2.) When the water spray exits from the top it will freeze up the nozzle...
3). In any case the rate of flow through such a long water pipe is misiscule
4). Even if none of the above....the ambient temperature is so low the water will freeze
The ship will have a large coal-fired generating plant to power the pumps, the heat tapes on the pipe, and the nozzle heaters.
If they manage to balance the system correctly, it will cancel out the CO^2 created to keep it running.
They can think up their own solution to the pressure & flow rate problems.
Unfortunately, I can just hear them a DU ‘solving’ the pumping problems by invoking the surface-stratosphere pressure differentional to suck the water up the pipe like a straw; and by using LOTS of tiny pipes to act as capillaries. I make myself laugh just imagining them.