torr

The torr (symbol: Torr) is a non-SI unit of pressure defined as ¹⁄₇₆₀ of a 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 1 mmHg. Note that the symbol is spelled exactly the same as the unit, but the symbol is capitalized, as is customary in metric units derived from names. It was named after Evangelista Torricelli, an Italian physicist and mathematician who discovered the principle of the barometer in 1644.^[1]

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 millimeters of mercury (abbreviated mmHg) came to be regarded as the standard atmospheric pressure. In honor of Torricelli, the torr was defined as a unit of pressure equal to one mmHg.

In 1954, the definition of the atmosphere was revised by the 10e Conférence Générale des Poids et Mesures (10th CGPM)^[2] to the currently accepted definition: one atmosphere is equal to 101,325 pascals. The torr was then re-defined as ¹⁄₇₆₀ of one atmosphere. This was necessary in place of the definition of a torr as 1 mmHg, because the height of mercury changes at different temperatures and gravities.

SI units of pressure

The SI unit of pressure is the pascal (symbol: Pa), defined as one newton per square meter. Other units of pressure are defined in terms of SI units.^[3][4] These include:

• The bar (symbol: bar), defined as 10⁵ Pa 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.^[5] The torr, a more convenient unit for low pressures, is used in high-vacuum physics and engineering.

Example reading:  1 Pa = 1 N/m²  = 10⁻⁵ bar  = 10.197×10⁻⁶ at  = 9.8692×10⁻⁶ atm, etc.

Manometric units of pressure

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.^[6] Nevertheless, manometric units are used routinely 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.^[7] Under most conditions, 1 mmHg is approximately equal to 1 torr.

There are several things to notice about this definition:

• A fluid density of 13.5951 g/cm³ was chosen for this definition because this is the approximate density of mercury at 0 °C. The definition, therefore, assumes a particular value for the density of mercury. The density can depend on temperature, exogenous pressure, and other similar variables, so those have to assume certain conventional, normal values as well.
• The definition assumes a particular value for the acceleration of gravity: the 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 even make sense.

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 millimeter 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.

—^[8]

The performance of modern transducers approaches the precision required to distinguish between the torr and the millimeter 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 millimetre 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
• Venous ulcer compression regime

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 millimetres of mercury.

Conversion factors

The mmHg is defined as (13.5951 × 9.80665) Pa = 133.322 Pa, 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, one torr is equal to 101325/760 Pa. The decimal form of this fraction (133.322368421...) is, unfortunately for practical use, an infinitely long, periodically repeating decimal, as is its reciprocal.

The relationship between the torr and the mmHg is:

• torr = 0.999 999 857 533 699... mmHg
• 1 mmHg = 1.000 000 142 466 321... torr

The mmHg and the torr differ from one another by less than 2 × 10⁻⁷ torr. The difference between one atmosphere (101.325 Pa) and 760 mmHg (101325.0144354 Pa) less than 0.2 μPa/Pa (less than 0.00002%). This small difference is negligible for most applications outside metrology.

Notes

See also

• Inches of mercury
• Pressure
• Pressure head
• Atmosphere (unit)
• Conversion of units
• cmH₂O

External links

• NPL - pressure units
• Pressure Measurements and Conversions