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# Pascal's law

In the physical sciences, Pascal's law or Pascal's principle states that for all points at the same absolute height in a connected body of an incompressible fluid at rest, the fluid pressure is the same, even if additional pressure is applied on the fluid at some place.

The difference of pressure due to a difference in elevation within a fluid column is given by:

$\Delta P =\rho g (\Delta h)\,$

where, using SI units,

ΔP is the hydrostatic pressure (in pascals), or the difference in pressure at two points within a fluid column, due to the weight of the fluid;

ρ is the fluid density (in kilograms per cubic meter);

g is sea level acceleration due to Earth's gravity (in meters per second squared);

Δh is the height of fluid above (in meters), or the difference in elevation between the two points within the fluid column.

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.

## Applications

• Pascal's principle underlies the hydraulic press.
• Used in artesian wells, water towers, and dams.
• 'Pascal's burst barrel demonstration': a long and narrow vertical pipe is connected to the contents of a large, sealed barrel. Adding water to the pipe increases the pressure throughout the system. Adding a small amount of water to the pipe is enough to burst the barrel. Scuba divers must understand this principle. At a depth of 10 meters 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.