Physics for Geologists, Second edition

128 Fluids and fluid flow
Water flowing through the pores of the sand does not flow in a straight
line over the distance 1 in Figure 12.8 but takes a much longer path, the mean
length of which for all particles of water is I,. This aspect of fluid flow through
porous media is called tortuosity, defined 1,/1. It is dimensionless; and it is
a vector in the sense that the value of tortuosity in sedimentary rocks usually
varies with direction, being much larger across the bedding than parallel to
it. Tortuosity is the only component of permeability in sedimentary rocks
that varies with direction, and therefore must account for anisotropy of
permeability in rocks.
We conclude, therefore, that intrinsic permeability includes tortuosity and
the square of the hydraulic radius. For a more detailed analysis in terms of
measurable rock parameters, see Chapman (1981: 49f). For a more detailed
mathematical analysis, see Hubbert (1940, 1969).
Finally, there is the matter of the energy of water. The total head, h, as
we have seen, is an energy per unit of weight of the liquid; the term gh is an
energy per unit of mass of the liquid. The potential of a fluid is its energy
per unit of mass, gh, and has the symbol @. So,
The potential gradient is therefore gAh/l.
Important groundwater definitions
(If you find definitions at variance with these, examine the physics carefully to
determine which is correct.)
Artesian Wells or aquifers in which the energy of the water is sufficient to
raise it above the level of the ground without artificial aid are said to be
artesian. An aquifer is artesian if its total head is greater than the elevation
of the land surface above the same datum.
Equipotential line or surface A line or surface on which points of equal
energy, equal fluid potential, equal total head, lie. See Potential.
Head Refers to the vertical length of a column of fluid, usually liquid. It
is an energy per unit of weight, with dimensions of length, not pressure.
Ambiguous when not qualified. See Figure 12.7.
Elevation head or simply elevation: the potential energy per unit of weight due
to elevation, that is, the elevation of the point at which pressure p is measured,
above (+) or below (-) an arbitrary horizontal datum. he = z.
Pressuve head: the vertical length of a column of liquid supported, or capable
of being supported, by pressure p at a point in that liquid. h, = plpg.
Velocity head: head due to the kinetic energy of the liquid. Negligibly small in
most geological contexts. h, = V2/2g
Total head: the algebraic sum of the elevation and pressure heads (neglecting
velocity head). It is proportional, lacking only the factor g, to the energy of
Copyright 2002 by Richard E. Chapman