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In the physical sciences, Pascal's law or Pascal's principle gives the fluid pressure at mechanical equilibrium (see also fluid statics), on which only gravity forces are taken into account. More specifically, this law is actually a set of principles or laws discovered in 1648 by the scientist, Blaise Pascal,summarized as: "In a body of equally dense fluid at rest, the pressure is the same for all points in the fluid so long as those points are at the same depth below the fluid's surface." (Franzini and Daugherty 1977) (See also Pascal's Contributions to the physical sciences .)

[edit] Formula

The intuitive formulation is that the pressure at the base of a column of water is due to the weight of the column.

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 or volumic mass of the fluid, g the acceleration due to gravity, and h1, h2 are elevations.

[edit] Applications

  • 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.
  • Any change in pressure applied at any given point on a confined and incompressible fluid is transmitted undiminished throughout the fluid.
  • 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.
  • 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.
  • Pascal's principle underlies the Hydraulic press.

[edit] References

Daugherty, R.L., and Franzini, J.B. (1977). Fluid Mechanics with Engineering Applications, Seventh Edition, New York: McGraw-Hill, p. 26.

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