Physics for Geologists, Second edition

24 Force
the weights - that is, their volumes are equal. Weights determined on spring
scales are always in error by a buoyancy amount that is small for dense
objects, but could reach about 112 per cent for objects of small density.
In a swimming pool, as we all know, our weight is further reduced because
it is reduced by the weight of the water displaced by our body. A body floats
only when it displaces less than its volume of water, that is, its bulk density
must be less than the density of water. This is why steel ships float. This
principle is used for separating 'heavy' minerals from 'lighter' (that is the
jargon; but we would be more accurate if we used 'denser' and 'less dense'
or 'more massive' and 'less massive').
Consider the following3 in order to clarify your thoughts on buoyancy:
There is a lake with no inflow and no outflow. A depth gauge is in the water.
On the bank there is a dinghy, a rock and a piece of wood. You put the
dinghy into the water: what is the effect on the water-level of the lake? You
get into the dinghy: what is the effect? Someone hands you a stone: what is
the effect? You are then handed the piece of wood: what is the effect?
You row out into the middle of the pond and throw the stone overboard:
what is the effect? Then you throw the piece of wood overboard: what is
the effect? (You are at University now, so only look at the answer given in
the Appendix on page 138 when you are satisfied that you have the correct
answer.)
Buoyancy acts also on fluids. When you take a hot shower in winter, the
shower curtain tends to be sucked in on you, because the warm water warms
the air, which rises because it is now less dense, and the cold air tries to flow
in to replace it. If a river brings sediment-laden water to a lake, as the Rh6ne
does to Lake Geneva, the dirty, denser, water may flow down the slope to
the bottom of the lake, displacing the cleaner water. This is the position
of minimum potential energy. The speed at which it flows depends on the
density contrast, the slope of the bottom and perhaps its smoothness, and
the viscosity of the water - at least. Figure 2.4 shows the essentials, but is
rather nai've. If you would like greater detail, see Turner (1973: 178ff.).
Buoyancy is the main driving force of convection because fluids expand
when they are heated, and so become less dense - but the energy may come
from an outside source such as the flame under the saucepan. Remembering
that in geology we regard as fluids substances that are certainly solids on
a short time-scale, the force of buoyancy acts on any volume of less dense
rock that is overlain by denser rock (Figure 2.5).
The drill pipe paradox - or fallacy
In the 1950s, development drilling in several oil fields around the
world was hampered by the drill pipe's sticking against formations that
3 This was probably an examination question, but I have been unable to trace it. I therefore
apologize to whoever owns the copyright - but it is too good to omit.
Copyright 2002 by Richard E. Chapman