STANLEY N. DAVIS
.Piezometer, manometer, or well
ί Π β ί Ι
Ρ/γ = Depth of water in
manometer.
Datum Plane
(sea level)
Fig. 3. Components of Hubbert's force potential. In most groundwater calculations,
the hydraulic head is assumed to be equal to the elevation of the water in the
well (manometer), p is the pressure at the bottom of the manometer, z the
elevation of the manometer above the datum, and h is the hydraulic head.
subsurface. For this, Darcy's law must be used. One form of this law is
Q = -KA
dh
ds
(2)
in which Q is the volume of water flowing per unit time; K is a proportionality constant called hydraulic conductivity; A is the cross-sectional
area normal to the direction of flow; and dh/ds is the hydraulic gradient.
Equation (2) can be modified for flow in the horizontal direction x y
by noting that for most natural flow systems
and
so that
Ah/As ~ Ah/Ax
Q/A =(?
q = -K(Ah/Ax)
(3)
This equation tells us that the amount of water flowing through a given
cross section is directly proportional to both the hydraulic conductivity,
K, and the hydraulic gradient, Ah/Ax.
A further modification of Darcy's law is useful for certain purposes.
If a portion of a region of flow is subdivided as shown in Fig. 4, the follow6