Page 49 - Hydrogeology Principles and Practice

HYDC02 12/5/05 5:37 PM Page 32

32 Chapter Two

Fig. 2.14 Condition of pressure head, ψ,
for the unsaturated and saturated zones
of an aquifer. At the water table, fluid
pressure is equal to atmospheric (P ) and
o
by convention is set equal to zero. Note
also that the unsaturated or vadose zone
is the region of a geological formation
containing solid, water and air phases
while in the saturated or phreatic zone,
pore spaces of the solid material are all
water-filled.

By substituting this expression for pressure into the gh = gz + P
equation for fluid potential, equation 2.16, then: ρ eq. 2.21

+
−
−
ρ
z
gh
P
P
+
=
o
o
Φ [( ) ] eq. 2.19 The pressure at point P in Fig. 2.13 is equal to ρgψ,
gz
ρ and so it can be shown by substitution in equation
2.21 and by dividing through by g that:
and, thus:
h = z + ψ eq. 2.22
Φ = [gz + gh − gz] = gh eq. 2.20
Equation 2.22 confirms that the hydraulic head at a
The result of equation 2.20 provides a significant rela- point within a saturated porous material is the sum of
tionship in hydrogeology: the fluid potential, Φ, at the elevation head, z, and pressure head, ψ, thus pro-
any point in a porous material can simply be found viding a relationship that is basic to an understanding
from the product of hydraulic head and acceleration of groundwater flow. This expression is equally valid
due to gravity. Since gravity is, for all practical pur- for the unsaturated and saturated zones of porous
poses, almost constant near the Earth’s surface, Φ is material but it is necessary to recognize, as shown in
almost exactly correlated with h. The significance is Fig. 2.14, that the pressure head term, ψ, is a negative
that hydraulic head is a measurable, physical quantity quantity in the unsaturated zone as a result of adopt-
and is therefore a suitable measure of fluid potential, ing the convention of setting atmospheric pressure
Φ. to zero and working in gauge pressures. From this, it
Returning to the analogy with heat and electricity, follows that at the level of the water table the water
where rates of flow are governed by potential gradi- pressure is equal to zero (i.e. atmospheric pressure).
ents, it is now shown that groundwater flow is driven In the capillary fringe above the water table, the
by a fluid potential gradient equivalent to a hydraulic aquifer material is completely saturated, but because
head gradient. In short, groundwater flows from re- of capillary suction drawing water up from the water
gions of higher to lower hydraulic head. table, the porewater pressure is negative, that is less
With reference to equations 2.16 and 2.20, and, by than atmospheric pressure (for further discussion, see
convention, setting the atmospheric pressure, P , to Section 5.4.1). The capillary fringe varies in thickness
o
zero, then: depending on the diameter of the pore space and