In the physical sciences, Pascal's law or the Principle of transmission of fluid-pressure states that "pressure exerted anywhere in a confined incompressible fluid is transmitted equally in all directions throughout the fluid such that the pressure ratio (initial difference) remains the same." The law was established by French

French people

The French are a nation that share a common French culture and speak the French language as a mother tongue. Historically, the French population are descended from peoples of Celtic, Latin and Germanic origin, and are today a mixture of several ethnic groups...

 mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

 Blaise Pascal

Blaise Pascal

Blaise Pascal , was a French mathematician, physicist, inventor, writer and Catholic philosopher. He was a child prodigy who was educated by his father, a tax collector in Rouen...

.


where

is the hydrostatic pressure (given in pascals in the SI system

Si

Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric 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

Standard gravity

Standard gravity, or standard acceleration due to free fall, usually denoted by g0 or gn, is the nominal acceleration of an object in a vacuum near the surface of the Earth. It is defined as precisely , or about...

 in metres per second squared

Metre per second squared

The metre per second squared is the unit of acceleration in the International System of Units . As a derived unit it is composed from the SI base units of length, the metre, and the standard unit of time, the second...

);

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

The intuitive explanation of this formula is that the change in pressure between two elevations is due to the weight

Weight

In science and engineering, the weight of an object is the force on the object due to gravity. Its magnitude , often denoted by an italic letter W, is the product of the mass m of the object and the magnitude of the local gravitational acceleration g; thus:...

 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.
Equation: (P₁)(V₁) = (P₂)(V₂)

Applications

• The siphon
  Siphon
  The word siphon is sometimes used to refer to a wide variety of devices that involve the flow of liquids through tubes. But in the English language today, the word siphon usually refers to a tube in an inverted U shape which causes a liquid to flow uphill, above the surface of the reservoir,...
  
  
• The underlying principle of the hydraulic jack and hydraulic press
  Hydraulic press
  A hydraulic is a machine using a hydraulic cylinder to generate a compressive force. It uses the hydraulic equivalenta mechanical lever, and was also known as a Bramah press after the inventor, Joseph Bramah, of England. He invented and was issued a patent on this press in 1795...
  
  
• Force amplification in the braking system
  Hydraulic brake
  The hydraulic brake is an arrangement of braking mechanism which uses brake fluid, typically containing ethylene glycol, to transfer pressure from the controlling unit, which is usually near the operator of the vehicle, to the actual brake mechanism, which is usually at or near the wheel of the...
  
   of most motor vehicles.
• Used in artesian
  Artesian aquifer
  An artesian aquifer is a confined aquifer containing groundwater under positive pressure. This causes the water level in a well to rise to a point where hydrostatic equilibrium has been reached. This type of well is called an artesian well...
  
   wells, water tower
  Water tower
  A water tower or elevated water tower is a large elevated drinking water storage container constructed to hold a water supply at a height sufficient to pressurize a water distribution system....
  
  s, and dam
  Dam
  A dam is a barrier that impounds water or underground streams. Dams generally serve the primary purpose of retaining water, while other structures such as floodgates or levees are used to manage or prevent water flow into specific land regions. Hydropower and pumped-storage hydroelectricity are...
  
  s.
• Scuba divers
  Scuba diving
  Scuba diving is a form of underwater diving in which a diver uses a scuba set to breathe underwater....
  
   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.

Also see

• Pascal (unit)
  Pascal (unit)
  The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre...
  
  
• Fluid statics
  Fluid statics
  Fluid statics is the science of fluids at rest, and is a sub-field within fluid mechanics. The term usually refers to the mathematical treatment of the subject. It embraces the study of the conditions under which fluids are at rest in stable equilibrium...
  
  
• Pascal's contributions to the physical sciences