Pascal’s law: Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. The hydraulic lift (Fig. 12.7) illustrates Pascal’s law. A piston with small cross-sectional area A1 exerts a force F1 on the surface of a liquid such as oil. The applied pressure.
p = F1/A1 is transmitted through the connecting pipe to a larger piston of area A2. The applied pressure is the same in both cylinders, so
The hydraulic lift is a force-multiplying device with a multiplication factor equal to the ratio of the areas of the two pistons. Dentist’s chairs, car lifts and jacks, many elevators, and hydraulic brakes all use this principle. For gases the assumption that the density r is uniform is realistic over only short vertical distances. In a room with a ceiling height of 3.0 m filled with air of uniform density 1.2 kg/m3 , the difference in pressure between floor and ceiling, given by Eq. (12.6), is
or about 0.00035 atm, a very small difference. But between sea level and the summit of Mount Everest (8882 m) the density of air changes by nearly a factor of 3, and in this case we cannot use Eq. (12.6). Liquids, by contrast, are nearly incompressible, and it is usually a very good approximation to regard their density as independent of pressure.