Well I'm going back to when I was very young, in the 1960s.
I'm not sure when the Baths went from being salt water to the plain chlorinated water they use now.
The laundry as it was ( the flying pigs boarded up building ) had large sinks near the window and big industrial machines further back, driers I think. It smelt of carbolic soap and heat. This was in the days when you could hire towels from the Baths and they were laundered in this building.
There must have been drying rooms and maybe storage in there. The ladies that worked there always seemed to be busy.
As for the tower the settling tank was up some steps- wooden i think - but can't say for definite , I'm not sure what was on the ground floor but the tank was on the first floor, dark, squarish, not sure how deep, it had a wee fish living in it and anenomes.
I remember it as cold, drafty, dank. I dont think the sides had glass or anything but I recall criss cross patterns made by light. I think the walls were sort of rough concrete.
To be honest at the tie I wasn't paying much attention I was chumming my Granpaw to see the fishy and was being careful not to drop his black note book, important job to carry the notebook
I later realised this was where he made a note of the salinity, noted the specific gravity of the water etc.
Maybe the manager of the Baths would know who to approach for keys
Or maybe enquire through
http://www.edinburgh.gov.uk/info/1034/land_and_propertyThe salt water was draw in from the sea, the pipe can sometimes be seen at low tide.
It was pumped to the tank to let the sand settle, must have gone through some other filters, then pumped to the boiler across the lane ( behind the big black doors ). In those days I think the boiler was heated by coal. She was called Bessie