Torr - Manometric Units of Pressure

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. 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. 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.

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.