Pascal's law
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In the physical sciences, Pascal's law or Pascal's principle states that the fluid pressure at all points in a connected body of an incompressible fluid at rest, which are at the same absolute height, is the same, even if additional pressure is applied on the fluid at some place.
On the other hand, the difference of pressure between two different heights h1 and h2 is given by:
where ρ (rho) is the density of the fluid, g the acceleration due to gravity, and h1, h2 are elevations. The intuitive explanation of this formula is that the change in pressure between two elevations is due to the weight of the fluid between the elevations.
Note that the variation with height does not depend on any additional pressures. Therefore Pascal's law can be interpreted as saying that any change in pressure applied at any given point of the fluid is transmitted undiminished throughout the fluid.
[edit] Applications
- Pascal's principle underlies the hydraulic press.
- Artesian wells, water towers, dams
- 'Pascal's barrel experiment': a long and narrow vertical pipe is connected to the contents of a large barrel. If you put water into the pipe, even in small quantity, the height of the fluid within the pipe will sharply increase, and can induce the break of the barrel.
- The pressure under water increases with depth, a fact well known to scuba divers. At a depth of 10 m under water, pressure is twice the atmospheric pressure at sea level, and increases by about 100 kPa for each increase of 10 m depth.
- Atmospheric pressure diminishes with height, a fact first verified on the Puy-de-Dôme and the Saint-Jacques Tower in Paris, on the instigation of Blaise Pascal himself. Following the explanation given above, as height increases the mass of air above each unit of surface area decreases.
