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Units of Pressure

07th Aug 2019 @ 30 min read

Physical Chemistry

What is pressure? The pressure is the force to perpendicular to a unit surface. In other words, it is the perpendicular force per unit area. The pressure is a scalar quantity and has the dimension of the force divided by the area.

P =\frac{F}{A}

The pressure is a widely used quantity; it is found in physics, chemistry, engineering, and biology. Because of the wide usage of pressure, it has adopted various units to express it. And it is necessary for us to know the relationship between various units of pressure.

Pressure Converter

Enter a value and choose desired pressure units.




List of Important Pressure Units

The table below list important units of pressure with its symbols.

Table 1: Units of Pressure
SymbolUnitComment
atmatmospherea standard unit of pressure
attechnical atmosphereIt is a non-SI unit and a unit value of it is equivalent to 1 kilogram-force per square centimetre
N m−2 or Panewton per square metre or Pascalthe SI unit of pressure
µPamicropascala metric unit, derived from the pascal
hPahectopascala metric unit, derived from the pascal
MPamegapascala metric unit, derived from the pascal
GPagigapascala metric unit, derived from the pascal
barbara non-SI metric unit
mbarmillibara non-SI metric unit, derived from the bar
dbardecibara non-SI metric unit, derived from the bar
Torrtorra non-SI standard unit of pressure
mmHgmillimetre of mercurya manometric unit based on mercury
cmHgcentimetre of mercurya manometric unit based on mercury
inHginch of mercurya manometric unit based on mercury
ftHgfoot of mercurya manometric unit based on mercury
mmH2Omillimetre of watera manometric unit based on water
cmH2Ocentimetre of watera manometric unit based on water
inH2Oinch of watera manometric unit based on water
ftH2Ofoot of watera manometric unit based on water
mswmetre sea wateran underwater diving unit
fswfoot sea wateran underwater diving unit

Other Units of Pressure

The other nonstandard units of pressure are listed below.

Table 2: List of Nonstandard Units of Pressure
SymbolUnitComment
kgf cm−2kilogram-force per square centimetrea gravitational metric unit
gf cm−2gram-force per square centimetrea gravitational metric unit
dyne cm−2 or Babaryethe CGS unit of pressure
psi or lbf in−2pound per square inch or pound-force per square inchthe most used imperial unit of pressure
ksikilopound per square inchan imperial unit of pressure, derived from psi
Mpsimegapound per square inchan imperial unit of pressure, derived from psi
lbf ft−2pound-force per square footan imperial unit of pressure
kip in−2kip per square inchan imperial unit of pressure, derived from psi
ozf in−2ounce-force per square incha US customary unit
ozf ft−2ounce-force per square footan imperial unit of pressure
pdl in−2poundal per square inchan imperial unit of pressure
pdl ft−2poundal per square footan imperial unit of pressure
tf m−2tonne-force per square metrea metric unit based on tonne
tf cm−2tonne-force per square centimetrea metric unit based on tonne
tf in−2long ton-force per square incha UK (imperial) unit based on ton
tf ft−2long ton-force per square foota UK (imperial) unit based on ton
tf in−2short ton-force per square incha US (customary) unit based on ton
tf ft−2short ton-force per square foota US (customary) unit based on ton
pzpiezea unit in metre-tonne-second system

Conversion Table

The conversion table below gives the relationship between some important units of pressure.

Table 3: Pressure Units Conversion Table
UnitsPabarTorrpsiat (≡ kgf cm−2)atm
1 Pa11 × 10−57.500 62 × 10−31.450 38 × 10−41.019 72 × 10−59.869 23 × 10−6
1 bar1 × 1051750.06214.503 81.019 720.986 923
1 Torr133.3221.333 22 × 10−311.933 68 × 10−21.359 51 × 10−31.315 79 × 10−3
1 psi6 894.766.894 76 × 10−251.714 917.030 70 × 10−26.804 60 × 10−2
1 at (≡ kgf cm−2)98 066.50.980 665735.55914.223 310.967 841
1 atm101 3251.013 2576014.695 91.033 231
Note: The above values are accurate up to six significant digits, and the values marked by † are exact values.

How to use the conversion table?

The above table is divided into units and values; the values are conversion factors. The first row and the first column represent the units and the remaining cells are the values. A unit in the first column has a unit value (e.g., 1 Pa, 1 bar) while a unit in the first row have a value of its conversion factor.

Consider an example of Torr to Pa.

1 \,\text{Torr} =133.322 \,\text{Pa}

In the above equation, 1 Torr is the unit from the first column has a unit value, and the right-hand side of the equation, 133.322 Pa, is formed from the first-row unit and the conversion factor.

\underbrace{1 \,\text{Torr}}_{\text{1}^\text{st} \,\text{column}} = \underbrace{133.322}_{\text{conversion} \, \text{factor}} \,\underbrace{\text{Pa}}_{\text{1}^\text{st} \,\text{row}}

Similarly for Pa to Torr,

\underbrace{1 \,\text{Pa}}_{\text{1}^\text{st} \,\text{column}} =\underbrace{7.500\,62 \times 10^{-3}}_{\text{conversion} \,\text{factor}} \,\underbrace{\text{Torr}}_{\text{1}^\text{st} \,\text{row}}

Conversion Scales

mmHg to atm

 mmHg and atm Conversion Scale
Figure 1: mmHg and atm Conversion Scale

psi to bar

psi and bar Conversion Scale
Figure 2: psi and bar Conversion Scale

psi to kPa

psi and kPa Conversion Scale
Figure 3: psi and kPa Conversion Scale

Pascal

The SI unit of pressure is the pascal (Pa) or the newton per square metre (N m−2) or (kg m−1 s−2). The unit pascal is christened after French mathematician Blaise Pascal. One pascal is a force of one-newton perpendicular to a surface of one square metre.

One pascal is a force of one newton applied perpendicular to a surface of one square metre
Figure 4: One pascal is a force of one newton applied perpendicular to a surface of one square metre.

The pascal is the recognised SI derived unit of pressure and can also be expressed in terms of SI base units.

1\,\text{Pa} =\frac{1\,\text{N}}{1 \,\text{m}^{2}} =\frac{\text{kg}\,\text{m}\,\text{s}^{-2}}{1 \,\text{m}^{2}} =\text{kg} \,\text{m}^{-1}\,\text{s}^{-2}

The pascal can also be expressed in terms of the joule, which is the SI unit of energy.

1 \,\text{Pa} =\frac{1 \,\text{N}}{1 \,\text{m}^{2}} =\frac{1 \,\text{N} \,\text{m}}{1 \,\text{m}^{3}} =\frac{\text{J}}{\text{m}^3}

The International Union of Pure and Applied Chemistry recommends 1 × 105 Pa as a reference standard pressure.

The common derivatives of the pascal are the micropascal, the hectopascal, the kilopascal, the megapascal, and the gigapascal. The relationship among all follows as:

1 \,\text{Pa} &=1 \times 10^{3} \mu\text{Pa} \\ &=1 \times 10^{-2} \,\text{hPa} \\ &=1 \times 10^{-3} \,\text{kPa} \\ &=1 \times 10^{-6} \,\text{MPa} \\ &=1 \times 10^{-9} \,\text{GPa}

The pascal is a very small unit, the micropascal is the smallest among them. The kilopascal is a widely used unit often atmospheric pressures are reported in kPa. The mechanical quantities like Young’s modulus, shear modulus, tensile strength, stiffness are displayed in the kilopascal (kPa) and the megapascal (MPa). The gigapascal (GPa) is preferred by geophysicists since the stresses and pressures within the Earth are in a large order of magnitude.

The hectopascal (hPa) is used by meteorologists to measure the pressure of air.

Note: one hectopascal is equivalent to one minibar.

1 \,\text{hPa}= 1 \,\text{mbar}

Bar

The bar is another common unit used to measure pressure. It is a metric non-SI unit and defined exactly to 1 × 105 Pa.

1 \,\text{bar}=100 \,00 \,\text{Pa}
Pressure Gauge Scaled in the bar
Figure 5: Pressure Gauge Scaled in the bar

The bar is slightly less than an atomophere (1 bar ≈ 0.986 923 atm).

The most common derived units of the bar are the millibar (mbar), the centibar (cbar), the decibar (dbar) and the kilobar (kbar).

1 \,\text{bar} &= 1 \times 10^{3} \,\text{mbar} \\ &= 1 \times 10^{2} \,\text{cbar} \\ &= 10 \,\text{dbar} \\ &= 1 \times 10^{-3} \,\text{kbar}

The bar was introduced by Norwegian scientist Vilhelm Friman Koren Bjerknes. He was a well-known meteorologist and contributed to modern weather forecasting. Since then, the bar, precisely the minibar, remains a widely used unit in meteorology. The atmospheric pressures are reported mostly reported in mbar. Some scientists use the hectopascal hPa, the bar equivalent in SI, as a standard unit.

Pressures in the map is reported in mbar.
Figure 6: Pressures in the map is reported in mbar.

The bar is also an accepted unit in oceanography, engineering instead of the pascal.

Standard atmosphere

The standard atmosphere or one atmosphere (atm) is a standard pressure defined as 101 325 Pa. It is a standard reference pressure recommended by the National Institute of Standards and Technology (NIST). It is a widely used unit of pressure. The value of 1 atm approximately equals the atmospheric pressure at sea level.

The relation between 1 atm and other units are as follows:

1\, \text{atm} &= 101 \,325 \,\text{Pa} \\ &= 101.325 \,\text{kPa} \\ &= 1.013 \,25 \,\text{bar} \\ &= 760 \,\text{Torr} \\ &= 1.013 \,25 \,\text{bar} \\ &= 14.695 \,9 \,\text{psi} \\ &= 1.033 \,23 \,\text{kg}_\text{f} \,\text{cm}^{-2} \\ &= 1 \,013 \,250 \,\text{dyne} \,\text{cm}^{-2}

Millimetre of Mercury (mmHg)

The millimetre of mercury is a common unit of pressure. It is a manometric unit based on mercury. One millimetre of mercury is defined as the pressure exerted by one millimetre of a column of mercury at 0 ℃.

Figure 7: Mercury Manometer
[Image Source: Wikimedia]
1 \,\text{mmHg} &= 1 \,\text{mm} \,\rho g \\ &= 10^{-3} \,\text{m} \times 13\, 595.1 \,\text{kg} \,\text{m}^{-3} \times9.806 \,65 \,\text{m} \,\text{s}^{-2} \\ &\approx 133.322 \,\text{Pa}

It is often used in aviation, medicine, meteorology, vacuum system, refrigeration. Blood pressure is mostly measured by a sphygmomanometer, which is a mercury-based manometer.

a sphygmomanometer
Figure 8: Sphygmomanometer
[Image Source: Medisave]

Other related units to it are the centimetre of mercury (cmHg), the foot of water (ftHg), the inch of water (inHg).

1 \,\text{mmHg} &=0.1 \,\text{cmHg} \\ &=0.003 \,280 \,83 \,\text{ftHg} \\ &=0.039 \,370 \,1 \,\text{inHg}

mmHg vs Torr

There is a small difference between mmHg and Torr. This difference is very small and can be ignored for practical purposes. The table below distinguishes both.

Table 4: Difference between mmHg and Torr
mmHgTorr
1 mmHg is defined as the pressure exerted by 1 mm of a column of mercury.1 Torr is defined exactly equal to 1760 of one standard atmosphere.
1 atm ≈ 759.999 891 7 mmHg1 atm = 760 Torr

As we can see from the above table, the difference between mmHg and Torr is marginal, and it will not affect the practical calculations.

1 \,\text{mmHg} &=1.000 \,000 \,142 \,466 \,32 \,\text{Torr} \\ &\approx 1 \,\text{Torr}

Centimetre of Water (cmH2O)

The centimetre of water (cmH2O) is a unit of pressure calculated from a column of water. One centimetre of water is the pressure exerted by one centimetre of a column of water at 4 ℃.

1 \,\text{cmH}_2\text{O} &= 1 \,\text{cm} \,\rho g \\ &= 10^{-2} \,\text{m} \times 999.972 \,0 \,\text{kg} \,\text{m}^{-3} \times9.806 \,65 \,\text{m} \,\text{s}^{-2} \\ &\approx 98.063 \,8 \,\text{Pa}

Other related units to it are the millimetre of water (mmH2O), the foot of water (ftH2O), the inch of water (inH2O).

1 \,\text{cmH}_2\text{O} &=10 \,\text{mmH}_2\text{O} \\ &=0.032 \,808 \,3 \,\text{ftH}_2\text{O} \\ &=0.393 \,701 \,\text{inH}_2\text{O}

Pound per Square Inch (psi)

The pound per square inch or the pound-force per square inch is denoted as psi or lbf in−2. It is an avoirdupois unit of pressure. It is defined as a force exerted by one pound-force on the surface of one square inch.

1 \,\text{psi} &=\frac{1 \,\text{lb}_\text{f}}{1 \,\text{in}^2} \\ &=\frac{1 \,\text{lb} \times g}{1 \,\text{in}^2} \\ &=\frac{0.453 \,592 \,37 \,\text{kg} \times 9.806 \,65 \,\text{m} \,\text{s}^{-2}}{0.025 \,4^2} \\ &\approx 6 \,894.757 \,\text{Pa}

The derived units of it are the kilopound per square inch (kpsi) and the megapound per square inch (Mpsi).

1 \,\text{psi} =1 \times 10^{-3} \,\text{kpsi} =1 \times 10^{-6} \,\text{Mpsi}

psi is usually used to measure gauge pressure i.e., pressure relative to atmospheric pressure.

Water Pressure Gauge in psi (Inner Scale) and bar (Outer Scale)
Figure 9: Water Pressure Gauge in psi (Inner Scale) and bar (Outer Scale)

Technical Atmosphere (or Kilogram per Square Centimetre)

Technical atmosphere (at), also known as the kilogram per square centimetre or the kilogram-force per square centimetre (kgf cm−2), is the force of 1 kgf (one kilogram-force) exerted on the surface of 1 cm2.

1 \,\text{at} & = 1 \,\text{kg}_\text{f} \,\text{cm}^{-2} \\ & = \frac{1 \,\text{kg}_\text{f}} {1 \,\text{cm}^2} \\ & = \frac{1 \,\text{kg} \times 9.806 \,65 \,\text{m} \,\text{s}^{-2}}{1 \times 10^{-4} \,\text{m}^{2}} \\ & = 98 \,066.5 \,\text{Pa}

The technical atmosphere is a deprecated metric unit. The gram per square centimetre (gf cm−2) is a derived unit of it.

1 \,\text{kg}_\text{f} \,\text{cm}^{-2} = 1 \times 10^{3} \,\text{g}_\text{f} \,\text{cm}^{-2}

Barye

Barye is the CGS unit of pressure. It is also known as barad, bary, baryd, or baryed. One barye equals one dyne per square centimetre.

1 \,\text{Ba} &=1 \,\text{dyne} \,\text{cm}^{-2} \\ &=1 \times 10^{-5} \,\text{N} \times 1 \times 10^4 \,\text{m}^{-2} \\ &=0.1 \,\text{N} \,\text{m}^2 \\ &=0.1 \,\text{Pa}

Metre Sea Water (and Foot Sea Water)

The metre sea water (msw) is a unit of pressure and defined as 0.1 bar. Thus, one metre sea water is one-tenth of one bar.

The US navy drivers check the pressure gauge during a training dive.
Figure 10: The US navy drivers check the pressure gauge during a training dive.
1 \,\text{msw} =0.1 \,\text{bar}

It is a common unit used by drivers. Another common unit is the foot sea water (fsw). The value of 1 fsw is calculated using a depth of 1 ft and seawater density of 64 lb ft−3.

1 \,\text{fsw} &= 1 \,\text{ft} \times 64\,\text{lb} \,\text{ft}^{-3} \times g\\ &= 0.3048 \,\text{m} \times 64 \times \frac{0.453 \,592 \,37}{0.304 \,8^3}\,\text{kg} \,\text{m}^{-3} \times g\\ &= 3064.34 \,\text{Pa}

Note: The relation between msw and fsw is different from the metre and the foot.

1 \,\text{fsw}=3.263 \,34 \,\text{msw}

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