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Q: Unit Conversion of Pressure (in Unusual Units) ( Answered ,   2 Comments )
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 Subject: Unit Conversion of Pressure (in Unusual Units) Category: Science > Math Asked by: tfpsoft-ga List Price: \$50.00 Posted: 18 Aug 2006 12:37 PDT Expires: 17 Sep 2006 12:37 PDT Question ID: 757433
 ```I've actually got a couple of related questions about the conversion of units of pressure. First, what is the difference -- if any! -- between "psi" (pounds per square inch) and "pound-force per square inch" (lbf/inch square). I assume that pound force is like foot pound or newton meter, but how far am I moving that pound for the word "force" to become part of the term? Same idea: if I were metric, explain the difference between newtons per square meter and kilograms per square meter. Is kilograms per square meter even a valid unit of measure of pressure? I'm working with a system where the base units of measure are decimeters for length, and kilograms for mass. Forces are therefore measured in terms of kilogram decimeters per second squared. (i.e. 1 unit of force will move a mass of 1 kilogram 1 decimeter, or .1 meters) This makes the force unit like a decimeter version of a newton. For reference, this makes the force of gravity 98.1 instead of the usual 9.81. Knowing this base system of measure, what would be the correct units to use for pressure? From this unit, please provide unit conversions to the following: 1 unit = ? psi 1 unit = ? pascal 1 unit = ? inch hg 1 unit = ? newton per sq meter 1 unit = ? inch water 1 unit = ? bar 1 unit = ? atmosphere Please explain thoroughly--I've inexplicably botched this calculation myself several times already. Thanks!```
 Subject: Re: Unit Conversion of Pressure (in Unusual Units) Answered By: elmarto-ga on 18 Aug 2006 14:21 PDT Rated:
 ```Hello tfpsoft-ga! There is no difference at all between psi and lbf/inch square. Always bear in mind that pressure is measured as: Pressure = Force / Area As such, the term in the numerator, must be a unit of force, such as "pound-force". The word "pound" in "pounds per square inch" is a bit ambiguous, because it's actually referring to units of pound-force (which is obviously a unit of force and not of mass). A unit of pound-force is not in the same category as a unit of Newton meter, as you mention in your question. The pound-force is a unit of *force*, while the Newton meter is a measure of *energy*. A pound-force is defined as the force due to gravity on a mass of one pound at the surface of the Earth. Similarly, a pound-force can be defined as the amount of force needed to accelerate a mass of one pound by 9.80665 meters/second square (the acceleration of gravity on the surface on Earth). A pound-force can be a compared to a Newton, which is the amount of force needed to accelerate a mass of one kilogram by 1 meter/second square. In fact, the equivalence between these is 1 lbf = 4.448222 Newton. Finally, "kilogram per square meter" would not be a valid measure of pressure. As I mentioned above, pressure is measured Force / Area; yet kilogram is a measure of mass, not of force. On the other hand "kilogram-force (kgf) per square meter" could very well be a measure of pressure. It would be possible to compare "kgf per square meter" to "Newton per square meter". The former represents a force of 1 kgf applied to an area of 1 square meter; while the latter represents a force of 1 Newton applied to that same area. Since 1 kgf = 9.80655 Newton, then 1 kgf/square meter = 9.80655 Newton/square meter. Let's now define a suitable unit of pressure for your system, which uses kilograms for mass and decimeteres for length. In order to do this, it will be convenient to find a unit of force within your system, since pressure = force/area. As I mentioned earlier, we have that the Newton is the amount of force needed to accelelerate a mass of one kilogram by one meter per second square. This measure already uses kilograms, as in your system. Therefore, we could define the "deci-Newton" (let's abbreviate it as "dN") as the amount of force needed to accelerate a mass of one kilogram by one decimeter per second square. We would then have the equivalence: 1 Newton = 1 kg * m / s^2 = 10 dN = 10 kg * dm / s^2 The "dN" uses kilograms and decimeters, as in your system. Given this, a logical measure of pressure for your system should be "deci-Newton per decimeter square" (let's abbreviate it as dN/dm^2). This can also be written as: 1 dN/dm^2 = 1 kg * dm / (s^2 * dm^2) = 1 kg / (dm * s^2) In order to establish the equivalences with your other units of measurements, it will be convenient to first find the equivalence of this measure with the most similar of the ones you provided. The most similar unit of measurement to the one we've just defined is the Pascal: 1 Pascal = 1 kg / (m * s^2) [In words, one Pascal is the pressure exerted by a force equal to the force needed to accelerate a mass of one kilogram by one meter per second square (=1 Newton) on an area of one meter square] From the given definitions, it's clear that: 1 Pascal = 0.1 dN/dm^2 Now we can easily establish the equivalences between the dN/dm^2 and all the other units of measurement: 1 dN/dm^2 = 10 Pascal 1 dN/dm^2 = 0.0014504 psi 1 dN/dm^2 = 0.0029610503 inch Hg 1 dN/dm^2 = 10 Newton per square meter 1 dN/dm^2 = 0.0401856577 inch water 1 dN/dm^2 = 0.0001 bar 1 dN/dm^2 = 0.0000986923 atm This equivalences were taken from the following calculator: http://www.sengpielaudio.com/calculator-pressureunits.htm [Simply enter "10" in the "Pascal" field - since we've found that 1 dN/dm^2 is equal to 10 Pascal. This will yield the equivalences in many other units of pressure] Google search terms conversion inch hg pascal pound force psi newton force I hope this helps! If you have any doubt regarding my answer, please don't hesitate to request clarification before rating it. Otherwise, I await your rating and final comments. Best wishes! elmarto```
 tfpsoft-ga rated this answer: and gave an additional tip of: \$1.00 ```Doh, force of gravity, should have realized. Makes sense, I knew the pounds in psi couldn't possibly be a mass. Thank you very much. I just ran your conversion units through my test case and they work out exactly as expected.```

 `I'm glad it worked out. Thank you for the tip!`
 ```Hi! If you have a PDA, try and get a program on it called YAUC that does all this and more. It is fantastic and invaluable for Maths and Physics.```