On Jan 21, 3:30*pm, jbriggs444 wrote:

Suppose you have 10 miles of oil in the Alaskan pipeline bearing down
on a closed valve at a rate of one meter per second buffered by a 2
meter air bubble at 1 atmosphere directly adjacent to the valve.
(Some idiot closed the valve abruptly)

Assume that all relevant safety devices have been disabled and no
other air bubbles exist.

I think that the rate of increase of air pressure with respect to time
and with respect to distance are both super-exponential (or are best
modelled by a curve that is super-exponential) right up to the point
where the pipe breaks.

Yes, this is another example. One needs only to formulate the diff.eq.
to see that this is super-exponential in the ideal case.

If the oil has infinite motivating force and the pipe infinite
strength, we have P = 1/(t'-t) where t' is when the bubble is crushed.
This is equivalent to

P' = P^2

which clearly grows faster than the exponential P' = P .

Andrew Usher