# Pascal's Principle

Blaise Pascal, the French mathematician and scientist (1623- 1662)
said that pressure applied to a confined fluid increased the pressure in the entire space by the same amount. For example, in a closed system such as the one pictured to the right, the pressure would
be the same at P1, P2, P3, and P4, and in fact would be the same

at all points in the system. This is really useful when designing flow
systems and especially when designing hydraulic systems that make use of Pascal's Principle to apply a mechanical advantage.

Consider the system below:

By Pascal's Principle, the pressure at P_{1} is equal to the
pressure at P_{2}. Since P = F/A, this implies that

F_{1}/A_{1} =
F_{2}/A_{2}.

This gives us a mechanical advantage.

*Example:*

Suppose a force of 100 N is applied to a piston with a cross sectional area of .0005 m^{2}. What would be the force out (F_{2} ) if the size of the piston out was .01m^{2}?
From Pascal's Principle, F_{1}/A_{1} = F_{2}/A_{2} so 100 N / 0.0005m^{2} = F_{2}/0.01m^{2}, or F_{2} = 2000N. A common application of
this is the brakes of your car, where a small piston at the pedal causes a larger force at the brake pads due to an increase in piston size. (Plus some power assist for cars with power
brakes.)

The *mechanical advantage* of a hydraulic system is given by the
ratio of the output force to the input force, and equals the ratio of the output area to input area, or

To learn more about Pascal’s Principle, go to

http://hyperphysics.phy-astr.gsu.edu/hbase/pasc.html

http://www.grc.nasa.gov/WWW/K-12/WindTunnel/Activities/Pascals_principle.html.

For Practice Problems, Try: *Giancoli Multiple Choice PracticeQuestions (It will be a few lessons before all of this is covered)*