I agree with Steve, either tankering or setting a treatment unit on the island would be more cost effective. (also, I agree with his flow and reservation estimates)
The investment cost only for the installation of such a pipeline (50km long, on the ocean floor) would make the potable water very expensive for the islanders.
I am here in Lindi Tanzania - water is brought across the bay through a hDPE 200 dia line but it is only about 7 km long. It is around 30 years old and experiencing failures at the welds and once with blood moon tide a section of 500 m was ripped out - the anchor blocks failed due to liquefaction of the sand on which it lay.
Hi Ben. We have large experience in submerged pipe and similar types of underwater crossings, for shorter distances. I am trying to enclose a presentation we made about a recent project we designed in Spain. Though it is in Spanish, I think that it is easy to understand, as it has many images. If you have any doubt, do not hesitate to contact me.
Hi there Ben. Certainly use of polyethylene is now well established and it can be gradually sunk by attaching concrete weights occasionally. You are going to need a flow of around 100 l/s as a design and will need storage on the island to even out demand of some 10,000 m3. You might look at tankering as an alternative. This is used quite commonly and tanker costs are surprisingly low. I know that water is taken by tanker from the US to the Bahamas for example. Also consider how you might limit demand or exploit reuse / treatment on the island. Hope this helps?