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Understanding Pascal's PrinciplePascal, Pressure, Force, Physics of Fluids, & Hydraulic Engineering
Pascal's principle, along with the relationship among pressure, force, and area, forms the basic foundation for all hydraulic engineering.
A mechanic wanting to work underneath a car drives it onto a hydraulic lift, pushes a switch, and watches the car rise. Large pieces of earth moving equipment use hydraulics to exert large forces on the earth or boulders being moved. These hydraulic devices all depend on Pascal's principle and the relationship among pressure, force, and area. Pressure, Force, and AreaPressure is defined as the force divided by the area, so that the force is the pressure times the area. A given force can result from a large pressure over a small area or a small pressure over a large area. Hence even a small pressure exerted over a large area exerts a large force. All hydraulic devices depend on this idea to exert large forces. Blaise Pascal discovered the fundamental principle that makes this pressure concept useful for hydraulics. Pascal's PrinciplePascal's principle states that a pressure applied to an enclosed fluid is transmitted everywhere in the fluid. Hence, if a pressure is applied to one side of an enclosed fluid, all the other walls containing the fluid feel the same pressure. The pressure is transmitted without being diminished. In physics the term fluid refers to either a liquid or a gas. If a pressure is applied to a compressible gas, Pascal's principle still applies, but the volume of the gas will change. For Pascal's principle to be useful to hydraulics, the fluid should be an incompressible liquid, which will transmit the applied pressure without changing its volume. HydraulicsTo understand how Pascal's principle applies to hydraulics imagine an enclosed fluid as in the figure. The enclosure has two movable pistons. Now imagine that one of the pistons has a small cross sectional area and the other has a large cross sectional area. If a force pushes the smaller piston into the fluid, this force results in a pressure that is transmitted to the larger piston. The pressure on both the small and large pistons is the same according to Pascal's principle. Because the total force equals the pressure multiplied by the area the total force on the larger piston will be greater than the total force on the smaller piston. In a hydraulic device, the larger piston multiplies the force exerted on the smaller piston. For example, if the pistons are both circular, the smaller piston has a 1 inch radius, and the larger piston has a 10 inch radius, then the area of the larger piston is 100 times as large as that of the smaller piston. (The area of a circle equals pi times the radius squared.) Hence this larger piston multiplies any force applied to the smaller piston by 100 times. Thus a hydraulic jack with pistons of these dimensions can use a 20 pound force to lift a 2000 pound car. However nothing is free. Energy must be conserved. The 20 pound force will have to push the smaller piston 100 times the distance the mechanic wants to lift the 2000 pound car. Therefore hydraulic devices might by design multiply the force by smaller amounts to reduce the distance traveled by the smaller piston. Hydraulics is just one of many applications of the fundamental physical concept of pressure. Further ReadingKnight, R.D., Physics for Scientists and Engineers with Modern Physics, Pearson, 2004. Wilson, J.D., Buffa, A.J., and Lou, B., College Physics 6th ed., Pearson, 2007.
The copyright of the article Understanding Pascal's Principle in Physics is owned by Paul A. Heckert. Permission to republish Understanding Pascal's Principle in print or online must be granted by the author in writing.
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