A pitot tube experiment
Just for my own curiosity, I took an old Rosemount "L" shaped pitot tube and did an experiment to see how rapidly it would clear water out of the bleed ports. This particular probe has two .028" (~.7 mm) bleed holes located just aft of the elbow to the sensor pressure connection. I calculated that approximately 45 inches of water column would equate to 270 knots CAS. By hooking a clear tube up to the end of the tube and sealing the pressure connector, I found that the tube could clear a full load of water in approximately 2-4 seconds with approximately 45 inches of head pressure.
AF447 had the Thales pitot tubes of course, but I am assuming that its water clearance rate would be comparable. Feel free to check my calculations in any way you wish.
FWIW, a pitot with frozen up bleed holes will have zero air flow velocity through the front part of the tube, thus if pitot heat is on, the mass of frozen water that might be trapped in the tube will have to heat up and will eventually become water which then apparently will then clear in a matter of seconds if the pitot inlet is open.