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Q: Unit Conversion of Pressure (in Unusual Units) ( Answered 5 out of 5 stars,   2 Comments )
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.

Subject: Re: Unit Conversion of Pressure (in Unusual Units)
Answered By: elmarto-ga on 18 Aug 2006 14:21 PDT
Rated:5 out of 5 stars
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

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:
[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!
tfpsoft-ga rated this answer:5 out of 5 stars 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.

Subject: Re: Unit Conversion of Pressure (in Unusual Units)
From: elmarto-ga on 18 Aug 2006 16:39 PDT
I'm glad it worked out. Thank you for the tip!
Subject: Re: Unit Conversion of Pressure (in Unusual Units)
From: borisshah-ga on 18 Aug 2006 22:06 PDT

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

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