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 P1 is equal to the pressure at P2. Since P = F/A, this implies that

F1/A1 = F2/A2.

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 m2. What would be the force out (F2 ) if the size of the piston out was .01m2? From Pascal's Principle, F1/A1 = F2/A2 so 100 N / 0.0005m2 = F2/0.01m2, or F2 = 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