Pascal's law

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]

Derivation

Pressure is the result of a force applied over a specific area and that pressure is therefore measured by the formula P = F / A or "pressure equals force divided by area". When a force is applied to an incompressible fluid, the area in question is the contact area between any two molecules of the fluid. That area is the same for any pair of molecules within the fluid. Because an incompressible fluid accepts and applies forces evenly throughout itself, the pressure will be equal at all points within the fluid. The molecules that are in contact with the surface of the container will push against that surface with the same pressure as between any two molecules anywhere else within the container because they have the same contact area with the molecules of the container as with each other.

If we consider that this container and its fluid contents are subject to gravity as an additional force then we must consider that the difference of pressure due to a difference in elevation within a fluid column is given by:

where

ΔP is the hydrostatic pressure (given in pascals in the SI system), 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 in the SI system);

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

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

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

• The underlying principle of the hydraulic press
• Used for amplifying the force of the driver's foot in the braking system of most cars and trucks.
• Used in artesian wells, water towers, and dams.
• 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 105 kPa for each increase of 10 m depth.

See also

• Pascal (unit)
• Fluid statics
• Pascal's contributions to the physical sciences

References