torr (torr) to centimeters of water (cmH2O) conversion

What is torr?

Torr is a unit of pressure measurement commonly used in vacuum applications. Let's delve into its definition, origin, and relevance.

Definition of Torr

The torr is a unit of pressure defined as 1/760 of standard atmospheric pressure. In other words, 760 torr is approximately equal to one atmosphere (atm).

$$1 \text{ torr} \approx \frac{1}{760} \text{ atm}$$

It is also nearly equal to one millimeter of mercury (mmHg). More precisely:

$$1 \text{ torr} \approx 1 \text{ mmHg}$$

Origin and History

The torr is named after Italian physicist and mathematician Evangelista Torricelli (1608–1647), who invented the barometer in 1643. Torricelli's experiment demonstrated that air pressure could support a column of mercury, paving the way for pressure measurement.

Relation to Pascal (Pa)

The pascal (Pa) is the SI unit of pressure. The relationship between torr and pascal is as follows:

$$1 \text{ torr} \approx 133.322 \text{ Pa}$$

Therefore, to convert from torr to pascals, you can use the formula:

$$\text{Pressure in Pa} = \text{Pressure in torr} \times 133.322$$

Real-World Examples and Applications

Torr is commonly used in fields that involve vacuum systems, such as:

• Vacuum pumps: Vacuum pump performance is often rated in torr or millitorr (mTorr). For example, a roughing pump might achieve a vacuum of 10⁻³ torr.
• Scientific instruments: Mass spectrometers, electron microscopes, and other analytical instruments require high vacuum conditions, often specified in torr or microtorr (µTorr).
• Semiconductor manufacturing: Vacuum processes, such as chemical vapor deposition (CVD) and sputtering, use vacuum levels measured in torr to control deposition rates and film quality.
• Space research: Simulating space environments requires extremely low pressures, which are measured in torr or even smaller units like picotorr (pTorr).
• Vacuum Furnaces: Sintering, brazing, and heat treating of materials at reduced pressures, which improves the properties of the final product.

Interesting Facts

• While torr and mmHg are often used interchangeably, they are technically slightly different due to variations in the definition of standard gravity.
• The unit "micron" (µ) is sometimes used as a unit of pressure, where 1 micron = 1 mTorr.
• The lowest pressure ever achieved in a laboratory setting is on the order of $10⁻¹⁷$ torr.

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.