Flow net: definition, properties, uses

A flow net is a graphical representation of two-dimensional steady seepage, made of two families of curves that cross at right angles: flow lines and equipotential lines. It gives the discharge, pore pressures and exit gradients directly.

• Flow line (stream line): the path followed by a water particle through the soil from upstream to downstream. No water crosses a flow line.
• Equipotential line: a line joining points having the same total head. Water level in a piezometer is the same at all points of the line.

     ==========  upstream
     |  |  |  |    flow lines  ----->
  ---+--+--+--+---  equipotentials  |

Properties

1. Flow lines and equipotential lines intersect at right angles.
2. The fields (elements) are approximately squares, so that a circle can be drawn touching the four sides of each.
3. The same quantity of flow takes place in each flow channel ($\Delta q$ is equal).
4. The head drop between two adjacent equipotential lines is the same ($\Delta h = h/N_d$).
5. Flow lines never cross each other; equipotential lines never cross each other.
6. The smaller the field, the greater the velocity and gradient.
7. Boundaries: an impervious surface is a flow line; the upstream and downstream ground surfaces under water are equipotentials.

Applications

• Seepage discharge: $q = k\,h\,\dfrac{N_f}{N_d}$
• Pore water pressure at any point (for stability and uplift on dams, weirs)
• Exit gradient and check against piping
• Seepage force and uplift pressure under hydraulic structures
• Design of the length of sheet piles, filters and drains
• Location of the phreatic line in an earth dam.