Page 52 - Hydrogeology Principles and Practice

HYDC02 12/5/05 5:38 PM Page 35

Physical hydrogeology 35

BO X
Flow nets and the tangent law
2.3

The construction of a flow net, for example a water table or poten- 5 If squares are created in one portion of one formation, then
tiometric surface map, and the interpretation of groundwater flow squares must exist throughout that formation and throughout all
lines, requires the implicit assumption that flow is perpendicular to formations with the same hydraulic conductivity with the possible
the lines of equal hydraulic head (i.e. the porous material is exception of partial stream tubes at the edge. Rectangles will be
isotropic), with flow in the direction of decreasing head. All flow created in formations with different hydraulic conductivity.
nets, however simple or advanced, can be drawn using a set of basic The last two rules are particularly difficult to observe when drawing
rules. When attempting to draw a two-dimensional flow net for a flow net by hand but even a qualitative flow net, in which ortho-
isotropic porous material by trial and error, the following rules must gonality is preserved but with no attempt to create squares, can help
be observed (Fig. 1): provide a first understanding of a groundwater flow system. In sim-
1 Flow lines and equipotential lines should intersect at right angles ple flow nets, the squares are actually ‘curvilinear squares’ that have
throughout the groundwater flow system. equal central dimensions able to enclose a circle that is tangent to
2 Equipotential lines should meet an impermeable boundary at all four bounding lines (Fig. 2).
right angles resulting in groundwater flow parallel to the boundary. In Fig. 2, a flow net is constructed for groundwater flow beneath
3 Equipotential lines should be parallel to a boundary that has a a dam structure that is partially buried in an isotropic and homo-
constant hydraulic head resulting in groundwater flow perpendicu- geneous sand aquifer. To calculate the flow beneath the dam, con-
lar to the boundary. sider the mass balance for box ABCD for an incompressible fluid.
4 In a layered, heterogeneous groundwater flow system, the tan- Under steady-state conditions, and assuming unit depth into the
gent law must be satisfied at geological boundaries. page, the flow into the box across face AB with width, ∆w, will equal

Fig. 1 Simple rules for flow net construction for the cases of (a) an impermeable boundary, (b) a constant head boundary (here shown
as a river) and (c) a water-table boundary.