Dave, this may be slightly tangential......I remember having a discussion with a colleague about how to measure the coast line of Britain. We came to the conclusion that it was.....infinite! Why? Well, imagine that Britain is a simple triangle (lop off Wales for the time being...). Then measure the sides of that triangle - fine. Now, start to add in more angles to reflect the true coastline - and it becomes longer.....and the more detailed you go with your measurement, the longer the coastline becomes.
In principle, I am thinking that the same applies to a meandering river....the length depends on the scale of measurement.

See also http://en.wikipedia.org/wiki/How_Long_Is_the_Coast_of_Britain%3F_Statistical_Self-Similarity_and_Fractional_Dimension

David (Cronshaw) -

But are you comfortable enough with Zeno's paradox to stand in front of someone pointing a gun at you and pointing the trigger? :-)

- Keith

But are you comfortable enough with Zeno's paradox to stand in front of someone pointing a gun at you and pointing the trigger? :-)
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....well, granted that could present me with an intractable problem. I would need a bit more context to be able to answer your question, as it does present some complexities.

Dave
Your stance must always be that mouths of rivers and estuaries are complex (and in fact abstract inventions) and vary so considerably that linear measurement from a similar fixed boundary on all rivers is impossible.

However the best lead I can find comes from New South Wales http://www.dnr.nsw.gov.au/estuaries/factsheets/physical/limits.shtml
and states
"we find that In hydraulic terms, the downstream boundary of an estuary can be considered as the location where any change in bottom topography has no substantial effect upon tidal behaviour within the estuary.” But if you can't find that boundary "a convenient geographical location is usually selected as the downstream limit of the estuary"

You win some, you lose some.

Cheers, Ron