A flow net consists of a set of equipotential lines, which illustrate the distribution of hydraulic head in a flow system, and a set of flow lines, which illustrate the paths of groundwater flow through the flow system. For construction of a flow net, the flow system needs to be in a steady state and two-dimensional in either a vertical cross-section or a horizontal plane (without areally distributed recharge). A flow net can be constructed graphically with pencil and paper according to the criteria delineated in this book, or it can be generated numerically using a computer model. In both cases, the resultant set of equipotential lines and flow lines satisfy the equation of groundwater flow.

Graphical construction of flow nets is limited to flow systems with homogeneous and isotropic hydraulic conductivity. Certain types of anisotropy can be handled by geometric transformation of the system to an isotropic equivalent. Graphical construction requires that equipotential lines and flow lines are drawn to intersect each other at right angles, and that the two sets of intersecting lines form shapes with constant aspect ratios, preferably curvilinear squares to facilitate maintaining a constant ratio and to use Equation 2 for calculating flow through the system. When these requirements are satisfied, equipotential lines have uniform increments (contour interval) from one line to the next, and all flow tubes carry the same volumetric flow rate. The exception is a partial (or fractional) flow tube, which can occur in some circumstances at the edge of a flow domain. If the hydraulic conductivity is known, the volumetric flow rate through the flow system can be calculated.

When groundwater flow is simulated by numerical computer models, equipotential lines and flow lines are used primarily to display model results rather than to calculate flow rates, which has already been done by the model. Thus, there is greater flexibility for drawing equipotential lines and flow lines. For example, equipotential lines can have irregular increments and flow tubes can have different flow rates. Nonetheless, the equipotential lines and flow lines satisfy the equation of groundwater flow and therefore, together, they constitute a flow net.

Flow nets can be used to understand some basic features of groundwater flow. For example, if a flow tube becomes narrower, the principle of mass conservation requires specific discharge in the flow tube to increase. Additionally, according to Darcy’s Law, higher specific discharge indicates a higher hydraulic gradient if hydraulic conductivity is homogeneous. Therefore, narrowing of a flow tube (converging flow lines) in a homogeneous hydraulic conductivity setting is associated with equipotential lines getting closer to each other.

The flow net for a homogeneous flow field will be distorted by the presence of a zone of different hydraulic conductivity. If the zone has a lower conductivity, a flow tube gets wider as it enters the zone and becomes narrower as it exits the zone; and equipotential lines are closer to each other within the zone. The opposite occurs when the zone has a higher hydraulic conductivity, where a flow tube becomes narrower as it enters the zone and wider as it exits the zone; and equipotential lines are spaced further apart within the zone.

In anisotropic (but homogeneous) systems, flow lines do not meet equipotential lines at right angles as is the case in isotropic systems, but transformation of the system geometry allows for graphical construction of a flow net, which can then be transformed back to the original geometry to illustrate flow paths.

Note on Transient Groundwater Flow Systems

For transient systems, a formal flow net cannot be drawn in the same manner as presented in this book for a steady-state system. Although equipotential lines can be drawn for a flow system at a given point in time, the time-varying flow system makes it impossible to draw flow tubes that represent a constant rate of flow along the tube. Consequently, to visualize flow for transient systems, equipotential lines can be drawn at any time in the transient evolution of the system and velocity vectors can be sketched on the equipotential line map to indicate the direction and magnitude of flow at various locations in the systems for a snap-shot of flow patterns at that time.