Middle School Activities On Pascal's Principle

A change in pressure applied to an enclosed fluid is transmitted undiminished to every point of the fluid and to the walls of the container. This is a statement of Pascal's Principle, which is the basis of the hydraulic jack you see lift cars at the garage. The relatively small force input at one piston drives the second piston under the car upward, because the pressure is transferred from one piston to the other through an intermediary fluid. You can demonstrate this transfer of pressure in the classroom without the use of pistons or other complex equipment.

Step on a balloon and the increase in pressure is spread throughout the inside of the balloon. The thinning of the walls and its possibly even popping demonstrate this transmission of pressure increase. This example is quite simple, and doesn't really convey the subtlety of the principle.

Place an egg in a plastic bag, as a precaution. Then try to crush the egg with one bare hand, making sure to wrap your fingers around as much of the circumference of the egg as possible. The egg won't break, because the outside pressure is evenly distributed, and the liquid inside the egg pushes back in an evenly distributed manner. It's akin to dropping the egg into a mile-deep ocean. It would still not break a mile down, because the pressure inside and outside build and oppose each other evenly.

Far more dramatic is the glass bottle demonstration of Pascal's Principle. Select a glass bottle with a screw-on cap. Fill it with water almost to the top. Screw on the cap. Hold the bottle over the classroom lab sink. Slap the cap with the ball of the thumb (the thenar eminence). With enough sudden force, the bottom of the bottle will drop out, as well as all the liquid inside. The circular seam where the bottom is joined to the rest of the bottle during manufacturing is where the break occurs. This demonstration is easier to perform with a rubber mallet, however.

The reason this demonstration works is because the sudden increase in pressure is transferred throughout the bottle, by Pascal's Principle. An even distribution of force presses on the bottom of the bottle. The seam just above the bottom just happens to be the weakest "joint" in the bottle, so that's where the bottle gives way. Note that because the bottle cap is much smaller than the bottom of the bottle, the liquid inside exerted more force on the bottom than the hand exerted on the fluid. Furthermore, the bottom need be moved outward only on a molecular scale—the width of a few atoms—to break the seam around the bottom, while the hand hits the cap inward over a far greater distance. Therefore, the bottom drops out by being subjected to a greater force, albeit over a shorter distance.

Recall that energy, as work, is force times the distance over which the force is applied. Therefore, energy is conserved in this demonstration because the force on the bottle bottom moves the bottom such a small distance. Like a mechanic's car lift, the bottle demonstration is a mix of both Pascal's Principle and the concept of leverage in magnifying force while still conserving energy.