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Pressure units and unit conversion BEAMEX Calibration White Paper

Pressure units and pressure unit conversion

It’s a jungle out there! To say that in a formula: There is a lot of different pressure units in use around the world and sometimes this can be very confusing and may cause dangerous misunderstandings. N kg In this article we will discuss the basics of different pressure Pa = = 2 units and different pressure unit families. m m × s

Pascal is a very small pressure unit and for example the What is pressure? standard is 101325 Pa absolute. When I talk about pressure in this post, it does not refer to the Out of ’s definition, the kg can be replaced with you may be suffering in your work, but to the physical different units like g (gram) force, and meter can be replaced quantity. It is good to first take a quick look at the definition with centimeter or millimeter. By doing that, we get many of pressure, this will also help to better understand some of other combinations or pressure units, such as kgf/m², gf/m², the pressure units. kgf/cm², gf/cm², kgf/mm², gf/mm², just to list a few. If you remember the studies of physics in school … as most The unit “” is still often used in some areas. It is based on of us don’t remember… a short reminder is in order: pressure , but is not part of SI system. Bar being 100000 is defined as force per area perpendicular to the surface. That times Pascal (100 times kPa) it is anyhow easy to convert. In is often presented as formula p = F/A. Pressure being indicated some areas (like NIST in USA) the bar is not recommended with the letter “p”, although capital letter “P” can also be seen to be used widely. being used in some occasions. And like for all pressure units, SI or not SI, we can use So what does this force per area mean in practice? It means the common prefixes/coefficients in front of them, most that there is certain force effecting to a specified area. When commonly used are milli (1/100), centi (1/10), hecto (100), kilo we look at force, it is specified being Mass x Gravity. As there (1000) and mega (1000000). To list a few examples, that already are so many different engineering units used for both mass gives us different Pa versions, all being commonly used: Pa, and area, the number of combinations of these is huge. Plus kPa, hPa, MPa. The unit bar is most commonly used without there are also a lot of pressure units that do not directly have prefix or with prefix milli: bar, mbar. the mass and area in their names, although it often is in their But taking all mass units and combining those with all area definition. units from SI system, we get many combinations. It is good to notice that in practice the “force” is not always Although the SI system is used in most of the countries, included in the pressure unit names. For example pressure unit there is still a lot of other pressure units also being used. So force per square centimeter should be indicated as let’s take a look at those next. kgf/cm², but often it is indicated just as kg/cm² without the “f”. Similarly, force per square inch (pfsi) is normally indicated as pounds per square inch (psi). In countries using Imperial system (like USA and UK), the engineering units used both for mass and area are different International System of Units (SI system) / Metric than with SI system. Therefore this also creates a whole new Let’s start to look at the pressure units by looking at the SI set of pressure units. Mass is being measured commonly in system, which is the International System of Units, derived pounds or ounces, and area and distance with inches or feet. from metric system. Now that I mentioned the metric system, So some pressure units derived from these are lbf/ft², psi, I can already see some of you taking a step back… but please ozf/in², iwc, inH2O, ftH2O. stay with me! In United States, the most common pressure unit is pounds SI system is the world’s most widely used system of per square inch (psi). For process industries, a common unit measurement. It was published in 1960, but has a very long is also inches of (inH2O), which is derived from level history even before that. measurement and the historical measurements of pressure For pressure, the SI system’s basic unit is Pascal (Pa), which differences with water in a column. is N/m² ( per square meter, while Newton is kgm/s²). www.beamex.com Pressure units and pressure unit conversion 2 BEAMEX Calibration White Paper

Liquid column units (mmHg). The older devices were often made by A common industrial application for use of column using liquid in a transparent U-tube. If the pressure in both pressure units is to measure the liquid level in a tank. For ends of the tube is the same, the liquid level in both sides are on example, if you have a water tank that is 20 feet (or 6 meters) the same level. But if there is a difference in the , then high and you want to measure the water level in that tank, it there is a difference in the liquid levels. Level difference being pretty logical to install a pressure indicator with a scale linearly proportional to the pressure difference. In practice you 0 to 20 feet of water, as that would tell straight what the water can leave one side of the tube open to the room’s atmospheric level is (13 feet in example picture). pressure and connect the pressure to be measured to the other side. As referred to the atmospheric pressure, it is a pressure type being measured.

P P

20 Scale feet

h 13.0 ftH O Liquid

Back to water column: It is clear that when the length indication was made to a U column, many different length units have been used, both metric and non-metric. This has The pressure scale is marked in the tube so you read the generated many different pressure units. pressure by reading the difference in liquid levels. When Although a liquid column sounds very simple, it is important pressure is applied it will change the liquid level and we can to remember that the of the liquid depends on the local read the value. This sounds very simple, no electronics and no gravity, so if you calibrate the column in one place and take wearing parts, so what could possibly go wrong… well, let’s it to another (distant, different elevation) place, it may not be see about that. measuring correctly anymore. So gravity correction is needed The most commonly used liquid in the column was to be precise. obviously water. But in order to be able to measure higher Also, the of the liquid effects to the of pressure with smaller U-tube, heavier were needed. One the liquid and that also effects slightly the readings of a U-tube. such liquid is (Hg) as it is much heavier than water There are various different liquid column based pressure (13.6 times heavier). When you use heavier liquid you don’t units available, having the liquid temperature specified in the need to have that long column to measure higher pressure, so pressure unit, most commonly used are 0 °C, you can make a smaller and more convenient size column. 4 °C, 60 °F, 68 °F. But there are also water column units, which For example, was earlier (still sometimes is) have no indication of the water temperature. These are based measured with a mercury column. Mercury is mainly used on a theoretical density of water, being 1 kg/1 liter (ISO31-3, because a water column for same pressure range would be so BS350). In practice, the water never has that high density. The long it would not be practical to use it in a normal room, highest density that water have is at +4 °C (39.2 °F) where as water column is about 13.6 times longer than mercury it is approximately 0.999972 kg/liter. The density of water column. As a result of this, even today the pressure unit that gets lower if the temperature is higher or lower than +4 °C. blood pressure is typically expressed is millimeter of mercury Temperature can have a pretty strong effect on the density, www.beamex.com Pressure units and pressure unit conversion 3 BEAMEX Calibration White Paper

for example going from +4 °C to +30 °C changes the water And some more… density about 0.4%. In addition to all the above pressure units, there are still plenty Finally, the readability of a mechanical liquid column more existing… is typically pretty limited, so you can’t get very accurate Just to mention, for example in a Beamex MC6 calibrator, measurements. And due to the mechanical limitations, you there are over 40 different pressure units, plus still a few can’t use a U-tube for high pressure. custom units for the thrill seekers. All of these above mentioned issues makes a U-tube liquid column not very practical to use. Also, modern digital pressure measurement devices have replaced the liquid columns. But Pressure unit conversions standards many of the pressure units created in the era of liquid columns If you work with pressure, you know that it is very common have remained and are still used today. that a pressure is indicated with certain pressure unit and you To shortly summarize the liquid column based pressure need to convert it into another pressure unit. units: Pressure units are based on standards and the conversion between units should also be based on standards. Most • For the length we have many units; mm, cm, m, inch and common standards for pressure units are: feet. • SI system • Then we have columns for different liquids, like water • ISO31-3, edition, 1992-09-01 (H2O) and mercury (Hg). • BS350 Part 1: 1974 • We have water column units for different density at • PTB-Mitteilungen 100 3/90 temperatures, like 0 °C, 4 °C, 60 °F and 68 °F and for • Perry’s Chemical Engineer’s Handbook, 6th ed, 1984 theoretical .

By combining all of these, we get a long list of pressure units, just to mention a few: mmH₂O, cmH₂O, mH2O, mmHg, cmHg, mHg, iwc, inH2O, ftH2O, inHg, mmH2O@4°C, mmH2O@60°F, mmH2O@68°F, cmH2O@4°C, cmH2O@60°F, cmH2O@68°F, inH2O@60°F, inH2O@68°F, inH2O@4°C, ftH2O@60°F, ftH2O@68°F, ftH2O@4°C and so on.

Atmospheric units For measurement of the atmospherics’ absolute pressure, dedicated pressure units have been created. One of such is PRESSURE UNIT CONVERTER TOOL the standard (atm) which is defined being 101325 Pascal. To add confusion, there is also a technical atmosphere I tried to make a conversion table between different (at) which is pretty close, but not quite the same as atm. pressure units, but that table started quickly to become a The technical atmosphere is one kilogram force per square huge matrix that would not be easy for you to use at all. centimeter. So 1 at equals about 0.968 atm. So instead of making a conversion table, we developed an Another pressure unit used for measuring atmospheric online pressure unit converter into our web site. With this absolute pressure is , being 1/760 of standard atmosphere. converter you can easily convert a pressure reading from So torr is an absolute pressure, although that is typically one unit into other units. Please click the link below to not mentioned, you just need to know it, which can cause check out the pressure unit converter: confusion. Torr was initially meant to be the same as 1 millimeter of mercury, although the later definitions show www.beamex.com/resources/pressure-unit-converter/ a very small difference in between. Torr is not part of the SI system. www.beamex.com Pressure units and pressure unit conversion 4