millimeters of mercury (mmHg) to bar (bar) conversion

What is millimeters of mercury?

Millimeters of mercury (mmHg) is a unit of pressure, often used in medicine (especially blood pressure) and meteorology. It represents the pressure exerted by a column of mercury one millimeter high at a standard temperature. Let's delve into its definition, history, and applications.

Definition and Formation

Millimeters of mercury (mmHg) is a manometric unit of pressure. Specifically, it's the pressure exerted at the base of a column of mercury exactly 1 millimeter high when the density of mercury is 13,595.1 kg/m³ and the local acceleration of gravity is exactly 9.80665 m/s². It's not an SI unit, but it is accepted for use with the SI.

While not an official SI unit (Pascal is the SI unit for pressure), mmHg remains widely used due to its historical significance and practical applications, especially in fields like medicine.

History and Torricelli's Experiment

The unit originates from Evangelista Torricelli's experiments in the 17th century. Torricelli, an Italian physicist and mathematician, invented the mercury barometer in 1643. He filled a glass tube with mercury and inverted it into a dish of mercury. The mercury column would fall, leaving a vacuum at the top, and the height of the column was proportional to the atmospheric pressure. This led to the standardized measurement of pressure using the height of a mercury column. Read more about it in Britannica.

Relation to Other Units

• Pascal (Pa): The SI unit of pressure. 1 mmHg is approximately equal to 133.322 Pascals.

  $$1 \, mmHg \approx 133.322 \, Pa$$

• Atmosphere (atm): A standard unit of pressure. 1 atm is equal to 760 mmHg.

  $$1 \, atm = 760 \, mmHg$$

• Torr: Named after Torricelli, 1 Torr is very close to 1 mmHg. For most practical purposes, they are considered equivalent.

  $$1 \, Torr \approx 1 \, mmHg$$

Real-World Examples and Applications

• Blood Pressure: In medicine, blood pressure is commonly measured in mmHg. For example, a blood pressure reading of 120/80 mmHg indicates a systolic pressure of 120 mmHg and a diastolic pressure of 80 mmHg. The first number represents the pressure in the arteries when the heart beats (systolic pressure) and the second number represents the pressure in the arteries between beats (diastolic pressure).

• Atmospheric Pressure: Meteorologists often use mmHg to report atmospheric pressure. Standard atmospheric pressure at sea level is 760 mmHg. Changes in atmospheric pressure are often precursors to changes in weather.

• Vacuum Gauges: Many vacuum gauges, particularly older or specialized instruments, display pressure in mmHg. Low pressures in vacuum systems, such as those used in scientific experiments or manufacturing processes, are often expressed in mmHg or fractions thereof (e.g., milliTorr, which is approximately 1/1000 of a mmHg).

• Aircraft Altimeters: Aircraft altimeters use atmospheric pressure to determine altitude. While the actual scale on the altimeter might be in feet or meters, the underlying pressure measurement is often related to mmHg.

Important Considerations

While mmHg is widely used, it's essential to be aware of its limitations:

• Temperature Dependence: The density of mercury varies with temperature, so precise measurements require temperature corrections.
• Local Gravity: Although standardized, the local acceleration due to gravity can vary slightly depending on location, potentially affecting accuracy.

What is bar?

The bar is a metric unit of pressure, widely used in science, engineering, and industry. It's a convenient unit because it is close to standard atmospheric pressure on Earth. Below is detailed information about bar, it's origin, and some real-world examples.

Definition of Bar

The bar is defined as exactly $100,000$ Pascals ($10⁵ Pa$). The Pascal (Pa) is the SI unit of pressure, defined as one Newton per square meter ($N/m^2$). Therefore:

$1 \, bar = 100,000 \, Pa = 10⁵ \, N/m^2$

Origin and History

The bar was introduced by British physicist Sir Napier Shaw in 1909. The goal was to have a unit of pressure that was close to atmospheric pressure but based on the metric system. The term "bar" comes from the Greek word "βάρος" (baros) meaning "weight."

Relation to Atmospheric Pressure

Standard atmospheric pressure at sea level is approximately $1.01325$ bar. Because of this proximity, the bar and millibar (1 mbar = 0.001 bar) are frequently used in meteorology to measure atmospheric pressure. Historically, meteorologists used millibars, but now the SI unit, the hectopascal (hPa), is also widely used (1 hPa = 1 mbar).

Real-World Examples and Applications

• Tire Pressure: Car and bicycle tire pressures are often measured in bar or PSI (pounds per square inch). For example, a car tire might be inflated to 2.5 bar.
• Weather Reports: Atmospheric pressure in weather reports can be given in millibars or hectopascals, where 1013.25 mbar is standard atmospheric pressure.
• Scuba Diving: Divers often use bar to measure the pressure of compressed air in their tanks. A typical scuba tank might be filled to 200 bar.
• Industrial Processes: Many industrial processes, such as hydraulic systems and pressure testing, use bar as a convenient unit of measurement.
• Geology: Pressures deep within the Earth are often measured in kilobars (kbar), where 1 kbar = 1000 bar.
• Vacuum: While bar is not commonly used for measuring high vacuum, it's relevant when discussing rough or backing vacuum levels. For high vacuum, units like Torr or Pascal are more typical.

Interesting Facts

• The bar is a metric unit but not an SI unit. The SI unit for pressure is the Pascal (Pa).
• The millibar (mbar) is commonly used in meteorology.
• 1 bar is approximately equal to 0.987 atmospheres (atm).