I question the model, not the math. I don't think a huge impeller is not the most energy efficient or dollar efficient way to increase the gpm of a pump, but it works. Instead try this: $40 motor + this $125 waterproofed esc + 6-8 LiFePO4 20 AH prismatic cells in series (You probably already have these) and a well balanced impeller around 1.1 to 1.25 inches in diameter. 6 cells should get you to around 30K rpm, and would fit in a Nagato or NC easily. I can verify over 3 gpm at slightly under 20K rpm with a 1.1 inch impeller for 300 Watts. The setup above would easily be capable of 4 gpm. The limiting factor is: Beyond about 400 Watts you will have trouble storing enough energy for a full 2 sortie battle in a class 6 battleship even with LiFePO4 batteries, a class 7 like Yamato could handle carrying 700-1000 watts for the pump, but your back pays for it. Of course two 150 Watt pumps can output over 5 gallons a minute in a class 5 for the total same energy input as a 300 watt pump takes to do slightly over 3 gpm so there is not much to recommend using a 4-5 gpm pump that sucks 1000 watts or so and drains your batteries in 10 minutes.
the problem you get with short impellers is a poor hydrodynamic efficiency due to (amongst other things) the high loading of the blades and really bad cavitation on the blades when everything is not just perfect... it really is just a balance of what you want to do. I started looking at low speed (relatively) large impellers after finding several papers on those type of impellers at low specific speeds with reasonably decent hydrodynamic efficiencies compared to most that I had seen in our range. Using the above from jch72, if you pull 300W nominal right now at 3 gpm and then change the speed to 30k, power consumption should go up to ~1kW give or take a lot if the pump's hydrodynamic efficiency changes significantly. it would probably get you the pressure (again with same caveats) to get to 4-4.5gpm). There comes a point however where cavitation near/on the blades (or a lack of sufficient pressure to avoid inlet cavitation) will kill the expected performance gain and the affinity laws break down. Onto batteries, you can change batteries in IRC after every sortee per section C.6.a so you just halved your battery needs if you have some to swap.
