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Physical hydrogeology 31

Fig. 2.12 Work done in moving a unit mass of fluid from the
standard state to a point P in a groundwater flow system. Fig. 2.13 Relation between hydraulic head, h, pressure head,
ψ, and elevation head, z, at a point P in a column of porous
material.
2.8 Groundwater potential and hydraulic head
As described in the previous sections of this chapter,
the porosity and hydraulic conductivity of porous Given that groundwater velocities in porous material
material characterize the distribution and ease of are very small, the kinetic energy term can be ignored
movement of groundwater in geological formations. such that at the new position, P, the fluid potential, Φ,
When analysing the physical process of groundwater or mechanical energy per unit mass (m = 1) is:
flow, analogies are drawn with the flow of heat
through solids from higher to lower temperatures P
=
+
and the flow of electrical current from higher to Φ P d eq. 2.15
gz
lower voltages. The rates of flow of heat and electric- ρ
ity are proportional to the potential gradients and, in P o
a similar way, groundwater flow is also governed by a
For incompressible fluids that have a constant den-
potential gradient.
sity, and therefore are not affected by a change in
Groundwater possesses energy in mechanical,
pressure, then:
thermal and chemical forms with flow controlled by
the laws of physics and thermodynamics. With refer- ( )
− P
P
=
ence to Fig. 2.12, the work done in moving a unit Φ +gz ρ o eq. 2.16
mass of fluid from the standard state to a point, P, in
the flow system is composed of the following three
To relate the fluid potential to the hydraulic head
components:
measured by Darcy in his experiment (Fig. 2.3), Fig.
1 Potential energy (mgz) required to lift the mass to
2.13 demonstrates that the fluid pressure at position P
elevation, z.
2
2 Kinetic energy (mv /2) required to accelerate the in a column containing porous material is found as
follows:
fluid from zero velocity to velocity, v.
3 Elastic energy required to raise the fluid from pres-
P = ρg ψ + P eq. 2.17
sure P to pressure P. o
o
The latter quantity can be thought of as the change
where ψ is the height of the water column above P
in potential energy per unit volume of fluid and is
and P is atmospheric pressure (the pressure at the
found from: o
standard state).
It can be seen that ψ = h − z and so, substituting in
P P
v d P equation 2.17:
=
m p d m eq. 2.14
m ρ
P o P o P = ρg(h − z) + P o eq. 2.18