Hahaha sorry. I'm just trying to get a handle on these equations. You know us pesky engineers with our equations and explanations.
I assume you're using the PV=nRT equation here and assuming that the compression process is isothermal, correct? That makes sense. Half the volume, double the pressure if temp stays the same.
Here's where I'm confused. For the first part to be true, it has to be isothermal. Otherwise the PV=nRT equation doesn't fit.
But if it is isothermal, then the discharge temps would be identical, which simply isn't true in the real world.
So where's the disconnect? Well, the process isn't isothermal for starters. Compression increases temperature. I don't think that's a linear process, but I don't have my thermal fluid systems book here so I can't double check that.
Basically what I'm getting at is that the smaller motor would have to make more than 30psi to match the 700hp because for each PSI it makes, the temperature changes and thus the volume does as well. Unfortunately, this starts delving into differential equations and all that fun stuff.
Does that sound about right? I'm about to go make an excel sheet and plot these values to see how much PSI the smaller motor would actually need. It might not be much more than 30 anyways.