# Pascal (unit)

The pascal (symbol: Pa) is the SI derived unit of pressure used to quantify internal pressure, stress, Young's modulus and ultimate tensile strength. It is defined as one newton per square metre.[1] It is named after the French polymath Blaise Pascal.

Common multiple units of the pascal are the hectopascal (1 hPa = 100 Pa) which is equal to one millibar, and the kilopascal (1 kPa = 1000 Pa) which is equal to one centibar.

The unit of measurement called standard atmosphere (atm) is defined as 101325 Pa.[2] Meteorological reports typically state atmospheric pressure in millibars.

Pascal
A pressure gauge reading in psi (red scale) and kPa (black scale)
General information
Unit systemSI derived unit
Unit ofPressure or stress
SymbolPa
Named afterBlaise Pascal
Conversions
1 Pa in ...... is equal to ...
SI base units:   kgm−1s−2
US customary units:   1.450 × 10−4 psi
atmosphere:   9.869 × 10−6 atm
bar:   10−5 bar

## Etymology

The unit is named after Blaise Pascal, noted for his contributions to hydrodynamics and hydrostatics, and experiments with a barometer. The name pascal was adopted for the SI unit newton per square metre (N/m2) by the 14th General Conference on Weights and Measures in 1971.[3]

## Definition

The pascal can be expressed using SI derived units, or alternatively solely SI base units, as:

${\displaystyle {\rm {1~Pa=1~{\frac {N}{m^{2}}}=1~{\frac {kg}{m\cdot s^{2}}}=1~{\frac {J}{m^{3}}}}}}$

where N is the newton, m is the metre, kg is the kilogram, s is the second, and J is the joule.[4]

One pascal is the pressure exerted by a force of magnitude one newton perpendicularly upon an area of one square metre.

## Standard units

The unit of measurement called an atmosphere or a standard atmosphere (atm) is 101325 Pa (101.325 kPa).[5] This value is often used as a reference pressure and specified as such in some national and international standards, such as the International Organization for Standardization's ISO 2787 (pneumatic tools and compressors), ISO 2533 (aerospace) and ISO 5024 (petroleum). In contrast, International Union of Pure and Applied Chemistry (IUPAC) recommends the use of 100 kPa as a standard pressure when reporting the properties of substances.[6]

Unicode has dedicated code-points U+33A9 SQUARE PA and U+33AA SQUARE KPA in the CJK Compatibility block, but these exist only for backward-compatibility with some older ideographic character-sets and are therefore deprecated.[7][8]

## Uses

The pascal (Pa) or kilopascal (kPa) as a unit of pressure measurement is widely used throughout the world and has largely replaced the pounds per square inch (psi) unit, except in some countries that still use the imperial measurement system or the US customary system, including the United States.

Geophysicists use the gigapascal (GPa) in measuring or calculating tectonic stresses and pressures within the Earth.

Medical elastography measures tissue stiffness non-invasively with ultrasound or magnetic resonance imaging, and often displays the Young's modulus or shear modulus of tissue in kilopascals.

In materials science and engineering, the pascal measures the stiffness, tensile strength and compressive strength of materials. In engineering use, because the pascal represents a very small quantity, the megapascal (MPa) is the preferred unit for these uses.

Approximate Young's modulus for common substances [9]
Material Young's modulus
nylon 6 2–4 GPa
hemp fibre 35 GPa
aluminium 69 GPa
tooth enamel 83 GPa
copper 117 GPa
structural steel 200 GPa
diamond 1220 GPa

The pascal is also equivalent to the SI unit of energy density, J/m3. This applies not only to the thermodynamics of pressurised gases, but also to the energy density of electric, magnetic, and gravitational fields.

In measurements of sound pressure or loudness of sound, one pascal is equal to 94 decibels SPL. The quietest sound a human can hear, known as the threshold of hearing, is 0 dB SPL, or 20 µPa.

The airtightness of buildings is measured at 50 Pa.[10]

### Hectopascal and millibar units

The units of atmospheric pressure commonly used in meteorology were formerly the bar, which was close to the average air pressure on Earth, and the millibar. Since the introduction of SI units, meteorologists generally measure pressures in hectopascals (hPa) unit, equal to 100 pascals or 1 millibar.[11][12][13][14][15][16][17] Exceptions include Canada, which use kilopascals (kPa). In many other fields of science, the SI is preferred, which means Pa with a prefix (in multiples of 1000) is preferred.[18][19]

Many countries also use the millibars. In practically all other fields, the kilopascal (1000 pascals) is used instead.

## References

1. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 118, ISBN 92-822-2213-6, archived (PDF) from the original on 2017-08-14
2. ^ "Definition of the standard atmosphere". BIPM. Retrieved 2015-02-16.
3. ^ bipm.fr Archived 30 June 2007 at the Wayback Machine.
4. ^ Table 3 (Section 2.2.2) Archived 18 June 2007 at the Wayback Machine., SI Brochure, International Bureau of Weights and Measures
5. ^ "Resolution 4 of the 10th meeting of the CGPM". Conférence Générale des Poids et Mesures (CGPM). 1954. Retrieved 2010-04-05.
6. ^ IUPAC.org, Gold Book, Standard Pressure
7. ^ "CJK Compatibility" (PDF). 2015. Retrieved 2016-02-21.
8. ^ "The Unicode Standard, Version 8.0.0". Mountain View, CA: The Unicode Consortium. 2015. ISBN 978-1-936213-10-8. Retrieved 2016-02-21.
9. ^ "Tensile Modulus - Modulus of Elasticity or Young's Modulus - for some common Materials". Retrieved 2015-02-16.
10. ^ "Chapter 7 ResNet Standards: ResNet National Standard for Home Energy Audits" (PDF). ResNet. 2010. Archived from the original (PDF) on 26 July 2011. Retrieved 3 March 2011.
11. ^ "KNMI - Weer - Waarnemingen". Retrieved 4 December 2016.
12. ^ "Comment convertir la pression? - IRM". Retrieved 4 December 2016.
13. ^ DWD
14. ^ "Japan Meteorological Agency - Weather Maps". Retrieved 4 December 2016.
15. ^ MDD Archived 6 May 2006 at the Wayback Machine.
16. ^ NOAA
17. ^ Kingdom, Met Office, FitzRoy Road, Exeter, Devon, EX1 3PB, United. "Key to symbols and terms". Retrieved 4 December 2016.
18. ^ CTV News, weather; current conditions in Montreal Archived 4 June 2011 at the Wayback Machine.
19. ^ Canada, Environment. "Montréal, QC - 7 Day Forecast - Environment Canada". Retrieved 4 December 2016.

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