Sounds to me like Blue broke rule 11 at the time of the third luff.  Blue put themselves in a position where Yellow no longer could alter course in both directions without hitting Blue.  Textbook failure to keep clear.

Blue cannot 'call for water'.  This has no meaning under the rules.  First, it will be rule 19 not 20 that applies once the boats are actually at the bridge.  Second, rule 20 would not apply in this situation anyway as the boats are not close-hauled.  Once they actually get to the bridge and if they are still overlapped then Yellow, as the outside boat, will have to give Blue room to go between her and the bridge.  If they are not overlapped then neither boat is required to give room.  But Yellow does not have to give Blue room until they are actually passing the bridge, that is Blue cannot turn to starboard without hitting the bridge.  Yellow is under no obligation to give Blue room prior to that.

How was the overlapped established -- did yellow come from behind, or did blue come from behind, or was it established via a jibe?

Al, Blue came from behind to establish the overlap.

John, How would you have Blue hail for room at an obstruction if she cannot 'call for water'?  I'm quite happy that rule 19 governs - I never meant to imply that rule 20 was at issue.  Still, if there is a point at which Blue needs room at an obstruction she needs to be able to hail something.  Rule 19 doesn't mention any specific terminology that is to be used or, conversely, is forbidden. (This post edited for clarity RE rule 19 and 20 references)

On hailing - Case 107 points out that hailing is one way that a boat may act to avoid contact.

On this case - Blue will be entitled to room  at the obstruction. However, when Yellow luffs for the third time both boats are a considerable difference from the bridge and the wall/causeway to the bridge, so rule 19 does not yet apply. At the last position shown on the diagram, I would argue that the boats are not yet 'at the obstruction' unless there is shallow water or rocks between them and the bridge.

My 2 cents
Rules that are On and Off.
Rule 17 always off. Blue was passing windward.
Rule 11 is On. Yellow ROW.
Rule 16.1 could be On Limiting Yellow. 
Luff 1 OK
Luff 2 OK but blue started bear down and got too close to the Yellow after the luff.

Luff 3  Blue failed under Rule 11 at Luff 3 unless Blue can claim 16.1 on Yellow.   
OR 
Blue thinks she is getting to close to the continuing obstruction that can only be pass one way. The obstruction is the bridge and also lack of safe sail-able water be it  shallow water or rocks and is getting to close. This is blue's call on safety grounds.
Then Rule 19 turns On and then 19.C.2 "Rules 10 and 11 do not apply". Rule 11 is off.
Blue is the inside boat Yellow has to give room. Rule 19 does not require a hail or call for water.        

So its really question is there a obstruction at luff 3 or not?

I am understanding that Y did not establish overlap from clear astern, so the luffs are appropriate.  And, at each luff, B responded promptly, including at the 3rd luff, so no foul there.   B was also within her rights to bear off each time Y did, and it does not appear that she did so without failing to keep clear. Getting quite close to Y is also within her rights.  She has no obligation to provide Y room to do anything she pleases.  It is not clear from the facts presented, but from the diagram it looks like B may not have been able to come up further than she did at the third luff without swinging her stern into Y.  This is a common limitation, and Y has to deal with it.  I see no Rule 11 or 16.1 issues.  The rules kept the boats apart.  

As for “water” at the bridge, Y as the outside boat was going to have to bear away eventually.  B was just communicating her plan to ask for room when 19 turns on.  No problem there either.

In summary, no rules broken.  Y may have taken them both out of contention for the day, but maybe that’s what she needed to do.

Between positions 10 and 11 did blue take immediate action (turning up) in response to yellows luff? Or did she wait until yellow got too close for her to turn up?   If the action by blue was ASAP then no foul and no contact (blue was able to keep clear so 16.1 does not apply). However if blue waited until she was no longer able to keep clear (it was clear she had some room to keep clear at position 10) and yellow broke off the luff because blue did not keep clear blue broke  rule 11 and should be DSQ.   It would be up to a PC to find facts to support a violation of 11.  Avoiding contact on boats this size is always a desirable outcome. I would be hard pressed to give blue a pass unless they could present evidence that  yellow broken rule 16.1

Note, the description of the case does not include anything about shallow water or rocks in the area of the bridge, so the assumption is that a boat can safely sail right up to the bridge as drawn.

Jon - First, rule 20 will not come into play at all here.  Rule 20.1 outlines when it applies.  One requirement is that the hailing boat must be sailing close-hauled or above, which clearly the boats are not.

Blue does not have to hail for room at the obstruction.  There is nothing in rule 19 about hailing, which will be the rule that applies when the boats actually reach the obstruction.  As they are not 'at a continuing obstruction' yet (roughly 3 boat lengths from it) yet or 'at the obstruction' (6-7 boat lengths from the opening), Yellow is under no obligation to give Blue room and could even continue to luff Blue if she chose to.  Yellow let Blue off the hook here.

Rule 20 is the only rule where hailing comes into play.  In fact, an argument can be made that Blue's hail actually broke rule 20.1.  There is no such thing as a hail that you will need room in the future, just a hail that you need room at that moment.  If Yellow had been really devious, she could have hailed 'you tack' and then protested Blue for not tacking immediately or improperly hailing.

Eric - B is required to keep clear of Y.  By coming down with Y after each luff, Blue closed the distance to the point where Y could no longer change course in either direction without immediately making contact B is not keeping clear.  B broke rule 11 in position 9, before the 3rd luff.  See (b) in the definition of keep clear.

Gordon - I'm not sure how 107 fits in here.  There is a big difference between hailing to avoid a collision and asking for room.

All, this is a deep water bridge with no rocks or shallows in the area near the bridge.

Gordon - Yellow never hailed that she wanted to come up or wanted Blue to give room to come up.

Paul - yes Blue's actions were immediate in each case.  The wind was light, the sea was flat, so there was little to distract.  At each change in course by Y, B responded immediately.

John - sorry about my second comment.  I reversed 19 and 20 there and have edited to correct.  Ooops.  With that in mind, you say that there is no such thing as a hail that you will need room in the future, and I agree that such a hail isn't mentioned in the rules.  But, is it against the rules?  We commonly hail that we will be calling for water at an obstruction before we get to the obstruction.  Especially when racing with unfamiliar boats.  This just seems like a basic safety precaution at an obstruction to make sure no-one ends up on the rocks because of confusion in the moment.

John - in your response to Eric, you say Blue broke 11 at position 9, before the 3rd luff - but Yellow was able to change course without immediate contact and she did just that.  Subsequently, the gap close to about two or three feet at the beam.

Eric - concludes accurately that at position 11 Blue couldn't come up without swinging her stern into Yellow.  If this therefore limits Yellow's luffing rights, it must be the heart of the matter.  (I am open to the idea that preceding events created this moment.)  In that moment, do Yellow's luffing rights cease?  Yellow says that Blue has a continuing obligation to keep clear and that her inability to come up further without touching means 11 was broken - full stop.  Yellow further contends that she had an initial obligation under 16.1 but that it did not continue.

John, I disagree with your conclusion that B is not entitled to follow Y down.  I contend that she was smart and correct to do so.  Even at the 3rd luff, B responded promptly and allowed Y to make a significant course change, however, Y is required to allow B room to keep clear as well, and if Y had come up further, and B could not respond, B is protected by 16.1.  See Team reach call A3 for this interpretation, which consistent with every other interpretation of this situation that I have heard.  To your good point about the definition of keeping clear, it is clear from the diagram that B did provide Y room, up to a point. The key is that she has no obligation at any time to anticipate Y’s luffs and leave room for Y to come head to wind at any time.  Another way to think about that is at the start line.  If everyone had to leave room for everyone below them to come up hard, there wouldn’t be room for anyone at the line.  We see boats lined up, often with just inches or feet (depending on the size of the boats) between them, yet the rules provide limits that keep them separated.   

Eric -  I have no problem with Blue following Yellow down.  However, in the OP says that by the third attempt to luff, the two boats are very close and Y cannot turn up more than shown without hitting B.  How did they get this close?  Because Blue pressed down on Yellow each time Yellow curtailed her luff and and kept closing the gap between them, Blue put herself in a position where she was and could no longer keep clear.  Blue had every opportunity to not close the gap as much as she did and failed to do so.  Had Blue maintained the gap between the boats that existed during the second luff there would not have been an issue.  This is an easy call.  Take a look at Match Racing call A1

Blue is not protected by rule 16.1. Rule 16.1 is a rule of part 2 section B, it does not protect the Keep Clear boat, it limits the actions of the right-of-way boat, "When a right-of-way boat changes course, she shall give the other boat room to keep clear."

Based upon the fact "the two boats are very close, and Y cannot turn up more than shown without hitting B." It appears that at position 9, Yellow cannot change course in both directions without immediately making contact. Therefore, Blue is not keeping clear and has broken rule 11.

John, you bring up a good point, and I checked out the match racing case.  I stand by my decision though, but only because the parallel course that is equivalent occurs only after Y comes up at least 30 degrees between positions 9 and 10, and Blue promptly reacted to keep clear.  At some point, Y is limited by 16.1.  If Y had been unable to change course from position 9 without making immediate contact,  I would be in complete agreement, as B would be not be keeping clear.  As it looks in the provided diagram, Y was, in fact able to make a significant (but not unlimited) course change. I recall this scenario coming up in a rules seminar, and was used to show how the leeward boat has to be aware of the limitations on their rights.  Certainly B put herself in a risky position with respect to how this might be interpreted.  Difficult call, for sure, and we likely won’t agree, but I appreciate the discussion.

If Y remained close hauled, what would requires Y to give B room at the bridge to sail towards the mark?

It seems to me from the diagram that Y could sail close hauled all the way up to the bridge to a point where Y has just enough room to bear away but B is forced to tack to avoid the bridge and then subsequently gybe to get back on course.

If Y was sailing close hauled then B would never be between Y and the Bridge.  Would Y not be in the inside boat and B the outside boat? So would B need to give Y room to bear away 19.2b

If Y is close hauled then B is always able to avoid the obstruction, just in completely the wrong direction.

Rowan -  I'm not sure you have the same picture of this situation as others do.  In this case the wind is coming from the right hand side, not the top, of the page, so the boats will be running down to the bridge opening from the last position shown. The boats are reaching/running towards an opening in a bridge which is at the top left of the diagram.  Other than needing to go through this opening to get to the next mark, there is no indication of where that mark is.  B will be the outside boat if the boats go through the opening on the left hand side.  Y will be the outside boat if they go through the opening on the right hand side.

If the boats sailed all the way up to the bridge and then ran along side it, then the bridge a continuing obstruction and 19.2(b) governs if the boats are overlapped when they reach the obstruction and 19.2(c) governs if they are not overlapped.  If they just sail from the last position shown then the bridge is not a continuing obstruction and it is governed by 19.2(b).  In the Match Racing Call Book, calls B15, B16, B19, there are a bunch of examples of how to apply rule 19 as boats approach an obstruction.  These would apply to fleet racing as well as these rules aren't changed by Appendix C.

I'm with Mark and John that Rule 11 is broken at point 9. We already KNOW B's proper distance from Y based on the second luff-up.
However, if Y wants to be more sure, she can hold course at points 9 or 10 followed by further luffing.

Based on this good discussion (thank you all) and on reading Team Racing call A3 and Match Racing call A1, it seems there is a real ambiguity here.  I appreciate that John says its an easy call, but doesn't that total dismiss TR call A3.  And in Case 92, the preamble says "When a right-of-way boat changes course, the keep-clear boat is required to act only in response to what the right-of-way boat is doing at the time, not what the right-of-way boat might do subsequently."  How can B be breaking rule 11 at position 9 or even 10 unless you are anticipating a subsequent change in course? 

Let me ask it a different way - what limits, if any, does 16.1 put on Y at position 9, 10, or 11?

The original post had a fact "the two boats are very close and Y cannot turn up more than shown without hitting B."

That seems to indicate that at about position 9 or 10 Blue is not keeping clear, Yellow has to curtail her luff to avoid contact. Yellow cannot alter course without fear of making contact, so Blue has broken rule 11. Rule 11 required B to "keep clear" of Y. "Keep clear" means something more than "avoid contact"; otherwise the rule would contain those or similar words.

Read WS Case 88. A boat may avoid contact and yet fail to keep clear.