Physics for Geologists, Second edition

40 Gravity
Figure 3.8 The siphon at rest. The tube joining the two containers of water is
filled with water, providing a continuum from one to the other. The
water in the tube is in tension - at less than atmospheric pressure -
but no water moves because the energy at each end of the tube is the
same.
petrol from one container to another. The physics of this siphon requires
some careful thought. It is easily misunderstood. Let us begin with the two
containers at the same level, with a water-filled tube passing from one to the
other. What is going on here? Clearly nothing. The pressure at the surface
of the water in the containers is atmospheric, whatever that might be. In
the tube connecting the two, the pressure decreases upwards from each con-
tainer and is at a minimum at the crest of the tube. The water here then is
in tension. How high can the tube rise above the levels in the containers and
still maintain continuity of the water in the tube? The limit is the height at
which a vacuum (vapour pressure) will be formed at the arch. That is a little
more than 10 m. This is the limit at which water in a well can be raised by
a suction pump at the surface. In general, though, the tube can rise and fall
between the two containers as long as it remains within the limits.
If you were to make a hole in the connecting tube at the crest, the water
would subside on both sides into the containers, and air would be sucked in
through the hole. Likewise, if the wall of the tube is not strong enough, it
would flatten at the crest.
The essential feature of the siphon at rest, as it were, is that the tube
filled with water provides a continuum from one container to the other. The
water in the tube has higher potential energy than that in the containers, but
nothing moves because the potential energies of each side are the same. To
move the water involves work, which requires energy.
If you now raise one of the containers without breaking the continuity
of the water in the tube (Figure 3.9), what changes? The most significant
change is that the potential energy in the higher container becomes greater
than that in the lower. Provided the water is continuous in the tube, the water
flows from the higher to the lower container. It flows from larger pressure to
smaller pressure in the short arm of the tube, and from smaller pressure to
Copyright 2002 by Richard E. Chapman