The Units of Pressure Measurement

Michael McKeown

This article was originally presented in Volume 1, Number 4 of the Bell Jar

Michael McKeown notes that he is a European happy to live in the USA despite this country's insistence on measuring everything in Imperial Units. He is the Marketing Manager for Kurt J. Lesker Company. My thanks to Michael for providing this lighthearted review of vacuum units. - Ed.

That wonderful commentator, James Burke, gave an excellent account of the beginnings of vacuum science in his PBS program “Connections.” The following is based on my recollection of Burke’s story and is not, therefore, guaranteed to be accurate. The nationality slurs are my own. Burke is too polished to sink to this level.

All vacuum problems started with the Italians. There was one obstacle to mining in Italy in the early 1600s ... Water. It was everywhere. Before the miners could dig, the water had to be pumped to the surface. It irked them that their ‘suction’ pumps could only ‘suck’ water up to a height of 32 feet above flood level (or rather, the contemporary equivalent of 32 feet). At that point, the pump effluent had to be spilled into vats and another pump used to suck the next 32 feet. Why couldn't they use one pump for the whole distance? What was magical about this height of 32 feet?

They posed the problem to Galileo but he did little with it until three months before his death when he tossed it to a mathematician named Torricelli who came to study under him. Torricelli had been kicking around ideas about ‘oceans of air’ surrounding us and concluded that he could bring this pump problem to a manageable size by using a fluid denser than water. Mercury seemed a good choice. He had his assistant fill a glass tube (closed at one end) with mercury, placed the open end in a dish with more mercury, and raised the closed end. The mercury reached a level equivalent to 32 feet times the ratio of the densities of water to mercury. What would be above the mercury if the glass tube was long enough? A vacuum, of course!

Ah, there's the rub, as Shakespeare said about the same time. Galileo believed that vacuums (vacua?) could not exist and he had already been put under house arrest by the Church for saying things like the earth went around the sun. There was no way Torricelli was going to broadcast the results of the ‘vacuum experiment’ himself. But he did write to a friend in Rome who copied the letter as sent it to a Father Mersenne in Paris. Mersenne, a minorite friar, acted as sort of a medieval computer bulletin board. He promptly copied the letter again (where was Xerox when it was needed most?) for his friend Blaise Pascal who lived close by and therefore, at a sufficient distance from Rome to ignore the Church’s word - to a certain extent.

Pascal, being a literal kind of man, set up the experiment in full scale using water and mirabile dictu confirmed the existence of a vacuum. It followed from Torricelli’s ideas that if the weight of air pushed mercury so far up the tube, then the mercury level would be reduced if the test were done at higher elevations. Blaise Pascal’s brother-in-law lived in central France in an area surrounded by mountains and was apparently adventurous (and strong) enough to march a complete mercury barometer to the top of the nearest mountain. The rest (to use a very bad pun) was downhill from there.

In my opinion, Torricelli, a mathematician, was a premature software guy. Blaise and his brother-in-law got the job of proving the prediction worked on a grand scale and up a mountain, less because of the Church’s decree and more because Torricelli was reluctant to get his hands dirty. Whatever the reason, Torricelli was honored later by someone naming the pressure measurement unit of 1 millimeter of mercury, the torr.

Nice story, but the Battle of the Units had only just begun. Life with torr would have been lovely, except the Brits had to tinker with it. Liking everything to be in Imperial Units, they converted the 760 mm Hg pressure of the standard day to 29.92 inches Hg. Well, if you like inches, that’s ok. But notice how the weather forecasters on American TV long ago forgot that it was the height of mercury they quote every night. Every one of them says, “The barometer is 29 inches and rising.” What’s this ... psycho-kinesis?

The inch thing really got out of hand when manufacturers of rough pumps came on the scene. Rough pumps are arbitrarily defined as those used for: in-house vacuum systems; meat packing; impregnating lumber and transformer coils; making freeze dried coffee, tea or foods (got ya!). That is, any pump that hauls great loads of gas and vapor day-after-day to a modest vacuum level. These manufacturers noted that if atmospheric pressure was 29.92 inches Hg, they would be shooting for 0 inches. That would look bad in their brochures. So, they calmly inverted the scale. Atmospheric pressure is 0 inches Hg and the best possible vacuum is 29.92 inches Hg, they said. Which left the rest of us struggling with converting inches Hg to torr. (First, subtract the given inch pressure from 29.92 inches, then multiply the answer by 25.4.)

Since the standard meter and kilogram are kept in Paris, I blame the French for the metric system. Not that I really object to it. After all, I accept 760 torr is really 760 mm Hg without too much argument. But someone, somewhere, noted that 760 mm Hg could not be related to any basic measurement units. The column’s height depended on the mercury’s density and that wasn't basic in anyone's scheme. “Let's make the pressure unit conform to the cgs (centimeter/gram/second) system” they said with glee, knowing how much they would confuse the rest of us.

And how is this done? First, we must understand that “pressure” is force per unit area. What’s the unit of force in the cgs system? Remember way back at school, your science teacher smacked your knuckles for not remembering that the dyne is that force which gives 1 gram an acceleration of 1 centimeter per second per second? You really should have listened because pressure in the cgs system is measured in dynes per square centimeter or, to give its proper name, microbar. Why micro (millionth) bar? Well, try this for an explanation. One million microbars (or 1 bar) is 750.06 torr. That is, the atmospheric pressure of the standard day is 1.0133 bar which is easier to remember than a number which must be multiplied by ten to the ‘minus oh-dear-I've-forgotten.’ The cgs advocates rounded off this part of the story by declaring pressures will be measured in millibar (because it’s close in value to the torr?). Indeed, to this day, millibar is the unit used for recording both vacuum and weather pressures in Europe.

If I can blame the French for the cgs system, what defence can they offer for the next leap? Some august body set up an international standard for measurements called Systéme International d'Unités (or SI). What could be more French than that? They threw out the cgs system's claim to fame and installed the MKS (meter/kilogram/second) system. The unit of force in SI units, that is the force to accelerate 1 kilogram at 1 meter per second per second, is called the newton. Don't you get the flavor of collusion between Brits and French here? And what do you think the MKS pressure unit (1 newton per square meter) is called? You've got it - the pascal! I rest my case.

Of course, since the units of length and mass in cgs and MKS are all related by powers of ten, millibar (mbar) and pascal (Pa) have the simple correspondence:

100 Pa = 1 mbar ( = 0.75 torr)

But does that really make you sleep easier at night? If you want nightmares, try this one. In pressure measurement, when does a milli equal a micro? Answer: consider the humble torr. If one torr equals 1 millimeter of mercury, then 1 millitorr must be equivalent to 1 micrometer of mercury, right? And what do we call a micrometer? - a micron. All of which says that:

1 millitorr = 1 micron Hg

But how often have you heard someone quote a pressure of “250 microns of mercury?” We all think of the unit as “micron” leaving the neophyte vacuum person with the impression that a milli (unit) equals a micro (unit). Just remember, like the weather forecasters we have simply forgotten to add “mercury” to the microunits.

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