Psi to bars, or: A physics lecture

[Jaap Bouma <j.h.bouma@xxxxxxxxxxxxx>]

CAUTION: Lengthy, largely boring message. Don't say you weren't warned....

Hi all,
following the recent spate of postings on pressure units, I couldn't resist
the temptation to enlighten the collective with The Definitive Answer On
Units Of Pressure. (ho hum indeed; that's what holding a PhD in mechanical
engineering gets you. Sad, isn't it?)

Basically, the unit of pressure is force per unit area. In the (metric) SI
system of units, force is expressed in Newtons (N). One Newton is the force
required to give a mass of 1 kilogram an acceleration of 1 meter per second
squared. The area is expressed in square meters. 
Thus, the unit of pressure becomes Newton per meter squared, more commonly
referred to as Pascal: 
1 Pa = 1 N / m^2

However, outside the cozy and orderly world of the SI system, other units
of force (poundforce, dyne) and area (square inch, square centimeter) leads
to different units of pressure. As a result, there are five commonly used
units of pressure: Pascal, bar, atm, at and psi.

Bar is the closest to the SI unit: 
1 bar = 10^5 Pa  or 100,000 Pascal 

Atm (used in the past in physics) stands for atmosphere, or atmospheric
pressure. In the old days, when people used mercury barometers, the average
reading was found out to be 760mm (or 29.9 inches), giving an atmospheric
pressure 1013 millibar, so the definition of atm is:  
1 atm = 101,325 Pa

At (used in technical circles) is defined as kilogramforce per square
centimeter. Kilogramforce is defined as the vertical force exerted by a
mass of 1 kilogram in the earth's gravitation. As the gravitational
acceleration of the earth (on average) is about 9.81 m/s^2, the definition
of at becomes:

1 at = 1 kgf/m^2 = 98,066.5 Pa

Psi stands for poundforce per square inch. Poundforce is, like
kilogramforce, the vertical force exerted by a mass of 1 pound (0.4536 kg)
in the earth's gravitation. So: 1 lbf = 0.4536 kgf = 4.448 Newton. Armed
with the knowledge that one inch equals 0.0254 meter, we can calculate one
psi to be:
1 psi = 1 lbf/in^2 = 6894.76 Pa


Using the above (I'm really beginning to sound like a lecturer, aren't I?):

1 psi = 0.0689 bar = 0.0680 atm = 0.0703 at = 0.0703 kgf/m^2

Conversely:

1 at = 1 kgf/m^2 = 14.224 psi
1 bar = 14.516 psi
1 atm = 14.705 psi

By the way, the f in kgf/m2 is often omitted, giving kg/m^2, which is the
unit you sometimes see on pressure gauges. So 1 kg/m^2 = 14.224 psi.
Unfortunately, bar and kg/m^2 are often confused or taken to be the same.
With this in mind the data given by the esteemed Mister Hertzman can be
checked:
1.5 kg/cm = 21 PSI (21.336)
1.7 kg/cm = 24 PSI (24.181)
1.8 kg/cm = 26 PSI (25.603)
1.9 kg/cm = 28 PSI (27.026)
2.0 kg/cm = 29 PSI (28.448)
2.2 kg/cm = 31 PSI (31.293)
2.5 kg/cm = 35 PSI (35.560)
So he is not too far off: with the exception of the 1.9 and 2.0 figures,
rounding the calculated psi data corresponds to the figures given by JohnH.
At this point, I could launch into another lecture on significant digits
and all that, but I think I'd better not...

JohnH further wrote:
>I thought the conversion from bar to PSI for Jochen Tydecks' friend would be
>the usual ho-hum look it up, but quickly found that a bar is a unit of
>pressure equal to one million dynes per square centimeter, and that a dyne is
>the unit of force which would give a free mass of one gram an acceleration of
>one centimeter per second per second. That is as far as I got (it IS late)
but
>I would bet that the dyne is a unit introduced in the recent past along with
>others intended to finesse the slight inaccuracies of the eighteenth
century's
>archaic Metric System definitions. 

Actually, there are two metric systems: the CGS and the MKS systems of
units. The CGS system was introduced in 1874, and proposed a system of
units based on the Centimeter, the Gram and the Second. The dyne falls into
this category. This system is still in use today in certain fields, but
less and less so.
It is gradually being replaced by the MKS system, in which all the units
are based on Meters, Kilograms and Seconds. This system was proposed in
1889, and is the basis of the current SI (Systeme International des Poids
et Mesures, or the Int'l System of Weights and Measures) standard. So the
dyne actually predates the metric system currently in use.

Well, that's your bit of large irrelevant information for today. Anyone
interested in finding out more, check the Dictionary of Units of
Measurement (http://www.unc.edu/~rowlett/units/index.html), which I used to
look up the dates in the above.

Obligatory Alfa content: I really should give my GTV6 a wash, but I'm too
busy writing excessively long e-mail messages...


Met vriendelijke groeten, regards
Dr.Ir. J.H. Bouma  <j.h.bouma@domain.elided>
University of Twente, Dept. of Energy Technology
tel.: (0)53 - 489 40 98
fax: (0)53 - 489 36 63

------------------------------

End of alfa-digest V7 #259
**************************