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how important is it to get my head wrapped around these equations before I move on to the next lesson. I seem to get hung up understanding every details of the equations. Especially how to convert psi to lb/ft3.
You will find over time you start to remember them more and more. The great thing about having these courses is they are yours for life and if you forget an equation you can always come back and re-watch the lesson again.
Things like pressure conversions are helpful when you're using different softwares with different forms of reading pressure, I.E A fuel table which axis is based on MAP could read in PSI, MAP, MGP, Bar etc. Knowing how these all work out to a value you understand is extremely important. Although you will also find more ECU manufactures now give you the capabilities to select your preferred unit of measurement.
Over time you will learn how these all relate to each other and you will be working it out in your head automatically, just keep referring to the courses as you need to and eventually you won't need to anymore. You will also find search engines like Google helpful to find a conversion calculator if needed.
Well, part of that problem might be you're looking at two different things, pressure and density, which are related but require, at a minimum, temperature as part of the equation.
PSI kPa, or bar
lb/ft^3 kg/m^3
It does make your head hurt a bit, but if you ever get into engineering, proper, there are a LOT of equations that also use greek symbols for you to learn.