Looking for a sci fi book that started out with an individual
demonstrating a Houdini water trick that went sour and that indidual
ended up on the stage still wet and in chains.  Come to find out he
had the ability to physically transport himself to another location by
his mental powers.  This ability spread to the populace till almost
all were able do the same.

Hi,

   The book you're looking for was written by Alfred Bester and was
published in 1956, firstly in instalments in 'Galaxy' magazine, and
then as a book with two titles: in the United Kingdom as 'Tiger!
Tiger!' and in the US as 'The Stars My Destination'. It has since been
republished in the UK as 'The Stars My Destination'. A new version,
with text restored from an alternative version, was produced in 1996.

   The ability to transport yourself using your mind is called
'Jaunting'. The scene as the beginning doesn't really involve a
Houdini trick, but it does involve an individual being put into a tank
of water! I've quoted the relevant section:

"The experimenters sealed Jaunte into an unbreakable crystal tank.
They opened a water valve, feeding water into the tank, and let Jaunte
watch them smash the valve handle. It was impossible to open the tank;
it was impossible to stop the flow of water. The theory was that if it
had required the threat of death to goad Jaunte into teleporting
himself in the first place, they'd damn well threaten him with death
again. The tank filled quickly. The observers collected data with the
tense precision of an eclipse camera crew. Jaunte began to drown. Then
he was outside the tank, dripping and coughing explosively. He'd
teleported again." Cited from 'The Stars My Destination', by Alfred
Bester. Orion Books edition (1999).

I obtained the above information from a copy of the book I own, but
I've found a website which I hope will provide adequate confirmation
for you:

Discursive Review
http://www.infinityplus.co.uk/nonfiction/starsmy.htm

Search Strategy: alfred bester "stars my destination"

I hope this fully answers your question, if not, please post a
clarification and I'll follow it up! Yours, robw-ga

I think you're looking for "The Stars My Desitination" by Alfred Bester