Geoscience Reference
In-Depth Information
all of his ideas. With their knowledge of mathematics and physics being inadequate
to build upon his suggestions, they struggled for several decades just making
empirical correlations between soil texture and fi eld capacity or permanent wilting
point. After working only 4 years in the US Department of Agriculture, Buckingham
spent the remainder of his career in the US Bureau of Standards publishing many
novel ideas including his well-known
ˀ
theorem of dimensional analysis applicable
to many scientifi c disciplines including those of soil science.
We described capillary pressure in Sect.
8.2.
and soil water potential in Sect.
8.4
.
Since the surface pressure of a plane water level is higher than the surface pressure
of the curved water level in the capillary (at complete wetting), the capillary poten-
tial is negative with its magnitude designated in units of kilopascals (kPa). One kPa
represents the 10-cm height of a water meniscus in a vertical capillary tube. Next,
we demonstrate simple examples showing that water fl ows from places where it has
a higher potential to places where it has a lower potential.
We measured the soil water potential at the same depth of 60 cm in two experi-
mental pits. The potential in pit No. 1 was −15 kPa and that in pit No. 2 was −30 kPa.
Inasmuch as −15 kPa is greater than −30 kPa, before digging the pits, water was
fl owing horizontally from pit No. 1 to pit No. 2.
However, dealing with vertical fl ow, we have to add the gravitational potential to
the soil water potential in order to obtain the total potential because the driving force
is the total potential gradient. For example, at a depth of 30 cm below soil surface,
our measurements reveal a soil water content of 35 % at a soil water potential of
−20 kPa. At the depth 50 cm, our measurements revealed the same values of 35 %
and −20 kPa. However, it does not mean that there is no water fl ow, since we have
yet to add appropriate values of the gravitational potential. Taking the soil surface as
the zero reference level of the gravitational potential, the total potential at the 20-cm
depth is −23 kPa and that at the 50-cm depth is −25 kPa. And remembering that
water fl ows from higher to lower values of total potential, we learn that at that instant
water is fl owing downward. Moreover, we obtain the rate of water fl ow by multiply-
ing the gradient of the total potential with the value of the unsaturated conductivity.
However, the soil water potential at the 50-cm depth increases with time until the
gradient of the total potential is equal to zero and fl ow stops. At that time, the soil
water content at 50-cm depth being higher than that at 30-cm depth, we also verify
that soil water content differences are not suffi cient to elucidate soil water fl ow.
With the soil water content changing due to the unsaturated water fl ow, the value
of the unsaturated hydraulic conductivity also changes. Below we shall describe the
footsteps of only a handful of physicists during the past century to heed the stimu-
lating experimental and theoretical suggestions of Buckingham to consider the fl ow
of water in unsaturated soil as a simple diffusion process. Because several aspects
of diffusion differ from those of classical hydraulics, we continue with a couple of
simple examples of diffusion that happen in everyday life.
While grilling a chicken in your kitchen with its door and windows closed, you
suddenly become aware that you have overcooked it because your eyes tell you that
it is a dry chunk of coal-like meat and your nose reveals its stinky odor everywhere
throughout the enclosed kitchen. After you open the kitchen door, the bad odor
