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 differents heights h₁ and h₂ is given by :

[P_2 - P_1=- \rho g (h_2-h_1)\,]

where ρ (rho) is the density of the fluid, g the acceleration due to gravity, and h₁, h₂ are elevations. (The intuitive interpretation of this formula is that the pressure at the base of a column of fluid is greater due to the weight of the column.)

Note that the variation with height does not depend on any additional pressures, therefore Pascal's law can be formulated by 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.
Artesian wells, water towers, dams
'Pascal's barrel experiment': a long and narrow vertical pipe is connected to the content 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 100 kPa for every extra 10 m of depth.
On the other hand, 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. As the atmosphere gets lighter with height, the atmospheric pressure varies exponentially with height. This is expressed functionally through the barometric formula.

Pascal's law

Applications

See also