And how does water increase boost pressure anyways?
Physics....
First, the greater the Delta T (temperature differential), the FASTER the heat/BTU transfer.
You are correct that water absorbs more BTUs(970) going form 212* water, to 212* steam.
BUT, you need that larger Delta T to get a FASTER change in temp/state. You DO NOT want a BLEVE.
NOW, part of the reason that Water Injection increases boost..
What drives a turbo? AIR(yes, I know exhaust gasses etc, for the sake of conversation lets just say air, easier on my typing), and heat.
223 cu ft of steam come from 0.135 cu ft of water. (Nominal at standard conditions)
The colder the water is, the more dense it is, THUS, per cu ft could make even MORE steam, thus, increasing CU/FT of "air" moving over the turbine, increasing speed, and spool up.
DISCLAIMER< forgive me if my math is a little off, a bit distracted with my rampant 5 y/o....
Chase