Can I Convert PSI to kPa Using Dimensional Analysis?

[JoeMaxwell92]

Ok, so I was at lowes and I was trying to figure out the gauge pressure of a certain air compressor that used psi measurements. I don't have an iPhone or anything that can pull up internet converters so I figured I would have to do the conversion dimensionally. This posed a problem though as the pounds to kilograms converter on my phone doesn't recognize pounds as a force, but as a mass. I was wondering if there was some sort of calculus involved with dimensionally converting psi to kPa.
1 lb = .4536 kg_{in Earth's gravity}
with respect to time, pressure is the second derivative of kg/meter

 

[PhanthomJay]

Ok, so I was at lowes and I was trying to figure out the gauge pressure of a certain air compressor that used psi measurements. I don't have an iPhone or anything that can pull up internet converters so I figured I would have to do the conversion dimensionally. This posed a problem though as the pounds to kilograms converter on my phone doesn't recognize pounds as a force, but as a mass. I was wondering if there was some sort of calculus involved with dimensionally converting psi to kPa.



1 lb = .4536 kg_{in Earth's gravity}

an object with a mass of 0.4536 kg has a weight of 1 pound on Planet Earth (that's about 4.45 Newtons).

with respect to time, pressure is the second derivative of kg/meter

No need for calculus...1 psi is 1 pound/square inch...convert pounds to kN (1 pound is 0.00445 kN) and convert square inches to square meters , and you end up with 1 psi is 6.9 kPa, or 1 kPa is 0.145 psi, approximately.

 

[JoeMaxwell92]

So I guess what you are saying is there is no way of converting pounds directly into Newtons by dimensional analysis without a definition, in Newtons, of what a pound is, or without multiplying the conversion from lbs to kg by the gravitational acceleration constant?

 

[PhanthomJay]

So I guess what you are saying is there is no way of converting pounds directly into Newtons by dimensional analysis without a definition, in Newtons, of what a pound is, or without multiplying the conversion from lbs to kg by the gravitational acceleration constant?

That's right, you need a definition. It's all in the definition of the unit and the conversion factors between units. That is true even within the chosen system of measure itself. For example, a kN is the force required to accelerate 1000 kg of mass at a rate of 1 meter per second per second. But you first need to define the kilogram and meter and second per an international standard.