Page 55 - Hydrogeology Principles and Practice

HYDC02 12/5/05 5:38 PM Page 38

38 Chapter Two

BO X
Continued
2.3

Fig. 4 Refraction of groundwater flow
lines at a geological boundary.

materials. Unlike in the case of light that obeys a sine law, ground- layered aquifer systems, as shown in Fig. 5, the outcome of the tan-
water refraction obeys a tangent law, as explained below. gent law is that flow lines have longer, horizontal components of
In Fig. 4, a stream tube is shown with flow from a region with flow in aquifer layers and shorter, vertical components of flow
hydraulic conductivity K to a region with hydraulic conductivity K , across intervening aquitards. The aquifer layers act as conduits for
1 2
where K > K . Considering a stream tube of unit depth perpendicu- groundwater flow. If the ratio of the aquifer to aquitard hydraulic
2 1
lar to the page, for steady flow, the inflow Q must equal the conductivities is greater than 100, then flow lines are almost hori-
1
outflow Q ; then, from Darcy’s law (eq. 2.5): zontal in aquifer layers and close to vertical across aquitards. This is
2
commonly the case, as the values of hydraulic conductivity of nat-
h d h d ural geological materials range over many orders of magnitude
=
Ka 1 Kc 2 eq. 8
1 2 (Table 2.1).
l d l d
1 2
where dh is the decrease in head across distance dl and dh is the
2
1
1
decrease in head across distance dl . In that dl and dl bound the
2
2
1
same two equipotential lines, then dh equals dh ; and from a con-
2
1
sideration of the geometry of Fig. 4, a = b ⋅ cos q and c = b ⋅ cos q .
1
2
Noting that b/dl = 1/sin q and b/dl = 1/sin q , equation 8
2
1
1
2
now becomes:
cos q cos q
K 1 1 = K 2 2 eq. 9
sin q sin q
1 2
or
K tan q
1 = 1 eq. 10
K tan q
2 2
Equation 10 is the tangent law for the refraction of groundwater Fig. 5 Refraction of groundwater flow lines across a layered
flow lines at a geological boundary in heterogeneous material. In aquifer system.