Last time I offered this equation as a rough description of the pressure gradient inside a disc pump:

Now I'd like to do a study in compression ratios with some real numbers, to get an idea of how this math will drive the design. To start, we'll do some algebra to make this spit out the compression ratio:

Interestingly, the compression ratio achieved from one pair of discs (this will be one "stage" in our pump) primarily depends on Vw, the tangential velocity of the outside edge of the discs. So, large discs spinning kinda sorta fast could have the same compression ratio as small discs spinning super fast. For my goals, I need a total compression ratio of 7.6x10^9, to go from a vacuum of 1.33x10-5 Pa to atmospheric pressure of 1.01x10^5 Pa. So, given a specific edge velocity Vw, I can figure out how many stages I need to reach my goal with this:

I made that one up, I think it's right, but not completely sure. I lost the scrap of paper I derived it on, haha. Documenting is so much work! Here's a table I made of what this looks like for various Vw's:

As you can see, faster Vw is exponentially more better. So why don't we just spin one disc at 2000 m/s for a single stage pump and call it a day? Tune in next time...