Could the Titanic have stayed afloat a bit longer if she kept moving, either in forward or reverse? I was reading this question: Was Titanic's captain's decision correct? @oakad commented about a Russian vessel keeping itself afloat by going in reverse, using hydrodynamic pressure to keep its damaged bow high enough to prevent fatal flooding.  This got me wondering...
My main question(s):
The Titanic stopped not long after it collided with the iceberg.  Could she have stayed afloat a bit longer if she kept moving, either in forward or reverse?  How much longer (or shorter, as the case may be?)
Would moving have had a net beneficial effect?  For example, would the benefits of moving be outweighed by an increased rate of flooding due to the flowing water further widening the gash, or a reduced rate of pumping because less steam was available to be diverted to the pumps?
What are all of the phenomena that would have an effect on this scenario?
 A: Interesting question. I suppose one should compare several scenarios


*

*Lie still

*Go forward - either straight, or hard to port, or hard to starboard

*Go in reverse


The rate at which water enters the ship is (to first order) proportional to the pressure differential - lower the pressure and live longer. Maybe even long enough for the Carpathia to come and rescue you...
If you think about the bow wave of a ship, its presence tells you that pressure builds up in front of the ship. Titanic cold not turn hard enough to port to pull a void on the starboard side, so I don't think any of option 2 is viable.
This leaves the question whether (3) would allow the bow to come (relatively) out of the water. I honestly think that once they realized they were surrounded by ice bergs, nobody would have much stomach for trying to go full steam astern (not very fast, with only two of the props turning the right way) in an attempt to change the equation of mass.
There were multiple small gashes far below the water line - where the rivets popped due to the stress of the impact. Based on investigations of the wreck, this is roughly what they might have looked like:
 
The draft of the ship was about 34 feet (10 meters), putting the deeper gashes about 6 meter or so below the water line. The fractional change in pressure that you could effect by any maneuver to raise the bow / change the profile of the water line would be at most 2 meter (being generous here), which in the very best case would have slowed the sinking by an hour. Tops. And in the process I am not sure what they might have run into, going backwards.
I hope someone has a hydrodynamic model to put a better confidence interval on my "two meters tops" number. I expect that it is very high.
A: As another hypothetical: If the Titantic had some way of distributing its buoyancy (i.e., pumping the incoming water aft) then it might have been possible to trim the bow far enough out of the water by making the hull aft-heavy to slow or stop the rate of water intrusion, and then powering up to full speed ahead.
Submarines on patrol can perform this trick because they have trim tanks into which ballast water or leaked water can be pumped aft to raise the bow and produce a  vertical thrust component which helps bring the sub towards the surface.
A: If reverse was maintained and if course was adjusted toward the Carpathia, in reverse, not only would the 2h & 40m time it took to sink may have been lengthened an hour by raising the bow up 6ft, as expressed above, and shortened the rescue ETA of 4-hrs, which left 1,496 in the icy water for at least 1-hr & 20m, to possibly converging in only 2-hrs, in plenty of time to save everyone.  Also, if that was not enough, the inertia of reverse would push water forward and out; and, the rush of water passing by the gashes may have also created a suction outward, extending its survival even longer.  If that extension was also an hour, the Titanic would have met up with the Carpathia in plenty of time before its demise, saving all 1,496 that perished from hypothermia.
