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.

 

[rdl]

*secondYes, you can use dimensional analysis to convert PSI (pounds per square inch) to kPa (kilopascals). Dimensional analysis is a mathematical method used to convert units of measurement by using the relationships between different units. In this case, the relationship between PSI and kPa is:

1 PSI = 6.894757 kPa

This means that for every 1 PSI, there are 6.894757 kPa. To convert from PSI to kPa, you can use the following equation:

kPa = PSI * (6.894757 kPa/ 1 PSI)

This equation uses the conversion factor of 6.894757 kPa/ 1 PSI to convert from PSI to kPa. By multiplying the value of PSI by this conversion factor, you can convert the units to kPa.

There is no calculus involved in this conversion process. Dimensional analysis is a method that is based on simple algebraic equations and does not require any advanced mathematical concepts. So, you can use this method to convert PSI to kPa without any issues.