Inches of mercury (inHg) to centimeters of water (cmH2O) conversion

What is Inches of mercury?

The "inches of mercury" (inHg) is a unit of pressure commonly used in the United States. It's based on the height of a column of mercury that the given pressure will support. This unit is frequently used in aviation, meteorology, and vacuum applications.

Definition and Formation

Inches of mercury is a manometric unit of pressure. It represents the pressure exerted by a one-inch column of mercury at a standard temperature (usually 0°C or 32°F) under standard gravity.

The basic principle is that atmospheric pressure can support a certain height of a mercury column in a barometer. Higher atmospheric pressure corresponds to a higher mercury column, and vice versa. Therefore, the height of this column, measured in inches, serves as a direct indication of the pressure.

Formula and Conversion

Here's how inches of mercury relates to other pressure units:

• 1 inHg = 3386.39 Pascals (Pa)
• 1 inHg = 33.8639 millibars (mbar)
• 1 inHg = 25.4 millimeters of mercury (mmHg)
• 1 inHg ≈ 0.0334211 atmosphere (atm)
• 1 inHg ≈ 0.491154 pounds per square inch (psi)

Historical Context: Evangelista Torricelli

The concept of measuring pressure using a column of liquid is closely linked to Evangelista Torricelli, an Italian physicist and mathematician. In 1643, Torricelli invented the mercury barometer, demonstrating that atmospheric pressure could support a column of mercury. His experiments led to the understanding of vacuum and the quantification of atmospheric pressure. Britannica - Evangelista Torricelli has a good intro about him.

Real-World Applications and Examples

• Aviation: Aircraft altimeters use inches of mercury to indicate altitude. Pilots set their altimeters to a local pressure reading (inHg) to ensure accurate altitude readings. Standard sea level pressure is 29.92 inHg.

• Meteorology: Weather reports often include atmospheric pressure readings in inches of mercury. These readings are used to track weather patterns and predict changes in weather conditions. For example, a rising barometer (increasing inHg) often indicates improving weather, while a falling barometer suggests worsening weather.

• Vacuum Systems: In various industrial and scientific applications, inches of mercury is used to measure vacuum levels. For example, vacuum pumps might be rated by the amount of vacuum they can create, expressed in inches of mercury. Higher vacuum levels (i.e., more negative readings) are crucial in processes like freeze-drying and semiconductor manufacturing. For example, common home vacuum cleaners operate in a range of 50 to 80 inHg.

• Medical Equipment: Some medical devices, such as sphygmomanometers (blood pressure monitors), historically used mmHg (millimeters of mercury), a related unit. While digital devices are common now, the underlying principle remains tied to pressure measurement.

Interesting Facts

• Standard Atmospheric Pressure: Standard atmospheric pressure at sea level is approximately 29.92 inches of mercury (inHg). This value is often used as a reference point for various measurements and calculations.

• Altitude Dependence: Atmospheric pressure decreases with altitude. As you ascend, the weight of the air above you decreases, resulting in lower pressure readings in inches of mercury.

• Temperature Effects: While "inches of mercury" typically refers to a standardized temperature, variations in temperature can slightly affect the density of mercury and, consequently, the pressure reading.

What is the centimeter of water?

The centimeter of water (cmH2O) is a unit of pressure equal to the pressure exerted by a one-centimeter-high column of water under standard conditions. It is used heavily in medicine and respiratory therapy, where small pressures are common.

Definition

The conventional centimeter of water is defined as the pressure of a 1 cm column of water with a density of 1000 kg/m³ under standard gravity (9.80665 m/s²):

$$1\ \text{cmH2O} = 98.0665\ \text{Pa}$$

This is the conventional value. Because water density varies with temperature, more precise variants exist (for example, cmH2O at 4 °C uses water's maximum density of about 999.972 kg/m³, giving roughly 98.064 Pa).

Origin and History

The unit comes directly from the water manometer, an instrument in which pressure is read as the height difference of a water column. Water was chosen for low pressures because it produces a taller, more readable column than mercury (water is about 13.6 times less dense). The convention fixes water density and gravity so the unit has a single agreed value independent of local conditions.

Law and Notable Facts

The centimeter of water is not an SI unit but is permitted in medical contexts, where it remains standard for measuring airway, ventilator, and cerebrospinal-fluid pressures. Roughly 1 cmH2O equals 0.7356 mmHg, so about 1.36 cmH2O make up 1 mmHg.

Real-World Examples and Conversions

• Mechanical ventilators typically deliver positive end-expiratory pressure (PEEP) of 5 to 10 cmH2O.
• Normal cerebrospinal-fluid opening pressure in a lumbar puncture is roughly 10 to 18 cmH2O.
• 1 cmH2O ≈ 98.0665 Pa ≈ 0.098 kPa.
• A standard atmosphere equals about 1033.2 cmH2O.