Re: A pipe line and pressure change

On Jan 23, 5:09 pm, "hhc...@xxxxxxxxx" <hhc...@xxxxxxxxx> wrote:
On Jan 23, 2:01 pm, Jeffrey Drake <jptdr...@xxxxxxxxx> wrote:





If a pressure change were to take place at one end of a 300 km
pipeline, containing water, how long would it take for the pressure
change to make it to the other end of the pipeline neglecting
friction?

This is the jist of an example question given in a class.

The answer given by the professor is 'instantaneous', meaning for all
practical purposes it is instant.

I was not comfortable with that answer, so a friend suggested that it
would be the speed of sound. The reasoning is that sound is just a
series of compressions (and because liquid does have some measure of
compressibility). The answer to this may be around 200 seconds, given
1500 km/s speed of sound.

Another teacher who does piping from a millwright perspective, said
that it would be virtually instantaneous because in a closed vessel
the pressure change is immediate.

I would like to have a qualified opinion from a more theoretical
perspective.

- Jeffrey Drake.

Jeff, notice no one asked how large in diameter the pipe is.  I find
this rather telling about readers of your question.

Also, all the little details that would be of importance to
physicists, such as how elastic the material of the pipeline is, and
what is the viscosity of the fluid. Then too, enter Reynold's number
into the consideration.

http://en.wikipedia.org/wiki/Reynolds_number

Evidently the profession who taught you this bit of crap is not a
physicist (or an engineer), else he would realize that the answer that
he gave you was total bull***.

The speed of sound in a liquid has nothing to do with the question.
Fluid mechanics has everything to do with arriving at the correct
answer.

Really?

Interesting second order oolie answer.

If we eliminate the pipe, and create a ping in open water, the speed
of sound would seem to have something to do with the propagation speed
-- although I was never comfortable with ignoring the difference
between the propagation speed of the peak, and of some information.
The latter might be only limited by molecular velocity -- or indeed,
by the speed of light -- since the molecules are essentially in
contact via the electric fields of their electron shells. And as Greg
Neil said, if we want to add "practically", we have evaluate the
context.

If we now confine the water to a pipe, then it's plausible the signal
transmission velocity -- assuming we've got around deciding what
exactly we mean by that -- changes with geometry: maybe shows
dispersion even when the free medium shows none. As you also point
out, if we allow the pipe envelope to have some elastic properties,
that too would influence the propagation of some kind of coupled mode
between the pipe and the fluid.

I'm not sure I'd accept that the speed of sound has "nothing" to do
with this, which seems too contrarian, but I like the fact that you've
dismissed the obvious first order oolie answer.
.

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