Pascal's Principle
Pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid, as well as to the walls of the container.
A common application of this is a hydraulic lift used to raise a car off the ground so it can be repaired at a garage. A small force applied to a small-area piston is transformed to a large force at a large-area piston. If a car sits on top of the large piston, it can be lifted by applying a relatively small force to the smaller piston, the ratio of the forces being equal to the ratio of the areas of the pistons.
Formula
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Demonstration
This video shows a Cartesian Diver which shows Pascal's Principle in action. The Cartesian diver demonstrates not only buoyancy, but the implications of the ideal gas law and Pascal's Principle as well. Squeezing on the top of the sealed plastic container decreases the volume and therefore increases air pressure above the water. By Pascal's principle, that pressure is transmitted to all parts of the container. This increases the pressure inside the small glass vial. The increased pressure decreases the volume of air at the top of the vial, and in so doing, decreases the amount of water displaced by the vial. This decreases the buoyant force on it enough to cause it to sink.
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