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Modeling groundwater flow with the help of flow nets

FLOWNET CONSTRUCTION

Although the following procedures are more or less sequential, be certain you read through and

understand all the procedures and suggestions before you begin to actually construct a flow net.

1. Ensure that the use of a flow net is valid.

(a) Flow is steady state.

(c) Boundary conditions are known or can be approximated well.

2. Prepare for a trial-and-error solution: there is no unique solution.

3. Ensure that the boundaries of the flow field are drawn to scale.

4. Define the boundaries, and determine the nature of each boundary.

(a) equipotential, or constant-head, boundary

(b) flow line, or no-flow, boundary: commonly an impermeable boundary

(c) known-head boundary; commonly the water table

(d) most often encountered, two equipotential boundaries and two flow line boundaries.

5. Determine the symmetry of the flow field, if any. This may reduce the work involved-for

example, bilateral symmetry would require construction of only half of the flow net.

6. Begin iterative construction of flow lines and perpendicular equipotential lines.

(a) Draw flow directions at equipotential boundaries.

(b) Draw predefined, or boundary, flow lines.

(c) Visualize the number of flow lines that provide a smooth transition between the boundary

flow lines.

(d) You will draw only a few of these, perhaps two or three.

7. A fundamental requirement of a flow net is that flow in each of the flow tubes must be equal.

Thus, because tubes that are longer will have a lower hydraulic gradient, they must therefore

be wider in order to carry the same flow. For this reason, when you draw a flow net that

curves (e.g., the flow field under the dam in Figure 1), you must draw flow tubes that are

progressively wider with an increase in path length or radius of curvature. In Figure 1, flow

tubes will widen with depth.

8. In terms of flow net construction, a simpler restatement of the above is in order to maintain

“squares” (Δw = Δl), Δw must increase as Δl increases.

9. Start at the most constricted part of the flow field, and lightly sketch a few flow lines and

equipotential lines.

10. Each area you construct must be correct before continuing (if there is any error, all further

work will be pointless).

11. Construct smooth lines that define equidimensional enclosures, or “squares”. (You can check

this by drawing circles inside the enclosures that are tangential at the four midpoints, or you

can connect midpoints of the sides with curved lines and see if they are of equal length.)

12. All intersections of lines must be orthogonal.

13. Adjust by trial and error. Your first attempt at drawing a flow net like that in Figure 1 may

take an hour or more.

14. Maintain a sense of humor.

15. When your flow net looks complete, you can check your construction by lightly sketching

diagonals across the squares. These diagonals also will form a flow net that is smooth,

encloses squares, and has perpendicular intersections.

You can do it this way, or you can do it your way. There are no required steps or procedures, but the

suggestions above should help you avoid problems. A net that goes astray can usually be traced back

to a violation of one of the above steps (most commonly to steps 8 and 10).

In the exercise that follows, before starting any flow net construction, think the problem through.

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