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Pascal (unit)
Pascal (unit)
Pascal (unit)
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pascal
A pressure gauge reading in psi (red scale) and kPa (black scale)
General information
Unit systemSI
Unit ofpressure or stress
SymbolPa
Named afterBlaise Pascal
Conversions
1 Pa in ...... is equal to ...
   SI base units:   kg⋅m−1⋅s−2
   US customary units:   1.45038×10−4 psi
   atmosphere:   9.86923×10−6 atm
   bar:   10−5 bar
   barye (CGS unit)   10 Ba

The pascal (symbol: Pa) is the unit of pressure in the International System of Units (SI). It is also used to quantify internal pressure, stress, Young's modulus, and ultimate tensile strength. The unit, named after Blaise Pascal, is an SI coherent derived unit defined as one newton per square metre (N/m2).[1] It is also equivalent to 10 barye (10 Ba) in the CGS system. Common multiple units of the pascal are the hectopascal (1 hPa = 100 Pa), which is equal to one millibar, and the kilopascal (1 kPa = 1,000 Pa), which is equal to one centibar.

The unit of measurement called standard atmosphere (atm) is defined as 101325 Pa.[2] Meteorological observations typically report atmospheric pressure in hectopascals per the recommendation of the World Meteorological Organization, thus a standard atmosphere (atm) or typical sea-level air pressure is about 1,013 hPa. Reports in the United States typically use inches of mercury[3] or millibars (hectopascals).[4][5] In Canada, these reports are given in kilopascals.[6]

Etymology

[edit]

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.[7][8]

Definition

[edit]

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

where N is the newton, m is the metre, kg is the kilogram, s is the second, and J is the joule.[9]

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

Standard units

[edit]

The unit of measurement called an atmosphere or a standard atmosphere (atm) is 101325 Pa (101.325 kPa).[10] 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.[11]

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.[12][13]

Uses

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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 the megapascal (MPa) is the preferred unit for these uses, because the pascal represents a very small quantity.

Approximate Young's modulus for common substances[14]
Material Young's modulus
(GPa)
Nylon 6 2–4
Hemp fibre 35
Aluminium 69
Tooth enamel 83
Copper 117
Structural steel 200
Diamond 1220

The pascal is also equivalent to the SI unit of energy density, the joule per cubic metre. This applies not only to the thermodynamics of pressurised gases, but also to the energy density of electric, magnetic, and gravitational fields.

The pascal is used to measure sound pressure. Loudness is the subjective experience of sound pressure and is measured as a sound pressure level (SPL) on a logarithmic scale of the sound pressure relative to some reference pressure. For sound in air, a pressure of 20 μPa is considered to be at the threshold of hearing for humans and is a common reference pressure, so that its SPL is zero.

The airtightness of buildings is measured at 50 Pa.[15]

In medicine, blood pressure is measured in millimeters of mercury (mmHg, very close to one Torr). The normal adult blood pressure is less than 120 mmHg systolic BP (SBP) and less than 80 mmHg diastolic BP (DBP).[16] Convert mmHg to SI units as follows: 1 mmHg = 0.13332 kPa. Hence the normal blood pressure in SI units is less than 16.0 kPa SBP and less than 10.7 kPa DBP. These values are similar to the pressure of water column of average human height; so pressure has to be measured on arm roughly at the level of the heart.

Hectopascal and millibar units

[edit]
Main article: Bar (unit)

The units of atmospheric pressure commonly used in meteorology were formerly the bar (100000 Pa), which is close to the average air pressure on Earth, and the millibar. Since the introduction of SI units, meteorologists generally measure atmospheric pressure in hectopascals (hPa), equal to 100 pascals or 1 millibar.[17][18][19][20][21][22][23] Exceptions include Canada, which uses kilopascals (kPa). In many other fields of science, prefixes that are a power of 1000 are preferred, which theoretically excludes hectopascal from use.[24][25]

Many countries still use millibars to measure atmospheric pressure. In practically all other fields, the kilopascal is used instead.[26]

Multiples and submultiples

[edit]

Decimal multiples and submultiples are formed using standard metric prefixes.

Multiples Submultiples
Value Name Symbol Value Name Symbol
101 Pa decapascal daPa 10−1 Pa decipascal dPa
102 Pa hectopascal hPa 10−2 Pa centipascal cPa
103 Pa kilopascal kPa 10−3 Pa millipascal mPa
105 Pa bar (non-SI unit) bar
106 Pa megapascal MPa 10−6 Pa micropascal μPa
109 Pa gigapascal GPa 10−9 Pa nanopascal nPa
1012 Pa terapascal TPa 10−12 Pa picopascal pPa
1015 Pa petapascal PPa 10−15 Pa femtopascal fPa
1018 Pa exapascal EPa 10−18 Pa attopascal aPa
1021 Pa zettapascal ZPa 10−21 Pa zeptopascal zPa
1024 Pa yottapascal YPa 10−24 Pa yoctopascal yPa
1027 Pa ronnapascal RPa 10−27Pa rontopascal rPa
1030 Pa quettapascal QPa 10−30 Pa quectopascal qPa

See also

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References

[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Pascal (unit)

View on Grokipedia
from Grokipedia
The pascal (symbol: Pa) is the coherent derived unit of and stress in the (SI), measuring force applied per unit area. It is defined as one newton per (1 Pa = 1 N/m²), which in terms of base SI units equates to one per (1 Pa = 1 kg⋅m⁻¹⋅s⁻²). The unit is named in honour of Blaise Pascal (1623–1662), the French mathematician, physicist, inventor, writer, and philosopher whose pioneering work on fluids and advanced the scientific understanding of . Pascal formulated what is now known as , which states that a pressure change occurring anywhere within a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere, providing a foundational principle for and modern . His brother-in-law, Florin Périer, conducted key experiments under Pascal's direction demonstrating that decreases with altitude, using barometers carried up the Puy de Dôme mountain to verify the weight of the air column above. The name "pascal" was officially adopted for the SI unit of newton per by the 14th General Conference on Weights and Measures (CGPM) in 1971, replacing earlier non-coherent units like the bar and per square in scientific and technical contexts. Although the pascal is the standard SI unit, its magnitude is small for many practical applications; for instance, standard at is exactly 101 325 Pa, often expressed as 101.325 kPa (kilopascals). The pascal is widely used in fields such as , , acoustics, and to quantify phenomena ranging from tire inflation to levels.

History and Naming

Etymology

The pascal (Pa), the SI unit of pressure, is named after Blaise Pascal (1623–1662), a prominent French mathematician, physicist, inventor, philosopher, and theologian whose pioneering work in hydrostatics and fluid mechanics provided foundational insights into pressure concepts. The name "pascal" was officially adopted by the 14th General Conference on Weights and Measures (CGPM) in 1971 as a special name for the SI coherent derived unit of pressure, equivalent to one newton per square metre. In English, the unit is typically pronounced /ˈpæskəl/, approximating the original French pronunciation /paskal/.

Historical Development

The concept of pressure has roots in ancient hydrostatic principles, notably ' work in the BCE, which described the buoyant force on immersed objects as arising from differences in fluid . This laid the groundwork for quantitative understanding of pressure in fluids, though early measurements remained qualitative. In the 17th century, advanced the field by inventing the mercury in 1643, enabling the first direct measurement of through the height of a supported mercury column. built on this in 1647–1648 by directing experiments using barometers and vacuums, including observations conducted by his brother-in-law Florin Périer on mountain, demonstrating that decreases with altitude. The 19th century saw proposals for standardized units to support growing scientific precision. suggested an absolute system based on the centimeter, gram, and second (CGS) in 1832, formalized by the British Association for the Advancement of Science (BAAS) in 1874 as a coherent mechanical framework. In this system, pressure was expressed in s, defined as one per square centimeter; the name "" was recommended by an international congress of physicists in 1900 to denote this unit, reflecting efforts to unify electromagnetic and mechanical measurements. Concurrently, the metre-kilogram-second (MKS) system emerged, with Giovanni Giorgi proposing its extension to include electrical units (MKSA) in 1901, addressing limitations of the smaller-scale CGS for practical engineering applications. Post-World War II, international efforts accelerated toward a unified metric framework amid global scientific collaboration. The International Committee for Weights and Measures (CIPM) authorized the MKS system in 1946 for deriving coherent units, particularly in electricity and magnetism. The 9th General Conference on Weights and Measures (CGPM) in 1948 approved supplementary MKS-based units, paving the way for broader adoption. These initiatives culminated in the 11th CGPM's establishment of the (SI) in 1960, defining pressure coherently as one newton per to replace disparate national standards. The 14th CGPM in 1971 formally named this pressure unit the pascal (Pa), honoring Blaise Pascal's contributions while integrating it into the SI structure. However, challenges arose in fully supplanting legacy units; the atmosphere (), defined as 101325 Pa based on historical barometric standards, persists in and due to its convenience for expressing near-sea-level pressures and entrenched usage in those domains. This coexistence highlights the tension between SI coherence and practical continuity in specialized fields.

Definition and Fundamentals

Formal Definition

The pascal (symbol: Pa) is the of and stress. It is defined as exactly one newton of per square metre of area, or 1 Pa=1 N/m21 \, \mathrm{Pa} = 1 \, \mathrm{N/m^2}. In physical terms, pressure PP is the FF applied perpendicular to a surface divided by the area AA over which it is distributed, expressed as P=FA,P = \frac{F}{A}, where FF is measured in newtons and AA in square metres. This definition ensures the pascal quantifies the intensity of distribution uniformly across scientific and engineering contexts. As a coherent derived SI unit, the pascal is not defined by reference to a specific physical artefact but arises directly from the SI base units through their fixed values tied to fundamental physical constants, particularly the definitions of the , , and second. This coherence allows for exact realization of the unit without reliance on prototypes, promoting universality and precision in measurements.

Relation to Base SI Units

The pascal (Pa) is expressed in terms of the SI base units as 1 Pa = kg·m⁻¹·s⁻². This dimensional formula arises from the definition of as per unit area. is measured in newtons (N), where 1 N = 1 kg·m·s⁻², derived from Newton's second law as F = m·a, with m in kilograms (kg) and acceleration a in meters per second squared (m·s⁻²). Area is measured in square meters (). Thus, P = F/A yields: Pa=Nm2=kg⋅m⋅s−2m2=kg⋅m−1⋅s−2.\mathrm{Pa} = \frac{\mathrm{N}}{\mathrm{m}^2} = \frac{\mathrm{kg \cdot m \cdot s^{-2}}}{\mathrm{m}^2} = \mathrm{kg \cdot m^{-1} \cdot s^{-2}}. In dimensional terms, the pascal has the formula [Pa] = M L⁻¹ T⁻², where M represents the dimension of mass, L of length, and T of time, corresponding directly to the base units kilogram, meter, and second. As a coherent derived unit within the (SI), the pascal requires no numerical conversion factors when expressed in terms of the base units, ensuring algebraic consistency in physical equations involving pressure. This coherence distinguishes it from some non-SI units that incorporate arbitrary constants.

Equivalents and Conversions

Common Equivalent Units

The pascal (Pa) relates to the imperial unit of pounds per square inch (psi) through the conversion factor 1 = 6894.757 Pa, or inversely, 1 Pa = 1.450×10−41.450 \times 10^{-4} psi (rounded). In atmospheric pressure contexts, 1 standard atmosphere () is defined as exactly 101 325 Pa, yielding 1 Pa ≈9.869×10−6\approx 9.869 \times 10^{-6} . Among other metric pressure units, the bar is exactly 100 000 Pa, so 1 Pa = 10−510^{-5} bar. The torr, commonly used in vacuum measurements, equals approximately 133.322 Pa, while the millimeter of mercury (mmHg, conventional) shares the same value of 133.322 Pa. For quick reference, the following table summarizes key conversion factors (values in bold are ; others approximate).
UnitValue in PaPa in UnitNotes
psi6894.7571.450×10−41.450 \times 10^{-4}
101 3259.869×10−69.869 \times 10^{-6}Standard atmosphere
bar100 00010−510^{-5}
133.3227.500×10−37.500 \times 10^{-3}Also applies to mmHg (0°C)
mmHg (conv.)133.3227.500×10−37.500 \times 10^{-3}Conventional; historical unit

Multiples and Submultiples

The pascal (Pa) is scaled using standard SI prefixes to create multiples and submultiples that accommodate a wide range of pressure measurements, from atmospheric conditions to extreme geophysical or material stresses. These prefixes, defined by the International Bureau of Weights and Measures (BIPM), enable the expression of pressures in decimal powers of ten, avoiding awkward large or small numerical values while maintaining coherence with the SI system. Common multiples include the kilopascal (kPa = 10310^3 Pa), which is extensively used in for moderate pressures such as those in pneumatic systems, tires, and load calculations. The megapascal (MPa = 10610^6 Pa) is applied in materials testing to quantify high stresses, including the compressive and tensile strengths of alloys, , and polymers under load-bearing conditions. For extreme environments, the gigapascal (GPa = 10910^9 Pa) measures pressures in high-pressure physics experiments, such as those simulating or shock-wave impacts on metals. Submultiples are employed for low-pressure regimes. The millipascal (mPa = 10−310^{-3} Pa) is infrequently used, as it remains too coarse for most sensitive measurements. The micropascal (µPa = 10−610^{-6} Pa) serves in acoustics to reference levels, particularly in environments where 1 µPa is the standard for calculations. In , the nanopascal (nPa = 10−910^{-9} Pa) quantifies subtle dynamic pressures, such as interactions with planetary magnetospheres. The hectopascal (hPa = 10210^2 Pa), while a multiple, is notably used in and equals one millibar. The following table summarizes key SI prefixes applied to the pascal, including their scaling factors and representative applications:
PrefixSymbolScaling FactorTypical Application
hecto-hPa10210^2Meteorological reporting
kilo-kPa10310^3Engineering and
mega-MPa10610^6Materials strength testing
giga-GPa10910^9High-pressure experiments
milli-mPa10−310^{-3}Rare low-pressure contexts
micro-µPa10−610^{-6}Acoustic levels
nano-nPa10−910^{-9}Geophysical pressure variations
SI prefixes enhance by standardizing the representation of pressures across orders of magnitude, facilitating international communication, precise calculations, and comparison in without reliance on disparate customary units. This systematic approach reduces errors in data interpretation and supports interdisciplinary applications in fields like engineering and physics.

Applications and Usage

General Uses in Science and Engineering

In physics, the pascal is commonly used to measure hydrostatic , which arises from the weight of a at rest, as described by Pascal's principle stating that pressure applied to an enclosed is transmitted undiminished throughout the and to the container walls. This principle underpins applications in hydraulic systems where pressure differences drive behavior. For dynamic in moving , the pascal quantifies the kinetic energy per unit volume, integral to , which relates , velocity, and elevation in flow, such as in and analysis. In engineering, the pascal serves as the unit for stress in materials, defined as per unit area, enabling analysis of deformation under load. , a measure of material stiffness, is expressed in pascals, with steel typically around 200 GPa, illustrating how the unit scales to gigapascals for high-strength applications like structural beams, while megapascals are used for moderate stresses in composites. In , tire is routinely specified in kilopascals, with standard car tires inflated to 200–250 kPa to balance load support, , and safety. In acoustics, sound pressure level is measured in pascals relative to a of 20 micropascals (20 µPa), the approximate threshold of human hearing at 1 kHz, converting to the scale via the 20 log₁₀(p / p₀) where p is the root-mean-square . This ensures standardized quantification of , from quiet environments at near 0 dB to industrial noise exceeding 100 dB. In vacuum technology, the pascal measures low pressures essential for semiconductor manufacturing, where high vacuum (10⁻¹ to 10⁻⁵ Pa) prevents contamination during processes like thin-film deposition and . For simulation chambers, pressures below 10⁻⁵ Pa replicate orbital conditions, testing components for and thermal effects under .

Specialized Uses in Meteorology and Other Fields

In , the hectopascal (hPa), equivalent to 100 pascals (Pa), serves as the standard unit for measuring due to its alignment with typical sea-level values around 1013 hPa. This unit facilitates the depiction of isobars on global maps, where contours of equal in hPa illustrate high- and low-pressure systems influencing weather patterns. The hectopascal was adopted internationally by meteorologists as a convenient multiple of the pascal, reflecting pressures that vary from about 850 hPa at 1500 meters to 500 hPa at 5500 meters. The hectopascal maintains equivalence with the millibar (mbar), where 1 hPa equals exactly 1 mbar or 100 Pa, a reinforced by international agreements to unify reporting in scientific contexts. This exact relation stems from the bar's definition as 10^5 Pa, making the millibar precisely 100 Pa, though the millibar originated earlier in the early for meteorological convenience before the pascal's formal SI adoption in 1971. Both units persist in and because of established conventions in settings and terminal forecasts (TAFs), where pressures are reported in hPa or mbar to ensure compatibility with global flight operations. In medical applications, is traditionally measured in millimeters of mercury (mmHg), but conversions to pascals are common in research for consistency with SI units, with normal systolic pressure approximating 16 kPa (equivalent to 120 mmHg). This conversion supports biomechanical studies and sensor development, where devices achieve sensitivities around 4.82 kPa⁻¹ to capture arterial pulses accurately. In , seismic wave pressures are quantified in pascals to assess ground motion effects, typically reaching a few thousand pascals—about 1% of —for moderate events. In , the pascal measures hydrostatic pressures in deep-sea environments, escalating to around 100 MPa at the ocean's greatest depths, such as the , where each 10 meters of descent adds approximately 0.1 MPa.

References

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  35. https://www.ess.uci.edu/~yu/class/ess200a/lecture.3.atmosphere.all.pdf
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