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この項目では、単位について記述しています。その他の用法については「トル (曖昧さ回避)」をご覧ください。 |
トル、トール
torr |
|
| 記号 |
Torr |
| 系 |
メートル法 |
| 量 |
圧力 |
| SI |
~133.322 368 Pa |
| 定義 |
101 325 / 760 Pa[1][2] |
| 由来 |
標準大気圧の760分の1の圧力 |
| 語源 |
エヴァンジェリスタ・トリチェリ |
| テンプレートを表示 |
水銀柱ミリメートル
millimeter of mercury |
| 記号 |
mmHg |
| 系 |
メートル法 |
| 量 |
圧力 |
| SI |
~133.322 Pa[3][1] |
| 定義 |
13.5951 × 9.806 65 Pa（SI[4]）
101 325 / 760 Pa（計量法[2]） |
| 由来 |
高さ 1 mm の水銀柱が与える圧力 |
| テンプレートを表示 |
トル（torr, 記号: Torr）は、圧力の単位である。トールとも言う。メートル法に基づくが、SI単位ではない。
この名は、17世紀のイタリアの科学者、エヴァンジェリスタ・トリチェリに因む。
現在、アメリカの国立標準技術研究所 (NIST) や日本の計量法は、101 325/760 Pa と定義する[1][5]。したがって、1 Torr = 約133.322 368 Pa である。
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目次
- 1 トルと水銀柱ミリメートル
- 2 定義
- 3 分量単位
- 4 他の水銀柱単位
- 5 使用
- 6 出典
- 7 関連項目
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トルと水銀柱ミリメートル
トルと水銀柱ミリメートル (mmHg) は、本来は同じ単位の別名である。mmHgは、「ミリ水銀」「ミリエイチジー」「ミリメートルエイチジー」と読まれることがある。
圧力を求める方法の一つに、その圧力によって支えられる流体の柱の高さを使う方法がある。流体は密度が一定のものならなんでもいいが、水のような比重の軽い液体では、柱の高さは非常に高くなってしまう（一応、水柱を使用した水柱メートル (mH2O) などの単位はあるが、標準大気圧を水柱で表すと10メートル近い値になる）。よって通常は密度の高い液体である水銀 (Hg) が使われる。標準大気圧は約 760 mm の水銀柱を支えることができる。すなわち、標準大気圧の760分の1は1 mmの水銀柱を支えることができ、その圧力を1水銀柱ミリメートル (mmHg) (または1ミリメートル水銀柱) と呼ぶ。
定義
慣習的に、標準大気圧が760Torrすなわち760mmHgとみなされてきた。一方、1954年、第10回国際度量衡総会 (GCPM) で標準大気圧が 101325 Pa と定められた。
これらに基づくと、1 Torr = 101325⁄760 Pa ≒ 133.322368 Pa となる。アメリカの国立標準技術研究所 (NIST) や日本の計量法が定めるトルの定義も、これに則っている。 ただし計量法では、mmHg も Torr と同じ定義を採用している[6]。
mmHg の現代的な定義は Torr とは異なる。国際単位系 (SI) では、慣用ミリメートル水銀柱 (conventional millimeter of mercury) を、水銀柱の高さという本来の定義に則り、1 mmHg = 13.5951×9.80665 Pa と定義する。13.5951 g/cm3 は0℃での水銀の密度（として採用された厳密値）、9.80665 m/s2 は標準重力加速度である[4]。この値は計算上約 133.322387 Pa となり、101325⁄760 Pa より約700万分の1だけ大きい。ただし通常、水銀の密度を厳密に定めることに意味がないとして、値は約133.322 Pa とされる。
分量単位
以下の分量単位が使われる。
- ミリトル (mTorr) = 10−3 Torr
- マイクロトル (μTorr) = 10−6 Torr
他の水銀柱単位
mmHgと同様に、水銀柱の高さに基づく
- 水銀柱メートル (mHg) = 1000 mmHg
- 水銀柱インチ (inHg, ″Hg) = 25.4 mmHg
- 水銀柱センチメートル (cmHg) = 10 mmHg
がある。
使用
SI
国際単位系 (SI) では、圧力の単位はパスカルを用いることになっており、トルや水銀柱ミリメートルが併用単位にもなっていない非SI単位であることは共通しているが、水銀柱ミリメートルの方が、次の3点でトルよりも認められている単位である。
- SIについての国際度量衡局 (BIPM) の正式文書[7]では、「SI と併用される非 SI 単位，及び基礎定数をよりどころとする単位」のひとつとされ、表8[8]に、海里やオングストロームと並んで記載されている。（トルは同文書に掲げられていない）
- 「圧力」全般の計量に使用できる。
- その数値は、約133.322 Pa とされている。
トルは、SIでは、石油のバレルやインチ、ヤードと同様に「使うことが推奨されないその他の非 SI 単位」[9]とされて、同文書に全く扱われておらず、したがって定義も定められていない。なお、NISTのSIガイドでは、トル及び水銀柱ミリメートルの換算値として、133.3224 Paを掲げており、これ以上の桁数は水銀の圧縮率や密度の安定性の点で無意味としている[10]。
各国
いくつかの国では、水銀柱ミリメートル(またはミリメートル水銀柱)を血圧に使うことができる[3]。
ヨーロッパでは、1979年欧州経済共同体 (EEC) の Council Directive 80/181/EEC により、mmHg は「血圧および他の体液の圧力」に使用が限定された[11]。
日本の計量法は、トル、ミリトル、マイクロトル、は「生体内の圧力」の計量に限って、水銀柱ミリメートルは「血圧」の計量に限って、認めている。未だに真空工学等の分野ではトルが使用されることが多いが、これはパスカルへ置き換えることが推奨されている。また、2013年9月30日までは「生体内の圧力」の計量に限って水銀柱メートル・水柱メートルの使用が認められている[12]（当初は1999年9月30日までであったが、猶予期限が何度か延期されている）。
出典
- ^ a b c NIST Guide for SI（英語）
- ^ a b 計量単位令
- ^ a b Non-SI units accepted for use with the SI, and units based on fundamental constants
- ^ a b 『物理化学で用いられる量・単位・記号 第3版』、講談社、2009年
- ^ 計量単位令別表第6 11
- ^ 計量単位令別表第6 12
- ^ The International System of Units (SI) (PDF)（英語）
- ^ BIPM - Table 8 - 翻訳は、「国際単位系（SI）」 (PDF)のp.40
- ^ BIPM - other units (contd) - 翻訳は、「国際単位系（SI）」のp.41
- ^ NIST Guide to the SI Units - Footnotes（英語）
- ^ conventional millimeters of mercury（英語）
- ^ 計量法附則第四条の計量単位等を定める政令
関連項目
圧力の単位
|
パスカル（SI単位） |
バール |
工学気圧 |
気圧 |
トル |
psi |
| 1 Pa |
≡ 1 N/m² |
= 10-5 bar |
≈ 10.2×10-6 at |
≈ 9.87×10-6 atm |
≈ 7.5×10-3 Torr |
≈ 145×10-6 psi |
| 1 bar |
= 100 000 Pa |
≡ 106 dyn/cm² |
≈ 1.02 at |
≈ 0.987 atm |
≈ 750 Torr |
≈ 14.504 psi |
| 1 at |
= 98 066.5 Pa |
= 0.980665 bar |
≡ 1 kgf/cm² |
≈ 0.968 atm |
≈ 736 Torr |
≈ 14.223 psi |
| 1 atm |
= 101325 Pa |
= 1.01325 bar |
≈ 1.033 at |
≡ p0 |
= 760 Torr |
≈ 14.696 psi |
| 1 Torr |
≈ 133.322 Pa |
≈ 1.333×10-3 bar |
≈ 1.360×10-3 at |
≈ 1.316×10-3 atm |
≡ 1 mmHg |
≈ 19.337×10-3 psi |
| 1 psi |
≈ 6894.757 Pa |
≈ 68.948×10-3 bar |
≈ 70.307×10-3 at |
≈ 68.046×10-3 atm |
≈ 51.7149 Torr |
≡ 1 lbf/in² |
For the standard botanical author abbreviation Torr., see John Torrey.
The torr (symbol: Torr) is a non-SI unit of pressure with the ratio of 760 to 1 standard atmosphere, chosen to be roughly equal to the fluid pressure exerted by a millimeter of mercury, i.e., a pressure of 1 torr is approximately equal to one millimeter of mercury.
The torr unit was named after Evangelista Torricelli, an Italian physicist and mathematician who discovered the principle of the barometer in 1644.[1]
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Contents
- 1 Nomenclature
- 2 History
- 3 Manometric units of pressure
- 3.1 Manometric units in medicine and physiology
- 4 Conversion factors
- 5 See also
- 6 References
- 7 External links
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Nomenclature
The symbol (Torr) is spelled exactly the same as the unit (torr), but the letter case differs. The unit is written lower-case, while the symbol of the unit (Torr) is capitalized (as upper-case), as is customary in metric units derived from names. Thus, it is correctly written either way, and is only incorrect when specification is first made that the word is being used as a unit, or else a symbol of the unit, and then the incorrect letter case for the specified use is employed. The torr is frequently coupled with the metric prefix of milli to form millitorr (mTorr) to represent 0.001 Torr. When following the SI convention of not-mixing unit names and unit symbols[2] the torr can be mixed with SI units to form, for example, torr · liters / second (Torr·L/s). The torr is sometimes improperly assigned the symbol "T" which is reserved for the SI unit for tesla.
History
Torricelli attracted considerable attention when he demonstrated the first mercury barometer to the general public. He is credited with giving the first modern explanation of atmospheric pressure. Scientists at the time were familiar with small fluctuations in height that occurred in barometers. When these fluctuations were explained as a manifestation of changes in atmospheric pressure, the science of meteorology was born.
Over time, 760 millimetres of mercury came to be regarded as the standard atmospheric pressure. In honour of Torricelli, the Torr was defined as a unit of pressure equal to one millimetre of mercury.
In 1954, the definition of the atmosphere was revised by the 10e Conférence Générale des Poids et Mesures (10th CGPM)[3] to the currently accepted definition: one atmosphere is equal to 101325 pascals. The torr was then redefined as 1⁄760 of one atmosphere. This was necessary in place of the definition of the torr as one millimetre of mercury, because the height of mercury changes at different temperatures and gravities.[citation needed]
Manometric units of pressure
See also: Pressure measurement#Liquid column
Manometric units are units such as millimeters of mercury or centimeters of water that depend on an assumed density of a fluid and an assumed acceleration of gravity. The use of these units is discouraged.[4] Nevertheless, manometric units are routinely used in medicine and physiology, and they continue to be used in areas as diverse as weather reporting and scuba diving.
The millimeter of mercury (symbol: "mmHg") is defined as the pressure exerted at the base of a column of fluid exactly 1 mm high, when the density of the fluid is exactly 13.5951 g/cm3, at a place where the acceleration of gravity is exactly 9.80665 m/s2.[5] Under most conditions, 1 mmHg is approximately equal to 1 Torr.
There are several things to notice about this definition:
- A mercury density of 13.5951 g/cm3 was chosen for this definition because this is the approximate density of mercury at 0 °C (32 °F). The definition, therefore, assumes a particular value for the density of mercury. The density depends on temperature (as evidenced by a mercury thermometer) and atmospheric pressure, meaning that certain conventional, normalized values must be assumed.
- The definition assumes a particular value for the acceleration of gravity, standard gravity (g0 = 9.80665 m/s2). In theory, the precise acceleration would vary, and the measurement would have to be recalibrated against the local value; in weightless conditions, this kind of measurement would not be possible.
- The definition does not address the quality of the vacuum, including the vapor pressure of the mercury, above the column of fluid.
In practice, of course, measurements are made using local values, which vary little enough at the Earth's surface. These assumptions limit both the validity and the precision of the mmHg as a unit of pressure.
According to the UK’s National Physical Laboratory (NPL):
The need to assume fixed and exact—but ultimately incorrect—values of liquid density and acceleration due to gravity will inherently limit knowledge of the relationship between the millimetre of mercury and the pascal. By contrast, the magnitude of pressure values expressed in the SI pressure unit, the pascal, can flex (albeit not by much) to take account of technological improvements in the underlying definitions of mass, length and time—the SI base quantities from which pressure is derived.[6]
The performance of modern transducers approaches the precision required to distinguish between the torr and the millimetre of mercury.
The NPL concludes
Thus, in the near future, the accuracy claims being made for otherwise state-of-the-art instruments scaled in manometric units will become inherently inferior.
Even now, confusion and large errors abound through the use of differing definitions, including alternative values of "standard" gravity and varying assumptions about the density and temperature of the fluid.
Misunderstandings about temperature assumptions alone can lead to errors of several tenths of a percent and there are many stories of this leading to major mistakes in pressure measurement.
Manometric units in medicine and physiology
In medicine the millimeter of mercury (measured with a sphygmomanometer) is the "gold standard" for blood pressure measurement.
In physiology manometric units are used to measure Starling forces. Other applications include:
- Intraocular pressure (tonometry)
- Cerebrospinal fluid pressure
- Intracranial pressure
- Intramuscular pressure (compartment syndrome)
- Central venous pressure
- Pulmonary artery catheterization
- Mechanical ventilation
Manometric results in medicine are sometimes given in torr. This is usually incorrect, since the torr and the millimetre of mercury are not the same thing. Pressures obtained with a manometer (or its transducer equivalent) should be reported in millimeters of mercury.
Conversion factors
The millimeter of mercury by definition is 133.322387415 Pa (13.5951 g/cm3 × 9.80665 m/s2 × 1 mm ), which is approximated with known accuracies of density of mercury and gravitational acceleration.
The torr is defined as 1⁄760 of one atmosphere, while the atmosphere is defined as 101.325 kPa. Therefore, 1 Torr is equal to 101325⁄760 Pa. The decimal form of this fraction (133.322368421...) is an infinitely long, periodically repeating decimal, as is its reciprocal.
The relationship between the torr and the millimetre of mercury is:
- 1 Torr = 0.999999857533699... mmHg
- 1 mmHg = 1.000000142466321... Torr
The difference between one millimetre of mercury and one torr, as well as between one atmosphere (101.325 kPa) and 760 mmHg (101.3250144354 kPa), is less than one part in seven million (or less than 0.000015%). This small difference is negligible for most applications outside metrology.
The millimetre of mercury as used in medicine is in general given relative to the atmospheric pressure. This means that when a doctor tells you you have a blood pressure of 100 mmHg, this is 100 mmHg above atmospheric. So on a day when the barometric pressure is 760 your absolute pressure is actually 860 millimetres of mercury (115 kPa).
The SI unit of pressure is the pascal (symbol: Pa), defined as one newton per square metre. Other units of pressure are defined in terms of SI units.[7][8] These include:
-
- The bar (symbol: bar), defined as 100 kPa exactly.
- The atmosphere (symbol: atm), defined as 101.325 kPa exactly.
- The torr (symbol: Torr), defined as 1⁄760 atm exactly.
These four pressure units are used in different settings. For example, the bar is used in meteorology to report atmospheric pressures.[9] The torr is used in high-vacuum physics and engineering.
Pressure units
|
|
pascal |
bar |
technical atmosphere |
standard atmosphere |
torr |
pounds per square inch |
| Pa |
bar |
at |
atm |
Torr |
psi |
| 1 Pa |
≡ 1 N/m2 |
10−5 |
1.0197×10−5 |
9.8692×10−6 |
7.5006×10−3 |
1.450377×10−4 |
| 1 bar |
105 |
≡ 106 dyn/cm2 |
1.0197 |
0.98692 |
750.06 |
14.50377 |
| 1 at |
0.980665 ×105 |
0.980665 |
≡ 1 kp/cm2 |
0.9678411 |
735.5592 |
14.22334 |
| 1 atm |
1.01325 ×105 |
1.01325 |
1.0332 |
≡ p0 |
≡ 760 |
14.69595 |
| 1 Torr |
133.3224 |
1.333224×10−3 |
1.359551×10−3 |
1.315789×10−3 |
≈ 1 mmHg |
1.933678×10−2 |
| 1 psi |
6.8948×103 |
6.8948×10−2 |
7.03069×10−2 |
6.8046×10−2 |
51.71493 |
≡ 1 lbF/in2 |
See also
- Inch of mercury
- Pressure
- Pressure head
- Atmosphere (unit)
- Conversion of units
- Centimetre of water
- Pascal (unit)
- Outline of the metric system
References
- ^ Devices similar to the modern barometer, using water instead of mercury, were studied by a number of scientists in the early 1640s (see History of the Barometer). Torricelli’s explanation of the principle of the barometer appears in a letter to Michelangelo Ricci dated 11 June 1644.
- ^ "Rules and style conventions". NIST. http://physics.nist.gov/cuu/Units/rules.html. Retrieved 2012-09-29.
- ^ BIPM – Resolution 4 of the 10th CGPM
- ^ National Physical Laboratory: Pressure units
- ^ Conventional millimetres of mercury
- ^ National Physical Laboratory: Pressure and vacuum
- ^ Cohen E.R. et al. Quantities, Units and Symbols in Physical Chemistry, 3rd ed. Royal Society of Chemistry, 2007 ISBN 0-85404-433-7 (IUPAC pdf copy)
- ^ DeVoe H. Thermodynamics and Chemistry. Prentice-Hall, Inc. 2001 ISBN 0-02-328741-1
- ^ Note that a pressure of 1 bar (100000 Pa) is slightly less than a pressure of 1 atmosphere (101325 Pa).
External links
