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pascal

What is a pascal?

The pascal (Pa) is the unit of pressure or stress in the International System of Units (SI). It is named after the scientist and mathematician Blaise Pascal. One pascal is equivalent to 1 newton (N) of force applied over an area of 1 square meter (m2).

The pascal is also used to measure stress, specifically tectonic stress in the Earth's plates. For most engineering problems, the unit is too small to properly represent pressure or stress, which is why it is often expressed in its multiples, like the kilopascal (kPa), megapascal (MPa), millibar (100 Pa), etc.

Understanding pascal

Pressure is the force applied over an area. In the meter-kilogram-second system, it is expressed in pascals. Specifically, a pascal measures the pressure applied by 1 N of force applied on an area of 1 m2 at a right angle. SI accepted it as the standard unit of pressure in 1971 and named it after Blaise Pascal.

In mathematical terms, pressure can be expressed as the following:

  • Pressure (P) = Force (F) / Area (A)

If F is measured in newtons and A in square meters, a pascal can be expressed as the following:

  • 1 Pa = 1 N / m2 = 1 N x m-2 or 1 N per m2

Reduced to base units in SI, 1 Pa is 1 kilogram per m/s2 -- that is, 1 Pa = 1 kg x m-1 x s-2.

Larger pascal units are expressed as follows:

  • 1 kPa = 1,000 Pa = 103 N/m2
  • 1 bar = 105 Pa = 105 N/m2
  • 1 MPa = 106 Pa = 106 N/m2

Blaise Pascal is also the namesake behind the well-known Pascal's law, which is used to develop hydraulic systems. A principle in fluid mechanics, it states that a change in pressure in a fluid creates the same change everywhere within the body of the fluid.

Measuring pressure in pascal

Here is an example of how pressure is measured in pascal.

Consider an object being pushed against a wall with a force of 400 N. The surface area that the object makes with the wall is 0.0008 m2. Using this data, pressure can be calculated as follows:

  • P = 400/0.0008 = 500,000 Pa or 500 kPa

Since pressure and surface area are inversely related, an object of a smaller surface area generates a higher pressure than a larger object. This explains why a small pin or screw can penetrate a concrete wall when only a small or moderate force is applied, but a human thumb fails to do the same even if the force applied is larger.

Young's modulus and pascals

Young's modulus is a mathematical constant that describes the elasticity of solid materials. When compression or tension is applied to the modulus, the material is either elastic or inelastic -- or some version between these properties. If Young's modulus is high, the material is less elastic and vice versa. The pascal is used to measure this value and to understand if a material is elastic or not and to what extent.

Pascal versus PSI

In some countries, such as the U.S., pressure is expressed as pounds per square inch (PSI). But, in most other countries that use metric and SI measurements, the pascal is used to measure pressure.

Unlike units such as PSI where the pressure value may vary, the pressure value represented by 1 Pa remains unchanged, regardless of where it is used. Additionally, the unit is independent of other factors, such as ambient temperature, media density or local gravity.

Uses of pascal

A pascal is useful for ultralow gas pressure applications, such as ventilation systems where pressure differences need to be measured. For measuring midrange pressures, higher pascal units, such as kilopascal, megapascal and hectopascal (hPa) are used.

Geophysicists use the unit to study tectonic stresses acting on the Earth's plates. Material scientists use it to measure the elasticity, stiffness, tensile strength and compressive strengths of different materials.

Meteorologists also use the unit to measure air pressure, which is usually expressed in hectopascal.

Common conversions among different pressure units

Pascal is not the only unit of pressure. It is useful to understand some common conversions among these different units:

  • 1 Pa = 0.00001 bar or 1 bar = 100,000 Pa
  • 1 Pa = 0.0000098692316931 atmosphere (standard) and 1 atm = 101.325 kPa
  • 1 Pa = 0.00014503773801 PSI or 1 PSI = 6,895 Pa

Pascal, pressure and vacuum

Any pressure value that falls below standard atmosphere pressure is considered a vacuum.

  • 1 atm = 101,325 Pa
  • 5 Pa = ~0.005% of atmosphere

A value of 5 Pa below atmospheric pressure would create a small suction pressure, whereas 5 Pa above atmospheric pressure would create a strong vacuum at the opposite end of the vacuum scale. 5 Pa below is also known as -5 Pa gauge, while 5 Pa above is also known as 5 Pa absolute. A perfect vacuum would correspond to absolute zero pressure.

See also: gas constant, power take-off and table of physical constants.

This was last updated in May 2022

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