FredGarvin said:
Gee...does anyone know where we can get a pump to overcome that head? Let's see...you have about, what...60 miles, that's 316800 ft of static head right there (assuming constant gravity which I know it's not), not to mention the pressure drop you'd encounter over the length of a Ø.250" tube, especially at a flow rate to make this all worth the while. I'll have to go and work the numbers just for kicks.
Actually, head wouldn't be an issue if pumping hydrogen: its lighter than air, so it'll rise through the pipe without anything more than air pressure pushing behind it.
For flow-rate vs pressure drop, yeah, I'm guessing someone didn't consider friction inside the pipe when they came up with that 1/4" dia. I can't imagine getting useful flow out of anything less than a foot diameter pipe.
A 12" pipe with a fairly generous pressure drop of .05" w.g. per 100 feet (I design HVAC ductwork for a living...) is good for 480 cubic feet per minute. At 22,000 miles to geostationary orbit, that's a total pressure drop of 4840' w.g. or about 2000psi.
Now, of course, since hydrogen is compressible, pumping it at 2000psi will add a pump-head issue...
And then, of course, is construction difficulty...
And hey - welcome aboard: you sound like an engineer...?
Errorist, I didn't put much effort into trying to understand that equation, but it looks suspiciously like gibberish. I don't see anything having to do with friction or flow rate, for example.