it is often the case that “narrow” is
replaced with “in” and “wide” is replaced with “out.”
It may seem that we “are getting more out of the system than we’re putting into it.” After all, in the example above
we only needed to input 1,000 N in order to output 9,000 N.
As you may suspect, this is not the case.
If we wish to raise the car, work must be done. And energy conservation tells us that we can never get more energy
out of a system than we put into a system. In fact, because of friction, we always need to put more energy in than
we get out.