Pascal's law

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See also: Pascal (unit)

In the physical sciences, Pascal's law or Pascal's principle states that "a change in the pressure of an enclosed incompressible fluid is conveyed undiminished to every part of the fluid and to the surfaces of its container."[1]

Pressure at any elevation within a column of fluid is consistent, but each elevation within that column is subject to a unique amount force being applied by the gravity of the weight of the fluid above it. This is known as hydrostatic pressure and it is non-existent in the absence of gravity. Note that the statement is in reference to "a change in the pressure..." and describes the consistency with which that change is distributed. If you leave gravity aside for the sake of summing up a fluid's properties as to its nature to displace pressure resulting from an introduced force, then this principle is still and will always be of value. If gravity is a pertinent factor in your application there is useful information to follow this brief elaboration of Pascal's Principle.

So then, to elaborate a little: Pressure is the result of a force applied over a specific area and that pressure is therefore measured by the formula of P = F/A or "Pressure = Force divided by Area". When a force is applied to a fluid which cannot be compressed, the area in question is the combined total of all points of contact between any two molecules of this fluid. And that area of contact is equal between any two molecules within the fluid. Therefore, by the formula you simply see that the pressure is the same by the same force being applied to the same size area at any point. Because this fluid, by the sheer nature of fluid will accept the applied force this consistently and evenly throughout its entire volume, the resulting PRESSURE will be EQUAL at any point because it has the same FORCE being divided over the same AREA. The molecules that are in contact with the surface of the container will be against that surface with the same measureable pressure as can be found between any two molecules anywhere else within the container because they have that exact same pressure between them and the molecules that are pressing them against the surface of the container.

Now if we consider that this container is and its fluid contents are subject to gravity as an additional force then we must consider the following.

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 metre);
g is sea level acceleration due to Earth's gravity (in metres per second squared);
Δh is the height of fluid above (in metres), 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.

In summary, this is the principle of a change in the pressure of fluid and it holds true if you aim it at a change in the force applied to the fluid, or if you aim it at the change in pressure that can be found at different elevations in a column of fluid that is subject to gravity. For either purpose this principle exposes a valuable property of fluids which can be exploited for the purposes of at least the applications listed below.

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 2x 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 metres under water, pressure is twice the atmospheric pressure at sea level, and increases by about 105 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.

See also

References

  1. ^ Bloomfield, Louis (2006). How Things Work: The Physics of Everyday Life (Third Edition). John Wiley & Sons. pp. 153. ISBN 047146886X. 
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