Although your first-principles approach is admirable, it's also an order of magnitude out from what the original researchers are presenting (for a 30m sphere):
> Assuming the spheres would be fitted with existing 5 MW turbines that could function at that depth, the researchers estimate that each sphere would offer 20 MWh of storage with four hours discharge time.
Looks like you are assuming a 1.5m wall thickness, and then scaling that linearly to the 30m version, neither of which are correct.
> Also, 700m depth? That is the limit for saturation divers and current nuclear submarines can't go deeper than 500m before getting crushed!
I'd be surprised if they were making a claim like this without some justification that they can build at that depth. As a counter-anecdotal number, oil pipelines can be constructed at 2km depth [1]. These spheres are neither pipes nor submarines; I'm guessing they know (at least roughly) what pressure their spheres can tolerate. FWIW, the depth was chosen based on the depth limits of the turbines[2].
> Assuming the spheres would be fitted with existing 5 MW turbines that could function at that depth, the researchers estimate that each sphere would offer 20 MWh of storage with four hours discharge time.
Looks like you are assuming a 1.5m wall thickness, and then scaling that linearly to the 30m version, neither of which are correct.
> Also, 700m depth? That is the limit for saturation divers and current nuclear submarines can't go deeper than 500m before getting crushed!
I'd be surprised if they were making a claim like this without some justification that they can build at that depth. As a counter-anecdotal number, oil pipelines can be constructed at 2km depth [1]. These spheres are neither pipes nor submarines; I'm guessing they know (at least roughly) what pressure their spheres can tolerate. FWIW, the depth was chosen based on the depth limits of the turbines[2].
[1]: http://www.offshore-mag.com/articles/print/volume-71/issue-8... [2]: http://forschung-energiespeicher.info/en/projektschau/gesamt...