Not quite...
First, the specific gravity of water is around 1. It varies, slightly, based on temperature and degree of contamination (how pure it is).
Second, did you take the square root the tire pressure? Note, the formula I cited is based upon tire pressure expressed in Kg/cm*2 (not pounds per square inch).
I've read several places that the principle of 9 X the square root of the tire inflation pressure (in lbs/in*2) has been re-evaluated. Some engineers consider a more accurate formula as 7 X the square root of the tire inflation pressure (in lbs/in*2).
Then, there's the theory (I've read this somewhere, but I honestly can't remember where,) that the formula is incorrect if, upon touchdown, there is no initial wheel spin-up, i.e. a real greaser of a landing on a runway that is contaminated with water after a heavy rain storm. In this case, you may never realize any braking action.
Interesting stuff.
In any event, it's important to note that the coefficient of friction (mu) is very low with standing water. In fact, I've seen figures published where the mu with standing water is not much higher than that of wet ice.
To some degree, tire wear plays a role, too. How much tread is on the tire has some bearing...but not as much as you might think.
Years ago, Professional Pilot magazine had a really good series of articles on braking, hydroplaning, coefficient of friction, etc. You may be able to retrieve these somehow via the internet.
In ProPilot treatise, the author discussed how a pilot in a typical runway over-run accident, many times, experiences all three types of hydroplaning. Initially, the pilot is faced with dynamic hydroplaning. As the landing roll continues, reverted rubber hydroplaning comes into play. Finally, as the aircraft skids through the touchdown zone of the other end of the runway, viscous hydroplaning is experienced.
In countries that are lesser developed (a nice way to put it), the runways are not crowned, not grooved, and not regularly pressure-sprayed (to remove rubber and other contaminants). Attempting to land during or immediately after a heavy rain puts a pilot into the 'test pilot' category. Whether or not he'll get stopped...well, all bets are off.
PantLoad