Perpetual drip and the Keswick gravity siphon
Let a closed system have the following setup:
-a large, vacuum sealed bell jar to eliminate atmospheric pressure,
minimally filled with some fluid
-connect a pipe with a small diameter d1 to a pipe with a large diameter
d2 to form an upside down J.
-place the open end of d1 in the fluid
-have the other end d2 open the vacuum at a height above d1.
-fill the pipes with the fluid and start the system
How will the system behave?
I think the downward pressure on the surface of the fluid of d2 will
force the fluid in d2 to "drip" because the mass of the fluid column d2
will be greater than the mass of the fluid column d1. At the same time,
fluid will be "sucked" up d1 by the siphon. So the cycle of perpetual
"drip" will commence in this Keswick gravity siphon.
Is this perpetual motion? Can a turbine in d1 be used to create
I also want a formula to describe the pressures and velocities involved
as a function of fluid density, fluid viscosity (friction in the pipes),
column diameters, heights, surface tension (intermolecular bonds), etc.
I am not sure I have this system visualized absolutely correctly but it
sounds like you are trying to pull water up d1. The driving force, if I
understand you, is the larger mass of fluid in d2 (shorter pipe but
larger diameter, large enough to contain a greater mass of fluid than
d1). Now let us think about this a bit. If the fluid in d2 were replaced
by a solid piston of the same mass you would indeed pull fluid out of the
reservoir through d1. This is the way a hand-pumped well works. Work
is done on the piston which then pulls the water up the pipe. (In our
case work was done on the piston by moving it to the top of d2) But,
when the piston falls out of d2 what will happen? Fluids flow. The
fluid in d2 will drip out of d2 but it will be replaced, not by more
fluid from d1 but by air (or partial vacuum in your bell jar)
Now, you referred to surface tension as being important to your experiment.
and perhaps, if the surface tension were high enough, you might get a
little flow down d2 and pull a little fluid up d1 -- but that would stop
when the flow reached the opening in d2 -- surface tension would hold it
there and not allow it to drip. If the surface tension was low enough
to allow a drip to form it could also allow a reverse drip (or a bubble)
to form and the pipe would empty of fluids -- stopping all flow.
Hope this helps.
gregory r bradburn
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Update: June 2012